Talk:Mass–energy equivalence/Archive 2

question
From the article: "Conversely, active energy in the form of kinetic energy or radiation can be converted to particles which have rest mass." What is an example of radiation converting to a particle?


 * Gamma rays of more than 1.022 Mev, when passing through matter, may give raise to pair production of electrons and positrons. S  B Harris 12:16, 22 November 2006 (UTC)

Romanticizing about Albert Einstein and perpetuating myth
The current introduction to the article states: "In these, he [Albert Einstein] showed that a unified four-dimensional model of space and time ("spacetime") could accurately describe observable phenomena in a way that was consistent with Galileo's Principle of Relativity, but also accounted for the constant speed of light."

That is pure myth. Historically, the fusion of space and time originated with Minkowski in 1908, who in fact stole the unification of space and time from the geometrization of relativity by Henri Poincaré. See http://www.univ-nancy2.fr/DepPhilo/walter/papers/einstd7.pdf

For that article, titled, Minkowski, Mathematicians, and the Mathematical Theory of Relativity, one directory states, "Minkowski claimed scientific priority for a great, new, geometric theory of relativity at the Cologne lecture of 1908, based largely on the work of Poincaré. Poincaré was purposely excluded from the meeting. 42 pages." http://www.everythingimportant.org/relativity/directory.htm --e.Shubee 19:27, 16 January 2007 (UTC)


 * Please remember in all this that people had been thinking of "unifying" space and time for a long time before 1907. Riemann worked on his geometry with this explicity purpose, 50 years before. It's one thing to think about unifying space and time, and something else to have the quantitative equations which give you the proper relationship between the two! Which in this case is a sort of hyberbolic geometry which which, even in flat space, isn't obvious. It was Einstein who came up with the quantitative relationships needed. It was Minkowski who realized they could be made into a new geometry. If it was Poincaire who supplied the program for this, or even Reimann, that's fine. Put them down as cheerleaders. Remember, mathematicians are very good at this sort of thing, once they are given the physical clues as to which of the (very many) mathematical worlds describes the real one. It's the physicists who do that for them. David Hilbert, once told by Einstein what the requirements would be in a differential Riemann-style differential geometry to decribe gravity, worked out the math for of general relativity many times faster than Einstein had, and very nearly beat him into publication. That's fine. The point is that it took Einstein to set the physical constraints on the mathematical theory. For the early geometrization of SR, Minkowski gets credit for the geometric interpretation. For GR, Einstein managed to do it all himself, but Hilbert also got there independently, once Einstein told him what was needed. All these men were following in the footsteps of Riemann, Poincaire, and many others. But the crucial physical insight was Einstein's, and he gets the major credit. And should.  S  B Harris 20:02, 16 January 2007 (UTC)


 * You are in error on several points.
 * 1) Riemannian geometry was not Riemann's attempt to unify space and time.


 * 2) Poincaré was to first to geometrize special relativity in a mathematical sense.


 * 3) Minkowski got the credit for the geometric interpretation but only because physicists are good at creating fictional realities that have nothing to do with the real universe.


 * 4) Einstein is on record in opposing Minkowski's unified geometrization of space and time in 1908 with a silly whine saying it was too complicated. Read http://www.univ-nancy2.fr/DepPhilo/walter/papers/einstd7.pdf, which I have already cited.


 * 5) Einstein could not have discovered general relativity in 100 years without the mathematicians of his day. If Einstein only had library access and a team of translators for all the published books and articles of the world, it wouldn't have helped him. Solving the objective of GR required talented mathematicians much smarter than Einstein to work on the problem.


 * 6) Einstein didn't create GR all by himself. You are forgetting the contributions made by Marcel Grossmann, Tullio Levi-Civita, Hermann Weyl, Felix Klein, Emmy Noether, and a number of other mathematicians. See http://www.phys.uu.nl/~wwwgrnsl/abstracts/rowe990217.html


 * 7) Modeling gravity as spacetime curvature isn't as brilliant as you think. There are at least four distinct physical forces in the universe yet only gravity is modeled as the curvature of spacetime. Who is to say that Einstein didn't take us in the wrong direction? Alternative points of view haven't been ruled out. There is no computing of geodesics in a geometric model of electromagnetism, for instance, when trying to figure out the trajectories of charged particles.


 * 8) You're bringing up general relativity because the veneration of Einstein, a purely religious idea, is the essence of your denial.


 * 9) You're defending the myth that in 1905 Albert Einstein unified space and time into a four-dimensional geometric model, now called spacetime, ignoring cited evidence to the contrary. --e.Shubee 21:47, 16 January 2007 (UTC)


 * Yes, this article incorrectly credits Einstein. Einstein was not the one to unify space and time into a 4-dimensional spacetime, and he was not the first to publish E=mc². The article should just explain the mass-energy equivalence, and leave the history for elsewhere. Roger 00:46, 26 February 2007 (UTC)


 * Albert Einstein indicated that gravity distorts space-time as modeled in rolling a ball on a rubber-sheet with heavier balls as masses in the solar system. The layman understands this to mean that light rays are also bent when passing close to large masses.

Tom Bearden asserts, et. al., that because of this distortion in space from gravitational fields (the rubber sheet metaphor) we must use Riemannian geometry not Euclidean geometry to describe space (near large masses).

Additionally, Mr. Bearden asserts that Einstein’s famous equation, E = mc2, was over simplified, ignoring an electromagnetic wave effect on gravity. E2 = p2c2 + m2c4. I don't know what "p" is. Larry R. Holmgren 16:14, 10 March 2007 (UTC)

I think the problem is that when Einstein "developed" this concept of E=MC squared, he failed to recognize the true forfathers of the equation. Think of it this way: He was not working by himself when he came up with the "theory of relativity". He was merely attempting to translate something that he had read and tried to make it his own, ergo, Einstein's theory of relativity. User:69.229.109.185 30 March 2007

Merge with Mass-energy equivalence
I was surprised to find that there is another article on this same topic called Mass-energy equivalence. I would like to propose that information from that article be merged to this one. Additionally, I think Mass-energy equivalence is a more appropriate name for the article. Having an equation, however famous, as an article title is something of an anomaly on Wikipedia, and I think it would be far more appropriate for the article title to be the concept represented by the equation rather than the equation itself. (Naturally, E=mc² can and should redirect to Mass-energy equivalence following the merge.) Comments? Robert K S 14:59, 1 February 2007 (UTC)


 * I agree with the merger but think that E=mc² is a better topic title. --e.Shubee 22:26, 1 February 2007 (UTC)


 * I agree that the information should be condensed into one, since it refers to the same information. The title E=mc² is what most people would look for first (voice of experience here), but redirecting to the more appropriate title is a fine compromise. -- Haxwell 17:36, 11 February 2007 (UTC)


 * Can you think of any other articles on Wikipedia whose titles are equations? Even an article title of The Einstein equation (a la Ohm's Law) is more appropriate than E=mc² in this regard.  Additionally, I have my doubts that many users arrive at this article by searching on the string E=mc².  E=mc2, perhaps, but finding the superscript 2 special character and pasting it in, or using the Alt+numbered keypad code to generate it manually, is most unnatural.  I would be willing to wager that most of this article's traffic comes from redirects or links from other articles. Robert K S 05:14, 15 February 2007 (UTC)


 * I got here by searching E=mc2 (no special superscripts); and I like the title this way. Also, note to Robert K S, you are completely wrong on your opinion, the E=mc² expression is the most famous equation in the history of human kind.  Also, do you know how many equations Einstein has?  Moreover, did you happen to note the 147kb worth of talk on this page compared to the one comment worth of talk on the other page?  As to the merge, I'm ambivalent; the term "mass-energy equivalence" is common jargon, unrelated, necessarily, to Einstein.  As a matter of fact, I'm going to add a nice image to this page from the walk of ideas.  Later: --Sadi Carnot 06:17, 15 February 2007 (UTC)

I also got here by searching E=MC2. Whether it fits as a title is superseded by the simple fact that even non-science adults (me) know of it by that name, as do non-science 9-year-olds (the boy who specifically asked me about "E=mc²" by name). Terrance Carroll, 6 July 2007.


 * It is a nice image. You say I'm "completely wrong", but I think you may misunderstand my point.  From my first comment to this thread: "Having an equation, however famous, as an article title is something of an anomaly on Wikipedia..."  In other words, it doesn't matter how famous the equation is.  The English-language concept behind the equation, and not the mathematical notation of the equation itself, is the more appropriate article title on the English Wikipedia, because the words "mass-energy equivalence" have intrinsic meaning in English, whereas "E=mc²" does not have intrinsic meaning in English.  (On a math wikipedia, sure, let's have equations as article titles, go to town.  But here, English, not mathematics, is the language of choice, and should be used for article titles.)  The article title should convey the concept the article expresses right off the bat, but mathematical notation cannot ever do so. Robert K S 17:34, 15 February 2007 (UTC)


 * Support merge The two articles are totally redundant. I never would have thought of typing "mass-energy equivalence" into Wikipedia's search field to find information on E=mc2. I made a guess that "E=mc2" would get me to where I wanted to go and voilà, it took me to the right article. It was a good demonstraton of the power of Wikipedia. I was impressed. Even though Wikipedia can easily redirect, I think Mass-energy equivalence should be deleted, links to it redirected, and any of its unique and valuable text should be incorporated into this article. Greg L 19:39, 5 March 2007 (UTC)


 * Support merge The proposed merge would benefit individuals seeking information on the subject with no prior knowledge of it. The title "Mass-energy equivalence" is akin to the captions and various pictures in a newspaper, which serve the purpose of providing a general idea of the respective subject to busy readers. --69.156.210.102 18:17, 8 March 2007 (UTC).


 * Support merge The proposed merge is a great idea, there is no reason there should be two articles on the same topic.


 * Support merge also. It is a great idea to merge those 2 articles.Yelir55 15:24, 7 April 2007 (UTC)


 * Support merge with redirect on E=MC2 article page per nom and Haxwell. Looks overdue now... any volunteers? // Fra nkB  20:27, 7 April 2007 (UTC)


 * Merging underway. Here's my first crack at a merged article; feel free to edit it.  If there are no objections I will perform the merge in the next several days.  I would also appreciate advice on how to merge the talk pages.  Finally--is it just me, or does there seem to be a good deal of, if not original research, then original-sounding phrasing in the "Background" section of this article?  Phrases such as "A key point to understand..." and "Now, understanding the difference between rest mass and relativistic mass, we see that the equation E = mc2 in the title must be rewritten..." should be bothersome to anyone interested in maintaining consistent encyclopedic tone in this article. Robert K S 23:12, 9 April 2007 (UTC)


 * Merge completed. I also just transferred the talk page lock, stock, and barrel. Robert K S 12:35, 11 April 2007 (UTC)

Deleted statement suggesting that 100 C change in temp is equivalent to some quantity of energy or mass
I have deleted the following statement (now twice):

"Raising the temperature of an object by 100 °C increases its mass by 2.3043 × 10–36 g."

I hope the many reasons why it's false will be apparent. First, raising the temperature of a cup of water 100 C will require more heat than raising the temperature of a bathtub of water by the same amount. So there is OBVIOUSLY something wrong with the statement. Obviously, the statement is intended to be somehow particle or mass-specific, or intensive. That means we're talking about things like specific heat capacity to even have a chance to make statements like this one. However, even when we go to intensive quantities like numbers of moles or particles, we can't come up with an amount of energy or heat which is equalivalent to a given temperature change like 100 C, because different types of objects have different heat capacities, due to different compositions and different ways of storing heat. Thus, there is no direct comparison of temperature and energy in any system which holds, with a given constant converstion number. The reference given involves some confused use of Boltzmann's constant, and is applicable to heat capacities of ideal gases where heat capacity is 3/2 k per particle, but a specific energy (or mass) like this would still require a certain amount of gas, like perhaps one molecule. In fact, 2.3e-36 grams is 2.1e-22 J = 15 Kb per 100 C per particle. Somebody probably meant it to be 1.5 Kb, so it's off by a factor of 10, even talking about the amount of heat/mass which is stored as kinetic energy. But in any case, as noted, the mass of an object when heated increases as all the energy modes stored, not just the kinetic ones. A bad sentence all the way around. Wrong conceptually (in several ways), and quantitatively, too. S B Harris 05:01, 6 March 2007 (UTC)

A first order proof of E=mc^2
The following I will try to present in formulas as well (I have never used the formula translation tool before) but just to make sure, here goes the descriptive proof:

power = energy / time => (1) energy = power * time

(2) power = force * velocity

(1)+(2)-> (3) energy = force * velocity * time

(4) momentum = mass * velocity

(5) force = momentum / time

(4)+(5)-> (6) force = mass * velocity / time

(3)+(6)-> energy = mass * velocity / time * velocity * time =>

(7) energy = mass * velocity ^2

It has always bothered me, what people say, nothing travels faster than light. All of the equations used are elementary physics/mechanics and please notice that I havent used the sqare root adjustment for mass that uses the speed of light.

My proposal is simple. The above proof, if it holds, apart from being simple, makes no assumption about velocity, i.e. it holds for velocities greater than the speed of light, so maybe, much as people thought before breaking the sound barrier, the assumption that we can't go faster than light, is a myth. Naturaly if you believe in your heart its possible, this just removes any worries about you shrinking to nothing as you approach c. Your only other problem is a suitable "lane" to try this, most likely perpendicular to the plane of the solar system.

If you are intent to "shoot me down" my last defence will be to borrow a line from "Contact" [Carl Sagan,Zemeckis 1997, Jodie Foster, John Hurt] and say this: "Wanna go for a ride?"

Using formulas and using 'u' instead of 'p' for momentum to avoid confusing it with power:

$$P=E/t$$

$$E=Pt$$

$$P=Fv$$

$$E=Fvt$$

$$u=mv$$

$$F=u/t$$

$$F=mv/t$$

$$E=(mv/t)vt$$

$$E=mv^2$$

wbP —The preceding unsigned comment was added by Pelorios (talk • contribs) 18:23, 6 March 2007 (UTC).


 * Pelorios, if you attach numeric quantities at each stage in your above logic (keeping careful track of all your "ones" and "twos", and "1.414s"), you will find that indeed, mass times the square of velocity relates to energy. But, more specifically, you will also find that it's not E = m • v², it's actually E = ½ m • v². The latter is the classic formula for determining kinetic energy. Einstein's formula can not be arrived at via your method unless one leaves off such niceties as numeric values. An explanation for why nothing can go faster than the speed of light is more complex than this. Greg L 08:28, 7 March 2007 (UTC)


 * And Einstein's work did not and does not derive the constancy of the speed of light; this was known well before Einstein and served as one of his axioms. And I don't think you substantially appreciate the rather simple physical basis for special relativity and things like the Lorentz contraction (which in terms of time dilation is easily verified in the case of things like muons). --24.147.86.187 00:39, 8 March 2007 (UTC)


 * The base for the axiom that nothing can be faster than light is that the maximal speed an interaction can take place at is c. Therefore, if two objects collide with a speed relative of each other higher than c, the interaction between them would have to happen at a speed over c, breaking the above axiom. However, this is logical fallacy: motion doesn't necessarily imply interaction. Remember superfluids? An object moving in superfluid helium doesn't interact with the superfluid. Therefore, an object moving at a speed higher than c in a superfluid doesn't break the speed-of-interaction axiom. So, speed over c in a superfluid might be possible. Also remember that when 2 waves travel on the surface of the water, when they collide, they just pass through each other: they might interfere, but they don't interact. Louis de Broglie described in 1924 that particles are waves and vice versa, waves can be also thought of as particles. This is especially true for photons, which reach a wave state very easily. Therefore, 2 particles can travel through each other like waves without interaction, that is, they behave like superfluids for each other. Since it is interaction that is limited in speed to c, and not motion directly, and as we can see from the above examples (object vs. superfluid, photon vs. photon), motion doesn't imply interaction, we can conclude that 1. motion is not necessarily limited in speed to c, and 2. if the relative motion of 2 objects is higher than c, there can be no interaction between them. What one might glean from this is that as an object passes c, it becomes unable to interact, meaning that it will become invisible! We know that light always travels at c, independent of the viewpoint. From the "invisibility" conclusion, we can understand why we can't detect light waves (photons) that are faster than c. The cause for not being able to detect photons slower than c might be that such photons don't have enough energy for an interaction to take place. So, only photons traveling at c can be detected. The axiom that the speed of light is invariant was taken from the results of the Michelson-Morley experiment. In that experiment, the detected light waves/photons (they are essentially the same thing, as per de Broglie's work) were always traveling at c. That is, they couldn't detect photons with speed other than c. That doesn't imply that there were no photons that couldn't be detected! Our axiom, rewritten to address the conclusions above is: "The speed of detectable light is invariant". With this, I have just stated that there are light waves of different speed in our universe, but we can only detect ones with a speed of exactly c. Light travels in vacuum. So, this means, waves can travel in vacuum at different speeds. Waves can also travel in superfluids at different speeds, as Piotr Kapitsa has proven it. Could it be that vacuum is in fact a superfluid? Well, this is very similar to the ether theory, but it doesn't conflict with the results of the Michelson-Morley experiment! (Sorry if I wrote something incorrect, most of this was translated from a book of the Hungarian scientist Laszlo Gazdag. I might have omitted something, or translated something incorrectly, so bear that in mind if you notice a mistake.) --NetRolller 3D 22:05, 3 May 2007 (UTC)


 * Perlios, you also have a fundamental error in your derivation. Power does not equal energy/time.  Power = work/time and work = force * distance.  Substituting that into your derivation leads a result of velocity = distance/time at step 3.  Since that eliminates your energy term, you cannot arrive at Einstein's mass-energy equation. 64.73.44.244 (talk) 17:03, 18 June 2008 (UTC)

Matter losing mass as it falls down a gravity well
The below has been transplanted from Greg L’s talk page (Greg L 18:45, 14 March 2007 (UTC)): ––––––––––––––––––––––––––––––––––––––––––– "Anytime energy is added to a system, the system gains mass. For instance, lifting a one-kilogram mass upwards one meter against the force of one standard gravity increases its mass by 109.114 femtograms (1 fg = 1 × 10–15 g)."
 * There's a problem with this, and that is that it's not true! The energy is stored as potential in the system of Earth and mass as a whole, and not in the mass itself. So where exactly does this mass reside? Hard to say. Mass can be very tricky to locate, especially in g-fields. See mass in general relativity for some of the problems. In any case, if you actually do lift a 1 kg mass in Earth's gravity, nothing happens to the mass of the system at all. Since of course you just move mass from here to there, from the chemicals in your arm to the system of weight-raised-to-height. The gravitational field of the Earth as seen from a long way away, obviously does not change in processes like these (lifting things or avalanches, etc). Energy has to escape or enter the system for that. So, again a bad and wrong example for many reasons. S  B Harris 21:50, 7 March 2007 (UTC)
 * “ In any case, if you actually do lift a 1 kg mass in Earth's gravity, nothing happens to the mass of the system at all ” No, that statement is not true. If it were, then why did you leave the one about hydro water? Matter going up or down: there's no difference. Matter falling into a gravity well looses mass. That's Einstein's way of looking at it. To the engineer, matter traveling closer to the center of the earth (or a floor) loses potential energy. The extent to which matter loses mass as it travels down a gravity well is equal to the potential energy lost as it does so. The reverse of this is matter gaining potential energy by being raised upwards (traveling upwards out of a gravity well). It's as valid for the kilogram weight going upwards as it is for water falling downwards. Greg L 05:40, 9 March 2007 (UTC)
 * No, mass falling down a gravity well does NOT lose mass. If two masses come together, are you going to tell me which one of them looses the mass? Is it split according to their ratios? All this is bad thinking. The system loses the mass of the potential energy, IF it's radiated as heat (otherwise it's retained as heat, or retained before contact as kinetic energy). Otherwise, not. Where the mass assocated with the g potential is, before that, is up for grabs. Generally, it's usually regarded to be in the g-field, but it doesn't have a location. As for hydro power, no mass is lost or gained when water falls or rises, except as sunlight enters or leaves the system. That complicates things there, but not in the simple arm-raising the weight example, where the system is closed, and therefore mass-energy obviously is conserved and constant.  S  B Harris 17:02, 9 March 2007 (UTC)
 * “ No, mass falling down a gravity well does NOT lose mass ” You are dead wrong. This is a fundamental and elementary truth and you are embarrassingly incorrect. “ If two masses come together, are you going to tell me which one of them looses the mass? ” In the case of the Earth vs. a kilogram, where the latter one overwhelmingly does the moving, yes. It’s ultra-simple: Two pieces of matter that are close to each other have less energy than the same two pieces a long way apart because you have to expend energy to separate them against the gravitational force that is pulling them together. Energy is proportional to mass. Ergo, closer together = less energy = less mass. This concept doesn't just apply for a kilogram, it applies to the entire universe. The total energy of the universe is exactly zero. The matter in the universe is made out of positive energy. A gravitational field in this sense is negative energy. If all the mass of the universe is brought together in a "big crunch", the resulting energy is zero. The bottom line is: If you take a kilogram of matter and measure its mass, and then lower it in an elevator to the basement where you measure it, you will find it lost mass. Don’t believe that statement? See Paragraph 1.3, here as well as that article’s main page, Einstein's Theory of Relativity versus Classical Mechanics. Oh, and were you tempted to disagree with some of what I wrote above? Well, Stephen Hawking wrote much of it in his A Brief History of Time. Please also see Talk:E=mc2, where I have an expanded explanation on all of this. Greg L 18:21, 9 March 2007 (UTC)
 * Sigh. Consider a couple of masses stably held apart. Draw a sphere around it. It's now a closed system, no energy or mass in or out. Now let the masses go. As they fall inward they lose potential and gain kinetic E, but the Lagrangian doesn't change. When they hit, they heat up. During all of this, it remains a closed system, and the mass and energy inside does not change. There's a discussion of this in Feynman in the relativistic kinematics portion of book #1. Although he omits the gravity part, it's just as obvious with springs or when kinetic energy is converted to heat. Through it all, if it's a closed system, mass is conserved. No matter what you do to it, or it does to itself. A nuclear bomb could go off inside that sphere, and so long as you didn't let light or heat out, the mass of the thing would not change. That's the whole point of these exercises. S  B Harris 18:30, 9 March 2007 (UTC)
 * You're trying to change the subject. What you deleted was a statement that said that raising a kilogram upwards against Earth’s gravity increases its mass. I wrote nothing about how doing so increases the mass of the Earth/Kilogram system. Save me your "Sigh" business (I'm not going to bite on petty provacations), read the provided links, and then make your edits to the article. Greg L 18:35, 9 March 2007 (UTC)
 * I do not understand where your problem is. If raising the mass does not raise the mass of the system, it doesn't raise the mass of the mass, either. If you're suggesting that mass moves around inside the system during gravitational work, that's certainly correct (so long as none enters or leaves), but the location of gravitational mass is problematic, as I noted. None of your references are relevent to WHERE gravitational mass resides in a system where it's stored in a G-field. The article on mass in general relativity does bear on the issue, but if you read it, you'll soon take leave of the idea that when you lift a rock, the work you do against the field somehow "goes into" the rock (and not the Earth or field), and is nowhere else. Heck, you wouldn't even believe that in the case of work done against an electric field. Would you? If I had an electron and a positron close together, and I measured the electron mass by jiggling it back and forth, and then I put some work into the system by moving them apart against their mutual electic field, the whole system would mass more by the amount of work I put into it. But that work goes into the *field*. Actually the whole system. I couldn't detect it from trying to take the invididual mass of the electron again. It doesn't reside there. And no, I'm not changing the subject. The physical location of "mass" gained in work done against fields (ie, where in space IS the energy of the field) is exactly the subject. For gravity, it's an especially tricky one. S  B Harris 19:31, 10 March 2007 (UTC)


 * You didn’t read the articles I provided, did you? Then read Note 6, which I just added. Greg L 19:34, 10 March 2007 (UTC)


 * …And you know, it’s time-consuming writing responses to you. I really wish you would read 1.3: Mass-Energy Conservation at a Microscopic Scale. This is but one section from a single page from a comprehensive treatise on Einstein’s equations titled Einstein's Theory of Relativity versus Classical Mechanics by Paul Marmet. This treatise is one of many topics available on the Intute: Science, Engineering and Technology Web pages, which is a shared resource of the Consortium of Academic Libraries in Manchester, U.K. However, since you seem to be reluctant to actually read any of this, and instead apparently prefer to continue to believe what you want to believe, I’ve quoted some of 1.3 for you below:

According to the principle of mass-energy conservation, the mass of the hydrogen atom in the basement is now different from its initial mass mo on the first floor. It is slightly smaller than mo and is now equal to mb. Any variation of g with height is negligible and can be taken (with g) into account in equations 1.4 and 1.5.


 * And finally, just how the hell old are you? What is your education and background? Your profound self-confidence and the absolute certainty in your statements (“ There's a problem with this, and that is that it's not true! ”, “ Sigh ”, “ I do not understand where your problem is ”, and “ No, mass falling down a gravity well does NOT lose mass ”) over a fundamental and elementary point like how matter loses mass as it falls down a gravity well, is a hallmark of extreme youth. Why did you persist in twice writing again instead of first setting aside five minutes to read even the very first link I provided you? Lastly, your writing style seems intended to convey that you have some sort of uncanny insight into the deep inner workings of relativity and its equations (“ So where exactly does this mass reside? Hard to say. Mass can be very tricky to locate, especially in g-fields. ”). False claims of knowledge are another hallmark of extreme youth and can be rather embarrassing to watch when someone so predisposed fails to correctly fathom the relativity-equivalent of 1+1=2. Greg L 00:00, 11 March 2007 (UTC)


 * Um, I'm 49 years old, a fact you could have discovered from my user page, on which I wrote last year that I was 48. I'm sorry to have to report that you're the victim of a bad textbook. I don't know if it's written by a crank, or what his problem is, but he's giving you bad physics. The frequency shift of atoms or nuclei at the bottom of a gravitational well is simply due to the fact that time runs slower there, by a factor of 1-phi/c^2, as seen from flat space (if you view the whole process of emission from there, photons start with a low frequency, and simply keep it). Which is the same as saying that photons climbing out of such wells suffer a gravitational doppler shift of the same amount (this is from the perspective of the ground, where photons start at a normal frequency, and gain in frequency, as they rise, since from the ground's perspective, clocks in space run faster). Both perspectives are correct, as they result in the same prediction: Low frequency at the bottom of the potential well, higher frequency when out of it. This stuff about lower mass of atoms in the bottoms of g-wells is nonsense. If it were literally true, you'd have a double effect, and would get a frequency shift from both the gravitational time/doppler effect, AND this wierd and wacky mass effect that your poor author is trying to push. But only one effect actually happens. The standard interpretation of it is not the one you're reading, sorry. Your author says: "Since the red shift measured corresponds exactly to the change of the Bohr radius existing between the source and the detector, we see that it cannot be attributed to an absolute increase of energy of the photon during its trip in the gravitational field." Alas, that actually is the standard interpretation of modern physics. I'm sorry, but it is. The photon loses energy as it goes up, as seen from the ground. From above, it already had low energy due to general relativistic slowing of ground clocks. Again, BTW, I'm not trying to argue that mass is not lost when you lower something down a g-well and extract energy doing it. But that mass is lost from the system-as-a-whole, not particularly from the object that you lower. And oh, yes, atoms (and space itself) expand in a g-field (along ONE dimension!), so the Bohr radii are larger, indeed (but no longer "circular"). But that's a direct effect of gravity on the fabric of space itself-- the beginning of that black hole funnel. It's got nothing to do with atoms losing mass. Did I leave anything out? Oh, yes. Hawking is not God. He may be right about the universe having zero mass/energy total, or he may be wrong. There's intense debate on the subject right now in astronomy, and no general agreement. Also, since it's a system thing, it (again) has no direct bearing on our argument. A system gains mass as you add energy in any way (including pushing masses in the system apart). But in general with gravity it's impossible to say where the extra mass is LOCATED in space. It's the same situation with gravitational waves: energy is there, mass is there. But it has no particular location.  S  B Harris 04:31, 11 March 2007 (UTC)


 * 17:02, 9 March 2007 (UTC): “ No, mass falling down a gravity well does NOT lose mass. ”
 * 04:31, 11 March 2007 (UTC): “ I'm not trying to argue that mass is not lost when you lower something down a g-well and extract energy doing it. ”
 * Your arguments are clearly not consistent. Further, you are again trying to broaden the issue by arguing about frequency shifts and other topics that have nothing to do with what I wrote about (and you deleted). I don’t give a crap about Bohr radii and won't allow myself to be enticed off into the brush to chase a red herring. Further, your are now trying to say that 1) a comprehensive, thorough, and detailed Web site on relativity (Einstein's Theory of Relativity versus Classical Mechanics by Paul Marmet) should not be believed, 2) Stephen Hawking can’t necessarily be believed, and 3) you should be believed. This line of reasoning is pretty hard to swallow; particularly considering that your two statements above (a day and a half apart) are diametrically opposing positions.


 * E=mc2 and the principal of mass-energy conservation are straightforward concepts with clear and unambiguous ramifications. Paul Marmet and Stephen Hawking are consistent and logical in their descriptions of how matter loses energy and mass as objects come closer together. Here’s the the consequence of what they say: Two spherical diamonds, each made of 83⅓ moles of 12C and each with a diameter of about 8.16 cm, are in space with their centers of mass separated by 8.16 cm. They are touching each other. Let’s say that 83⅓ moles of 12C precisely defines a kilogram in space (far from Earth and its gravity). The two-sphere system thus has a mass very slightly greater than 2 kg because of the potential energy latent in the fact that their 166⅔ moles of carbon isn’t concentrated into a single sphere; their two centers of gravity are separated by a minimal amount. Then you separate them by an additional meter. You had to put in 3.0 × 10–9 J of work to accomplish this task. Their mutual gravitational attraction is 176 times weaker than when they were touching. According to E=mc2, the now-separated system has 179,751,035,747,363,528.000 000 0030 J of energy, which is a mass of 2 × 100 + 3.4 × 10–26 kg.


 * But where is this added mass located? Earlier (before you flip flopped), you were arguing that the added energy and mass isn’t bound in the matter but that it’s “ hard to say ” exactly where it is (Wow… that’s helpful), but you seemed to imply that it’s somewhere in “g-fields.” However, two objects poses a combined gravity field that doesn’t change in total magnitude as their relative positions change. If one accepts Stephen Hawking’s explanation that matter is “positive energy” and gravity fields are a “negative energy,” and that these two energies equal zero as the Universe disappears in a Big Crunch, then it must follow that matter loses mass as it falls down a gravity well and it must follow that matter gains mass as it rises out of a gravity well. If your earlier argument were true (that the added potential energy and mass due to separating objects is bound in the gravitational field somewhere), then the Big Crunch would leave a big ball of matter and no gravity! Stephen Hawking’s concept is borne out by Paul Marmet’s 1.3: Mass-Energy Conservation at a Microscopic Scale. I really doubt these guys invented any of this; they’re just explaining it for us simple folk. Further, Stephen Hawking’s explanation handily explains how something (the Universe) could come from nothing (empty space seething with zero-point energy): what looks like something (the observable local Universe surrounding us), is really nothing more than “zero” that has been stretched until it formed a ±precipitate of gravity and matter.


 * And please don’t beg off a story about how your second statement above is consistent with the first because it includes the caveat that “you must extract energy while the object is falling down the gravity well and if you don’t capture this during the drop, then it doesn’t lose any mass.” That would clearly be a big, steaming, metric butt-load of weapons-grade bullonium and you know it. You’re flip flopping. You incessantly complain that what I’ve written it isn’t true but offer no explanation of your own (“I know the extra mass is not in the matter but it’s hard to say just where it is” amounts to “Pay no attention to that man behind the curtain!”). Trying to debate a subject like this with you is like trying to swat a house fly: logic doesn’t work and you change positions all the time. Greg L 23:54, 11 March 2007 (UTC)


 * ANSWER: You can shout "BS!" till the cows come home, but the reason I carefully qualified the two statements above, so that they are different, is because they represent two different situations, and I understand that. If you lower a mass, you extract energy in the process, and mass-energy of the system decreases, because you're removing it. Whereas, if the mass simple falls down the well (you let it fall), you're NOT extracting anything, and the mass-energy of the system remains constant as the mass falls. Simple as that. Apparently, you'd like very much to prove I'm contradicting myself on this point, but what I've written is clear enough and I can let it stand as proof that I'm not talking about the same situation. Yes, I'm saying Marmet shouldn't be believed on this point about atoms getting less massive and enlarging in a g-field, and I gave a very clear reason why he's wrong. His prediction of enlargement and mass-decrease of atoms gives the well-known doppler gravitational frequency shift, and yet we know that's due to something else (gravity slowing of clocks), and NOT the effect Marmet describes. QED, he's wrong. There's no red herring here-- he's the one pointing out that his supposedly lowered mass gives what other physicists call the gravitational Doppler shift, not me. So he's the one who put his foot in it, not me. On your example: "However, two objects poses a combined gravity field that doesn’t change in total magnitude as their relative positions change." Who told you THAT? It's certainly not true in general. If you add mass-energy (in the form of simple mechanical work) to the 2-sphere system from the outside, in order to separate them, they end up as a system having more mass, after you're done. That shows up in an (over all) larger (stronger) G-field, as seen from a long way away. (Where the field is viewed down the axis joining the spheres: having one sphere approach MORE than makes up for the other moving away by the same distance. The field is weakened in the plane orthogonal to the radius between spheres, but not to the same extent.) And that would be just as true if they were held together by a spring, which you stretched using a couple of outside ropes. The extra mass-energy and G-field due to it, is not due to formation of any new carbon atoms (certainly), and (indeed) its location is hard to place. No, all the carbon atoms don't get a little more massive. For an electrical situation (one sphere pos and the other equally neg), the energy to separate them goes into the E-field, and (guess what?) there actually is a difference in what you see in the field from far away, to correspond to the work you put into the system. Because the field at a distance is not exactly zero, but is a 1/R^3 dipole field, and you increase the dipole moment when you put in the work (as I "back of envelope" it for the far-field, all derivatives of these field strengths (dF/da) with respect to sphere separation ("a") vary as the inverse cube of distance R to the spheres, but in the case of the direction plane orthogonal to sphere-sphere axis, there's an extra factor of a/R which diminishes the effect, as compared with the direction of the sphere-sphere line). The total energy of the field ends up increasing as "a" increases. A similar thing happens with the total G-field, when you separate two masses--- you change the gravitational quadrupole moment. (Incidentally, both of these processes result in EM and gravitational radiation, especially if done quickly, but I assume we're going to do it in the limit of very slow processes, in order to minimize that). Anyway, that's the way it works. Oh, as for Hawking. The total energy of the universe is really off topic, as it involves so many other kinds of matter and energy. Quite often cosmologists just ASSUME a flat universe and calculate things like dark matter and dark energy so total energy comes out to zero, using the estimates of positive energy (mass-energy) and negative potential (gravity) we have from observation. We certainly don't have enough data from observation to be able to tell directly any such value. Yes, G-potential-fields represent a sort of negative mass-energy, in the opposite sense of ordinary positive (non gravitational) mass-energy that shows up in the matter part of the matter+gravity stress-energy pseudotensor. Never said they didn't. Just said they were always hard to locate. A highly bound object is lighter (less massive) than a loosely bound one, but that doesn't mean that all the objects in it are somehow less massive. Do you think if the gravity of a neutron star or black hole gets large enough, it might just disappear in a zero-energy quantum fluctuation? Nope (although this very question did stop Einstein in the middle of the street once, when Szilard asked him about it). A neutron star masses less than the sum of its free neutrons, is all. Just as an atomic nucleus has a mass less than the total of the mass of its free nucleons. That doesn't mean each neutron in there somehow is individually less massive. The loss of mass associated with binding energy is a system property, and cannot be located to a place within the system.  S  B Harris 02:26, 13 March 2007 (UTC)


 * Gad, you’re still complaining that Dr. Paul Marmet is flat wrong about how atoms lose mass as they go down a gravity well. And Dr. Stephen Hawking’s theories are debatable. Tell you what hot shot: You go write a huge pile of Web pages on the subject of relativity that colleges in the U.K link to, and you go write a best-selling book on cosmology, and maybe people will one day cite you as an authority on the subject. Pardon me all over the place if I chose not to cite Sbharris at the moment. Greg L 20:00, 13 March 2007 (UTC)


 * Hey, you're free to talk to your physicist pals. Mine tell me I'm perfectly correct. When you pull apart two masses, using energy from the outside, that energy adds to the mass of the system. But there's no way of telling which of the two masses it "jumps" to--in fact the entire question is improper, because it presumes that it does. Or that it proportions itself somehow between the masses, and that you know the formula for how the proportionation happens. Yeah, what is it, Einstein? Anyway, Hawking doesn't speak to this point. Marmet seems to be saying the mass added all gloms onto the smaller (less massive) particle--- I presume he has a reason for that? And what if the two particles are closer to the same mass?  Basically, you haven't convinced me that he knows, or that you know. Your arguments are a mess and not self-consistant. Nor are Marmet's, for reasons discussed. I think I've said about all I have to say about it. I'll wait for inputs from people with degrees in physics.  S  B Harris 21:05, 13 March 2007 (UTC)


 * Who do you think you’re kidding? Well, please cite these experts of yours. Greg L 21:26, 13 March 2007 (UTC)

––––––––––––––––––––––––––––––––––––––––––– The following is the original, parallel debate originally posted here. Greg L 18:45, 14 March 2007 (UTC)

"Anytime energy is added to a system, the system gains mass. For instance, lifting a one-kilogram mass upwards one meter against the force of one standard gravity increases its mass by 109.114 femtograms (1 fg = 1 × 10–15 g)."
 * There's a problem with this, and that is that it's not true! The energy is stored as potential in the system of Earth and mass as a whole, and not in the mass itself. So where exactly does this mass reside? Hard to say. Mass can be very tricky to locate, especially in g-fields. See mass in general relativity for some of the problems. In any case, if you actually do lift a 1 kg mass in Earth's gravity, nothing happens to the mass of the system at all. Since of course you just move mass from here to there, from the chemicals in your arm to the system of weight-raised-to-height. The gravitational field of the Earth as seen from a long way away, obviously does not change in processes like these (lifting things or avalanches, etc). Energy has to escape or enter the system for that. So, again a bad and wrong example for many reasons. S  B Harris 21:50, 7 March 2007 (UTC)
 * “ In any case, if you actually do lift a 1 kg mass in Earth's gravity, nothing happens to the mass of the system at all. ” No, that statement is not true. If it were, then why did you leave the one about hydro water alone? Matter going up or down: there's no difference. Matter falling into a gravity well looses mass. That's Einstein's way of looking at it. You know that's true don't you? If you don't then you shouldn't be editing this article. To the engineer, matter traveling closer to the center of the earth (or a floor) loses potential energy. The extent to which matter loses mass as it travels down a gravity well is equal to the potential energy lost as it does so. Does that surprise you? It shouldn’t. See 1.3 - Mass-Energy Conservation at a Microscopic Scale. The reverse of this process is matter gaining potential energy by being raised upwards (traveling upwards out of a gravity well). It's as valid for the kilogram weight going upwards as it is for water falling downwards.
 * I left the hydro section alone because it's confused by the issue of mass-energy (sunlight) entering the system from the outside. In that case, mass of the system is increased if water is lifted (but not if it's lifted by energies internal to the system, such as the arm of somebody). But when sunlight does the job, it's the mass of the entire system that increases, not particularly the mass of the lifted water. The energy gained when sunlight is added to the system can be viewed as being stored in the gravitational field as much as anything else. In any case, it'd hard to say where it is, and it's certainly improper to view it as being stored as extra mass in the raised water. S  B Harris 03:51, 13 March 2007 (UTC)


 * “ The gravitational field of the Earth as seen from a long way away, obviously does not change in processes like these (lifting things or avalanches, etc). ” Sheesh. Yes, that's true. But it doesn't support your position one twit! Yes, the Earth system doesn't gain mass when one raises the kilogram upwards one meter. Do you know why? What if a bunch of Indiana Jones-style sand falling onto a seesaw platform lifted the kilogram weight upwards? See? Obviously, the sand lost potential energy — and mass — as the kilogram gained. Regardless of the type of machine (even if its a human machine) that is employed to to lift the kilogram’s weight upwards one meter, it ultimately accomplishes 9.80665 J of work while accomplishing the task. All that's happening is work and a transfer of energy (and small amounts of mass) from one object or system to another.


 * Yes, indeed, but you seem to believe that the mass and potential energy have "jumped" onto the raised kg like a flea onto a cat. That's a bad way to view it, and it's really without foundation. S B Harris 03:51, 13 March 2007 (UTC)


 * “ Since of course you just move mass from here to there, from the chemicals in your arm to the system of weight-raised-to-height. ”  There, although that sentence is mangled almost beyond recognition, I can tell what you meant: you had the proper concept right in front of you but you didn't grasp its significance in order to realize it’s a non sequitur that undermined your point! Chemical energy of the human metabolism was expended in the process of lifting the weight. Ultimately, the human body is a combustion machine that oxidizes carbohydrates. The reaction byproducts (mostly carbon dioxide and water) have a teeny bit less mass — about 0.1 µg per day — than the fuels going into the reaction. Except in this case, the inefficiency of the human body is such that it lost much more energy and mass into the ambient environment than ever went into the kilogram while lifting it. Again… All that's happening is work and a transfer of energy (and small amounts of mass) from one object or system to another.


 * The "system" which holds the gravitational potential energy of a lifted rock, is rock-plus-Earth. It's not the rock (or water, or sand) per se. It's improper to view it as such. S  B Harris 03:51, 13 March 2007 (UTC)


 * If you still doubt what I’ve written here, more good reading can be found at Einstein's Theory of Relativity versus Classical Mechanics as well as Stephen Hawking’s A Brief History of Time.


 * Since you didn't grasp this, then others will doubtlessly fail to do so too. Accordingly, I added two explanatory sentences right after the sentence in question to illustrate the concept. I also added three more sentences to the end of the paragraph regarding how this is all about the exchange of energy and mass. Greg L 06:37, 9 March 2007 (UTC)


 * By using the earth as your reference frame, you're implicitly sneaking in additional information about the combined system. You're only able to specify a location for that extra mass by taking the special case where you pick your frame of reference to be one of the bodies in a two body system. To define a location for that mass you still need information about the entire system, and then to arbitrarily pick a reference point within that system, which is exactly what SBHarris has been saying. What if I decide my reference point is the object being lifted? Then it's the earth that's getting heavier. KonradG 03:49, 13 March 2007 (UTC)
 * I don't know this stuff very well, but in "references" note #6 is not appropriate. It's a footnote, not a reference, and the webpage it links to is apparently a set of very short excerpts from A Brief History of Time.  The webpage does not include anything that helps me understand what you all are arguing about.   Could you all agree on what to say and how, and leave out the long footnote?  Enuja 23:33, 12 March 2007 (UTC)
 * One editor seems to think that Hawking's view that the universe has zero energy is relevant here. I happen to agree that it isn't. Not only that, but it's not even an agreed-on view in astronomy, however much Hawking might be enamoured of it. In any case, potential energy is stored in gravitational fields as well as electric and magnetic and other fields, and I feel this statement that mass and energy used in lifting a mass of water (if they come from sunlight, say) are stored completely on the lifted water (as in the example) and not (say) at all in the Earth or the gravitational field of the Earth, is improper. And wrong. Citing Hawking's views of the energy of the universe aren't going to help this bad view. S  B Harris 04:00, 13 March 2007 (UTC)


 * Gad, you’re still complaining that Dr. Paul Marmet is flat wrong about how atoms lose mass as they go down a gravity well (“ Yes, I'm saying Marmet shouldn't be believed… ”). And you say Dr. Stephen Hawking’s theories are debatable. Tell you what hot shot: You go write a huge pile of Web pages on the subject of relativity that colleges in the U.K link to, and you go write a best-selling book on cosmology, and maybe people will one day cite you as an authority on the subject. Pardon me all over the place if I chose not to cite Sbharris at the moment. For the complete history of Sbharris’s writings on this topic, see my user talk page.  Greg L 20:12, 13 March 2007 (UTC)


 * P.S.: I just got off the phone with one of the authors of The Apache Point Observatory Lunar Laser-Ranging Operation (APOLLO) paper (132 kB PDF, here) written by five people, some of whom work for the University of Washington, Dept. of Physics. This is the experiment where researchers are looking for extremely small violations in Einstein’s Strong Equivalence Principle (SEP) by measuring the Earth/Moon distance with lasers. Yes, raising a kilogram upwards against gravity increases its mass. That’s what he/she confirmed. I’ve e-mailed him/her the link to this Wikipedia article and asked him/her to review what I’ve added. In the mean time, please leave the disputed text alone so people with Ph.D.s and lots of expertise in this subject can review it. I’ll ask his/her permission to post his/her response here — and to cite his/her name — after he/she responds.  Greg L 20:48, 13 March 2007 (UTC)
 * Hillarious. So the extra mass "knows" to go into the raised kilogram and not the raised Earth. Remember, you're just separating two objects with a force, and yet all the energy of your doing so just jumps to one of them, and sits there. That's some smart energy. I can't wait for the equation which tells how your physicist friend knows this. Standing by (but I think you're in for a red-faced admission that the addded mass doesn't have a location in space you can point to). S  B Harris 21:12, 13 March 2007 (UTC)
 * The only thing that is hillarious, is your saying people should believe Sbharris, but to not believe Dr. Hawking and Dr. Marmet. Greg L 21:43, 13 March 2007 (UTC)
 * Greg, I think you're missing the point. It's not a question of whether you can measure a mass increase, but whether that measurement is *observer-independent*. Your example only works because you've arbitrarily defined your reference frame to be the two-body system minus the object being lifted. Of course the relativistic mass is going to appear in that object, since that's the only thing left. KonradG 22:59, 13 March 2007 (UTC)


 * KonradG: I don't understand why you feel I chose an "arbitrary" frame of reference. As I wrote, the frame of reference is an absolute one, i.e., relative to the center of mass of the two objects being separated. A mass measurement must be observer-independent; one can not have a situation where different observers (above or below the object) arrive at different mass measurements. Lifting a weight upwards one meter against Earth's gravity is simply an issue of adding potential energy into an object by increasing its separation from the center of the Earth. What I wrote is explicitly and unambiguously supported by Dr. Paul Marmet in his 1.3: Mass-Energy Conservation at a Microscopic Scale. This is but one section from a single Web page from a comprehensive treatise on Einstein’s equations titled Einstein's Theory of Relativity versus Classical Mechanics. The concept that matter loses mass as it falls down a gravity well is vividly illustrated by Stephen Hawking’s in his A Brief History of Time when he said that precisely zero energy remains if all the matter in the Universe fell down the entire gravity well of the Universe in a Big Crunch.


 * The only way that Sbharris has been able to deal with this fact is to simply declare that Dr. Marmet and Dr. Hawking are incorrect. Hey, life’s damn simple when you deal with problems that way, isn’t it? I don't know why I bothered to contact the researcher who participated in the APOLLO laser ranging experiment looking for any violation of Einstein’s Strong Equivalence Principle (SEP). Today, that individual said: “Yes, raising the height of an object above Earth increases its mass” and elaborated as to why this is the case. Kinda black & white don't you think? Sbharris’s solution to this bit of news: declare that the relativity researcher is incorrect too! Wow… As I said before, pardon me all over the place if I chose not to cite the likes of Sbharris and instead chose to cite experts like Dr. Marmet.  Greg L 00:35, 14 March 2007 (UTC)

This is a reference frame issue. From Chapter 20, Section 4, page 467 of Gravitation by Misner, Thorne, Wheeler (the bible of General Relativity):


 * "Anybody who looks for a magic formula for "local gravitational energy-momentum" is looking for the right answer to the wrong question. Unhappily, enormous time and effort were devoted in the past to trying to "answer this question" before investigators realized the futility of the enterprise.  Toward the end, above all mathematical arguments, one came to appreciate the quient but rock-like strength of Einsten's equivalence principle.  One can find in any given locality a frame of reference in which all local 'gravitational fields' (all Christoffel symbols, all gamma(alpha,mu,nu)) disappear. No gammas means no 'gravitational field' and no local gravitational field means no 'local gravitational energy-momentum.'


 * "Nobody can deny or wants to deny that gravitational forces make a contribution to the mass-energy of a gravitationally interacting system. The mass-energy of the Earth-moon system is less than the mass-energy that the system would have if the two objects were at infinite separation.  The mass-energy of a neutron star is less than the mass-energy of the same number of baryons at infinite separation.  Surrounding a region of empty-space where there is a concentration of gravitational waves, there is a net attraction, betokening a positive net mass-energy in that region of space (see Chapter 35).  At issue is not the existence of gravitational energy, but the localizability of gravitational energy.  It is not localizable.  The equivalence principle forbids."

An increase in gravitational potential energy therefore cannot be localized in any single mass or field in a way that is invariant for all observers. Whether the mass of an object raised in a gravitational field rises depends on where you look at it from. In particular, an observer remaining near the object raised, say in close orbit around the raised object, will not see the raised object's mass increase. On the other hand, an observer in a fixed position relative to the Earth would plausibly see the object's mass increase as it moves through the Earth's gravitational potential. Someone above wrote, "one can not have a situation where different observers (above or below the object) arrive at different mass measurements...." In fact, you can, just as in Special Relativity different observers arrive at different mass measurements of the same object depending on relative motion. It is meaningless to speak of mass changes without clearly specifying the observer dependence. Brian Wowk 06:35, 14 March 2007 (UTC)


 * Brian and Steve are correct: the kilogram mass remains mass-invariant as it is raised or lowered in a gravitational field. The energy change is accommodated by (i.e. stored in) the gravitational field itself.  I refer you to Alan Guth who says
 * "Since the negative energy of a gravitational field is crucial to the notion of a zero-energy universe, it is a subject worth examining carefully. In this appendix I will explain how the properties of gravity can be used to show that the energy of a gravitational field is unambiguously negative. The argument will be described [in the appendix] in the context of Newton's theory of gravity, although the same conclusion can be reached using Einstein's theory of general relativity."" (See Guth's "The Inflationary Universe" (ISBN 0224044486) Appendix A).
 * Guth considers the work that can be extracted from a collapsing spherically symmetric shell of matter; the argument has obvious application here also. --Michael C. Price talk 09:49, 14 March 2007 (UTC)

I looked at the Marmet web page that is used as a cite support the apparent absolute mass increase argument. Marmet discusses the famous Pound Rebka experiment in which a red shift of gamma rays is seen when gamma rays climb through a distance in Earth's gravity. He shows how this can be explained as mass change in the atoms lowered in the field. This is not surprising since it is common in physics for different interpretations to give equivalent and results. However the mass change interpretation of this experiment proves nothing about any absolute change of mass. For if the emitter and absorber are lowered together, rather than separated by a distance in the gravitional field, no red shift or apparent mass change will be recorded. It's all relative.

There is another problem that needs to be addressed. Marmet was a well-known iconoclast with unconventional interpretations of a great many topics in physics. Encyclopedia articles on important mainstream physics topics should cite mainstream sources when necessary. Listing of Marmet's writings on General Relativity on crank dot net (http://www.crank.net/einstein.html) is prima facie cause for not using Marmet cites in a mainstream encyclopedia article involving GR.

The current article text claiming that mass-energy increase is uniquely confined to single bodies rather than the composite system when gravitating bodies move apart is misleading, and should be changed. It isn't even true classically. Brian Wowk 16:25, 14 March 2007 (UTC)


 * Good quotes Brian. Thanks. I wish I had the book. But I carefully read what you quoted and believe you are misinterpreting its meaning. It’s clear to me what the first section (two paragraphs) you quoted are addressing: gravitational energy is not localizable. It does not address the issue of whether a matter-based body can be localized; that’s pretty much a “Well… Duhhh issue isn’t it? Further, the second paragraph in the first section you quoted from is merely supporting what I wrote: that according to the Einstein’s Strong Equivalence Principal, gravity’s self-energy has inertial and gravitational mass. The second paragraph you quoted says nothing more.


 * The third paragraph (the very last section you quoted) Brian, simply supports what Dr. Stephen Hawking wrote in his A Brief History of Time (and which I cited): that matter loses mass as it falls down a gravity well. More specifically, that when all the matter that exists falls down the biggest gravity well in existence, it looses all its mass and gravity disappears; there is zero net energy (mass) in the Universe. This is just an extreme example of scaling the effect to the largest possible dimensions. What Hawking — and now Guth — wrote both support what Dr. Paul Marmet wrote in his 1.3: Mass-Energy Conservation at a Microscopic Scale (and which I also cited), which simply states that when matter is lowered down a gravity well, it loses mass. Except that Dr. Marmet accomplishes this via an example at the other extreme: with a single hydrogen atom.


 * I simply wrote — and cited — what one author (a Ph.D. in the subject) explicitly wrote, and what two others support via analogy at a grand scale. I don’t have the supreme confidence that Sbharris and others do, where I would simply announce that I am so damn expert in the subject, that I will declare that a published Ph.D. author is flat wrong. Dr. Paul Marmet wrote his 1.3: Mass-Energy Conservation at a Microscopic Scale and I cited it. Please note that this citation is but one section, from a single page, from a comprehensive treatise on Einstein’s equations titled Einstein's Theory of Relativity versus Classical Mechanics. In turn, this treatise is one of many topics available on the Intute: Science, Engineering and Technology Web pages, which is a shared resource of the Consortium of Academic Libraries in Manchester. What did he exactly write? This:

According to the principle of mass-energy conservation, the mass of the hydrogen atom in the basement is now different from its initial mass mo on the first floor. It is slightly smaller than mo and is now equal to mb. Any variation of g with height is negligible and can be taken (with g) into account in equations 1.4 and 1.5.


 * Note further, that yesterday I contacted one of the researchers who helped test, to extreme precision, Einstein’s Strong Equivalency Principal (SEP), and who helped write The Apache Point Observatory Lunar Laser-Ranging Operation (APOLLO), T. W. Murphy, Jr. et al. University of Washington, Dept. of Physics (132 kB PDF, here). That individual also said "Yes, raising the height of an object on Earth increases its mass.” Sbharris declared this person to be wrong too (in addition to Dr. Hawking, Dr. Marmet, and apparently any other famous Ph.D. who disagrees with him).


 * It seems clear to me that the issue here is that Sbharris et al. feels that the added energy and mass caused by separating objects is bound in the gravity field, not in the object that was moved. I apparently don’t have anywhere near the brass to simply declare that because I am a Wikipedia contributor (*insert drum roll and heavenly voices here*), that I am expert enough to declare all these guys are full of crap. I do however, poses enough capacity to think logically to recognize the fallacy of thinking that separating two bodies against the force of gravity adds the energy (and equivalent mass) into the gravitational field and not the body that one accelerated and moved. Think: matter creates gravity. According to the Strong Equivalence Principal, gravity has a self-energy (and an equivalent mass). The only thing that creates a gravitational field in the first place is mass. The only thing. So why would someone think that added potential energy would add directly to the gravitational field and handily bypass the mass? This, in spite of the fact that all four authors mentioned above are consistently saying that matter loses mass as it goes down a gravity well?


 * Note too that while I was talking to the researcher who participated in the SEP experiment (using Lunar laser-ranging) the individual explained to me that an object falling down a gravity well doesn’t loose mass — at least at first. It loses only if it is lowered down a gravity well. Why? Because as it falls, stationary matter (and its equivalent energy), plus its potential energy (and its equivalent mass) become moving matter (and its equivalent energy), and kinetic energy of motion (and its equivalent mass). Please think about this. If you do, you will realize that this too fully supports the notion that the added energy and mass resides in the body. This also makes it logically impossible for the added energy and mass to go into the gravitational field. Here’s why I think this is the case:


 * A gravitational field can have no knowledge of the velocity of the falling object, only its position. The magnitude of the combined Earth/object gravity doesn’t change appreciably as an object is either lowered or falls towards the center of the Earth. Before an object falls, it has maximum potential energy and maximum mass. Shortly after it begins falling, it rapidly exchanges potential energy for the kinetic energy of motion. Let’s assume it’s falling in a vacuum so frictional losses aren’t an issue. Accordingly, (since some potential energy converted into kinetic energy) the object’s mass hasn’t hardly change at all. OK, stop. Let’s examine two scenarios at this point: 1) one object is falling and still retains the energy (and mass) associated with its kinetic energy; and 2) let’s consider another object that was lowered by a machine (human or mechanical) so there was no conversion of potential energy into kinetic energy. From the point of view of Earth’s gravity field, both objects are in the same position. So where is the missing energy and mass in the one that was slowly lowered? Answer: it’s in the object, not the gravity field. OK, let’s continue the drop. As the object continues to fall closer to the center of the Earth, Earth’s gravitational force on the falling object decreases so its potential and kinetic energies (and mass) diminishes. By the time the object creeps to the center of the Earth, its total energy is at a minimum. So too is it’s mass. However, if someone lowers the object one meter and accomplishes work against the force of gravity (but no conversion to kinetic energy), its total energy and mass diminishes. Note that the above logic is in accordance with the writings of all the above-mentioned published Ph.D. authors and doesn’t depend on the rather brassy argument of saying they’re all wrong. I will shortly revise what I wrote so some instances of “falling” are changed to “are lowered” (or equivalent words). Come to think of it, I'll leave the classic word “falling” alone with regard to Einstein’s teachings. What the SEP researcher said is a transitory condition. The concept of matter falling into a gravity well applies for a single atom being lowered to the basement just as well as for all the matter in the Universe falling into a Big Crunch. Greg L 18:33, 14 March 2007 (UTC)


 * I also carefully explained to you that there was a difference between letting the body fall, and lowering it. At that time, you ignored me and chose to believe I was contradicting myself. I'm glad now you chose to believe somebody else, explaining the same distinction. But now, if you'll continue with this same situation, you'll see that it actually does not support your point of view. A falling body does not contain the extra mass attributable to its kinetic energy, except in certain reference frames. In the frame of the body, it never appears, for example. Thus, kinetic energy is yet another example of mass in a system which isn't localizable, and may appear as a righteous and real quantity in a system (like this example one!), but yet doesn't have a location where you can point and say "Everybody agrees it's right THERE". A rock falling down a g-well trades gravitational potential for kinetic energy, and the mass of one sort of energy becomes the mass of the other sort. But YOUR problem in using this example is that (notice) the mass associated with the object's kinetic energy is not IN the falling object. It's in the system. From the object's point of view, it resides in the approaching Earth. From the Earth's view, it resides in the object. From frames intermediate, it is partitioned between them. Why would you imagine that mass from gravitaional potential in this system acts in any other way, than the mass associated with the kinetic energy being created as the system collapses? Come on-- you're being really recalcitrant here. Marmet's on the crank pages. Hawking is not a crank but is talking about the entire system of the universe, in which we reference total system mass (which is not localized to planets or suns or something). And your third lunar laser ranging guy hasn't got a name. Give it to me, and his statement, and I'll write him an email, explaining to him how and why he's wrong. I'll be glad to. S  B Harris 18:59, 14 March 2007 (UTC)


 * You know, when I was talking to that researcher and said I’d e-mail him/her a link to this article, we spent about 45 seconds agreeing on how I would write subject line for the e-mail; he/she wanted to be able to quickly find it. You know why? Because the researcher — who specializes in relativity — gets so much spam and e-mail from “cranks” (the researcher’s words). It’s funny since that is exactly what you are saying the researcher is. Sbharris, who adds to Wikipedia articles, will e-mail the researcher “explaining to him how and why he's wrong.” Authoring Wikipedia articles can be rewarding at times. This is a textbook example of why Wikipedia suffers in extremely technical articles. No reputable author will touch it because they don’t get attribution and any moron in a hurry can go and revise it all willy nilly. What are you, unemployed? I’ve got to get to work. I’ll be back on later tonight so see your latest. Greg L 19:22, 14 March 2007 (UTC)


 * …and then I checked my e-mail. Here’s the entire contents of what the researcher specializing in relativity e-mailed me (I asked him/her to review the Practical examples section):


 * Hello


 * here are a few comments on the first part of the article


 * "...rarely 100% efficient..." The conversion is always 100% efficient in the sense that the change in energy is always c^2 times the change in mass.
 * But it is rare to convert all the mass into energy.


 * the notion of "realtivistic mass" is outmoded and confusing. I would not discuss it al all.


 * the section on other works at the end doesn't serve much useful purpose because many of the references are only of vague historical (but not scientific) interest.


 * {closing salutation deleted}


 * {name deleted}


 * He/she didn’t seem to have a problem with what I wrote. Note too that the "...rarely 100% efficient..." is from the last paragraph of the “Practical examples” section. I had deleted most of that particular paragraph but one Mr. Sbharris put it all back in. My edits also make no mention of "relativistic mass" so this, in addition to the last comment, makes it clear that the researcher read much more than I asked the him/her to. I’ll e-mail back to make doubly sure the researcher reviewed my contributions. Well, I guess Sbharris has a mighty low opinion of this researcher now!! Tell me Sb, what are your qualifications that embolden you to challenge a published researcher who investigated Einstein’s Strong Equivalency Principal and makes you want to e-mail this individual “explaining to him how and why he's wrong.”? Do tell, what are your qualifications that make you so willing to challenge published experts. As I said earlier, I really need to get to work now. Back later. Greg L 19:58, 14 March 2007 (UTC)

I'm sorry that I haven't had the patience to read the entire flamefight before posting, so I hope this is not redundant. It should be obvious from reductio ad absurdum that the entire mass gain from raising a kilogram above the Earth cannot in principle reside completely in the kilogram in question. Imagine that the Earth weighed one kilogram, or rather, that you are somehow sitting between two identical kilogram objects somewhere in space. If you "raise" one of them by separating it from the other, where does the change in mass go? There's no way of choosing. Now, if you make one of them heavier, maybe you could argue that the majority of the mass change goes only to one of them. In the limit of infinite mass, you could say that all the mass change belongs to one object. However, the Earth does not have an infinite mass, although it may be a good approximation in practice when compared with one kilogram. I have the impression that Greg's point of view has a implicit geocentric assumption that should be made explicit to clarify why he assigns the change in mass to the kilogram. Leaving mass aside for a moment and going back to classical physics, it is basic knowledge that the potential energy change does not "belong" to the kilogram but to the Earth-kilogram interaction. Therefore the statement made in the footnote that "the potential energy — and mass — the kilogram gains by rising out of Earth’s gravity well is independent of its position relative to an observer" is simply not correct in principle. The kilogram does not gain potential energy--the system does. --Itub 10:44, 16 March 2007 (UTC)

Local conservation of energy in general relativity vs. other theories
Since the previous article is getting rather long, I'll start a new one to simply note that it was noted quite early by everybody that general relativity, unlike other field theories, doesn't have any local conservation of energy (and consequently no local conservation of mass or exact physical location [i.e., to any arbitrarily small volume] of gravitating mass-energy, in space). This bothered quite a few people, including Hilbert and Einstein. The basis for the underlying problem in terms of how the theory was constructed, was finally located by Noether, who merely noted that it wasn't fixable, and was indeed a feature of the math used in the theory itself. The following article has been pointed out to me, and contains a good discussion of the problem which bears on all we're discussing here. In a gravity field, you simply cannot finally locate and "conserve" mass-energy, except globally (by drawing your integral surfaces far away, in flat space). In gravitatinoal fields, mass-energy is impossible to pin down locally (to an arbitrarily small volume, so you can talk about an absolute mass-energy-density which everybody agrees on). This includes the absolute physical location of the total energy associated with the kg being raised in the g-field in our sample problem, and which is transfering potential energy TO that field (not just to the physical region where the kg is located). Here's a quote from the article, from a paper by a physicist at UCLA. "To illucidate these matters further, we discuss in some detail field theories of matter, gravity, electromagnetism, etc. in both special and general relativity. In special relativity these theories have a `proper energy theorem' in the sense of Hilbert and we will show how `proper energy theorems' give a principle of local energy conservation. In general relativity, on the other hand, the proper energy theorem becomes improper in that the energy-momentum tensor for which the theorem holds is gauge dependent. As will be shown below, there is transfer of energy to and from the gravitational field and it has not meaning to speak of a definite localization of the energy of the gravitational field in space(5). Consequently we do not have a principle of local energy conservation in spacetime regions in which there exist gravitational fields." S B Harris 20:22, 14 March 2007 (UTC)


 * You know, when I was talking to that researcher and said I’d e-mail him/her a link to this article, we spent about 45 seconds agreeing on how I would write subject line for the e-mail; he/she wanted to be able to quickly find it. You know why? Because the researcher — who specializes in relativity — gets so much spam and e-mail from “cranks” (the researcher’s words). It’s funny since that is exactly what you are saying the researcher is. Sbharris, who adds to Wikipedia articles, will e-mail the researcher “explaining to him how and why he's wrong.” Authoring Wikipedia articles can be rewarding at times. This is a textbook example of why Wikipedia suffers in extremely technical articles. No reputable author will touch it because they don’t get attribution and any moron in a hurry can go and revise it all willy nilly. What are you, unemployed? I’ve got to get to work. I’ll be back on later tonight so see your latest. Greg L 19:22, 14 March 2007 (UTC)


 * …and then I checked my e-mail. Here’s the entire contents of what the researcher specializing in relativity e-mailed me (I asked him/her to review the Practical examples section):


 * <tt>Hello</tt>


 * <tt>here are a few comments on the first part of the article</tt>


 * <tt>"...rarely 100% efficient..." The conversion is always 100% efficient in the sense that the change in energy is always c^2 times the change in mass.</tt>
 * <tt>But it is rare to convert all the mass into energy.</tt>


 * <tt>the notion of "realtivistic mass" is outmoded and confusing. I would not discuss it al all.</tt>


 * <tt>the section on other works at the end doesn't serve much useful purpose because many of the references are only of vague historical (but not scientific) interest.</tt>


 * <tt>{closing salutation deleted}</tt>


 * <tt>{name deleted}</tt>


 * He/she didn’t seem to have a problem with what I wrote. Note too that the "...rarely 100% efficient..." is from the last paragraph of the “Practical examples” section. I had deleted most of that particular paragraph but one Mr. Sbharris put it all back in. My edits also make no mention of "relativistic mass" so this, in addition to the last comment, makes it clear that the researcher read much more than I asked the him/her to. I’ll e-mail back to make doubly sure the researcher reviewed my contributions. Well, I guess Sbharris has a mighty low opinion of this researcher now!! Tell me Sb, what are your qualifications that embolden you to challenge a published researcher who investigated Einstein’s Strong Equivalency Principal and makes you want to e-mail this individual “explaining to him how and why he's wrong.”? Do tell, what are your qualifications that make you so willing to challenge published experts. As I said earlier, I really need to get to work now. Back later. Greg L 19:58, 14 March 2007 (UTC)

Let me check something. Greg, do you understand that as a box containing a heavy object is lowered by a rope into a uniform gravitational field at uniform speed that nobody inside that box will measure the mass of the object to decrease? Do you accept that the appearance of mass change depends on observer position? If so, maybe this can be resolved quickly.

By the way, toward the end of the last section the discussion was getting inappropriately personal. SBHarris is justifiably concerned about his position being misrepresented to the consulting physicist, whose position might in turn be misrepresented here. This can happen without malice simply because the issues are complicated. Brian Wowk 21:36, 14 March 2007 (UTC)


 * Last thing first. "Getting personal" with Sbharris is an unavoidable part of addressing a legitimate editorial problem: I'm citing reputable sources and his arguments basically boil down to "your Ph.D.s are all wrong but I’m right.” Further, he’s even prepared to e-mail a researcher who makes a living doing experiments on subjects like relativity (and who participated in a landmark paper on an experiment that confirmed Einstein’s Strong Equivalence Principal with remarkable precision) to tell them how and why they are wrong! Endlessly badgering contributors with that sort of crap doesn’t fly. And implicit behind all of this crap is that he'll sneak in and delete stuff that he disagrees with after the winds of disagreement with him die down. Again, pardon me all over if I cite world-recognized authors and choose not to cite Sbharris. Note further that the relativity researcher (working at a university) who I talked to and e-mailed took pains to instruct me on how to address the subject line of my e-mail because he gets so many e-mails from "cranks."


 * Now the first thing. Mass is the measure of a body’s resistance to accelerating (distance integrated across time squared). When you explicitly write that people inside the box (at the same level as the kilogram weight) observe no change in its mass, you seem to be implying that people outside the box will observe different masses for the kilogram inside the box depending upon their location relative to the box. Is that what you think? I might parenthetically add that I agree actually with your premiss at a certain level: if the people in the box drag out their "international prototype" (reference kilogram), and compare their test mass to their international prototype using a balance beam scale, there will be no observable change because both hunks of matter lost equivalent amounts of mass. But if one applies a force of one newton and watches the kilogram’s acceleration with a laser (which provides both meter-stick and clock effects), what do you think different people will see from different vantage points?


 * I've got to tell you that arguing endlessly about this stuff isn't my cup of tea. I don't like it. I've cited two sources that say that all matter in the universe loses all its mass as it falls down the largest gravity well in the Universe. Some of you don't think that means that matter going down a gravity well loses mass. I can't help that. I further cited a published Ph.D. who said lowering a single hydrogen atom to the basement makes it lose mass. Some of you say this Ph.D. is wrong too. I can't help that either. In response to endless challenges from you-know-who, I contacted a published expert in relativity who said "Yes, raising a kilogram upwards against the force of Earth's gravity increases its mass. The response from you-know-who is that the researcher is wrong and he wants to e-mail the researcher to tell him how and why he’s wrong. I asked that expert to review what I wrote and he/she responded with no problems (with what I wrote anyway). Well, we all know what you-know-who’s response will be to that: the expert is really really wrong now! Contributing to this particular article is about as rewarding as wiping my rear end with poison ivy because of the intellectual arrogance of a few (people who think they've got advanced concepts on relativity figure out better than the experts). I didn't know what I was getting myself into when I landed here.


 * Now, I'm done arguing with you people. Period. If you delete what I wrote. Fine. Cite your sources and do it well. If I think it's garbage, and feel like it, I'll be back. I might add Fact to it. I might revert it. Whatever I do, I'll politely and logically explain what I've done to the betterment of the article. As you can see from the entire sordid history written above (I'm talking the entire topic above this one too), I've patiently tried to patiently explain and justify what I've written. There has to be a logical conclusion to this process. Unfortunately, there simply can't be when arguing with certain types of people (the one's who think they've got it all figured out and the experts are all wrong). As much as Sbharris wants me to think that the researcher who helped conduct the APOLLO experiment and write the report is all wrong and Sbharris is right, any right-thinking person would think that notion is nutty on the face of it. This discussion page experience has been too weird for me to handle. This all simply demonstrates why the Wikipedia way of arriving at correctly written, highly technical articles is going to be a tough row to hoe. Goodbye. Greg L 23:19, 14 March 2007 (UTC)

Generally speaking, web-published papers by authors who have a listing on crank.net are not a good source for wikipedia articles.

See for instance http://www.newtonphysics.on.ca/BIGBANG/Bigbang.html as to why Paul Marmet deserves his crank.net entry as "Cranky".

Meanwhile, E. Noether's discovery of the deep connection between symmetries and conservation laws. (English)

also cited, has been published (at a conference proceeding), unlike the Marmet article.

[A] Teicher, Mina (ed.), The heritage of Emmy Noether. Proceedings of the conference, Bar-Ilan University, Ramat-Gan, Israel, December 2--3, 1996. Ramat-Gan: Bar-Ilan Univ., The Emmy Noether Research Institute of Mathematics, Isr. Math. Conf. Proc. 12, 67-81 (1999).

It's a much higher quality reference.

The statement that an object in and of itself gains mass when it raised is not, IMO, correct as written. It would need to be qualified significantly to be correct, and would need a much better citation than the one from Paul Marmet, or some "anonymous researcher".

Anonymous researchers are just not acceptable under WP:Verifiability

I think the statement that an object in and of itself gains mass when raised in a gravitational field could be justified if one considers only stationary systems and the Komar mass. (I do not have a suitable reference which directly says this at hand, however direct computation of the Komar mass supports this. Since the computation is rather technical, it probably needs a full reference to meet WP:Verifiability).

However, with more general notions of mass such as the ADM mass, while one can compute the mass of a system, one cannot in general assign that mass a location. This statement has been documented in the article by Mina Teicher previously quoted by SBHariss.

Thus I substantially agree with SBHaris on this issue, and disagree with Greg L.

I think that possibly some compromise could be worked out if Greg L. could qualify his statements more precisely, and find some better references (i.e NOT web-published papers by Paul Marmet).

Pervect 02:31, 15 March 2007 (UTC)


 * Thank you. I have considered this a good-faith discussion, but when it gets to the point that simple questions of logic are just referred off to the statement of some anonymous Ph.D. who I cannot contact to verify he thinks what he supposedly thinks about these specific issues, and the only cites in evidence are from a living crank (who is on Greg L's. side) and a dead recognized genius (who I think's on mine), we're in trouble. We could push the discussion along with we had somebody with credentials we could talk with. For example, we don't even know if Greg L's pet APOLLO researcher has been specifically asked to vet the specific sentence in question, and Greg L.'s been cagey about that very issue (see above). So what reason do I have to trust all this, at fourth-hand? Marmet seems to think all gravitational added energy shows up in the smaller of the masses, AS measurable mass, IF there's a big disparity in magnitude of the masses (as in the atom, or the kg, vs. the Earth). But what if the two masses pushed apart, have the same mass? Do they equally divide the energy and equally increase in mass? Is there a (purportedly linear) equation to describe this? I'm skeptical. I have a right to be. I don't believe it. Neither do the other posters so far, of whom I have good reason to believe one is a relativist, and the other of which I know is a Ph.D. physicist. Greg L, if your response is "Sionara, but my secret Ph.D. says you're full of it, and my published Ph.D.'s a crank, but at least is published" I don't think you'll fly. We'll eventually get Thorne or somebody on this page to discuss the issue, and that will be the end of it. S  B Harris 20:01, 16 March 2007 (UTC)


 * Actually Marmet died in 2005. There is great irony that Marmet would be cited in a discussion that decries Wikipedian ignorance about subtleties of General Relativity when Marmet's main claim to fame was repudiating the entire field of relativity in favor of his own cranky theories. Would the anonymous relativity worker cited in this thread, who has such trouble with crank emails, have accepted an email from Marmet?? Brian Wowk 23:20, 16 March 2007 (UTC)

In any case, it's been two days since Greg L declared that he refuses to continue the discussion, apparently abondoning any attempts at reaching a consensus. As all the other participating editors (SBHarris, MichaelCPrice, Brian Wowk, Pervect, Itub and myself) seem to be in agreement, I believe we now have a consensus by default. KonradG 04:55, 17 March 2007 (UTC)


 * I fixed the contentious sentence that started this enormous thread. Someone else needs to fix the hydroelectric power generation example, which suffers from the same problem. Hydroelectric power has so many complex E=mc2 issues that I don't think it's pedagogically useful in this article, and should be deleted. Brian Wowk 06:45, 17 March 2007 (UTC)

Challenges to E = mc²
I just reverted some changes by an editor who modified the lead to "correct" the mass-energy equivalence formula to some supposed limited special case it actually applies to. The point of the article is to introduce E = mc², and I don't think it's a good idea to muck things up too much in the lead. Any challenges to the verity or applicability of the formula should be (a) made further down in the article and (b) well-sourced. My $0.02. Robert K S 04:48, 20 May 2007 (UTC)


 * The lead is now even simpler. I believe that the lead of every article should make an attempt to be both correct and comprehensible by the non-specialist. Original references (and online copies) have been added.


 * The edit reflects the current view in physics, that has been mainstream for more than 50 years now. The previous version also had material that is already available elsewhere in WP, which material is now linked to instead of copied again. So, the article got leaner. Please let me know if you have any other specific question. Thanks. Edgerck 12:14, 20 May 2007 (UTC)


 * corrected also the part on atomic weapons. Contrary to popular belief, the strong nuclear binding energy is the main reason for the power of nuclear fission and nuclear fusion atomic weapons, not E = mc². The main energy contribution is due to binding energy conversion to other forms of energy, not mass conversion.Edgerck 14:19, 20 May 2007 (UTC)


 * I am not an expert. However, I fail to understand how a view that has not been "mainstream for more than 50 years"--that in theory mass has an energy equivalence and energy has a mass equivalence--could remain in the lead of this page and its predecessors for a year, with dozens of parties qualified to challenge it having vetted it by virtue of the text being allowed to stay as-is.  Then you come along and tell us everything you know is wrong, rewriting the article with minimal references and obliterating quite a bit of the work that has been built over the months.  Except for the minimal references, none of the above is objectionable on Wikipedia, but you may need to build consensus for each section of the text before your rewrite is fully implemented.  Please don't give up, and please keep contributing.  But don't be surprised that you're having your work reverted, when it seems to go so completely against the grain of the former versions of the article. Robert K S 14:35, 20 May 2007 (UTC)


 * Please do not delete content from articles on Wikipedia. Your edits appear to be  vandalism and have been reverted. If you would like to experiment, please use Sandbox for test edits.   DavidCBryant 14:23, 20 May 2007 (UTC)


 * I am not experimenting and my changes are correct, all of them. Editors are encouraged to be bold in WP. Especially when content is mostly incorrect, and off-topic, as it was. Hope this helps. Edgerck 14:33, 20 May 2007 (UTC)


 * WP:BB is a great policy, and you have followed it correctly. However, you now must deal with the unpleasant aftermath of boldness: cranky conventional conservatism, which can be as harmful in its inertia as it is helpful in its moderation and self-regulation of major upheavals.  The appropriate steps to now take are to discuss your changes with those who might disagree with you, and to provide good sources.
 * Speaking of being bold, please be careful about your use of bold text in the leads of Wikipedia articles, as it has a special meaning in the lead. Also, note that equations should be properly formatted with their variables in italics (but not numerical superscripts). Robert K S 14:40, 20 May 2007 (UTC)


 * Thanks, point taken in bold. Anyone is welcome to improve on the equations. I just saw that the article was again reverted to its old and incorrect version. I am not going into edit wars. My version speaks for itself, and (as far as I see it) has all the references required. If someone would like to question it, or ask for additional references, please refer to the specific point(s) in question. I am available here. I ask for Robert K S to please re-revert the old version to my last edit -- as I said, I am not into edit wars but to contribute. Again, edits are welcome. Hope this helps. Edgerck 14:50, 20 May 2007 (UTC)


 * Hi Ed, It's not about edit wars, it's about discussion. Your version doesn't speak for itself (it doesn't include all the requisite sources), but more importantly, it doesn't speak to the previous versions of the article which had apparent consensus.  I'm reading your second source  right now, and it's helping me to understand your objections.  Please keep in the discussion, even though immediate and total reversion to your version seems a little much to ask, as it is a drastic change, and removes a lot of material that had good reason for being there, especially in the "History" section. Robert K S 15:06, 20 May 2007 (UTC)


 * Robert: Please take your time to read the references I provided. That reference [2] is an updated summary of "The Concept of Mass", in Physics Today, June 1989, free online at []. The old "History" section had repetitive material, which now comes from the links and references (including Einstein's paper, available online in a link in my edit). Edgerck 15:15, 20 May 2007 (UTC)


 * I have finished reading your reference #2, which is a rhetoric rather than a study, on why rest energy (i.e., E0 = mc²) should be promoted over rest mass/relativistic mass (i.e., E = mc²), but it acknowledges that the issue is controversial. Given this controversy, is it entirely appropriate to rewrite the article in favor of one side of the controversy, without making mention of the controversy?  (I am not expert enough to definitively evaluate for myself the correctness of the argument made by the source, and am not suggesting either side is "right".  But I hope I've made my point that the changes require discussion.) Robert K S 15:43, 20 May 2007 (UTC)


 * The "controversy" not longer exists in physics and is not central to the article Mass-energy equivalence. Therefore, in my edit it was moved to the links referred to in the article.


 * The previous version had a photo of a nuclear navy ship formation that, considering how E=mc^2 is not even a major part of nuclear propulsion power, is clearly off-topic. There are many other such examples in the previous version, including entire paragraphs that are off-topic.


 * The previous version also copies "by value" what should be given "by reference". Linking material makes it possible to keep the article updated when the references change.


 * Hope this helps. Edgerck 16:03, 20 May 2007 (UTC)


 * Concur re: submarine and value vs. reference (for the most part--in some cases copying by value is required for completeness, and always ends up in the article anyway via editors who come along and say, "Why isn't this in here?") But re: controversy: your source shows that the controversy existed in 2005.  Are you suggesting that it is resolved as of 2007? Robert K S 16:16, 20 May 2007 (UTC)


 * Thanks. The new version can easily point to Mass in special relativity where the "controversy" is discussed in depth. Please note that, in physics, the controversy ended around 1950 but took about 30 years to taper off. Today, almost no peer-reviewed scientific paper in physics uses "relativistic mass". It's also a question of improved mathematics understanding -- mass is a Lorentz scalar but "relativistic mass" is not. I'd say that for the non-specialist audience perhaps another 30 years might be required ;-) But that's why Mass in special relativity exists -- physicists don't need any of it. Edgerck 16:25, 20 May 2007 (UTC)


 * I note that your contributions to mass in special relativity have also been extensive and controversial . Robert K S 16:39, 20 May 2007 (UTC)


 * That's why I cited it here. You'll find more arguments for the update there, and some "familiar" stuff. In photon, OTOH, we are still dealing with a pesky footnote [3] on "relativistic mass" for ol' time sake. Thanks.Edgerck 16:44, 20 May 2007 (UTC)


 * Consolidated changes. Improved references (accessible); cited historical relativistic mass use. Cited sections of Lev Landau and Lev Okun book references can be read without cost at . Hope this helpful. Edgerck 00:35, 21 May 2007 (UTC)

A single proton forms the nucleus of a hydrogen atom. Two protons are found in the nucleus of a helium atom. This is how if we see in the periodic table the elements are all the way up to the heaviest naturally occuring substance, uranium, which has 92 protons in its nucleus. It is possible to make two free protons (Hydrogen nuclei) come together to make the beginnings of a helium nucleus. This requires that the protons be hurled at each other at a very high speed. This process occurs in the sun,or in the center of an atomic bomb. The process is called nuclear fusion. What makes it interesting is that when the two protons are forced to combine, they don't need as much of their energy (or mass). Two protons stuck together have less mass than two single separate protons! When the protons are forced together, this extra mass is released as energy.Typically this amounts to about 7% of the total mass, converted to an amount of energy predictable using the formula

Conservation of mass and energy
I just deleted this incorrect block. There is some major editing going on right now, which I am not involved with, so I will leave the article alone.

The original text:
 * The concept of mass-energy equivalence complements but does not unite the concepts of conservation of mass and conservation of energy. While any mass can be converted to energy (such as kinetic energy, heat, or light), not every energy can be converted to mass. In relativity theory, in spite of popular philosophical discussions otherwise, mass and energy are not two forms of the same thing.  [6]

Edgerck's version--a revert
User:Edgerck did a rewrite of this page which I reverted several times previously on the basis that it introduced too many changes at once and deleted too much material, as well as introducing a conception of the material I considered controversial. I have reverted the page again, though this time not on any of those bases, but instead on the basis that cleaning up Ed's version just got too discouraging. Among other problems: etc. It would be great if Ed could humor the rest of the editors on this article by implementing his changes more patiently, one at a time. The present article, we can all agree, needs improvement, but I cannot see the Ed version as on the whole an improvement. Of course, the elephant in the room in Ed's version is that it declares that there is not really a mass-energy equivalence in mass-energy equivalence. For my own edification, if for nothing else, this needs a little more discussion and explanation. Robert K S 02:48, 25 May 2007 (UTC)
 * The formatting on almost all of the equations got mucked up.
 * The lead was substandardly written, with such phrasing as "this energy" without it being clear what the "this" was referring to.
 * No link or reference at all to the Annus Mirabilis Papers.


 * Robert: I'm not quite following your points. The last version of my revision is Revision as of 04:28, 24 May 2007. Please tell me in my last version where the problems are, both in style and content, and I'll gladly address the issues. You can create a new page with it, to facilitate editing, or sand box. Thanks. Edgerck 03:29, 25 May 2007 (UTC)


 * BTW, the version that I see used right now seems very close (if not the same) to the one that really got me inspired to Be BOLD in this article. It shoots out in too many directions, and misses all the shots that matter. Edgerck 05:27, 25 May 2007 (UTC)


 * I have just read the article "The concept of mass" you linked. It contains an error in equation 5. The argument presented for not using the rest mass and instead the total mass on the bottom of the same page is wrong. It considers the border case of v << c, but in this border case m approaches m_0 and there is no disagreement. In the case of the sections written by Einstein, it is clear that Einstein refers to the rest mass when he talks about the mass and uses an unqualified m to denote it (you can see that from the vector notation on top). Please see the Feynman Lectures on Physics I, Equation 16.13 for the correct verison of equation 5 and a detailed explanation surrounding it.


 * Richard Feynman in The Character of Physical Law wrote "The energy associated with motion appears as an extra mass, so things get heavier when they move." This POV is outdated and not used in physics today. I am sourcing this, according to WP:RS, to (inter alia) Mass.


 * Regarding the "error" you claim in Okun's paper, I kindly suggest you follow WP:RS policy. You can publish your correction of it in a peer reviewed publication at least as authoritative as the popular science "Physics Today" and then use it in this discussion. Otherwise, you are not following WP:NPOV and WP:RS. Thanks for your participation. Edgerck 19:05, 25 May 2007 (UTC)


 * I actually *gave* you a reference that claims exactly the opposite of what Okun writes in that specific section. However the usenet article on the subject is very good. You also had a very nice link to "Ist die Trägheit eines Körpers von seinem Energieinhalt abhängig?" in your private version of the article. Why don't you try to put these two in the current article to improve it? The references section in the current version surely needs an improvement.

No sig, hmmm. No reference that's not old-POV Feynman. Ok. I am replying below. Edgerck 02:37, 26 May 2007 (UTC)

WP:NPOV and WP:RS violations
Richard Feynman in The Character of Physical Law wrote "The energy associated with motion appears as an extra mass, so things get heavier when they move." This POV and the associated name "relativistic mass" are outdated and not used in physics today. The opposite view, that ("things do not get heavy when they move") and that the only type of mass is invariant mass, is not the least controversial today (see WP:RS source below). This article is in violation of WP:NPOV and WP:RS. Historical references may mention the previous use of "relativistic mass", as done in the Revision of 04:28, 24 May 2007.

I am sourcing this comment under WP:NPOV and WP:RS, to (inter alia) Mass which is a link to http://math.ucr.edu/home/baez/physics/Relativity/SR/mass.html

Regarding the "error" claimed in the "Revision 04:28, 24 May 2007" referenced Okun's paper, I again kindly suggest that editor to follow WP:RS policy. You can reference (or publish there your correction of it) from a current (past Okun's paper) peer reviewed publication at least as authoritative as the popular science "Physics Today" and then use it in this discussion. Otherwise, you are not following WP:NPOV and WP:RS.

The last version that is not in violation is of 04:28, 24 May 2007.

Again, I formally request the editor(s) who reverted from 04:28, 24 May 2007, or anyone else in the current dialogue, to reinstate that version in a timely manner, preventing other WP editors from working on the current version visible -- with the subsequent loss of work.

Thanks. Edgerck 02:37, 26 May 2007 (UTC)


 * Now after this comments that read like letters from my lawyer, what are we going to do?


 * The reason for me to visit this page for the last week was that I just accidentally stumbled upon the page in EdGerks version. I immidiately started to remove some passages from the article. That should at least contribute to EdGerks experiment, how long his edits will last. Not long for sure. Some minutes later I discovered that there was actually a completely different original version of the article, the one that is currently live.


 * Count Iblis (http://en.wikipedia.org/wiki/Talk:Mass_in_special_relativity) and I independently found out after talking to EdGerk, that he uses a completely different definition for the rest mass of a system of objects than we know. I think his definition is either plain inconsistent or at best bizzare. That is the root cause of this disagreement and it has caused some chaos in this page and the other one.

''EdGerck here: Please report truthfully. The mass definition I used is the magnitude of the energy-momentum 4-vector, which is standard in SR, and is the same as the rest mass for isolated (free) bodies at rest.''Edgerck 22:51, 28 May 2007 (UTC)


 * So it is. But then whence your odd idea that closed systems can change this mass at will, so that their "rest mass" (total 4-vector norm) goes up or down when they (say) emit a photon (which is still counted within the closed system)? Which emission you claim elsewhere DOES change the system mass? The "magnitude of the 4-vector," which is conserved across reactions, and also invariant, applies to systems just as well as single particles, and it defines the invariant mass of systems. It applies to any system in isolation. It applies to atom bombs, as causes them to have mass conservation even as they blow up, as Taylor and Wheeler make clear on pp. 248 and 249. Do I need to quote them? The problem here is that you quote correct principles, then fial to apply them when it comes to examples. S  B Harris 17:45, 29 May 2007 (UTC)


 * Thanks, Sbharris. I refer you to the standard, authoritative, current textbooks that I cited according to WP:NPOV and WP:RS, for any such notions as discussed here. I fully agree with those sources and don't think these issues are the least controversial today. Older texts, including Einstein's 1906 paper, may vary. Edgerck 18:26, 29 May 2007 (UTC)


 * So how can we get rid of the tag? Well, I mean apart from calling it vandalism and removing it how it was done in the mass article. I just went through the list of editors and found that User:Timb66, a Professor of Astrophysics has edited the Mass in special relativity article in the beginning of may. He also followed the discussion, but has not participated much. Maybe he could be asked to do an expert review on this article or at least provide someone else who is competent to do it (a.k.a. force a postdoc).


 * Yeah! A thankless, unrewarding, boring and nasty task. Where's our grad student...? LOL. Yes, in TALK on Mass in special relativity we did indeed find that Ed Gerck = Edgerck somehow seems to have missed the idea of defining mass (also called invariant mass or proper mass) as the norm of the system 4-momentum, since he accuses me of discussing 4-momentum as an off-topic subject when it comes to mass! And this guy is a physicist! Very odd.

''EdGerck here: Please report truthfully. My version IS in the archives and is not what you say. My comment that you were off -topic is because you were talking about 4-momentum conservation, which does NOT imply mass conservation and has nothing to do with E=mc2. ''Edgerck 22:51, 28 May 2007 (UTC)
 * What?? If mass is defined as the 4-momentum norm (which it usually is, and ought to be) then 4-momentum conservation most CERTAINLY and directly and inevitably implies mass conservation. What is it about this incredibly simple logic that you disagree with? Where is your sticking point in the inference chain, since you just repeat this wrong stance over and over? Are you just messing with me? You quote Landau and Lifschitz to back it. What page, please? I'm tired of this and I'm calling you on it. Cite your reference properly, or stop and be done with it. S  B Harris 08:46, 29 May 2007 (UTC)


 * Anyway, Dr. Gerck asks (see immediately above in this header topic) for referreces on the definition of mass more recent than Okun's 1989 paper--- and has been provided with two: Taylor and Wheeler's 1992 text SpaceTime Physics (last edition 1998), a relevant section of which is actually quoted in the Baez article which Ed Gerck seems to think supports his position Mass, though it certainly does not (it support's Einstein's notion of mass as 4-momentum norm, not total E/c^2). Also, I gave him a reference to Kip Thorne's current (2003) physics text, which is available online, and which also discusses and proves the invariance and conservation of 4-momentum in system interactions. That ought to be enough, if you accept mass as 4-momentum norm. Considering that the Baez article which Edgerck likes to quote from, explicitly makes it clear that most physicists prefer the 4-momentum derived mass definition over relativistic mass (though of course when total momentum is zero, they are the same). S  B Harris 19:25, 28 May 2007 (UTC)

There seems to be some confusion by Sbharris and CI about what I said or did not say, or what my position is (even though all the relevant WP archives are online). So, let me summarize, again. My position is that the article version according to my last revision is correct according to WP:NPOV and WP:RS and that the current version is NOT. So, I ask for whoever reverted it from my revision to go back to it as the current version. That is all. As to the physics, and mass definition, anyone interested can take a look at the answers here. Thanks. Edgerck 20:59, 28 May 2007 (UTC)


 * I was the one who reverted it, and I explained why above. You said, "Please tell me in my last version where the problems are, both in style and content, and I'll gladly address the issues", apparently ignoring that I had done so in bulleted points.  If you want to make headway on this article, I would like to propose that you reintroduce changes slowly, one at a time, and watch consensus magically build.  But (a) please be careful in your formatting of equations (properly use italics, non-breaking spaces, and subscripts when not using the math markup), (b) please don't allow your writing to entirely neglect viewpoints or controversies (just because, for example, relativistic mass is used infrequently in present-day academic publishing doesn't mean it's wrong, as one of your sources points out) and (c) please don't go willy-nilly with the deletion of material, much of which accrued here as a matter of necessity over a long period of time (I speak especially with regard to the "contributions of others" section, which, if incomplete, will be amended by various parties vexed that their E = mc² originator doesn't get a mention).  I hope you will also take my suggestion and start elsewhere than the lead.  If you're going to pressure for the lead to take a strong stance on the asymmetry of mass-energy equivalence, please take the time to build up the definitions that lead to this asymmetry in other parts of the article.  Remember, you're not writing for physicists (especially in the lead), you're writing for a general audience (terms like "massless energy" and "energyless mass" are bound to be particularly perplexing to the uninitiated reader—they've stumped me).  Thanks for your patience and keep up the good work.  Robert K S 23:06, 28 May 2007 (UTC)

Thanks. Your suggestion is reasonable and could be a good way. I'd like a suggestion as to where to begin and a group consensus to not revert if there is a disagreement -- rather, let's discuss in the talk list. As the article will probably be inconsistent while this goes on, I'd like a suggestion on a tag to warn readers. I hope this is useful. Edgerck 23:26, 28 May 2007 (UTC)


 * You may also want to read WP:FN before playing with references. (All of the cites on your user page are formatted in a way that does not conform to the Wikipedia Manual of Style.  There should be no space between periods and footnote markers, and no spaces or commas between adjacent footnote markers.)  I prefer to use  templates; they're not required, but they sure make citation formatting a heck of a lot more consistent.  All the best, Robert K S 23:30, 28 May 2007 (UTC)

Feel free to improve them. "Misteaks are a catalyst for collaboration." Thanks. Edgerck 06:17, 29 May 2007 (UTC)


 * You can do whatever you want on your user page, but if you replace an article with properly formatted citations or equations with one with improperly formatted citations or equations, I'm going to do the easy thing and revert rather than spending a lot of time fixing things up. Robert K S 06:23, 29 May 2007 (UTC)

Gimme a break. I don't buy it. If you want to delete correct and verifiable information because a couple references have an extra space, or a formula may be written differently in math-HTML, then I think you are just not balancing things according to WP policy. Imagine if every editor would that? Not even some top WP articles would survive. BTW, I did not mean you editing my user pages, as you correctly said. I can do (almost) whatever I want on my user page. Edgerck 18:31, 29 May 2007 (UTC)


 * I ask again: Why don't we try to find an expert to review the article for factual accuracy?

Robert and all: I thought about it more and, even though you kindly invited me to edit the article piecemeal, I prefer to let other people edit the information I already provided and sourced. That version is not lost, it's in the archives. I'm sure it can be much improved. I am interested in the great big question of trustworthiness of information in WP, and the binding force between editors and articles is, any way I see it, a negative factor. So, I want to reduce my own binding force to zero and simply observe once in a while what's happening with the work I already did. I don't want to be a Sisyphus. Thanks for all your nice words and keep up the good work. Edgerck 18:41, 29 May 2007 (UTC)

Merge with mass in special relativity?
I don't think we need two seprate articles on essentially the same thing. This article refers a lot to relativistic mass without syaing clearly that it is no longer used by mainstream physicists. I suggest deleting this article and redirecting to mass in special relativity (and concentrating our efforts there). Comments? Timb66 14:22, 8 June 2007 (UTC)
 * Just to provide some history, this article is already the merge of two articles, Mass-energy equivalence and E=mc². Robert K S 15:32, 8 June 2007 (UTC)

Too many digits
There are a ridiculous number of digits on the energy conversions. (yes, I know that the value of c is defined exactly, but the kg is not) This is bad science and should not appear in an encyclopedia. Timb66 02:24, 11 August 2007 (UTC)
 * If you're referring to the part where it says E = (1 kg) × (299,792,458 m/s)2 = 89,875,517,873,681,764 J (&asymp;90 × 1015 Joules), it seems to me that it's setting up a definition, not performing a calculation. Sig figs are irrelevant.  The 1 kg is meant to be exactly one kilogram, not some measurement with 1 significant figure of precision. Robert K S 10:46, 11 August 2007 (UTC)

Hi Robert. After I wrote this comment I edited the page. Look at the version on 10 Aug and you will see what I mean. Timb66 23:03, 11 August 2007 (UTC)

Derivation of E=mc^2
This "derivation" strikes me as merely a consistency check on the definition of the energy-momentum four vector. The energy-momentum four vector is defined to give you E= mc^2. Clearly, if you defined it differently, this "proof" would fall through. There seems to be almost no physics in this derivation.

It might be more interesting to put in Hasenorhl's original derivation, or Planck's. It seems to be a thermodynamic derivation is the most convicing.151.204.72.59 22:27, 22 August 2007 (UTC)Tony Rothman


 * Or Einstein's original argument, which is definitive. I added that. All the other discussions in this article just derive the momentum in special relativity, but they do not address the problem of showing that if energy is absorbed or emitted, the mass of the absorber/emitter changes. I think they should all be removed. Ditto for the ludicrous claim that Newton was aware of mass/energy. Likebox 04:54, 3 September 2007 (UTC)


 * One more comment--- Hasenorhl's derivation is about the inertia of radiation trapped by mirrors in a cavity. The idea is that if you boost the cavity, the light moving in one direction will apply more pressure than the light moving in the other direction, and thereby change the mass. This is correct, but it only includes the radiation field contribution to the mass, ignoring the container. If the container is included without the proper relativistic transformations for the container stress energy, the answer is wrong. This means that Hasenholr's derivation is not at all a derivation of E=mc2, but just yet another attempt to attribute mechanical mass entirely to electromagnetic mass. It was not just Einstein, but Poincare also, that realized that this approach was bound to fail, since non-electromagnetic stresses are necessary to confine an electromagnetic field. So to credit Hassenhorl with the result is not just contrary to established wisdom and in bad taste, it is also silly. I tried to modify the article to reflect that fact.Likebox 01:44, 5 September 2007 (UTC)

Complete historical section
I've re-arranged some sections to make an complete historical overview. I moved Einstein's 1905 derivation (made by User:Likebox) into the section Einstein (1905,1906). Also the connection Poincare(1900) and Einstein's 1906 paper ist highlighted. --D.H 08:02, 3 September 2007 (UTC)


 * While the historical discussion is mostly accurate, it is misleading because it overstates Poincare's contribution. While Poincare is certainly partly responsible for the special theory of relativity, he is not responsible for the mass-energy equivalence. Many authors in the late 19th century were aware of electromagnetic momentum, and realized that this would give a velocity-varying mass to the electron. These people believed that the electromagnetic mass would vary with velocity, while the newtonian mechanical mass would not. In this point of view, the relation between mass and velocity can reveal what portion of the mass is electromagnetic. Max Abraham, for example, predicted on the basis of a rigid spherical electron theory some now forgotten mass/velocity relation or other.


 * When Poincare talks about effective masses in fluids, he is talking about the mass caried by electromagnetic fields, not by the mass carried by mechanical objects. This is just the Poynting momentum in the field. He notes the failure of conservation laws, so he was aware that there is a consistency problem, but this is not the same as giving a consistent resolution.


 * Einstein's contribution was to place the symmetry principle--- invariance under Lorentz transformation--- at the foundation. Poincare and others saw the Lorentz transformation as a peculiar symmetry of the Maxwell equations, not as a symmetry of space time. From this symmetry law, they wished to deduce the properties of electromagnetic matter, using the Maxwell equations. Einstein started with the fundamental symmetry principle, and produced laws of mechanics consistent with the symmetry. The equivalence of mass and energy can't be deduced without assuming that all laws of physics, not just the Maxwell equations, are consistent with Lorentz transformations (and conservation of energy-momentum). Poincare was initially hostile to the Einstein point of view, since, in his words "Einstein assumed what all of us were trying to prove", referring to invariance under Lorentz transformations. If you are trying to prove the symmetry from the laws, it is clear that you consider the laws more fundamental than the symmetry.


 * Nevertheless, Poincare was aware that the Laws of physics, including the mechanical ones, needed to be Lorentz invariant, for purely empirical reasons. This is appropriate to mention in discussions of Special Relativity in general. But the mass-energy relation is Einstein's alone. For whatever reason, some people seem to want to knock Einstein off his pedestal, but this is not the place to do it. Likebox 02:06, 4 September 2007 (UTC)

It's true that Einstein was the first who derived the full consequences of mass-energy-equivalence, but I don't think Poincaré's contribution is overestimated. Poincare argued that the center of mass theorem can (partially) be saved by assuming that the center of mass frame is composed by the mass of matter and the mass of em-energy - and he used the correct formula (obviously he was following JJ Thomson, Poynting and Lorentz). Poincare's contribution to solve the center of mass problem by assuming the inertia of energy was acknowledged even by Einstein in 1906. But of course, Poincare didn’t arrived at the mass-energy-equivalence, because he didn't recognised that matter is loosing/gaining mass during the emission/absorption process and therefore he wasn't able to completely solve his radiation paradoxes. It was Einstein, who solved these problems (Darrigol, ref. 10) and the article clearly states this fact. So nobody (I hope so) wants "to knock Einstein off his pedestal". See also the article Lorentz ether theory. --D.H 10:29, 4 September 2007 (UTC)


 * This is again accurate, but I think it again misses the main point. The mass-energy relation is exactly the fact that "matter is losing/gaining mass during the emission/absorption process". It is not the fact that light waves have an effective mass. It is not the fact that light carries momentum. It is the fact that if you heat up your coffee, your coffee weighs more. Everything else is interesting work, but it isn't the mass-energy relation. The whole point of Einstein's $$ E=mc^2 $$ paper is that it is the first truly new result that Einstein could get, and not Poincare or Lorentz. It is so famous because it is a universal law, deduced from a symmetry principle, which applies in new domains beyond the narrow domain of electrodynamics which allowed you to figure out the symmetry. Poincare and Lorentz deduced from the equations of electrodynamics, and they therefore could never leave the domain of electrodynamics. So I still think that Poincare's contribution to mass/energy relation is overstated, although, of course, in kinematics and electrodynamics, he has priority on special relativity. Likebox 17:13, 4 September 2007 (UTC)

Derivation does not derive
Perhaps it should be moved to special relativity page. —Preceding unsigned comment added by Likebox (talk • contribs) 18:03, 4 September 2007 (UTC)

I just deleted the derivation--- and I want to apologize to the author because it is a correct derivation of the mass/velocity relationship. Unfortunately, the argument the author uses is inappropriate. He assumes that the work done on a fast moving particle in relativity is given by the formula dW=Fdx, which is true in the Newtonian limit, but requires justification in relativity. The notion of force is ambiguous in this equation. It could be $$dp/dt$$ or $$dp/d\tau$$. While a person who is well familiar with relativity would not get confused, I think that this derivation requires more assumptions than that which is to be shown.

While Einstein used this argument in his earlier paper on relativity, he was guided by a physical intuition about which force to use. The intuition is difficult to describe in an exposition such as this. This is why the argument in the mass-energy paper does not rely on the more complicated formulas from the earlier paper, but only uses invariance principles.

The only assumptions in Einstein's derivation is that conservation of energy and momentum hold, that the energy/momentum of light is described by Maxwell's theory, and that the momentum of a slow-moving body is described by Newton's theory. These are all incontrovertible. I hope the author can find a home for the derivation, as it is a valuable text. I just think it is not appropriate here, since it muddies the issue. —Preceding unsigned comment added by Likebox (talk • contribs) 18:53, 4 September 2007 (UTC)

Relativistic Mass/ Rest Mass
Nobody in the history of the world has ever gotten cofused about this point. Give it a rest! Relativistic mass is momentum over velocity. Rest mass is E^2-P^2. They are both useful. There is no need for all the grating repetitive clarification.

It is often claimed that Einstein had a problem with the concept of relativistic mass. He did. But as far as I remember, he had a problem with another type of relativistic mass that nobody remembers anymore. This is the ratio acceleration/force. This ratio gives two different types of mass--- the "transverse mass", which is the ratio of the transverse acceleration to the transverse force, and "longitudinal mass", which is the ratio of the longitudinal force to the longitudinal acceleration. Now the concept of longitudinal and transverse mass (which appear nowhere in the modern world) are fine things to rail against. But there's no problem with the concept of relativistic mass, and no one is confused on this point. Likebox 17:40, 5 September 2007 (UTC)

Just to add, I did a major edit, where I got rid of pompous language and repetitions, and shortened the discussion of relativistic mass/invariant mass. I also added some well known mechanisms for total mass/energy conversion. But these are very high energy processes, which are not yet observed, so perhaps they belong in their own section rather than in the "practical examples".132.236.173.27 20:36, 5 September 2007 (UTC)

I put the full conversions into their own section. I think that is clearer. Likebox 05:25, 6 September 2007 (UTC)

Abraham, Hasenöhrl
I've expanded the Hasenöhrl section to emphasize the role of Abraham. It's notable, that the corrected forumule (4/3)E/c² is from Araham, not Hasenöhrl. Also references to online available pages are included (in German). --D.H 09:41, 8 September 2007 (UTC)

Equivalent to vs. Is
Mass is energy. To say mass is equivalent to energy leads to much confusion. For example, many people have the mistaken view that when matter turns to heat the heat somehow no longer registers on a scale, because it is energy now. This is not true. I think that although it sounds like clarification, to say that mass is "equivalent to" energy as opposed to mass "is" energy seems like weasel words to me.Likebox 03:54, 28 September 2007 (UTC)


 * If the above commenter objects to the word "equivalence", what would he have the article be renamed to? Robert K S 04:26, 10 October 2007 (UTC)


 * Good point. It's ok to say equivalence every now and then, so long as the main point is not obscured by weaseling.Likebox 05:20, 10 October 2007 (UTC)

The equivalence of mass and energy is so perfect, that physicist today use the word "mass" in a different way. The "mass" as measured on a scale is just a synonym for energy, by Einstein's relation. Because it is silly to have two terms for one concept, physicists usually use the word mass to mean "rest mass". So when physicists say "light is massless", they do not mean that light would not have weight on a scale.

A box of light has weight on a scale. Although there are a lot of reverts, there is no disagreement about this.Likebox 20:38, 7 October 2007 (UTC)

Your mistake is in thinking that only mass can register on a scale. That is wrong. In General Relativity, all forms of energy (and pressure, too, in fact) contribute to gravity. An object weighs more when hot than cold because it has more energy. Similarly, a box of photons registers on a scale because it has energy. In modern usage, most physicists say photons have zero mass. Of course, if you define relativistic mass as energy/c^2 then photons have some. But relativistic mass and energy are the same thing, just in different units. So the term relativistic mass is no longer in common use by practising physicists (although it remains in many textbooks).


 * This is not a mistake, it is a convention. While you are right that, once you accept E=mc2, it is redundant and wasteful to use the useful short word "mass" just as a synonym for E/c2, it is inappropriate to use this convention when discussing the mass-energy relation itself. Always remember that you are writing for someone who is not already familiar with the equivalence of mass and energy, and for that person, mass is what is measured on a scale, while energy is an abstract quantity related to motion and heat. Once you establish that the quantity thst is measured on a scale is the energy, then it is OK to redefine the word mass to be the rest mass. But not until then.Likebox 01:21, 9 October 2007 (UTC)

Mass (i.e., rest mass, also called "invariant mass") is a form of energy. But it is misleading to say mass "is" energy. It is misleading to say one gram of mass (a dollar bill) "is" 89.9 terajoules. That is why I made the changes, and I will stand by this until you can find reputable physics textbooks that say "mass is energy". Timb66 22:56, 8 October 2007 (UTC)


 * But that equivalence goes both ways, contrary to your edit to the lead. And it's literally true that when you add energy to a box, whether in the form of heat or photons or whatever, then box weighs more on a scale, and the reason for that is that the box then has a higher mass.  The photons in a box don't have mass, but the mass of the box of photons has to include their energy.  Do you agree? Dicklyon 23:02, 8 October 2007 (UTC)


 * I am pretty sure that there is no disagreement on the facts, only on the language. There is a movement to use "mass" to mean "rest mass" exclusively, but rest mass is not additive, so it is difficult to do it consistently when dealing with composite systems. Likebox 01:39, 9 October 2007 (UTC)


 * Using mass to mean only "rest mass" is fine, but that doesn't make it hard to add up all the rest masses and energies of portions of a system to get the system's rest mass. But you can't leave out the energies, e.g. of those massless particles; they contribute to the rest mass of the box they're in. Dicklyon 05:02, 9 October 2007 (UTC)


 * Yeah, we all agree on all substantive issues. The only thing left to bicker about is the language. I am not really that committed to anything, so long as the message gets through that the energy has inertia and the mass can do work.Likebox 05:22, 9 October 2007 (UTC)


 * A dollar bill is 89.9 terajoules in the same way that a Proton is 980MeV. The dollar bill is at rest, and it can be used to produce exactly that amount of work and no more.Likebox 01:21, 9 October 2007 (UTC)

I have undone the lead that said: "mass–energy equivalence is the concept that any mass can be used to do work". It is a very unhelpful statement. I know what you are trying to say, but this is just plain wrong. Timb66 08:10, 9 October 2007 (UTC)


 * I agree that it is wrong in practice, but it is correct in principle. I can take any mass, throw it into a black hole, and use the radiation to lift weights or power my car, and the amount of work is equal to the mass (times c2). Why do you have a problem with that? Perhaps I should say "any mass can used to do work in principle"?Likebox 17:43, 9 October 2007 (UTC)


 * Better to say mass is a form of energy. This implies that it can be converted to other forms of energy, and therefore used to do work. But saying mass can be used to do work leaves out the middle step: the mass (or some of it) has to be "destroyed" in order to make the energy available. Timb66 00:14, 10 October 2007 (UTC)


 * Uncle. Likebox 19:09, 10 October 2007 (UTC)

There are two problems we are facing here. One is that some people are still equating mass with relativistic mass (total energy/c^2) rather than with rest mass. This explains how some people can argue that photons have mass. It is true that they have relativistic mass, but absolutely false that they have rest mass. So we first need to accept the modern convention that mass means rest mass.


 * I disagree that "we first need to accept the modern convention that mass means rest mass." You can do so, but you also still be clear and correct without that convention, by just clearly indicating when you mean rest mass versus when you mean relativistic mass. Dicklyon 14:25, 9 October 2007 (UTC)

The second problem is that rest mass is problematic to define for compound systems. As Dicklyon pointed out, it is sensible to say that a box of photons has a rest mass, even though the individual photons have zero mass.


 * So why are you saying it is problematic to define? It's very clearly the total energy equivalent, or sum of rest masses and energy equalivalents of the systems. Dicklyon 14:25, 9 October 2007 (UTC)


 * But the "total energy equivalent" of a system is dependent on the frame of reference, which you get to pick, so it's NOT clear what it is, or should be. It's not a single number, like the rest mass of a system, which is what the energy of the system is (divided by c^2) in the COM or zero-momentum frame. Or what the mass is, in the frame in which the system is in a box and the box has "settled down" (all the particles have bounced enough that the box now moves with the COM or CM frame velocity, which you can now freely pick as your inertial frame). In that THAT frame, the total box energy is its rest mass and relativistic mass and total energy and rest energy and so on. BUT if you pick any other inertial frame, the rest energy and rest mass of the system doesn't change, BUT the relativistic energy and relativistic mass DOES change. And so it's not all THAT obvious that the CM frame is the right frame-- it's just the most oonvenient one-- the one in which the total energy is also the rest energy, even if internal stuff is moving. There is no right frame. The easy example is two baseballs moving apart from each other in empty space, each with speed v from the observer. In this, the CM frame, their total energy is the sum of their rest energies, plus 2* [1/2mv^2] (or so). Which is their rest energies plus an extra mv^2, which is added by kinetic energy. This is the minimal energy of the system-- the least it can have by picking among the various inertial frames to look at it from. BUT, is that the REAL energy of this system? Is that the REAL mass of this system? No. The mass of the system is whatever you like! If you choose to move your observer to one of the baseballs (so that it's at rest for him), the system energy is the sum of the baseball rest masses, plus the kinetic energy of one remaining moving baseball, which is (1/2)m (2v)^2 = 2mv^2, which means it's now mv^2 more than it was when the observer saw each baseball moving at v, instead of just one, moving at 2v. Where did the extra mv^2 energy come from?? From nowhere. It's a property of space-time, that appears and disappears when you look at the system from different frames. So energy is not conserved, in that sense. It's a system property, and you get to choose the system. And gravity goes with it! Basically, that's why mass isn't well-defined in general relativity. The gravitational pull of a baseball in its rest frame is a certain amount. But if you choose your observation frame to go flying by it at speed v, its tangential gravitational pull is pretty close to 2*gamma more than it was. So it's not at all obvious what it's mass and energy are. The gravitomagnetic field is flattened. Do you integrate the whole thing to get the "true" mass and energy? Physicists haven't decided. It's a mess. See mass in general relativity. S  B Harris 05:20, 29 November 2007 (UTC)

We should be careful with language. It is sloppy (and I would say wrong) to write "a proton is 980MeV" (see above). We should say "the rest energy of a proton is 980MeV". Likewise, (rest) mass and (rest) energy are not the same (they have different units). Timb66 08:26, 9 October 2007 (UTC)


 * Agreed. We have to be very clear.  And the way to do that is not to introduce things like weight into the discussion.  But rest mass and rest energy are the same, which is the whole point; they just are expressed in different units. Dicklyon 14:25, 9 October 2007 (UTC)

Plaese don't break up comments by interspersing your own. It makes the discussion hard to follow. Timb66 00:09, 10 October 2007 (UTC)

Is E=m*c^2 an approximation?
So far as I can tell, the equation is only an approximation that disregards the higher ordered terms, which are significant in relativistic cases. Am I mistaken? Thanks. —Preceding unsigned comment added by 69.201.150.130 (talk) 19:52, 11 November 2007 (UTC)


 * Yes, you are mistaken. The equation is exact, for relating either rest mass to rest energy, or relativistic mass to total energy. Dicklyon 20:24, 11 November 2007 (UTC)


 * No, E=mc^2 is an aproximation for normal speeds. You must take into account that mass increases as you reach relatavistic speeds. The real equation for mass-energy equivalence is E=Γmc^2 where Γ is the Lorentz factor. Γ=1/(1-(v^2/c^2))^1/2. Nsnipe (talk) 18:21, 16 April 2008 (UTC)


 * But he (Dicklyon) said it was for converting rest mass to rest energy or relativistic mass to total energy. Saying you need a gamma in front of mc^2 is the same (at least mathematically speaking) as saying you use the relativistic mass to calculate total energy, isn't it?  —Preceding unsigned comment added by 70.90.239.241 (talk) 15:49, 12 May 2008 (UTC)

Light, energy and mass
Does light have mass? it is deflected by objects of mass therefore for that attraction to exist, light must have mass, as per Gmm'/r2, but it is travelling at the speed of light, so doesn't it have an infinite mass because of that. does that mean that an aluminium block with a mass of 5kg would have less mass than the same aluminium block heated by 100'c, having an increase in energy, therefore an increase in mass?Confused Physicist (talk) 09:50, 28 November 2007 (UTC)

No, particles of light (photons) have zero mass. The deflected of light by gravity can only be properly understood within General Relativity: a massive object curves the spacetime in its vicinity, and a light beam is deflected as it passes through that region. And to answer your second question: an aluminium block has a greater mass when hot than cold. Timb66 (talk) 11:23, 28 November 2007 (UTC)

No, particles of light (photons) have zero rest mass, and therefore only finite relativistic mass equal to E/c2. Dicklyon (talk) 04:18, 29 November 2007 (UTC)

Yes, I always means rest mass when I say mass. By the way, the use of finite to mean non-zero is a pet hate of mine (and a bad habit of many of my fellow physicists, sadly). :-) Timb66 (talk) 09:35, 29 November 2007 (UTC)


 * These sorts of confusions illustrate why it is best not to worry about definitions of words. To understand what is going on, you should focus on the experiments themselves, not on the labels that humans choose to give to things. Does light get deflected by gravity? Yes. Does a box of mirrors with light bouncing around inside weigh more? Yes. Does light have mass? That depends on what the human decides the word mass means. Light definitely has weight, and light definitely has inertia, but it does not have any rest-mass. So whether it has mass or not depends on the human you are talking to.Likebox (talk) 00:17, 26 December 2007 (UTC)
 * Very good answer. S  B Harris 00:37, 26 December 2007 (UTC)

True discoverer of E=MC^2
Why is there no mention of Olinto De Pretto, the true discoverer of E=MC^2?

http://www.guardian.co.uk/international/story/0,,253524,00.html

Graham Wellington (talk) 00:28, 6 January 2008 (UTC)


 * WP:SOFIXIT. Not sure what you mean by "true", but here are some sources you could draw on to fix it: . Dicklyon (talk) 00:55, 6 January 2008 (UTC)


 * It is dangerous to expose Einstein as a fraud. He is a sacred cow created by several generations of media hype. That is why I prefer to discuss this matter before editing the article. Graham Wellington (talk) 02:26, 6 January 2008 (UTC)


 * So you're worried for the author of some of those books if you report what they said? Because if you meant yourself, then yes, it would be a bad idea to go into this with the idea that you are exposing Einstein as a fraud; that's quite a POV. Dicklyon (talk) 04:19, 6 January 2008 (UTC)


 * If you read the end of the article they show that these claims have not been proven. They also say even if they are that De Pretto should not take away from Einsteins work. Nsnipe (talk) 18:53, 16 April 2008 (UTC)

Comment for Graham Wellington: Please read the historical section of the article to the end--- Olinto De Pretto's speculation is mentioned. He was not alone in his guessing game, and many others much earlier did as well. They are each mentioned in approximate historical order, and with due weight. This was the product of a long process which involved researching historical material, much of which is in German.

It is an untenable position to think that Einstein was in any way a fraud. I am speaking sincerely, as a reader of Einstein in English translation. Einstein's original papers soar above all contemporaries. They are clearer, simpler, more original, and turned out to be correct more often. There are also more of them. I am making no accusations, but historically, many people who have tried to discredit Einstein were motivated by jew-bashing, and hardly know anything about theoretical physics.

The reason De Pretto, Abraham, Poincare, Hassenhorl, and so forth are not credited with the result is that they did not and could not possibly understand it. The reason mass and energy are equivalent is because of the symmetries of space and time in relativity. Since these symmetries are present in the theory of electromagnetism, anyone who believed that mass was caused by electric fields would have come up with some sort of relation which looks like that. But to get the constants exactly right requires a good argument which links up both the mechanical and electromagnetic portions of the mass. DePretto didn't even do that, he was just doing dimensional analysis. It is ridiculous to assume that Einstein's argument, a beautiful thought experiment is in any way cribbed. This was discussed earlier on this very page.

Theoretical physics is not a guessing game. You don't get credit for guessing a result. For example, in the 19th century, maxwell predicted from his theory that one over square root of epsilon0 mu0 is the speed of light. Do you think he was the first person to notice the numerical coincidence? Probably every tenth schoolchild noticed this coincidence. But they couldn't figure out why. The contribution of DePretto is much like the contribution of those schoolkids, and Einstein's is like Maxwell--- he explained clearly what it was that is true, and why it is this way.Likebox (talk) 07:29, 6 January 2008 (UTC)


 * This is exactly what I predicted. Exposing Einstein as a plagiarist would immediately bring out fanatics who make baseless accusations of anti-semitism. The article should mention that De Pretto was the first to publish E=MC^2. This is an undeniable fact. Graham Wellington (talk) 19:05, 6 January 2008 (UTC)


 * It is an undeniable fact that a phrase like "...historically, many people who have tried to discredit Einstein were motivated by jew-bashing..." does not imply that Likebox is accusing any particular person of anti-semitism.
 * It is also an even more undeniable fact that the article says:
 * "... the correct equation E =mc2 was first published on 16 June 1903 by Olinto De Pretto, an industrialist from Vicenza, Italy."
 * I also think that is an as good as undeniable fact that it helps when one reads articles before one proposes amendments to it.
 * DVdm (talk) 19:44, 6 January 2008 (UTC)


 * "... the correct equation E =mc2 was first published on 16 June 1903 by Olinto De Pretto, an industrialist from Vicenza, Italy."
 * That information belongs at the top of the article, before any mention of Einstein. Graham Wellington (talk) 19:58, 6 January 2008 (UTC)


 * Surely that depends on whether the author really knew what he was doing. If some monkey had accidentally typed that equation in, say, 1850 and Bartocci had discovered the piece of paper, say, 150 years later, and had mentioned it as an aside in one of his articles, perhaps we should put the monkey before De Pretto. So, have you done your homework? From what you have found in the literature about De Pretto's relevance and pertinence, what can you share with us that would justify mentioning him at the top of the article?
 * DVdm (talk) 21:00, 6 January 2008 (UTC)

We all make mistakes. I made a mistake when I said SOFIXIT before checking the premise that there's "no mention of Olinto De Pretto". And Likebox made a mistake by bringing up a potential or historical motivation, diluting his argument that you just need to make sure any edits are sourced and with an appropriate level of emphasis based on the preponderance of evidence. See WP:NPOV. Let's keep our feelings and paranoias out of it, and stop pretending that anything we do here will "expose" Einstein in some way that he hasn't already been exposed in print. Dicklyon (talk) 22:15, 6 January 2008 (UTC)

There, I just made another one; forgot to look at your history first, Graham Wellington. I can see why Likebox might have brought up the motivation issue, since your history shows a preoccupation with jews and nazis. It's probably better if you don't bother to edit about such things, since there are enough unbiased editors to prevent you getting anywhere with it. Dicklyon (talk) 22:25, 6 January 2008 (UTC)


 * I am Jewish. Graham Wellington (talk) 22:41, 6 January 2008 (UTC)


 * Yep, it looks like you had made the lack of prejudice mistake, but you have put things straight now. Good for you.
 * Sorry, couldn't resist ;-) DVdm (talk) 22:38, 6 January 2008 (UTC)
 * Despite your sugar coating, the fact remains De Pretto published mass-energy equivalance two years before Einstein. Furthermore, Einstein never cited De Pretto's formula and published it as wholly his own. That is plagiarism. I understand that Einstein is a sacred cow and media sensation. Many invested a great deal of time and money in promoting him. Exposing his plagiarism would be an egg in the face of many honest scholars. Judaism teaches us to knock down false Gods. Graham Wellington (talk) 22:48, 6 January 2008 (UTC)


 * Why do you fixate on DePretto? It is not even clear that he meant "E is exactly mc2", he could have meant "E is roughly mc^2" or "E is mc^2/90". Who knows? He didn't justify his reasoning by any cogent argument, so how are we supposed to guess what he had in mind?


 * There are some issues with Einstein's scholarship with regards to Special Relativity. He probably should have cited Poincare and Lorentz in the Special Relativity paper. The only reason he didn't mention Lorentz is that he didn't know about it, and he mentions Lorentz later versions. But with Poincare, it was something else. Perhaps he felt that Poincare didn't have the physical picture right. I'm speculating. Maybe he wanted to emphasize that he wasn't relying on Poincare's work, anyway, he should have cited Poincare.


 * But with E=mc^2, and all his work after the Special Relativity paper, he isn't plagiarizing anything. In later work, he even took care to bring out obscure young people's work into the public light, giving Bose and DeBroglie somewhat more credit for their results than they deserved, when in fact it was Einstein who fleshed out the mathematics.


 * The reason I brought up anti-semitism is because the article needs to be in good taste. People should be aware of the historical issues. In other articles, it might be lots of fun to say "such and so didn't think Shakespeare wrote his plays" or "such and so didn't think that Romulus and Remus were historical figures", in this case, the historical links between "Einstein is a fraud" and "Jewish conspiracy" is too immediate, it just comes across as hateful. That's why I think it is good that any (not very) controversial priority claims are left to the end, in a balanced discussion, instead of being right out in front, where it looks like tastelessness. Graham Wellington is probably not motivated by prejudice, unless you call rooting for the underdog a prejudice. But history is history, and needs to be kept in mind.Likebox (talk) 23:34, 6 January 2008 (UTC)
 * We should begin the process of coming to terms with Einstein's plagiarism. Yes he is a media darling, yes he is a Jew, but that doesn't excuse him from stealing another man's formula without so much as giving partial credit! Bringing the truth to light will not be easy. Slowly we can chip away at the false legend that is Einstein & E=MC^2. Eventually others will accept the truth. Just look at Columbus and the Vikings. Graham Wellington (talk) 23:40, 6 January 2008 (UTC)


 * Could you please tell us exactly what was in DePretto's paper? Aside from $$E=mc^2$$ that is. I am relying on second-hand accounts.Likebox (talk) 23:45, 6 January 2008 (UTC)


 * After much searching, I found one secondary source that actually discusses more details of DePretto's particle-ether theory. Since his definition of kinetic energy is twice the ordinary one, I think he should be more accurately said to have discovered that 2E=mc2.Likebox (talk) 03:15, 18 January 2008 (UTC)
 * Mathpages is not a legitimate source. Graham Wellington (talk) 00:53, 19 January 2008 (UTC)
 * But given the unfortunate circumstances: 1.I don't read italian 2. De Pretto's paper is not translated anywhere I can find. 3. Nobody else says anything about the contents of the paper. 4. I don't have the time to do a comprehensive literature search
 * I think it is best for us to leave the description from the secondary source until someone who speaks italian can find the original. Unless you have any evidence that MathPages is lying about the contents, that is.Likebox (talk) 08:38, 19 January 2008 (UTC)


 * Likebox, why don't you tone it down a bit instead of overreacting to Wellington's provocation? There's no need to be calling things "bogus", unless you have a source that uses such language.  Dicklyon (talk) 08:48, 19 January 2008 (UTC)


 * I didn't mean to be inflammatory, it was like that before. I'll remove the language you object to.Likebox (talk) 08:51, 19 January 2008 (UTC)


 * Your edit is entirely based on an unverified source and a totally illegitimate source. It is best to remove all that you recently added until you back up those claims with real sources. This is an encyclopedia after all. Graham Wellington (talk) 00:27, 20 January 2008 (UTC)


 * Generally, I'm on board with you, although calling mathpages "totally illegitimate" is a little over the top. In this case, given the paucity of source material, it would be more constructive to provide a reference to the original paper. I read french badly, so it shouldn't take more than an hour or two to puzzle out the italian. Best if you would do it, or if there is a native speaker willing to help out.Likebox (talk) 02:10, 20 January 2008 (UTC)


 * Do you have a reliable translation for "Reale Instituto Veneto Di Scienze, Lettere Ed Arti" ? If not, I'll have no choice but to delete your edit. Mathpages is not a reliable source and you also seem to agree. Did it become reliable since yesterday? If not, I'll have to delete any information you added based on Mathpages. Graham Wellington (talk) 01:33, 21 January 2008 (UTC)


 * Its not based on mathpages anymore. Its based on the contents of the paper now. While I personally can only read italian with great effort, I have found people who can read italian fluently who have explained the contents of the paper.Likebox (talk) 02:06, 21 January 2008 (UTC)


 * I do not agree with adding an unsourced opinion ascribed to anonymous "historians" in order to produce an implicit editorial caveat. If we can't report on this from a neutral point of view using published reliable sources, then we should maybe not report on it at all. In no case are we free to invent our own material to fill the gaps. --Lambiam 08:39, 21 January 2008 (UTC)


 * It is not "inventing" when you are stating facts so obvious that they will not have a source. If somebody writes "Napoleon was a flesh eating zombie!", the burden of proof is on the person who is making the assertion. The lack of statement on the subject by historians is evidence enough that he wasn't. Similarly, if someone says Einstein cribbed De Pretto, it is so obvious that he didn't that the only historian who make a comment are the few that believe it happened. This is the WP:Undue_Weight policy, and it requires caveats on material that is accepted only by a small minority, so long as the unsourced caveats would be agreed upon by nearly everybody in the field.Likebox (talk) 10:02, 21 January 2008 (UTC)


 * So you think it is OK to add unsourced statements expressing opinions like: "Historians do not believe Napolean was a flesh eating zombie", "Historians do not describe Napolean as a mellow person", "Physicists think that Bartocci's claims are ludicrous", and so on. If it is so obvious, we do not need to state it at all. But we must not sneakily editorialize by inserting our own judgement of the situation, however obvious, while hiding behind anonymous sources. And isn't Bartocci a historian of science? In its generality, the statement is not even true. --Lambiam 16:52, 21 January 2008 (UTC)


 * Where are the contents of the paper in English? Claiming you understand Italian does not qualify. I have no choice but to delete your edits until you provide a reliable source in English. Graham Wellington (talk) 20:42, 21 January 2008 (UTC)


 * I agree. The less said the better. We can report an independent interpretation if we find one, but should not provide our own. So I shortened it. Dicklyon (talk) 20:50, 21 January 2008 (UTC)


 * Don't think so. See Verifiability - Non English sources:
 * "Because this is the English Wikipedia, for the convenience of our readers, English-language sources should be used in preference to foreign-language sources, assuming the availability of an English-language source of equal quality, so that readers can easily verify that the source material has been used correctly."
 * So, if/when you find a translation, you are encouraged to replace it. Otherwise you are discouraged to delete the sourced edits. DVdm (talk) 21:00, 21 January 2008 (UTC)
 * I don't believe your translation is reliable. We have no idea what is written in that article. Graham Wellington (talk) 03:45, 24 January 2008 (UTC)


 * Sure, but your (dis)beliefs are your problem. Analfabetics have no idea what is written in any article, yet that is no reason to remove all sources from the Wikipedia. Do have another look at WP:RSUE. DVdm (talk) 10:33, 24 January 2008 (UTC)
 * Likebox actually has stated "I don't read italian", giving a strong basis for doubt that his understanding of the text (if he has seen it at all) is accurate. --Lambiam 17:44, 24 January 2008 (UTC)
 * The only way you can aquire a "basis for doubt" is to go read the text yourself, or have someone else do it, and check what I wrote for accuracy. I went to a lot of trouble to do this, and I got an explanation of the original paper, not a secondary source, from a native speaker, so I am confident that the statements that I made accurately reflect De Pretto's text (and Preston's). But be my guest, verify it independently. The paper is reprinted in Bartocci, and there's no math in it, so there's no difficulty for any reader of Italian.Likebox (talk) 01:03, 25 January 2008 (UTC)

Why I think We Should Describe De Pretto's Nonsense
There are still some people in the world who think that something along the lines of what De Pretto describes is very close to what Einstein discovered. I think that the image many people have in their mind of what E=mc2 is about is De Pretto's. It will be useful to them to see that this hogwash is absolutely not what E=mc2 is about, so that they can think about it and learn it properly.Likebox (talk) 23:05, 21 January 2008 (UTC)


 * I don't disagree with your attitude about that, but I'm not sure that wikipedia is the place to be trying to straighten this out. This is obviously a contentious topic, and as long as we allow ourselves to deviate from WP:V, WP:RS, and WP:NOR by adding interpretations, we're not going to see the edit war settle down.  I'm not sure what the mathpages source is; if it didn't appear to be anonymous, it might be an OK source; does it say who wrote it?  If we could attribute an interpretation, that would make more sense.  Dicklyon (talk) 01:39, 22 January 2008 (UTC)


 * You might be right, considering the amount of heat. But I am trying to get the two objectors to agree to a text. If it's impossible, then what can you do. But I lean to the position that is a shame not to mention all the ideas that were floating around at the time, no matter how flawed, because I think an important part of Wikipedia is to record all the missteps and not just the successful solutions. While finding all the references, I found out that Preston used the same LeSage ether as De Pretto for his mass/energy relation, so it seems there was an active physics "counterculture" of LeSagians who were being marginalized by the mainstream. That seems notable and interesting. But if it leads to crap getting presented as a valid precursor to mass/energy, then I agree that it needs to be deleted on WP:Undue Weight grounds.Likebox (talk) 07:26, 22 January 2008 (UTC)


 * Which two objectors? As far as I can see everyone except Likebox could agree on this version. --Lambiam 14:37, 22 January 2008 (UTC)


 * If nothing better can be achieved, then that's not horrible. The only problem with this version is that it doesn't really describe these pre-Einstein ideas in any detail, so it makes it difficult for readers to understand the nature of the debate.Likebox (talk) 15:27, 22 January 2008 (UTC)


 * Same here. It would be good if we could say more to clarify or position this bit of history, but until we find a reliable source, attempting to do so will just be a fight. As for "the nature of the debate", I'm not sure there is one, and we shouldn't be creating one. Dicklyon (talk) 15:44, 22 January 2008 (UTC)


 * I meant the 19th century debate over what mass energy relation is correct. It seems that everybody had their own version. What are your objections to the current language?Likebox (talk) 16:42, 22 January 2008 (UTC)


 * Definitely that's good stuff to cover, perhaps even in the "others" section, but certainly not in the paragraph about de Pretto; if the source mentions de Pretto, is would be good to put a few words about that into the de Pretto paragraph. Otherwise, let it remain short and uncommented, to be interpreted by the reader in the context of whatever other coverage can be included from sources.  Don't dignify it by taking it seriously or including it in the discussion of information from sources where it was not mentioned. Dicklyon (talk) 21:40, 22 January 2008 (UTC)


 * How about this version?Likebox (talk) 04:28, 23 January 2008 (UTC)

Why You Absolutely Need Relativity to Get Mass-Energy
There's a universal issue with any purported non-relativistic "derivation" of E=mc2. Without relativity, the normalization of the energy and the normalization of the mass can be chosen largely arbitrarily. This is not apparent, because the form of the kinetic energy was chosen wisely in the 19th century, to make Hamilton's equation look nice, and this fixed the coefficient of 1/2 and the general normalization of E comes out the same as the low-velocity kinetic energy in relativity. But you can rescale E to be mv2 or 2mv2 without any significant damage to the formalism, and without rescaling mass, but you get an overall scale factor in Hamilton's equations. This doesn't break a symmetry, it just means that the you chose your units badly.

In relativity, the normalization of energy is determined by the fact that p=Ev/c^2. The only natural choice for energy is to make a four-vector with the momentum. So if people had screwed up the nonrelativistic convention for energy, relativity would have fixed it. Turned out we didn't screw up--- good work 19th century people. But this means that any claims of a pre-relativity derivation is completely unsupportable.Likebox (talk) 02:40, 20 January 2008 (UTC)

I was wondering why the 19th century people didn't screw this up, when Liebnitz did with the vis-viva. I have a completely speculative answer, but maybe somebody knows for sure. You can get the Galilean group as the limit of the ordinary rotation group, not the Lorentz group, just ordinary rotations in 4 space in the limit that the unit of time is very long compared to the unit of space. If you define the Galilean group this way, then it would be natural in Hamilton's formalism to define the energy with the 1/2. I wonder if historically this is what happened. Or maybe they just didn't want 2s cluttering their formulas, which was my first guess.Likebox (talk) 06:11, 20 January 2008 (UTC)


 * The factor of 1/2 is designed to make the Hamiltonian conjugate to the time variable in the same way that the momentum is conjugate to the space variable. This makes the 1/2 extremely natural even with just the Galilean group. Technically, though, if you are feeling perverse, I suppose you still could change the definition, but you would get idiotic numerical factors for the canonical transformation which performs a Galilean boost. I think Hamilton must have known this, but 19th century stuff is irritating to me, so I don't know.Likebox (talk) 19:40, 5 June 2008 (UTC)

Black Holes vs. Monopoles--- Which is Heavier?
This is a bit of a tricky question since the lower limit of a black hole is not perfectly well defined. In string theory, the black hole spectrum, appropriately interpreted, includes all the elementary particles since all the strings and branes are charged black holes in the classical limit.

So is there is a monopole which is lighter than the lightest recognizable (thermally radiating) black hole. The only true limit which you can put on the mass of the lightest magnetically charged particle is that its mass (in planck units) is less than its charge (in planck units), which means that it must repel other like particles magnetically more than it attracts them gravitationally.

The unit of magnetic charge is the invese of the unit of electric charge, so the maximum possible mass for the lightest monopole is about 3 or so planck masses, or maybe 9 planck masses if quark electric charges are the right unit for the quantization. There might be a recognizable semiclassical black hole already at 1-2 planck masses. I don't know. So while technically I think it is correct that the monopole can be heavier than the lightest black hole, it's not by much.Likebox (talk) 00:46, 11 January 2008 (UTC)

Observer chasing a photon
From the entry: "If an observer chases a photon faster and faster, the observed energy of the photon approaches zero as the observer approaches the speed of light." Care should be taking to define chasing a photon "faster and faster" since the entire time the observer's speed approaches the speed of light, the basic tenet of special relativity is that the photon will always be advancing at the speed of light in the observer's reference frame. I've forgotten to much relativity to figure out if an increasing observer speed relative to some inertial frame decreases the frequency the observer measures of photons (and thus the energy), but at first glance this seems wrong to me... I presume that the original entry is correct and my memory/intuition are faulty, but nonetheless, I feel this section should be elaborated on to explain this claim. 72.144.128.242 (talk) 02:35, 15 January 2008 (UTC)Jon
 * The photon would continue at the speed of light, but would decrease in energy. However, the argument doesn't have to be phrased this way. A person would accelerate away from a source of photons and observe the ones going past. The frequency and energy of THOSE would decrease to zero as a speed away from the source approached that of light. Of course, photons would still go past at the speed of light no matter what energy they had. S  B Harris 03:00, 15 January 2008 (UTC)


 * Just to elaborate--- a photon's frequency, but not its velocity, changes when you chase it. That's the Doppler shift--- the time between crest crossings increases if you are moving along with the photon. The speed of the wave crests stays constant, but the light gets redder and redder. The energy of the photon then decreases because redder photons have less energy.


 * Historically, Einstein formulated relativity and wave-particle duality for photons simultaneously, and he noted that when you chase a wave of light, the total energy in the wave changes in the same way as the total frequency. As the frequency gets redder, the energy decreases, as the frequency gets bluer the energy increases by the same factor. Einstein points this out explicitly in his relativity paper, since he was emphasizing that light can be consistently quantized with the quantum of energy proportional to the frequency.


 * This was essentially known to Wein too, but only for nonrelativistic speeds because he didn't know relativity, so his Doppler formulas and energy formulas would be wrong for large velocities. Wein considered reflection of light off a slow moving mirror--- the fraction increase in energy by light reflecting on a mirror moving towards it is proportional to the to fractional increase in frequency. It was this observation that allowed him to guess that the occupation of high frequency light modes would be suppressed by a Boltzmann-like factor of e^{-f}, which is usually supresses high energies, not high frequencies. This is a photon assumption, but he wasn't very clear on the physics.Likebox (talk) 05:43, 15 January 2008 (UTC)

Einstein and rest mass
The article says that "Einstein's original papers treated m as what would now be called the rest mass and some claim that he did not like the idea of "relativistic mass." This is wrong, because both in his electrodynamics paper and in another paper in 1906 he used (like Lorentz and Abraham) the velocity and direction dependent terms "longitudinal" and "transverse" mass, which was (based on F=ma) an early form of relativistic mass. So I rewrote the passage. --D.H (talk) 15:49, 26 January 2008 (UTC)


 * This is not completely accurate. The quantities "m" you are referring to are not exactly early forms of relativistic mass, they are two different experimentally measurable quantities, one of which (the transverse mass) is equal to the relativistic mass. Einstein did use these quantities, but he was aware of relativity, so what he called "m" was usually the values of these masses in the rest frame, where they are equal to the rest mass. He was, as I heard it, quickly convinced to stop talking about F/a masses by either Planck or Lorentz.Likebox (talk) 01:20, 27 January 2008 (UTC)


 * But that's exactly what you wrote.Likebox (talk) 01:23, 27 January 2008 (UTC)

I haven't said that the F/a masses are exactly the same as relativistic mass, but they are similar. Now, the article statet that Einstien never used (at least similar) concepts to relativistic mass, which is not correct. And yes, it was the influence of Planck, that Einstein abandoned the F/a mass concepts. Einstein admitted in an endnote, written in the 1913-edition of his paper, that "The definition of force here given is not advantageous, as was first shown by M. Planck. It is more to the point to define force in such a way that the laws of momentum and energy assume the simplest form." --D.H (talk) 10:02, 27 January 2008 (UTC)


 * Once I actually read what you wrote, it was precise and correct. Sorry to doubt.Likebox (talk) 12:16, 27 January 2008 (UTC)


 * Mass has to have a definition before you can make a meaningful derivation: E=mc2. These derivation is based on the definition of mass, which is in terms of inertia.  Relativistic mass is something newer, defined in terms of E=mc2 ~Paul V. Keller  16:48, 28 December 2008 (UTC)

e=mc2 can be used to calculate a specific frequency within the existance.
e=mc2 can be used to calculate a specific frequency within the existance. If we assume that the mass of the soul is 21 (21 comes from the weight loss noted when a person dies and the soul leaves the body) and that the velocity of the universe/ existance is 69 then the frequency from which we are currently experiencing the existance is 99981. XOXO —Preceding unsigned comment added by 129.142.24.98 (talk) 13:40, 4 February 2008 (UTC)

Perfect conversion problems with antimatter
Antimatter + Matter will convert to energy, but not all of it is useful energy. Up to 50% of that energy will come out as neutrinos, which have almost no interaction with matter at all (so in other words, it's useless). Maybe this could be added to the article to clarify. 64.236.121.129 (talk) 16:46, 14 February 2008 (UTC)

blackholes radiating thermally
Blackhole do not radiate thermally - that makes no sense, "thermally" means temperature, which is a property of matter. Does the author mean "radiate protons"? Because they don't. In blackhole evaporation they radiate particles, so you gain nothing from dropping particles on them - you get them right back. Ariel. (talk) 03:04, 15 February 2008 (UTC)


 * Thermally is the right word. Thermal radiation is blackbody radiation, and is a well accepted term. They Radiate protons, they radiate electrons, they radiate photons and gravitons. They radiate everything. It is not true that they radiate only the types of particles that fell in, although the outgoing particles have to have the same total charge and same total angular momentum as the particles that came in.Likebox (talk) 03:14, 15 February 2008 (UTC)


 * No. blackbody radiation is only photons. And blackholes do NOT radiate photons (or gravitons, unless they are moving). They ONLY radiate particles, and the only way to have the same total quantum numbers (everything, not just charge and angular momentum) emitted, is to emit the same particles as fell in. The thing about charge and angular momentum is that it is the only thing you can measure from outside the blackhole. It doesn't mean it doesn't actually have the other numbers. Ariel. (talk) 03:23, 15 February 2008 (UTC)


 * Black holes do radiate photons. Hawking's theory assigns a temperature to black holes based on equating the total outgoing energy to the amount of radiation that a blackbody would generate at that temperature.  It is in fact very common to talk about the temperature of black holes and thermal radiation in this sense.  The black hole emissions will preserve the sum of the quantum numbers that entered, but it doesn't mean you have to get the same collection of particles.  Dragons flight (talk) 07:01, 15 February 2008 (UTC)


 * Equating the two for calculation does not mean it's actual photons. How would a photon escape? Isn't that a contradiction in terms for a blackhole? And I'm pretty sure to get the quantum numbers right you do in fact have to have the same particles. But even if I'm wrong the article implies that blackholes eat mass and emit pure energy (the section is called "Perfect conversion"), and that is certainly not the case. They eat mass, and emit mass, no conversion happens. Ariel. (talk) 07:45, 15 February 2008 (UTC)


 * Photons escape the same way everything else escapes, through Hawking radiation, which can be described as quantum tunnelling through the event horizon or equivalently by virtual pair capture from outside. Actually, photons are one of the easiest particles to generate.  Mass is energy, energy is mass.  A 511 keV photon has the same gravitational mass as an electron sitting at rest.  In one sense what one should really say is that no conversion is possible.  However, what the article means is that black holes can convert particles with a significant rest mass into photons and light weight particles with high kinetic energy.  And no you don't need the same particles just the same total quantum numbers, which can be distributed among the particles in many different ways.  Dragons flight (talk) 09:01, 15 February 2008 (UTC)


 * I am willing to accept that I'm wrong about photons from blackhole, if you can show me what other lightweight particles you can turn protons into. But you can't, since protons are the lightest baryons. If you drop protons into a blackhole, protons must come out. That same it true for the charged leptons: the electron is the lightest. So I still fail to see how you can use a blackhole to convert matter to energy. I await your response, and won't change the article till then. Ariel. (talk) 21:55, 15 February 2008 (UTC)

(deindent) You have just stated one of the deepest properties of Hawking radiation. It doesn't give a hoot about Baryon number conservation, or lepton number conservation, or CP, or any other symmetry other than CPT and those charges which can be seen poking out the black hole through their electromagnetic field. This is the reason that black holes can be used to violate Baryon number, and is one of the deepest insights into quantum gravity to date. Hawking radiation implies that quantum gravity doesn't conserve anything except charge/momentum/angular momentum. It doesn't care about any global symmetry, only gauge symmetries.

The stuff that comes out of the black hole solution is coming out from a different classical region than the stuff falling in, and it is mostly photons and gravitons until the black hole gets small. That means that if you make a black hole out of neutrons and only out of neutrons, the solution outside doesn't know you made it out of neutrons because it's all just a gravity field. That's remarkable, as you say, because once the black hole decays, it has clearly violated Baryon number. This is true even if at the last stages an abnormal number of neutrons come out. That still will never make up for all those photons that were emitted earlier. This is the main reason people are very sure that quantum gravity only allows conserved quantities which are charges attached to a gauge field you can see outside the black hole with a gaussian surface.

A little after this was discovered, 't Hooft showed that Baryon number is not exactly conserved even in just the standard model, although to see the effect in an experiment is next to impossible in current understanding. Likewise, lepton number is almost surely being violated by the neutrino masses (if they are Majorana masses as people mostly expect). CP violation was observed long ago, and that's a complete list of the non-gauged conservation laws.Likebox (talk) 23:30, 15 February 2008 (UTC)
 * Yeah. You know, I still remember the chill I got when I realized this on my own about 1999. I hadn't read it anywhere in the literature for laymen. But I realized that if any neutral black hole turns into the same stuff, you can make them from a seed by dropping in anything neutral-- neutrons, atoms, neutrinos, photons, whatever. And the same thing comes out, according to Hawking. So right after "Black holes have no hair" you have "Black holes aren't so black" and the corollary if you believe both, is this one: "Black holes suck so much they've lost their flavor." (I figured Baryon number was a gonner anyway, and we've had discovered proton decay by now). For a while I called it the "Harris Lollipop Rule of Black Holes." But of course, it wasn't a new insight. Shame.  S  B Harris 00:41, 16 February 2008 (UTC)

This needs to be revised again. There is absolutely no violation at all, because things are not lost inside a black hole now concluded by Hawking himself. In July 2007 he retracted his statement, nd he now beleives that any that falls into one, actually quantum tunnels back out again. No violation, faulty text. Electrino —Preceding unsigned comment added by Electrino (talk • contribs) 18:09, 6 November 2008 (UTC)


 * It doesn't have to be revised. Hawking is talking about information loss in black hole evaporation, which is different than conservation laws. Please read the text above. If you form a black hole out of neutrons, it will decay into photons and gravitons. It cannot conserve baryon number, even if an abnormal number of neutrons come out at the end. This is true even if Hawking (or anybody else) were to say it is false (nobody does).


 * What Hawking concedes now is that the photons and gravitons that come out are not completely random, that there are subtle correlations in them which in principle encode the information that the black hole was formed from neutrons. If you were to exactly reverse all the photons gravitons and final explosion particles that come out, with all the subtle correlations reversed too, you could make a black hole that forms from gravitons and then emits neutrons out. Although this is thermodynamically impossible--- it lowers the entropy of the universe, it is possible in principle, the same as it is possible for a broken cup on the floor to spontaneously reassemble and jump back onto a table, as in a film run backwards. Notice that this reverse process creates neutrons, and violates the conservation law of Baryon number just as much as the forward process.


 * Before Hawking conceded this, he believed that any black hole process would always end in a thermal state of photons and gravitons no matter what subtle correlations there are in the initial state. This violates assumptions of quantum mechanics and it is now widely believed to be false.Likebox (talk) 20:39, 7 November 2008 (UTC)

Not linked to atomic energy?
There's a notion around in popular culture that Einstein's equation pointed the path to atomic weapons. There's an SF short story - I forget the title - in which survivors of an atomic war manage to send a destructive beam of energy back into the early 20th century, killing Einstein in his youth and thus changing history.

As I understand it, all this is sheer myth. Definitely H. G. Wells got the idea from Frederick Soddy's The Interpretation of Radium and popularised it in 1914 in The World Set Free (1914). I'd suppose that Einstein's work was useful in working out the details of how to make an atomic weapon, but it was around anyway.

Is this something that should be mentioned here? --GwydionM (talk) 21:41, 22 February 2008 (UTC)


 * Soddy's 1920 book seems worth a mention, though it was not the earlier analysis of radioactive decay energy. The Wells 1914 was probably inspired by something earlier. Dicklyon (talk) 05:27, 23 February 2008 (UTC)


 * Szilard, who came up with the idea of a nuclear chain reaction to generate energy (as opposed to a chemical one), actually cites Wells in his patent. Everybody knew from direct measurement that there was a huge amount of energy in radioactive decay-- the problem was how to get it out faster than it comes out naturally. Einstein even mentions in his 1905 E=mc^2 paper that the mass=energy theory might perhaps be tested with radioactive decay, which releases enough energy (the quantitative amount known roughly even by 1905) to possibly be "weighed," when missing. Now, Richard Feynman is responsible for the idea that energy would have been measured directly for fission anyway, so poor Einstein isn't responsible for the bomb or for understanding fission in any sense at all. But it's not that simple. When Lise Meitner realized on a walk in late 1938 that the nucleus was being split, or "fissioned," as she called it after the biological process in cells, part of her insight was due to knowing that this process was energetically favored-- something she could only have known from Einstein's theory, which involved knowing nuclide binding energies from measuring their masses and knowing the mass of protons and neutrons. To know the energetics, Meitner (and Frische, who shares credit) had to know the packing fractions of the nuclides, which is a concept straight out of Einstein (binding energy shows up as missing mass). She said they all had these numbers memorized. It hadn't been possible to calculate packing fractions until the neutron was discovered in 1932 and weighed, but shortly after that, these binding energy numbers were calculated for most of the common atoms, and that was how Meitner and Frische were so aware of them. We call his now the curve of binding energy. So yes, Einstein's E=mc^2 theory played a part in all of this-- in the fission discovery itself, as a concept. But much more subtly than usually understood. S  B Harris 06:05, 23 February 2008 (UTC)


 * To SBHarris: you seem to know a lot about it, why not add a section?--GwydionM (talk) 15:49, 23 February 2008 (UTC)

Took the plunge and added a section. Tried to keep a neutral view.--GwydionM (talk) 18:18, 26 February 2008 (UTC)
 * Good job but naturally now somebody wants cites. The Meitner story is told pretty well in Rhodes "The making of the Atomic Bomb." Feynman tosses out the offhand comment about blaming Einstein when he had nothing to do with it, in Vol I of his Lectures in Physics. I have them both and will try to stick in the two cites in such a way that they illustrate the two views (Einstein is everything to this, vs. nothing). Or course this is very much a different question than what would have happened if E had never lived, since obviously somebody would have discovered special relativity if E hadn't, and probably in time for 1938. I'm not certain we should go there (so that way of putting it goes farther astray than we want), as it's very speculative. Let's just stick to views on what the guy who actually existed, did to further the understanding of fission. There, I think we should take the word of Meitner over that of Feynman. Much as I admire Feynman, he wasn't infallable when it came to history (and he knew and admitted it, saying educated physicists have a lot of "just so" stories about how we came to understand stuff, that don't survive real historical analysis). S  B Harris 05:18, 27 February 2008 (UTC)


 * My point in calling for citations is that saying something is a "matter of dispute" is content free weasel wording. If there's a dispute, then say something about it, like what the sides are or who takes what position; if you can't find a source for a dispute, don't say there is one, even if there are multiple viewpoints; just summarize the viewpoints. Dicklyon (talk) 05:26, 27 February 2008 (UTC)

Origins
I am trying to figure out how the equation became standardized in the form of E=mc^2. While the opening section of this article attributes the mass-energy equivalence to Einstein's paper in 1905, that paper doesn't use E=mc^2 to describe the equation. I am looking to find out who said, in effect, "The best way to express what Einstein said in 1905 is E=mc^2. Let's all use that." --Metropolitan90 (talk) 06:05, 2 March 2008 (UTC)


 * Well, the the formula m=E/c^2 and m=(4/3)E/c^2 was used by Poincare, Wien and others before 1905. Also Einstein used the expression E/c² for mass in his 1905 paper. However, the expression E=mc^2 in explicit form (as far as I know) was used by Einstein for the first time in this paper in 1907. He wrote: German: "Die Masse &mu; ist in Bezug auf Trägheit äquivalent mit einem Energiegehalt von der Größe &mu;c^2." English (replacing &mu; with m): "The mass m is in relation to inertia equivalent to an energy content of the magnitude mc^2." Regards, --D.H (talk) 10:12, 2 March 2008 (UTC)

Einstein's 1905 derivation
There are some claims by Ives and the respected historians of science Jammer and Miller, that Einstein's 1905 dervivatin was invalid, because Einstein had assumed the result ot be prove at the outset. However, there are other opinions, see for example: Pandya: http://arxiv.org/abs/0705.0775. BTW: The derivation in the Wiki-Article given by Likebox is in principle very similar to Einstein's, but it's not the same. It think we shoud correct that (based on Pandya's description of Einstein's derivation in section 2 in his article). --D.H (talk) 18:12, 19 March 2008 (UTC)


 * Although I changed the language slightly, took the nonrelativistic limit with less care, and used the redshift formula for photons (Einstein used the energy transformation formula for EM waves, which is the same) the physical situation and relevant calculations are exactly parallel to those in Einstein's paper. They are self-evidently correct, which should explain why those authors that thought it was a wrong argument have disappeared into the mists of history. There was some controversy though, a long time ago.Likebox (talk) 02:20, 20 March 2008 (UTC)

E=Mc^2 in Popular Culture
Maybe there should be a section, on how, in popular use the formula has become shorthand, for an intellegent scientific formula. Most people have heard E=MC^2, and I'd hazard a guess that a lot of those people have no idea what it actually means. —Preceding unsigned comment added by 217.41.229.252 (talk) 16:13, 6 April 2008 (UTC)


 * There pretty much is a section like that; see the bit about nuclear energy at the bottom. I've added "and popular culture" to the subtitle. I think it says about as much as we need to say about the subject (that is, I'd rather not end up with one of those awful listings of everything that contains the equation, even if it is, horrifically, the latest Mariah Carey album). The equation doesn't really become mega-popular until after the atomic bomb is dropped, so talking about it in that context makes sense, to me anyway. --98.217.8.46 (talk) 20:44, 5 May 2008 (UTC)

E=&gamma;mc2
Could someone please explain this? --Espoo (talk) 16:17, 3 June 2008 (UTC)


 * That's the formula:
 * $$E={mc^2\over \sqrt{1-{v^2\over c^2}}}$$


 * in Einsteins unfortunate convention where the geometric factor


 * $$1\over \sqrt{1-{v^2/ c^2}}$$


 * goes by the name "$$\gamma$$". This formula is discussed in the article--- it's the expression for the energy of an object moving with velocity v whose rest mass is m. When the velocity is zero, the energy is the rest mass times $$c^2$$.


 * The reason why this factor $$\gamma$$ pops up everywhere in relativity is because the velocity is a slope, not an angle. If you imagine the trajectory of a particle as a path in space-time, the velocity is the amount you move per unit time, it's the ratio of the x displacement to the time displacement. This is a slope. The geometric transformations of relativity are analogous to rotating the time axis to match the slope of the moving particle.


 * Even if you rotate coordinates in plain old euclidean geometry to make the x-axis tilt by a slope "m", the new coordinates are related to the old coordinates by the following complicated looking rule:


 * $$ x' = {x+ my \over \sqrt{1+m^2}} $$
 * $$ y' = {y- mx \over \sqrt{1+m^2}} $$


 * which is formally almost identical to the Lorentz transformation. People don't usually write it out this way in geometry, because they work with the angle, and not the slope. In terms of the angle of the new x-axis:


 * $$ x' = x \cos(\theta) + y \sin(\theta)\,$$
 * $$ y' = y \cos(\theta) - x \sin(\theta)\,$$


 * and the geometrical factors are the trigonometric functions:


 * $$ \cos(\theta) = {1\over \sqrt{1+m^2}} $$
 * $$ \sin(\theta) = {m\over \sqrt{1+m^2}} $$
 * $$ \tan(\theta) = m \,$$


 * In relativity, the analog of the angle is called the rapidity, $$\alpha$$, in terms of which the geometric factors are:


 * $$ \cosh(\alpha) = {1\over \sqrt{1-v^2}} = \gamma\, $$
 * $$ \sinh(\alpha) = {v\over \sqrt{1-v^2}} = v\gamma\, $$
 * $$ \tanh(\alpha) = v \,$$


 * with space/time units chosen so that the speed of light c is equal to 1, and the hyperbolic functions trace out hyperbolas and not circles, so that:


 * $$ \cosh^2(\alpha) - \sinh^2(\alpha) = 1\, $$


 * The lorentz transformation then reads:


 * $$ t' = t \cosh(\alpha) - x \sinh(\alpha)\,$$
 * $$ x' = x \cosh(\alpha) - t \sinh(\alpha)\,$$


 * so that Einstein's gamma is just a pet notation for the hyperbolic cosine.Likebox (talk) 20:07, 5 June 2008 (UTC)

Relativistic Mass
This article contains an excessive amount of reference to "relativistic mass". This isn't horrible in itself, but surprise surprise, with it has come a horde of mistakes. For instance,

''The rest mass of a system, however, is not the sum of the rest masses of its parts taken one-by-one, free from the system[2]. The difference between the rest mass of the system and the rest masses of the (free) parts is the binding energy, which has been emitted in the formation of the system.''

''But the rest mass of a system is always the sum of the relativistic masses of its parts, in the frame where the system as a whole is at rest. Because the inertia (the relativistic mass) of a system (linked or free) is always the sum of all the inertias (all the relativistic masses) of its parts ; and the rest mass of a object could be seen as the particular value of its relativistic mass, when it's at rest.''

The first statement is mostly correct. This second statement, which introduces "facts" about the relativistic mass is not only incorrect, but in total contradiction to the first statement and betrays the basic message that it was trying to impart. This entire article looks like it was molested by a relativistic mass advocate.

CHF (talk) 22:22, 30 June 2008 (UTC)


 * Oh, it has. See mass in special relativity which treats the problem better. There's also a small article on invariant mass. The last two sentences you quote above are unclear and could go. Feel free to delete. I think the sentence about rest mass being the same as sum of relativistic masses when the "system is at rest" is talking about a system in which there is no net momentum (a bound system at rest, like a hot box of gas or any hot object). In that case (in that center of momentum inertial frame), relativistic mass and invariant mass are the same, even for bound compound objects and unbound systems. Many of us don't like the idea of "relativistic mass" and think that it adds nothing to the concept of "total energy" or "relativistic energy" (you just divide by c^2). But the idea that (simple) objects get more massive with velocity is so ingrained into the public consciousness that it seems necessary to write about the idea. Actually, objects get more or less massive in the only way that counts (increase in invariant mass) ONLY if their total energy changes in the center-of-momentum frame, where by definition the center of mass velocity is zero. But that's a more difficult concept to explain. Anyway, have at it. I'll back you up, at least. S  B Harris 01:23, 1 July 2008 (UTC)


 * The relativistic mass obviously adds nothing to the relativistic energy--- it is another name for the relativistic energy. But this article is discussing the equivalence of mass and energy, and a person who is not already intuitively familiar with the equivalence sees mass and energy as completely different things. Once mass and energy are seen to be the same, the term "relativistic mass" can obviously be thrown away as redundant. But this article is discussing that very equivalence, and so takes pains to distinguish between mass and energy even in cases where they are exactly the same. This is not advocacy, in my opinion it is clarity.Likebox (talk) 21:01, 8 July 2008 (UTC)


 * Recent edits relate to notes in this section. ~Paul V. Keller 16:42, 28 December 2008 (UTC)

Mistake
On the previous version of this page, it said that the energy in relativity can be redefined by subtracting the rest energy, and if no new particles are created, that this new definition is just as good, but has no rest energy. This is completely wrong, because Einstein's argument is a two photon emission, and it works with either definition--- the rest energy of the emitted photons is zero. The central body in Einstein's argument if the cockeyed alternative definition of energy is used would end up with a negative total energy, and its momentum would be altered by the inertia contribution of carrying the negative energy around. It's total nonsense. I should admit that I wrote that in a flash of temporary insanity.Likebox (talk) 19:10, 10 July 2008 (UTC)

I know I'm being facetious, but...
>>If the temperature of the platinum/iridium "international prototype" of the kilogram — the world’s primary mass standard — is allowed to change by 1°C, its mass will change by 1.5 picograms (1 pg = 1 × 10–12 g).

By definition, the prototype kilogram has a mass of 1.000000000000000000000 kg. If you heat it by 1 °C, everything else in the universe will get lighter by 1.5 × 10–15 of its original mass. 212.137.63.86 (talk) 14:17, 6 August 2008 (UTC)

question
E=mc^2, where c is the speed of light in vacuum (where gravity still exist), often expressed distance travel in time. Now gravitational time dilation is the effect of time passing at different rates in regions of different gravitational potential which was tested/ confirmed with difference of nanosecond recorded by atomic clocks at different altitudes.

Sun gravity decreases as we move away from it. This means that speed = distance/time of light is not constant because of the time difference due to time dilation. It should varies at each gravitational potential point while moving away from the sun.

Myktk (talk) 06:19, 8 August 2008 (UTC) zarmewa bewafa

wanted to point this out.. sorry
the article says: "...consequence of the symmetries of space and time"

-space and time are not symmetrical, they are orthogonal. duh! (just kidding). how this is related to matter and energy being equivalent as a general principle as a consequence of how time and space are positioned against eachother, i know not. 71.9.106.104 (talk) 14:09, 28 August 2008 (UTC)

Latent energy store
I've included some information on the theories of Rutherford and Soddy (1903) on "latent energy store" within matter as an explanation where the energy for radioactivity is coming from. Also an interesting speculation of Rutherford in 1904 is included. It seems, that he had changed his opinion of using atomic energy in 1930.... --D.H (talk) 18:13, 25 September 2008 (UTC)

Photons?
The article says: "any mass has an associated energy, and vice versa". But what about photons: certainly they have energy, but do they have an associated mass? - Regards, 87.160.77.23 (talk) 20:44, 7 October 2008 (UTC)
 * Photons have relativistic energy and relativistic mass, but no rest energy and no rest mass. Two types of mass are being spoken of here, and the statement is only true for the relativistic kind of mass, but is not always true for the invariant kind of mass. A single photon has energy but no invariant mass. Two photons moving in different directions, do have invariant mass. The basic problem with single photons is that their energy, and thus their "mass" is completely dependent on the observer, and can be reduced to arbitrarily low values. Thus, like the kinetic energy of a single particle, it's difficult to locate, and may well not exist as a "real" thing. S  B Harris 21:30, 11 October 2008 (UTC)


 * It's not really that difficult; both energy and (relativistic) mass are frame dependent in exactly the same way. Dicklyon (talk) 01:42, 12 October 2008 (UTC)
 * Sure enough, but there's another kind of mass which isn't. The tricky part for many to understand is that while the kinetic energy of ONE particle is entirely frame-dependent, the kinetic energy of TWO particles, as a system, so long as they're not moving in the same direction, is not. It contribues a minimal emergy value to the system below which you cannot go, by simply choosing frames. You can thus make some system kinetic energy go away by choice of frame, but not ALL of it. The invariant system mass is the (total system energy)/c^2, when seen in the frame which minimizes this total energy. That also is the center of momentum frame. S  B Harris 22:26, 3 November 2008 (UTC)


 * This is true, but why get hung up on frame invariance? I was riding the subway the other day, and I leaned against the pole. I was leaning in the direction of motion, and I was thinking--- gosh, force in the direction of motion, I'm doing a heck of a lot of work on this pole! Is this point of view wrong? No, it's just the station version of the story of the momentum flows in the subway through my feet and out the pole. Covariant quantities are just as physical as invariant quantities. Something called "mass" doesn't have to be the same in all frames, just as something called "energy" or "work" is not the same in every frame. What you call the "x-component of the electric field" changes when you rotate your frame. That doesn't mean its unphysical. The same goes for the time-component of the momentum.Likebox (talk) 22:40, 3 November 2008 (UTC)
 * Eh, but don't you think that quantities which are conserved and invariant no matter who looks, aren't somehow more real? I suppose this is a philosophical question, but what else do we mean by "real" except: "That which everyone measures the same, and thus agrees on" ? Thus, it's not this or that component of the field that is "real", but rather the amount of "charge" that gives rise to all components of the field, measured in all directions and integrated. Some of which vary accoding to observer, but each observer somehow sees the sum-total (some volume-integral through all space) as being the same. Invariant mass is sort of a gravitational "charge." S  B Harris 01:53, 4 November 2008 (UTC)


 * Accepting your opinion of which is "more real" does not in any way cause relativistic mass to disappear as a concept. Dicklyon (talk) 03:28, 4 November 2008 (UTC)


 * This is more of a philosophical answer: Is a vector real? I don't mean the length of a vector, I mean the direction. There is no definition of direction which is independent of frame, but the object itself somehow acquires a meaning even though the numbers that define it change from frame to frame. So it's a philosophical sort of question, but I think the answer is "the transformation law defines the object", so that even though an object with a transformation law is different in different frames, it is a well defined object as a whole. So the "relativistic mass" and the "relativistic momentum divided by c" four vector are the philosophical "quantity" that exists. But then the relativistic mass just by itself doesn't quite cut it, which perhaps explains all the animosity you guys have towards it. It's like the x-component of a vector--- you need to know the other components for the concept to make complete sense.Likebox (talk) 03:40, 4 November 2008 (UTC)

On the interpretation of the rest energy
One can show that the rest energy can also be interpreted as the infinite sum (or "integral") of infinitesimally-small increments of kinetic energies calculated in a Newtonian way. Here one considers a fictitious set of incremental motions of the particle towards the high-velocity limit $$\,v=c\,.$$ The details are as follows.

Let the particle move under the influence of a constant force $$\mathbf F$$. The relativistic equation of motion then leads to $$\frac{m^2\mathbf v^2}{1-\frac{v^2}{c^2}}=\mathbf F^2t^2\,,$$ or $$\frac{v^2}{c^2}=\frac{\frac{F^2t^2}{m^2c^2}}{1+\frac{F^2t^2}{m^2c^2}}.$$ This means that asymptotically for $$t\to\infty$$ the velocity $$\,v$$ approaches the limit c. Now a complete set of infinitesimal intervals is considered, becoming asymptotically identical with the orbit of the particle, and also two (not one!) associated infinitesimal quantities are considered. The first one, $$\epsilon_1\,,$$ descibes the approach to $$\,v=c$$. (In a pseudo-mathematical language: "for $$\epsilon_1\to 0$$ the velocity c is approached with arbitrary accuracy").

The second infinitesimal, $$\epsilon_2$$, is more complex: it is assumed to be so small that the Newtonian approach, which can be applied in a given one of our small intervals after a Lorentz transformation to the corresponding comoving coordinates of the center of that interval, can be linearized with respect to the increment of the kinetic energy  $$ T=(1/2)\,mv^2\,.$$ Thus, "for $$\epsilon_2\to 0$$,  the linearization becomes arbitrarily accurate in our interval", and $$\delta T=mv\cdot\delta v$$, i.e., the factor 1/2 has vanished. (Remark: a Newtonian approximation is posssible in any case, in the whole interval considered, since exactly in the center of that interval, where our comoving system is defined, the particle is at rest.)

Precisely: at first we let $$\epsilon_2\to 0$$, and only afterwards also $$\epsilon_1\to 0\,.$$ In this subtle limit, we obtain an infinite sum of infinitesimal increments of Newtonian kinetic energies, $$\sum\,\delta T$$, i.e. an "integral" which approaches the desired expression $$mc\cdot c\,.$$ (Here we use the following facts: for almost all terms of our infinite sum the velocity is almost c, and the sum of the increments $$\,\delta v$$ is also c, namely c-0.)

Highly fictitious, indeed, and very mathematical! But still interesting, perhaps, to some people. Not more, but also not less! In fact, that the orbit is fictitous and does not, e.g., correspond to a real motion preceding the genuine processes, can be proven by experiment, namely by comparison with photons. These would have $$\,v=c$$ everywhere, whereas for massive particles one has $$\,v=0$$ in the instantaneously comoving system and $$v=c\cdot (1-\epsilon_1 )$$ for large t. - 87.160.97.246 (talk) 12:48, 11 October 2008 (UTC)

"Corroboration" subsection
Can someone with the required knowledge read technical details here and here and rewrite the new "Corroboration" subsection that is just hype from the popular press? We would much appreciate it! McKay (talk) 10:10, 23 November 2008 (UTC)


 * That stuff is an attempt to stir up excitement in the media about lattice QCD. Periodically, people who do computer calculations try to get the public interested in their work. The news now is that they can get the mass of the proton about right.


 * What does this have to do with E=mc^2? Not much, other than the obvious fact that most of the mass of the proton is carried by glue and in the kinetic energy of quarks, not by the parameters which we call the "quark mass". The problem is that the quark mass is not like the electron mass, it doesn't have a simple interpretation as the weight of something isolated. It's a property of the propagator of the quark at short distances, it tells you how far a quark moves in a given very short time.


 * If you think of gluons as "energy" and quarks as "matter" (which is a pretty cockeyed division), and separate out the kinetic energy of the quarks from their mass, then you could say "most of the proton's mass is energy!", but you could also say "all of the proton's mass is energy!" by calling the quark masses energy too. The point is that the real content of the statement E=mc^2 is that changes in energy are reflected by changes in inertia and weight, and the energy in the proton is all locked up, since the proton is stable. So I don't think this is such a good illustration of E=mc^2.Likebox (talk) 02:31, 27 November 2008 (UTC)
 * Cockeyed or not, you'll see from its TALK page that a few people have decided to WP:OWN the article on matter, and define matter as "fermions" (eg, quarks and leptons) and everything else as "non-matter." Which means they want to define most (>98%) of what we handle as "ordinary matter" (like tables and chairs), as actually being non-matter which nevertheless has most of the mass. Sigh. I think "matter" should correspond to its historical usage, not some harebrained thought of accelerator guys about fermions vs. guage bosons. S  B Harris 04:12, 30 November 2008 (UTC)


 * I'm not owning anything, you're the one equating mass and matter, not I, and you're making me say things I di]dn't say. You know what a chair is made of? Molecules! You know what a molecule is made of? Atoms! You know what atoms are made of? Quarks and leptons (aka elementary fermions)! Aka tables and chairs are... matter! You don't have to like it, but it's how physicists define matter, just pick any book on particle physics. There's absolutely nothing being said about mass. Headbomb {{{sup|ταλκ}}<sub style="margin-left:-3.5ex;">κοντριβς – WP Physics} 22:29, 30 November 2008 (UTC)


 * Except that protons are not made of quarks only, they are also made of glue. The glue is most of the mass.Likebox (talk) 23:02, 30 November 2008 (UTC)
 * Yes. Saying that a chair is "made" of quarks and leptons is like saying a chocolate chip cookie is made out of chocolate chips. S B Harris 23:06, 30 November 2008 (UTC)
 * But the quarks are particles/quanta while the "glue" is just a configuration of the gluon field around the quarks. It's not like gluons (or cookie dough) which can lead an independent existence. People routinely use the word "electron" to mean the bare electron and its fields and its fields' fields..., and why not? It's not like you can have an electron without the fields. So I don't see the problem with saying that a chair is made of quarks and electrons. It's certainly a bound state of quarks and electrons. -- BenRG (talk) 00:13, 2 December 2008 (UTC)


 * The first difference is that the electromagnetic contribution to the mass of an atom is very small, aside from very very close to the electron and quarks. On the other hand, the mass of the proton is nearly entirely due to the mass of the glue field. One way of saying this is that if you changed the mass of the up and down quark to zero, the mass of the proton would only shift a few percent. But if you reduced the coupling constant of QCD, the value of the glue-glue coupling at a certain very high energy scale, the mass of the proton would change by an incredibly large amount.


 * I would say that it is not quite correct to say that the glue field is "due to" the quarks, like the electromagnetic field is due to electrons. The reason is that space is filled with glue field even in the absence of any quarks, meaning that the vacuum of QCD is full of low-momentum gluons. These low momentum vacuum gluons are hard to describe precisely as particles--- they are usually described as the value of the "glue condensate", a field, which is "|G|^2", the expectation value of the sum of the squares of the glue field components. But you can think of it like this--- at any momentum k which is smaller than about 200 MeV, the vacuum is full of a coherent superposition of vacuum gluons, and at high momenta, about 1000MeV or more, there aren't any vacuum gluons. Another way of thinking about it is that the electromagnetic field averages to zero at large distances, but the QCD field averages to a random field at large distances, and the randomization distance is about 1 fm approximately 1/300MeV, a nuclear radius of 10^-15 m or so.


 * When there are quarks around, they create a new gluon field nearby, like electrons create an electromagnetic field, but at long distances, the field collimates into a string. The reason is because of the all the glue field in the vacuum don't like to be aligned so that their average becomes a long ranged 1/r field like would be made by a free quark, they would rather be random. At distances greater than about 1fm, the field flux of a quark, which is not random but points in a particular direction, has to squeeze into the smallest possible area, which makes it into a 1fm in diameter string. The precise mechanism of collimation is a matter of debate, it's called the problem of confinement.


 * But there's a further complication. The light quarks, which are lighter than the scale at which the QCD field becomes full of glue, are so light that their number is uncertain in a box of radius 1fm. So the vacuum is full of a coherent state of these light quarks too. These light quarks form cooper-like pairs and condense, except the condensate is not superconducting, but is just a spontaneous symmetry breaking. The shaking of this condensate is called the pion. The pion is lighter than the QCD scale, and would be massless if the quarks were massless.


 * So that the proton is a bunch of quarks generating a glue field which interacts with vacuum glue, and generates a long ranged "pion tail" extending out about 7 proton radiuses out. To call this big bag of mess "three quarks" is a misdescription.Likebox (talk) 01:21, 2 December 2008 (UTC)


 * It's wrong to the extent that saying atoms are something made of "protons, neutrons and electrons" is wrong. Forget the photons, and you have no atom to speak of, all you got is protons, neutrons, and electrons flying around. Headbomb {{{sup|ταλκ}}<sub style="margin-left:-3.5ex;">κοντριβς – WP Physics} 02:17, 2 December 2008 (UTC)


 * You are sort of right, but it's misleading. The "photons" responsible for keeping the protons neutrons and electrons together are generating a Coulomb interaction, and you don't have to view them as photons. They have a very small percentage of the mass of the atom, and they may be well approximated by a non-relativistic potential. Then you can think of the atoms as protons and neutrons interacting with a potential to form the nucleus, and with the electrons by a Coulomb potential to form the atom, and you have a picture that's 98% right. The gluon interaction cannot be well thought of as a non-relativistic potential between quarks, the number of quarks in the proton is a quantum superposition of 3,5,7,9,11 etc, the "pion cloud", and the gluons contribute most of the mass of the object.Likebox (talk) 19:46, 2 December 2008 (UTC)

(unindent) And again, for clarity, I'm not talking about mass. It's completely irrelevant here. If one is ok with either the "implicitness" that electrons and protons will have photon fields which binds them to one another in the clumps we call atoms, then one has to be ok with the "impliciteness" that quarks will have gluon fields which binds them to one another in the clumps we call proton/neutron/baryon/pion/kaon/meson. Sure the fields' contribution to mass is greater (much greater) in one case than in the other, but mass is not something that is inherent to matter. Ws and Zs have mass too. Are they matter because of this? The literature says no. In the SM, neutrinos don't have mass. Are they then "not matter" (under the SM) because of this? The literature again says no. That's because matter is not defined in term of whether or not something has mass, matter is defined in terms of whether or not something is made of elementary fermions. If yes, it's matter, if not, it's a force carrier. The rest are technicalities, albeit very complex ones. And that's what the matter article, and articles on related topics, should reflect.Headbomb {{{sup|ταλκ}}<sub style="margin-left:-3.5ex;">κοντριβς – WP Physics} 02:30, 3 December 2008 (UTC)


 * Although the two people who wrote the "standard model of particle physics" poster decided that matter means "something with elementary fermions in it", and everything else is "force carriers", this is not a standard scientific definition and it's just rubbish. Is a pi meson or a rho meson matter? How about positronium? A photon is part of the time positronium, part of the time a meson. So does it start being "matter" the moment it quantumly fluctuates into a meson, then stops being "matter" when it goes back to being a photon? The pion is a force carrier, but it's got quarks in it. The separation is just bogus.


 * There is no definition of the word "matter" that's accepted. It usually means a bunch of stuff made of protons, neutrons, and electrons. It usually excludes classical black holes, and it usually excludes short-lived unstable particles. It's a word without precise scientific definition.


 * As for the proton, the glue field is not just due to the quarks. A lot of it is due to the QCD vacuum, too.Likebox (talk) 05:24, 3 December 2008 (UTC)


 * Rho mesons, pions, positronium, etc... are all made of elementary fermions so yes they are all matter. This goes well beyond the famous poster. Just pick any book about particles physics and you always have that distinct division between "particles of matter" aka the three generations of elementary fermions and "force carriers" aka the gauge bosons. See for example Beam Line 25(3) p.7 (in the bottom left corner).Headbomb {{{sup|ταλκ}}<sub style="margin-left:-3.5ex;">κοντριβς – WP Physics} 07:10, 3 December 2008 (UTC)


 * Maybe this is the accepted terminology in a bunch of particle physics books, but it's not very useful. The separation "matter=fermions" and "force carrier=boson" is sort of artificial. Consider for example the hypothetical case that we discover a skyrmion in nature--- a stable topological soliton in a purely bosonic field that behaves as a fermion. A skyrmion doesn't have any elementary fermions in it, but it would behave like a fermion, so it could be a constituent of some hypothetical matter. But this is not a completely hypothetical case, because the proton, neutron, and small nuclei can be approximated as skyrmions in the bosonic pion field, with about 10% accuracy (but the accuracy gets better if you add a fifth dimension and do some string theory, and there might be a systematic way of making this description exact--- this is still a subject of active research). But if you like the textbook separation, what can I say? It rubs me the wrong way, personally, but there's no content to disputes like this, it's all just language.Likebox (talk) 20:19, 3 December 2008 (UTC)


 * Well I'm not saying the current definition is perfect, or will stand the test of time, I'm just saying that this is the current definition used, and the reasons for using it. Anything else would be IMO, WP:OR, WP:MAINSTREAM, or WP:CRYSTALBALL. Perhaps matter will still be defined as "that which is made of elementary fermions", and exclude things like your skyrmion. Perhaps it will be extended to "that which is made of elementary fermions, or behaves as if it were". There is perhaps shortsightedness in this definition, but I doubt that this will be resolved anytime soon since no one seems really interested in studying the implications of defining what matter is. I (on a personal level) don't have any real problem with the current definition, as it's always implicit that elementary fermions (or clumps of them) are not standalone entities. Headbomb {{{sup|ταλκ}}<sub style="margin-left:-3.5ex;">κοντριβς – WP Physics} 02:41, 4 December 2008 (UTC)


 * This is not a mainstream definition among scientists. It's a faddish definition among popularizers of science. It is as bad as "the atom is mostly empty space", which started with Rutherford and was popular among popularizers in the past, or "motion in a gravity well is like a deformed rubber sheet" which started with Einstein and continues today. None of these statements is correct as science, even in the first approximation. They are only catchphrases, designed to grab the ear of the listener. This stuff really confuses young people. For example, when I was younger, I tried to work out the motion of a planet as a geodesic of a rubber sheet, and it's all wrong. The mathematically correct simplification for the planet is to say that the rate of clocks is different at different points. A popularization should turn into a correct mathematical picture, at least in some approximation, and this position is supported by WP:USEYOURCOMMONSENSE and WP:THINKFORYOURSELF.Likebox (talk) 19:48, 4 December 2008 (UTC)


 * I've never seen it defined otherwise in any book or publication dealing with particle physics. I can and did provide both "vulgarisation" articles and technical/peer reviewed articles that consider matter to be what is made of elementary fermions. If this is wrong, then show the refs.Headbomb {{{sup|ταλκ}}<sub style="margin-left:-3.5ex;">κοντριβς – WP Physics} 05:21, 5 December 2008 (UTC)


 * Here's a reference (neutrinos are not made of atoms, so they are not matter according to this definition).
 * Here's another one (dark matter is probably not made of the usual elementary fermions, but it is matter according to this source)
 * I will ask you a question: are glueballs matter according to your definition? In pure QCD, glueballs are made of pure glue, so that they would not be matter. But in the real world, glueballs mix with quark bilinears, meaening that every glueball looks exactly the same as a meson, and glueball states are not distinct from meson states.
 * There are no scientific articles that go into detail about the definition of "matter", because that's like trying to define "air". What is "air"? If you say the air on mars is thin, do you mean the same thing as "the air is humid today?". "Air" is a colloquial term, generally meaning the mix of gasses around you. "Matter" is a colloquial term for anything made of atoms.Likebox (talk) 16:12, 5 December 2008 (UTC)

(deindent) This discussion veered into ridiculous semantic debates. I am sorry for pushing too hard--- I was just venting frustration with "standard definitions". For the corroboration subsection, I moved it to "applications to nuclear physics".Likebox (talk) 07:50, 6 December 2008 (UTC)

Featured article
Can this article be nominated as a featured article? MathCool10 (talk) 05:22, 24 November 2008 (UTC)


 * It won't make it. There's an equation in it.Likebox (talk) 00:09, 25 November 2008 (UTC)
 * Good point. --Itub (talk) 23:00, 3 December 2008 (UTC)

Antimatter
The article states that "in our universe, antimatter is rare". I'm no physicist, but is it not true that it is simply not in abundance on Earth - perhaps making a re-write to "antimatter is highly expensive to produce" more appropriate? - RD (Talk) 12:48, 1 December 2008 (UTC)


 * I am writing based on the current consensus view that the preponderance of matter over antimatter in the universe is not a local fluctuation, it's true everywhere. The reason that this is widely believed is because if there were domains of matter and antimatter, there would be boundaries between them, where you expect to see a huge amount of e-plus e-minus annihilation, which would show up as X-rays. Since you don't see a big X-ray peak from any empty region in the sky, the conclusion is that the universe is everywhere matter.Likebox (talk) 20:49, 1 December 2008 (UTC)
 * Ah, I see. I think I got my wires crossed somewhere. Thanks for clarifying that for me. - RD (Talk) 01:30, 2 December 2008 (UTC)

Potential Energy/Circularity/Relativistic mass
One of the things that confuses people when learning mass/energy equivalence is potential energy. Where is the mass of the potential energy? For example, when I compress a spring, it weighs more. Where is that extra mass?

The solution is that In relativity, the potential energy of a particle is no longer an admissible concept--- it is replaced by the potential and kinetic energies of a field. The field energy is the potential energy in the non-relativistic limit. When the field gravitates, it's stress energy acts at the points where the field is nonzero. To make this statement precise, you also need to take into account the gravitational field energy. That is what the comments which were tagged with "citation required" were saying.

I don't think I can find a source for these comments, because they are too trivial. Everybody knows this. But maybe there is a source somewhere.Likebox (talk) 19:56, 28 December 2008 (UTC)

Similarly, the comment "The rest mass of a system is the sum of the relativistic masses of the parts in the frame where the system as a whole is at rest." is correct, and also well known. If it is required, it is possible to dig up a source.Likebox (talk) 20:01, 28 December 2008 (UTC)

The definition of relativistic mass is not circular--- it is the mass as measured on a scale. It is not defined experimentally in terms of energy, it is defined in terms of an experiment which weighs something. It is equal to the relativistic energy up to units, and this means that if you want, you can redefine it to be the energy. That's fine, if you already understand E=mc2, otherwise, it is confusing. This article went through a protracted discussion on the merits of relativistic mass, etc, and the consensus at that time settled on the current wording. The current wording mentions relativistic mass, but also emphasized that the concept is redundant, since it is a synonym for the energy.Likebox (talk) 20:01, 28 December 2008 (UTC)
 * See WP:VER. The burden is on you to produce evidence.  These are not trivial remarks.  See also WP:OR.  I see misunderstandings of energy concepts.  The linked definition of total energy is not the same as the definition on this page: they are not both right.  If relativistic mass were mass as measured on a scale (normalized, as I am sure you are conscious of the distinction with weight), it would just be mass. ~Paul V. Keller  20:34, 28 December 2008 (UTC)
 * I should clarify, my main concern is that only differences in energy have physical signifance. Of course, you can define a reference state with zero energy, then the absolute value of energy shows where you are in relation to the reference state.  But as the article already explains, the choice of the reference state is arbitrary.  The arbitrary choice causes much confusion when the concepts of mass-energy are used in connection with systems where it is convenient to represent thermal energy and other forms of energy separately from m0c2. ~Paul V. Keller  21:02, 28 December 2008 (UTC)

(deindent) Wikipedia policy is designed to deal with real existing points of controversy in the literature, not with some minor misunderstandings between editors. I am sorry, but I do not like to cite authority. When all knowledgable people agree on something, there is no need to dig up citations. On this stuff, everyone should be able to come to agreement by discussing in a reasonable way.

1. The relativistic mass is indeed just what you would call mass--- it is the resistance to changes in velocity. It is only different from the word "mass" when something is moving at a speed comparable to that of light, because there is also the invariant mass. The two are equal when an object is at rest (see mass in special relativity).

2. It is no longer completely true in relativity that only differences in energy have a meaning, because in relativity there is a natural reference state: the physical vacuum. Any object has nonzero energy relative to the vacuum, and if you can grab this object and shake it, then this energy is measurable as the mass of the object, how much it resists shaking. (I should point out that the energy of the vacuum is arbitrary in special relativity, you can set it to zero by convention, but it is not arbitrary in general relativity--- it is the value of the cosmological constant.)

3. Thermal energy is never separate from m_0. A hot cup of coffee weighs more than a cold cup of coffee.Likebox (talk) 02:00, 29 December 2008 (UTC)
 * If I thought you were right, I would not ask you for a cite. The question is far more subtle than you acknowledge.  Try http://plato.stanford.edu/entries/equivME/ for a starting point
 * For any definition to be meaningful, the terms used by that definition must be defined. If you look at the derivation, it is only the inertial mass that is used.  Only changes in energy are taken into account.  The link to relativistic mass gives a rearrangement of E=mc2.  Why would you link the definition to that page when the mass page already uses the inertial mass?
 * A "natural" reference state is your intuition at work. When you start looking at multi-body interactions, you will soon get into trouble.  I am not bothering about the point that vacuum potentially has some mass-energy, but I will say it is easier to think about many problems if you are not bogged down by a mistaken idea that energy is defined in absolute terms.  There is a huge history of science behind energy, and all concerns relative energy values.  The history of energy as an absolute quanitity is philosophical speculation, computational convenience, and tremendous confusion.
 * You can make the thermal energy separate from the rest mass if it is convenient, but then your would call less stuff mass and say the energy behaves like mass. http://plato.stanford.edu/entries/equivME/
 * I went into greater detail on some points in my response to you on my user talk page. ~Paul V. Keller 02:32, 29 December 2008 (UTC)


 * The vacuum is a natural reference state to define zero energy. That's not just my intuition, it is everybody's intuition, including all physicists, and including you yourself, if you think about it. The energy of a bunch of well-separated particles is the sum of the energy of the particles, relative to the energy of the vacuum. This is what the mass of a particle is in relativity--- the energy of one particle minus the energy of the vacuum. This is more or less an absolute--- it is only arbitrary to the extent that the vacuum energy can be redefined by adding a constant. The vacuum energy is not measurable in special relativity, but it is measurable in General Relativity because if there is energy in the vacuum it makes gravity--- the vacuum energy is called the cosmological constant.


 * There is no problem with multi-body interactions, I don't even know exactly what you mean by suggesting that. The energy of a bunch of interacting particles is determined by the kinds of fields that they make, by the particle-field coupling. For example, if there is a bunch of particles interacting with an electromagnetic field, the interaction energy is the charge density times the scalar potential, and you can define the total energy, and it will have a field energy which becomes the potential energy in the limit that every particle is moving slowly. If you use local fields there is no problem.


 * Of course you can define the total mass/energy as split up into some "mass" and some "energy", if you like, and then say that the "energy" has inertia, and the "mass" also has inertia. But it's stupid. It's like dividing all the charge in a region into "charge" and "schmarge", and declaring that charge and schmarge are different, but behave exactly the same as far as all experiments are concerned. Then you can get into an argument whether you have 2 coulombs of charge, or 1 coulomb of charge and 1 coulomb of schmarge, or maybe it's all schmarge. If two things behave the same way in all circumstances, they are the same thing, and that's what mass and energy are--- the same thing. You can split them up in some arbitrary way, but that would always be unproductive, and no physicist would ever do that. In physics, if two ideas are equivalent as far as the experiments are concerned, they are philosophically the same.Likebox (talk) 05:06, 29 December 2008 (UTC)

An unclear point
In the history section, under the title "Electromagnetic rest mass", I read: "... it was also suspected that the mass of an electron would vary with velocity near the speed of light". This refers to the work of:
 * J.J. Thomson: 1881
 * Oliver Heaviside: 1888
 * George Frederick Charles: 1896

How is this possible, knowing that electron was first discovered in 1896? I think these authors were talking about charged bodies, not electrons. —Preceding unsigned comment added by 212.50.110.1 (talk) 19:08, 29 January 2009 (UTC)

GA failed nomination
OK! I failed the GA nomination of this article because of some messed up reference links. We need to clean this article up and add more references. Scanning through almost any section, I see little to no references. This cannot do with a possible GA! We need to source most of the statements, as most statements are unsourced. Any advice, please?  Math Cool  10  Sign here! 01:27, 4 February 2009 (UTC)
 * Go through a standard text like Taylor and Wheeler's Spacetime Physics and just put in the refs where they go. Takes work. S  B Harris 02:19, 4 February 2009 (UTC)

Use Spacetime Symmetry to derive E=MC^2
Dear Editor, why did you say that E=MC^2 is the consequence of symmetry of space-time? Would you please show me how to use space-time symmetry to derive E=MC^2? Thanks a lot!

Sincerely,Wanchung —Preceding unsigned comment added by Wanchung Hu (talk • contribs) 02:36, 10 March 2009 (UTC)


 * The symmetry of space time is Lorentz invariance, which means that the physics is the same no matter how fast an observer moves. Einstein's derivation is in the article.

Merge with "Available Energy"
Available energy is not a great article--- I put some issues on the talk page there.Likebox (talk) 14:43, 16 March 2009 (UTC)

Bunch of nonsense
What does this diagram mean?

Properties_of_mass

I guess I understand--- it tells you what to multiply by to go from one mass representation to another. But it's empty of real content. What is the "quantum mass"? Is it the inverse of the compton wavelength? This table serves the purpose of obfuscation, not enlightenment.

This table is a perfect example of wrongheaded attempts at education.

The reason is that it is a table of unit conversion. If you use natural units, or at least know what natural units are, then this entire table is obvious. All the quantities are masses, and all are represented by the same letter, by the letter M. That's true of every quantity except r_s, the Schwartschild radius, which is twice the mass. The factor of two is included here for some unfathomable reason.Likebox (talk) 23:57, 9 April 2009 (UTC)

Contrary to Popular Belief
Anytime the words "Contrary to popular belief" are used, the remainder of the sentence is suspect. The reason is that this phrase is saying "see how much smarter I am than all those other people". Most of the time, the person making the claim has misunderstood popular belief, or distorted it so that it can be made to seem foolish.

If a popular belief is known to be genuinely wrong, like the Sun goes around the Earth, the result is that it stops being a popular belief. This particular sentence is particularly annoying: contrary to popular belief, mass energy equivalence does not explain the energy emitted in nuclear reactions. It depends on what you mean by "explain". The detailed mechanism is due to nuclear and electromagnetic forces. But the idea that it might be possible to extract energy from nuclei, and the amount of energy available, are both calculable from the general principle.

So contrary to people who say "contrary to popular belief", the popular belief that mass-energy equivalence has something indirectly to do with nuclear power is justified.Likebox (talk) 23:27, 9 April 2009 (UTC)


 * I agree that the sentence should usually be avoided (and I didn't write it), but there is one particular popular belief associated with E=mc^2 which is quite prevalent, which is that the mass involved in nuclear reactions is "converted" to energy, and thus disappears. Actually, it doesn't disappear so much as relocate (disappears from the system, but only because it can't be kept from doing so). When the energy is removed, the missing mass goes with it and is also removed, but it never disappears or is "converted." It adds to the mass of wherever it goes. One type of energy can be converted to another kind, and ditto with mass, but both energy and mass are separately conserved, and so neither can be changed to the other. In this sense the popular interpretation of the equation is wrong, even though it (usually) gives the right answer, since binding energies (thermal energies, kinetic energies, etc) are normally withdrawn completely from systems before their mass-defects are measured, so that the change in one thing is given by the change in the other. With small reaction-energies that's not always the case (often heat is not completely removed in chemistry) but this isn't noticed because the mass differences are too small to measure. Reactions which produce heat don't change in mass until the heat is removed! S  B Harris 00:31, 10 April 2009 (UTC)

Hi Steven: Are you suggesting the caption to this image is incorrect? Brews ohare (talk) 02:23, 10 April 2009 (UTC)


 * No--- he's just saying that the "mass" doesn't go away once the atoms split. It's still there in the heat and light. That's a reasonable thing to clarify. But I'm not sure how widely prevalent that misconception is. I think that the whole thing is explained pretty well in the body of the article though.Likebox (talk) 04:01, 10 April 2009 (UTC)


 * The equivalence of mass and energy has no more to do with nuclear reactions than it has to do with the springing of a mousetrap, yet we never mention E = mc2 in that context. No one would argue that the mass loss of the mousetrap explains how it releases energy, and no one would say that "some of the mousetrap's mass is converted to energy". It is true that nuclear energies are often found by making mass measurements but that doesn't mean the mass difference is the cause of the energy release; that is the same logical fallacy as saying that we "measure" lightning's distance by the time interval between lightning and thunder and therefore the time interval explains why the lightning struck at the distance it did. The fact that we can measure the mass difference in the nuclear case but not in that of the mousetrap is irrelevant. It does not mean that mass-energy equivalence explains a nuclear reaction in any sense in which it doesn't explain why a mousetrap springs. That is the same logical fallacy as saying that if we are too far away to hear the thunder then we cannot explain the reason for lightning striking at the distance it did as due to the time difference between lightning and thunder, but when we are close enough to hear the thunder then we can give that "explanation" of why the lightning struck at that distance. You wouldn't explain how a mousetrap works by invoking E = mc2, would you? The point of my "Contrary to popular belief..." statement is that E = mc2 has nothing whatsoever to do with why energy is released in a nuclear reaction.


 * As a side note, "contrary to popular belief" can be justified; if it [the E=mc2 "explanation" of nuclear energy release] is in science textbooks and is repeated on television and in newspapers invariably whenever the history of nuclear weapons and energy comes up, it is still wrong. It doesn't matter how many otherwise reputable sources say it; it is still just as wrong! In order for Wikipedia to help the world we must not spread such mythconceptions.

129.2.43.42 (talk) 18:03, 12 April 2009 (UTC)Nightvid


 * Everything you say is absolutely correct in terms of facts, but your interpretation is uncharitable. Logically speaking, E=mc2 has as much to do with nuclear energy as it does with mousetrap energy, as you say. But in terms of human history, mousetrap energy was predicted and understood long before E=mc2, while nuclear energy was understood after. The order of magnitude of the energy released by nuclear transformations, then the precise value, was estimated from the differences in nuclear masses, and this is important in terms of history.


 * The way to fix this is to explain that mousetraps also can be understood in terms of E=mc2, although nobody does this. This is done in the article in the part about the electricity generator in the dam. E=mc2 does not provide an explanation in any of these cases, as you say, because it's too general--- it doesn't deal with the specific forces and particles involved. But the article is phrased carefully now (hopefully to your liking).Likebox (talk) 18:39, 12 April 2009 (UTC)


 * I still think we could include a "contrary to popular belief" statement, but admittedly I have some deep emotional issues with explanations in physics that are influenced by history or in historico-chronological order rather than "pure". Mostly this is because it took me so long to really understand quantum physics since it was explained in a "historical" way rather than with the "pure" axiomatic approach. I suppose I can "live with" the way the article is now. 129.2.43.26 (talk) 18:14, 15 April 2009 (UTC)Nightvid

Disputed text
This text (and other additions) disrupt the flow of the text. The text says that a photon can have any energy, and any amount of relativistic mass. It then says that a photon is never at rest, and that if you try to get it to be at rest by chasing it, the energy goes to zero. So the photon has zero rest mass. It's a simple pedagogical paragraph.

But this text is inserted:

More precisely, it is known that the mass of the photon is less than 10−51 g, but if the photon.

Which simply has the effect of plugging the four references. It adds nothing to the paragraph. The bound on the mass of the photon is irrelevant. If the photon is not massless, you could substitute "graviton" or even "an idealized photon, one that moves at the speed of light". The point of the paragraph is kinematics, not details of photons.

This is actually something that comes up a lot in pedagogy of relativity--- some people get the sense that relativity has "something to do with light". But of course, that's nonsense. The addition has the unfortunate effect of distracting. It's accurate, though, and would be a good addition to photon.Likebox (talk) 03:09, 12 April 2009 (UTC)


 * The references and sentences about experimental observations supporting the prediction that photons have zero mass has nothing to do with confusing relativity with light; it is simply pointing out (i) some experimental support (ii) referring to a topic of great theoretical and experimental interest (iii)suggesting that whatever theory says, it is subject to observation. The topic is photons: not gravitons or kinematics. The references are not "plugged" they are supporting the point. Removal of such a documented relevant point is inadvisable. I've put the photon discussion in its own subsection to ease any "interruption of flow". Perhaps this is advisable also because zero rest mass is a special case. Brews ohare (talk) 15:03, 12 April 2009 (UTC)


 * I didn't accuse you of confusing relativity with light. I am worried that a reader, learning about the kinematics of massless particles, will confuse relativity with light. The only purpose the photon serves in that paragraph is as an example of a massless particle.Likebox (talk) 19:16, 12 April 2009 (UTC)

The photon is an example of a massless particle, and is the example chosen for most of the discussion. Switching to neutrinos is not adding clarity. To delete references about experiments concerning photon rest mass is pure caprice on your part; no response has been given to the reasons supporting its inclusion. I suggest you desist from deleting referenced material at your whim. Confusing relativity with light is a figment of your imagination: you have provided no reasoning to suggest why this could happen or what bearing it has upon the topic of this article. Brews ohare (talk) 04:01, 13 April 2009 (UTC)


 * You might be right. I'm sorry for being hasty. But then, please, introduce the discussion in a separate paragraph. For example, you can say:
 * The photon might not be a massless particle, in which case, it would not move with the speed of light. The speed of light would then not be the actual speed at which light moves, but a constant of nature which would be equal to the maximum speed that any object could theoretically attain. It would be the speed of gravitons, but not the speed of photons. The photon is currently believed to be strictly massless, but this is an experimental question. From studies of long-ranged magnetic fields, like galactic magnetic fields, the current bound on the photon mass is that it is lighter than 10^-50 grams (source).


 * I would have no objection to this discussion, but it is out of the main line of development. The confusion of relativity with properties of light, I am afraid, is not a figment of my imagination. There are people I have met who think that time dilation is caused by light signals reaching you at the wrong time.Likebox (talk) 17:21, 13 April 2009 (UTC)

Formula for Rest Mass
The article is written so as to be readable by anybody in the early parts. So the early parts are written without any mathematical formulas, not written in symbols, nor written out in words.

If you write "the rest mass is the energy squared minus the momentum squared" in the early section, you are confusing just as many people as when you write m^2=E^2-p^2. These people usually get confused is not because they can't understand what the equation means in words. The reason that they get confused is because they don't understand why such an exact, precise relation should be true. The human mind, given such precise information without a hint of a reason, rebels.

If the person is gullible, you can give a stupid reason, and the result might end up absorbed for a while. Then it will be lost the moment the person learns more and the reason no longer makes sense. At wikipedia, we are duty bound to give an accurate reason. In this case, that means that the reader should learn enough coordinate Minkowksi geometry, at least to the point where you understand that the length of a four vector has a minus sign in the time component.

This is why I delete the sentence which says how to calculate the rest mass of a photon in formulas.

But it is still possible to discuss the rest mass of a photon, without equations, and in a way that anyone can understand. That's by staying physical, giving an explanation of how to measure the rest mass of a photon, by chasing it, and measuring its mass in different frames. This is what the article does, and it is much easier to understand than a formula spelled out in words.Likebox (talk) 19:13, 12 April 2009 (UTC)


 * This source: is unclear in the part cited--- I am not sure what it is saying exactly. It says "consistent with nonzero rest mass of the photon" for various numbers, but then gives bounds which exclude those mass ranges. The book itself seems to be pushing the point of view that photons have a small nonzero mass.

About QCD
The recent edits to the "application to nuclear physics" section included a modification of the paragraph about QCD. I encourage the editor to read the previous discussion about that section.Likebox (talk) 19:42, 12 April 2009 (UTC)

Let me explain precisely what is wrong: the models people have in their head regarding the structure of the proton, even some experts, is totally wrong. They imagine that three quarks interact to make a proton much as a proton and an electron make an atom. This point of view was prevalent in the 1980's, and a lot of literature still clings to this simpleminded view.

That the proton is more complicated was suggested already in the 1960's, but was not rediscovered until the 1980s, and not widely accepted until much later. The correct point of view includes the effects of quark vacuum condensates, to produce a skyrmion picture of protons. Without the skyrmion picture, simpleminded constituent pictures based on three quarks get the physics wrong. The other alternative is a detailed lattice QCD, which of course is also correct.

But neither of these pictures has anything like a "three quarks plus interaction energy" approximation. This non-relativistic constituent quark model does not have any domain of validity ass far as I know. For the most obvious example where it fails, it can't explain the mass difference of the pion and the Kaon, and of those and the eta. Nambu just won the nobel prize for explaining that, and it is this type of field model that gives rise to skyrmions.

This subject has had a lot of turmoil in recent decades. We have to be careful here.Likebox (talk) 19:54, 12 April 2009 (UTC)


 * This is the offending sentence: Basically, much of the mass of hadrons is the interaction energy of bound quarks. Thus, most of what composes the "mass" of ordinary matter is interquark interaction energy.


 * That's only true in a nonrelativistic quark model, with a nonrelativistic potential. In QCD, the total energy of the proton is the extra kinetic energy of the quarks and gluons inside the proton bag, as compared to the usual sea of quarks and gluons in the vacuum. The "interaction energy" is only when the partons are sitting right on top of each other. Most of the interesting interactions is exchange into an out of vacuum condensates.


 * In this case, in addition to rewriting, the following sources were introduced:


 * This quote source 3 is given: the gluonic forces binding three quarks (total mass 12.5 MeV) to make a nucleon contribute most of its mass of 938 MeV. The quote is accurate, but interprets the gluons as "forces", and neglects the extra kinetic energy of quarks in a proton. It's being paraphrased into a falsehood in this case.


 * This quote from source 4 is given: A first-principles calculation of the nucleon mass has yet to be accomplished. The recent claim of lattice groups (and there is no reason to seriously doubt them) is that they can calculate the mass of the proton to about 1% accuracy from full QCD. Perhaps the accuracy is not as good as they claim, but nobody doubts that it's not in the ballpark. This was the news report that led to the original writing. So this quote is outdated.


 * Finally source 5 is a perturbative picture of the quark core. It is not distinguished from other pictures of the quark core in any particularly special way that I can see. Why is it included?


 * The problem here is promiscuous sourcing. You have so many sources for the given claim that to choose one over another amounts to an act of promotion. I think it is best to leave generally accepted claims unsourced, because we all agree on the facts, and talk about the content of the article in terms of clarity.Likebox (talk) 20:31, 12 April 2009 (UTC)

That this is "promiscuous sourcing" is your own opinion. Mine is that the sourcing provided is a great improvement over zero sourcing and reliance upon one person's opinion that is not found in any published source. You think it is best to leave "generally accepted claims unsourced", but I find that unacceptable because there is no evidence that the claim is "generally accepted" when no sources are provided. It is quite possibly a narrow or unbased opinion instead. Brews ohare (talk) 03:43, 13 April 2009 (UTC)


 * What claim is that?


 * BTW, the sources can be the original literature. That usually gives the credit to the right people.Likebox (talk) 04:01, 13 April 2009 (UTC)

The sources substituted by you are yahoo links to puffery. The sources provided previously include summaries of the published sources in reputable books and some published sources are directly cited (e.g. source 5). The claim that gluons have zero mass is not supported. You should try a bit harder to be scrupulous about your argument. Brews ohare (talk) 04:05, 13 April 2009 (UTC)


 * Look, if you read your sources as saying that gluons have nonzero rest mass, you read them wrong. The rest mass of a gluon is a shaky concept, because a gluon is confined. But in terms of physics, a massive spin-1 particle moves in a different way than a massless spin-1 particle, and gluons without any doubt have the propagator of a massless spin 1 particle. This is not contradicted by any of your sources.Likebox (talk) 04:14, 13 April 2009 (UTC)

I believe the point of the sources is related to the relativistic mass of the gluons. Brews ohare (talk) 04:40, 13 April 2009 (UTC)


 * I see. Sorry. But then why is it controversial to say that the gluons are massless? Massless doesn't mean "having zero energy"? If that was what massless meant, then nothing would be strictly massless.Likebox (talk) 16:31, 13 April 2009 (UTC)

DELETE THIS ARTICLE!
IT IS ABOUT! ORIGINAL RESEARCH. Who cares if it is a bout a theory that some hundread + year old physisist. Wrote. HIS THEORY WAS JUST A HUNCH! HE HOLDS AS MUCH CREDIBILITY AS I DO! --114.77.203.166 (talk) 11:12, 13 April 2009 (UTC)


 * Although this is an obvious troll--- this comment gives the opportunity to explain why this article is important. E=MC^2 is a famous equation that everybody has heard of, and many people propagate misinformation about what it means. This article can settle the issue once and for all, by providing a clear, readable, introduction, which anyone can understand, and which is available to everybody.


 * The paper establishing this result is the most physical and readable of Einstein's early work, providing a clear record of his inimitable clarity of thought. With a few lines of mathematics and a clear physical setup, he settled a decades long controversy about the relationship of mass and energy. This is a masterpiece of physics, which has the added benefit that it can be understood by any grade-school student.Likebox (talk) 18:16, 13 April 2009 (UTC)

1% QCD accuracy
The statement that hadron masses are theoretically accurate to 1% requires some documentation. For example, Lattice QCD calculations of the interactions among hadrons are notoriously difficult and require circumventing the Maiani-Testa theorem Some of the ingredients of these calculations are controversial. quark masses which don’t meet their physical values yet.the range of quark masses for which a given order of chiral perturbation theory is accurate is still under investigation. Brews ohare (talk) 13:16, 13 April 2009 (UTC)


 * You are absolutely right, which is why the news reports are slightly misleading. Let me tell you what I know about the state of the art, and it might not be the most accurate information. I can source it, but to settle this type of controversy requires additional evidence of consensus in the field.


 * The pion mass is the crucial parameter to say whether the quark masses are "light enough" to give an accurate estimate of the proton mass. The current lattices can (as I heard it) simulate pions at a mass of about 200-300 MeV. This is not the physical mass of 140 MeV, but it is close enough to allow for a reliable extrapolation. To make sure that the extrapolation is OK, you need to control for finite volume effects and finite lattice spacing effects, and it is hard for an outsider to objectively verify if this is done right, especially because we already know the answer from experiment.


 * But the accuracy of the proton mass with 200MeV pions I think is something like 5%. The lattice community claims that reliable extrapolation to 140MeV pions reduces the error to 1%. But this is not universally accepted: the best estimate of error would come from quantities like the rho width or the eta prime mass, which are more sensitive to the vaccuum condensate structure. But these quantities are not the focus of interest right now.


 * For sourcing, see this news report. I agree that it is painting a picture that is a little rosier than the actual state of the art. But the state of the art is at less than 10% error, even from earlier much more heavily quenched calculations. The recent paper is, and it is linked in the news article.Likebox (talk) 16:46, 13 April 2009 (UTC)


 * About the other comments: the Maini-Testa theorem is about the scattering of hadrons, their interaction, as you say, extracting these from the three point functions. It does not present any obstacle to calculating the masses of the hadrons, which is easy from the two point function. It's also not such a big deal to circumvent.Likebox (talk) 17:01, 13 April 2009 (UTC)


 * Ok--- the recent lattice paper has a bunch of different extrapolation procedures, and gives a median nucleon mass which is within 1% of the known answer, with a spread which is +/- 40 MeV, which is 4% accurate. I think better than 4% and no better than 1% is the most accurate thing to say. Electromagnetic corrections are going to effect things at 1%, so to do better you need to add lattice form-factor calculations.Likebox (talk) 19:53, 13 April 2009 (UTC)
 * Okay, but we're getting away from the big picture. Why is all this stuff in the article on mass-energy equivalence?? It has no more to do with mass-energy equivalence than any other technique used in particle physics. Stick it in the QCD WP article. There are even lattice QCD and perturbative QCD articles. It may be that the "techniques" section of the QCD article needs better main article refs and some fleshing out, but THIS article, which is relatively non-technical (or at least most of it is) is not the place to go heavily into the latest numerical QFT techniques as applied to hadrons. Come on! Likewise, the fact that the photon has been measured to have no mass or very nearly no mass (with the experimental limits not excluding no mass) merits about footnote in this article. If you have more on the subject, stick it in photon, or the relevent sections in quantum optics or standard model. Again, in my opinion (one more editor) here is not the place for it. S  B Harris 07:32, 16 April 2009 (UTC)


 * It wasn't my idea. I'd prefer if it wasn't here at all.Likebox (talk) 23:37, 16 April 2009 (UTC)


 * Okay, well you certainly have my vote to move it! Anybody else like to comment on the topic? S  B Harris 01:21, 17 April 2009 (UTC)

I'd agree the emphasis has strayed a bit. To take one thing at a time:
 * 1) Photon mass: the photon mass is an important special case of E=mc^2 and deserves its present discussion. The theoretical stance that the photon has zero rest mass has to be mentioned. Thereupon, it seems logical to me to ask what the experimental status of this theoretical stance might be. This question is not a footnote matter: it is the subject of extreme interest in (for example) quantum gravity and in cosmology, where the entire structure of relativity is being re-explored and tested. It is not an oddity.
 * 2) Nucleon mass: the issue here is whether E=mc^2 works at this level. That is a basic question. My original approach was simply to say that at the moment we don't know: backed up by a source. However, Likebox would like to make a stronger claim, and posted some yahoo news release puffery to the effect that this problem at last was resolved once and for all. That position now has been modified by adding the extra detail under discussion. My stance would be to move this discussion (which is worthwhile) to lattice QCD, and summarize it in this Mass-energy article with a "progress is being made, but the jury is still out". My view of the work by Durer et al. is that it is still "out there" and averaging 432 extrapolation methods that are all over the map and claiming a valid prediction because the mean is 1% from reality (which is still so far off that it cannot settle any issues of hadron structure) is not science but claim-staking. Brews ohare (talk) 23:18, 17 April 2009 (UTC)


 * Ok, the photon mass may not be exactly zero, but it sure is close. What's the point of cluttering up this page with speculation?


 * While the lattice QCD results have an interpolation spread of +/- 4%, that's not too bad! Maybe this is a form of undeserved claim-staking, and you are right that the claim would be stronger if the group had calculated some form factors in addition to masses. But the best solution is to replace the "yahoo puffery" with better sources.Likebox (talk) 01:47, 18 April 2009 (UTC)

Point 1 above says why it's worth mentioning the photon mass. The work on this topic is not just "speculation", but serious theoretical and experimental effort. Brews ohare (talk) 15:00, 18 April 2009 (UTC)

Point 2 above is supported by references. There are references to Durer for the latest "results" and there used to be a reference to Bressani among others stating "the jury is still out". Brews ohare (talk) 15:00, 18 April 2009 (UTC)


 * Point 1 is saying that relativity might be wrong. Ok maybe. Maybe rotational invariance is wrong too. There's no need to waste people's time with this type of speculation on this page, which is devoted to a prediction of relativity theory.


 * What part of Point 2 is supported by references? That the jury is still out on QCD?? Give me a break. But that's not the important point. The only point here is that most of the mass of the proton is not the rest mass of its constituents. Do you disagree with that statement?Likebox (talk) 15:48, 18 April 2009 (UTC)

Let me understand this: relativity theory should be presented as making predictions that are beyond experimental test or further reasoning? Or, at least, no-one should be burdened by any indication of such tests & examinations? Brews ohare (talk) 07:55, 20 April 2009 (UTC)

The point, you say, is that the hadron mass is not the rest mass of its constituents. I'd say the point that one would like to make, but cannot, is that the difference between the rest masses and the hadron mass is accounted for as the combined relativistic masses of the constituent quarks along with that of the gluons holding the whole thing together using E=mc^2. Averaging over methods and claiming the mean as a prediction is rather like averaging over liberals and conservatives and saying the US is a moderate country. Brews ohare (talk) 08:24, 20 April 2009 (UTC)


 * It's not that relativity shouldn't be tested, it should. But this is just not a particularly appropriate place to discuss bounds for the rest mass of the photon. It's not a good test of relativity, and it is only very tangentially related to mass/energy equivalence.


 * The "averaging over methods" is not something that the authors of the proton mass study do. Rather, they estimate the error in their calculations by the difference in different extraplation methods. The error is reasonable, and there is no deviation from the expected result. Also, this is a completely standard way of estimating errors. The results are perfectly in line with mainstream consensus for both the proton mass and the photon mass, and even if either of these were slightly off, what does that have to do with the subject of this article?Likebox (talk) 20:22, 20 April 2009 (UTC)


 * 1) The case of applying E=mc^2 to the photon has been raised, as ha s the zero rest mass issue. Therefore a simple reference to tests and examination of this point is entirely in order, takes very little space, and alerts the reader to some active issues that may be of interest.
 * 2) I agree that the mass of the nucleon is a side issue. I have proposed, as has Steve, that this discussion be transferred to another article, with simple reference to their paper as indicative (not repeating their accuracy claims) and a statement that work in this area is ongoing. Brews ohare (talk) 21:00, 20 April 2009 (UTC)


 * What you are missing here is that the masslessness of the photon is completely irrelevant as far as applying E=mc2 to photons. E=mc2 applies to massless and massive things just as well, and it means that "massless" things have a nonzero "mass" (in the sense of mass-energy equivalence), because they have a nonzero energy. It is this mass that is measured on a scale, or when you put things together in a box.
 * Ok, you can transfer the stuff, but the statement "most of the mass of the nucleon is not rest mass of constituents, but all the rest mass of the proton is it's energy" should stay, because it's a nice illustration of the concept. Maybe the reference is unnecessary.Likebox (talk) 22:54, 20 April 2009 (UTC)

Brews, did you ever see this web link? . The contents were published in some journal around about 1990.

The implication of it is that E = mc^2, c^2 = 1/εμ, and Newton's equation for waves in an elastic solid are all essentially the one equation, and that E = mc^2 relates to the binding energy between electrons and positrons in a dense electron-positron sea in which EM radiation constitutes disturbances. As you know, Maxwell directly linked the second two equations mentioned above at equation (132) in his 1861 paper. Permeability is the density and permittivity is the elasticity. David Tombe (talk) 10:37, 21 April 2009 (UTC)

What is missing?
Above Likebox says:
 * 1) What you are missing here is that the masslessness of the photon is completely irrelevant as far as applying E=mc2 to photons. E=mc2 applies to massless and massive things just as well, and it means that "massless" things have a nonzero "mass" (in the sense of mass-energy equivalence), because they have a nonzero energy. It is this mass that is measured on a scale, or when you put things together in a box.
 * OK, you can transfer the stuff, but the statement "most of the mass of the nucleon is not rest mass of constituents, but all the rest mass of the proton is it's energy" should stay, because it's a nice illustration of the concept. Maybe the reference is unnecessary.Likebox (talk) 22:54, 20 April 2009 (UTC)

In response to item 1 : the photon is a special case because its rest mass is zero. That occasions special treatment, as per Hecht, Prigogine etc. Many question what the significance of a nonzero rest mass may be. Examples are Evans and the authors cited in the article. These questions seem to strike you as a diversion from the Wiki article, as narrowly focused upon only the formula, but it seems to me that even for a general audience it is of interest that the mass of the photon is key to such matters as whether or not relativity applies at small scales, and the resulting logical questions lead to very interesting and demanding experimental work, things with ramifications like the failure of causality, or modifications of simultaneity that the ordinary reader is very possibly interested in, and that are not just "speculation" but examples of the machinery of science at work. Depending upon what is found, E=mc2 may be discovered not to be the entire answer to the mass of hadrons.

In response to item 2 : I have agreed with this statement entirely, with one exception: it is very poor practice to leave out references. Already any reader of Wikipedia has discovered that opinion often masquerades in Wiki for fact, and so suspicion is normal. References help to counter this natural skepticism. Brews ohare (talk) 21:46, 22 April 2009 (UTC)


 * Since everyone seems to agree on item 2, I will address item 1 only.


 * E=mc2 is no different for massless or massive things. It's about what happens when you shake a box of energy--- you feel the energy as inertia. The issue of masslessness is about the length of the energy-momentum, the mass-energy business is about the time-component, the energy.


 * This is confusing for some students and lay people, and the reason is that the concept-box for "inertia carrier" needs to get filled up with "energy", while the new relativistic concept of "mass" becomes not a measure of inertia, but a frame invariant "relativistic length of energy momentum vector". This transformation involves some shift in perspective, and this article is mostly pedagogical: it tries to help the reader in making this shift. All the issues are well understood. No one disputes anything. There is no need to cite authoritative sources on this stuff.


 * But for the photon mass, you are opening up a big bag of contested worms. None of the sources you say are discussing E=MC2, they are each doing something different.


 * Hecht is writing down the frequency/k relationship for photons in quantum field theory. This is the energy-momentum relation from relativity. This is discussed in a million places, you might as well have cited DeBroglie.
 * Prigogine is speculating that the frequency/k relationship is suspicious, because the "frequency" of a quantum particle should be associated with the particle's frame, the rest frame.
 * Evans is noting that the measurements of the photon mass don't definitely say the mass is zero. There is experimental room for it to be nonzero.


 * Prigogine's argument is not mainstream and is also ridiculous. The frequency is not a property of the "particle" in its own frame, really, it is a property of the wavefunction in the observer frame. Even if you go to a Feynman picture, so that the frequency is a functio of the particle's proper time, the mass is indefinite, and only becomes zero in the limit of long times (otherwise the particle is virtual, and can have any mass, with different probabilities). So this Prigogine argument is not valid.


 * Prigogine's "no massless particles" argument can be applied equally well to gravitons. For the graviton, we know that the mass is exactly zero. The only reason we don't know the photon is exactly massless is because the extra component in a massive but very light photon stops interacting with anything else. For spin 2 and nonabelian spin 1, massive and massless behave differently in the zero-mass limit.


 * These sources are not original literature for any well accepted part of physics. They are not directly related to the subject of the article. So including them is just an unwarranted act of promotion. They would be great for a "speculative ideas" section in photon or for an article on photon mass.Likebox (talk) 22:47, 22 April 2009 (UTC)

The idea here is not to debate various views and determine their credibility. The point is that there is bona fide debate going on with fundamental implications, and a pointer to such work is not out of place. The sources mentioned above are not perhaps the best, but that is not to say there are not reputable sources out there. Brews ohare (talk) 09:43, 23 April 2009 (UTC)


 * Unfortunately, in order to figure out where the views fit in the mainstream scientific consensus, it is necessary to debate various views and determine their credibility, with mainstreeam assumptions. If a view is not very credible, that doesn't mean that it should be censored, it just means that it should appear in an appropriately qualified article or section devoted to non-mainstream thinking. That's the principle of "undue weight". You have to make judgement calls about how mainstream an idea is.


 * The idea that the mass of a particle is defined along its worldline is not so out of the mainstream--- it's Feynman's path-integral approach to relativistic particle scattering. In this point of view, particles don't have zero mass, or positive mass, or any definite mass, because the propagator between finitely separated points is "off mass shell". This is the kernel of truth contained in Prigogine's observation, and indeed, the proper-time formulation is incompatible with a strictly zero photon mass. But the mainstream resolution of this not-so-confusing incongruity is that the photon is off-shell by a very small amount for any finite propagation time, not that it has a small positive mass.Likebox (talk) 13:17, 23 April 2009 (UTC)

Hi Likebox: You have a rather different context in mind. I was focusing more upon cosmology and quantum gravity. Take a look at cosmology and, Also, see Doubly-special relativity. Brews ohare (talk) 00:44, 24 April 2009 (UTC)


 * Again, each source is a different and interesting attempt to violate SR, and they would be great for a "tests of special relativity" article: Schaeffer is using emissions of light in distant objects to constrain light velocity (probably, the first sources for this should be found, in addition to the most recent), while Ellis et.al. are constraining relativity violating theories with high energy cosmic rays.


 * But a photon mass is different, because a tiny photon mass would not by itself violate special relativity. And none of these things are directly linked to the subject of this article. E=mc2 is a prediction of relativity. To put this discussion here would be like putting a discussion of recent measurements of gravity at short distance scales in the article on Kepler orbits.Likebox (talk) 15:32, 24 April 2009 (UTC)
 * You put your finger on something I wanted to say, which was that a non-zero photon mass would not affect relativity. The relativistic information-tranfer speed-limit c, which relates time and spacial dimensions and how they change with relative velocities, would merely NOT be the speed of light, but something slightly higher. It would remain the cosmic speed-limit in relativistic space-time motion (and thus the speed of gravitational disturbances). And for that reason the equation E = mc^2 would stay, but with the caveat that c is the speed of gravity waves. But photons would travel a whiff less than c, just as we (now) think neutrinos do, ala Majorana. So what? S  B Harris 07:46, 7 May 2009 (UTC)

E=mc2
Why can't the first equation be:


 * $$E = mc^2 \,\!$$

It looks better than normal font.  M C  10  &#124;  Sign here!  05:27, 7 May 2009 (UTC)


 * Well, it certainly looks like it's going faster! S  B Harris 07:32, 7 May 2009 (UTC)


 * TeX always has the prettiest fonts. But the math bracketed stuff processes into an embedded image, and I don't know if it shows up well on all browsers, like text browsers. That's probably not an issue in the modern world. Maybe it's still an issue for palm browsers, or for search databases. Anyway, I tried MC10's version. But is the same font available in regular wiki markup?Likebox (talk) 17:23, 7 May 2009 (UTC)

Big Words = Little ideas
Please avoid using jargon word "system", say "thing" "object", etc. You're talking about ordinary objects after all. Similarly "entity" is no good. Don't replace simple language with obtuse language for absolutely no reason.Likebox (talk) 17:40, 11 May 2009 (UTC)


 * A system is not the same as an object, nor it it the same as a thing. A system is only the same as an object in a very distinct circumstance, a differentiation should be made. Smittycity42 (talk) 03:12, 4 July 2009 (UTC)smittycity42


 * Yes, this was the original idea behind use of the "big words." An object is necessarily a bound system, with automatically momentum = 0 if you're in the object rest frame. By contrast, the "system "rest" frame" for UNBOUND systems (where system energy is minimal, and is invariant mass) must be artificially defined as the momentum = 0 (COM frame), so that gets a bit complicated. Nevertheless, invariant masses for unbound systems are a common physics concept, due to this simplicity and analogy. They correspond with the rest mass for bound objects, but it takes a bit of explaining to see why. S  B Harris 14:19, 4 July 2009 (UTC)

Rest Mass
This discussion is not productive. Relativistic mass is not useful as a word after a point, but when you are talking about "E=mc^2" you need to talk about the inertia associated with energy, and the easiest way is to say "relativistic mass" a little. This discussion has happened a million times already. Also, when rewriting, take care to make it sound literate: that means don't use big words unnecessarily, and write with specific examples instead of vague generalities.Likebox (talk) 17:45, 11 May 2009 (UTC)
 * Well, the problem is in leaving the COM frame where all those momentum terms appear in the energy-momentum equation. There's a price you pay for this! If you DO that, then you can't use E=mc^2 anymore without being FORCED to define the "mass" in the equation as something other than the rest or invariant mass. It now must be the "relativistic mass" if anything. So you have to choose: stay in the COM frame and use E=mc^2 for everything (including systems and bound objects containing internal energy, keeping the mass as rest and invariant mass), or else leave the COM frame, continue to use E-mc^2, and thus be required to ignore the momentum terms, and thus now be required to redefine your definition of "mass" to something, well, unnatural. Which relativistic mass is, at least to my mind. Likewise, the problem with considering single photons is that there is no COM frame for them, so the very act of thinking about them forces you to leave the COM frame. So now the dilemma: you can either abandon E=mc^2 and take notice of the momentum term and call the (rest) mass zero, or else you can still insist on using E=mc^2 and again (since not in the COM frame) as usual, be forced to use "relativistic mass" as the "m". S  B Harris 14:35, 4 July 2009 (UTC)


 * The issue is this: there's physics, and there's a formula. This page is about physics, not about the relativistic momentum energy forula. The physics of E=mc2 is that energy registers as inertia, and that inertia can be used to do work. That's the main bit. The distinction between rest mass and relativistic mass is so inconsequential as compared with a bombshell like that, that it is, in my opinion, ridiculous to talk about it in the lead. If you understand that mass and energy are the same thing, you will never get confused about the rest-mass relativistic mass distinction. Relativistic mass is energy, rest mass is energy in the rest frame. That's no more complicated than the distiction between "velocity" and "speed".Likebox (talk) 16:02, 4 July 2009 (UTC)
 * It's easy to get confused, because the "relativistic mass" is not the same thing as ordinary kinds of mass (invariant and rest mass). Relatistic mass won't make a black hole. It doesn't gravitate symmetrically enough to do that. It has funny inertia and momenta that vary by direction. It has all the attributes of a bad term made up so that somebody would have something to shoehorn into E/c^2 no matter what E was. And that's a bad idea. Some E's are different from others, that's all. Some E can make a black hole and other E can't, even if the same size. That is physics. S  B Harris 18:30, 4 July 2009 (UTC)


 * Yes--- you are right that a big relativistic mass won't make a black hole because its not in the rest frame. So what. The point that I think you are missing is that this is not the source of the confusion for the people who are confused. People who understand the physics well enough to understand what you are saying already clearly know what you are saying is true.


 * The point of E=mc2 is unit conversion. It is to tell you that the quantities "mass" and "energy" which look different and have different units are really the same thing. Once you understand that, the distinction between "mass" and "energy-momentum" is the same as the distinction between "speed" and "velocity". It's not a distinction that needs to be emphasized.


 * What needs to be emphasized is that hot coffee weighs more than cold coffee, that when you throw a baseball fast you end up losing more weight than when you throw a baseball slow, that fast moving gas molecules weigh more than slow moving gas molecules, that all energy shows up as inertia. That's easily summarized by slapping mass units on the quantity P_0, the time component of the energy-momentum vector. There's nothing wrong with that. You can use mass units for energy as well as energy units.Likebox (talk) 18:38, 4 July 2009 (UTC)


 * To clarify a little--- while you are right that a particle with a small rest mass can be boosted so that it has a huge relativistic mass but is not a black hole yet, this is not exactly for the reasons you are saying. If you whack two such particles together, or try to measure such a particle to see if it is a black hole, you will cause it to collapse immediately, so long as the particle is small enough.


 * When any energy is released, the mass goes down. Even if a massless particle like light is emitted, you lose mass. If you emphasize "rest mass" as the right definition of mass, then the equality of "rest mass" and "total internal energy" is not obvious. Keep in mind that the confusions about this are endless, while the actual thing is so obvious.Likebox (talk) 19:25, 4 July 2009 (UTC)

"Subtler"?
"But the rest mass of a photon is slightly subtler, because a photon is always moving at the speed of light&mdash;it is never at rest."

What does "subtler" mean in this context? If it means "smaller," I just need the OK before I can modify it. &mdash; La Pianista  ♫ ♪ 03:56, 18 May 2009 (UTC)


 * It just means "slightly subtler to define in terms of physical measurements" because there is no rest frame.Likebox (talk) 04:24, 18 May 2009 (UTC)

Mass and energy are the same thing?
The opening sentence says that "mass and energy are the same thing". I don't think many physicists would say that (I am one, by the way). Much better to say that there is energy associated with mass, so that mass can be thought of as a form of energy (and that there are other forms of energy, too). Timb66 (talk) 22:14, 12 June 2009 (UTC)


 * It depends on what you mean by "mass". If you have a box, and there is energy in the box, the inertia of the oscillation of the box on a torsion pendulum is the total energy inside the box. If the box is slowly moving, the coefficient of the velocity in the momentum is equal to the total energy. If you have energy "E" in a region of spacetime, it makes a gravitational potential at long distances like E/r^2, where E is the total energy. This means that all energy carries inertia, and that inertia means you have energy.


 * But rest mass is not the same as energy--- it is the length of the energy-momentum vector. So if you are concerned with the invariant quantity for a fast moving box, the mass as measured when moving along with the box, this is a different quantity than the total energy, and it differs by the extra kinetic energy. This is an annoying debate, because everyone agrees on the outcome of all the experiments. The only difference is what words you hang the ideas on.Likebox (talk) 22:56, 12 June 2009 (UTC)


 * Let me be more precise--- if you say that mass is a form of energy, and there are other forms of energy too, you might be misled into thinking that these other forms of energy don't carry a mass. So that if you have a spring that's compressed, it weighs the same as a spring that's not compressed (wrong), if you have a box with a hot gas it weighs the same as the same box when the gas is colder (wrong), etc, etc. The point of the conceptual identification is to make it clear that mass and energy are not "interconvertible", but that all energy is heavy, and that everything heavy is full of energy.Likebox (talk) 23:07, 12 June 2009 (UTC)

Well ok, these are subtleties related to the difference between rest mass and relativistic mass, which have be discussed here before. But a lead sentence is not the place for subtleties and it remains incorrect to say that "mass and energy are the same thing" and I don't know of any physicist who would disagree. And so I have deleted those words, so that the lead sentence now reads: "In physics, mass–energy equivalence is the concept that every mass has an energy equivalent and vice versa." Not perfect wording, but at least it is correct and much less confusing. Timb66 (talk) 12:06, 15 June 2009 (UTC)


 * These are not subtleties. They are not in any way subtle. They are the essence of mass-energy equivalence. Please do not delete stuff until you understand them.Likebox (talk) 14:07, 15 June 2009 (UTC)


 * Let me expand on that: The statement of "E=mc2" is that the quantity that appears on the right and the quantity that appears on the left are the same thing. The quantity that appears on the right is the "mass" of a body (at least when slow moving). The quantitity on the left is the energy content of the body. This means that mass and energy are the same thing. That's what Einstein means by "the inertia of a body is it's energy content." This is not a subtlety, it is the whole point.


 * If you think that saying that "mass and energy are the same thing" is confusing, then you don't understand the result. This is why it is a perfect introduction. If you read it and say "yes of course", you have already understood.Likebox (talk) 14:15, 15 June 2009 (UTC)


 * I agree with Timb66. I had concerns with the opening but didn't want to get into it with people so I let it be. If the article were 'the mass-energy equality' then saying they are the same thing would make sense. If mass has to be converted into energy and vice-versa then they are not the same thing.-Crunchy Numbers (talk) 14:59, 15 June 2009 (UTC)
 * Also, Likebox, reverting Timb66's edit and calling it a "good-faith edit" seems to imply that it was a step up from vandalism. If anything it was a bold edit by a knowledgeable person that improved the article. Do you have a reliable source that says they are the same thing? If not please allow others to improve this article.-Crunchy Numbers (talk) 15:49, 15 June 2009 (UTC)


 * Saying "good faith" means just that, good faith.


 * The source for this is Einstein's original paper, and every other secondary source since then: The inertia of a body, as measured by shaking it, is equal to the total energy in the body (up to a factor of c^2). I don't understand why this is controversial. It is what the equation means. I like to use units where c=1, and then the formula is an identity. The meaning of the formula is that two concepts, mass and energy content, which you thought were different before relativity, are the same up to units.


 * In terms of experiments this means two things:


 * Any energy in a body shows up as inertia of the body when you shake it.
 * Any massive body can be used in principle to do work (by throwing it into a black hole and using the emitted thermal light to run a steam engine)


 * So the concept of "total internal energy" and the concept of "Newtonian mass of a slow moving object" are identical, except for units. This is common knowledge within physics, it is not disputed by any physicist that I know of, it is what is written in the body of the article, and if it seems strange to you, then I urge you to understand it better.


 * When you have a fast moving object, there are two different "masses" you can have. The relativistic mass is just the total energy including the kinetic energy of the overall motion, while the rest mass is the mass in the rest frame, excluding the kinetic energy of the overall motion. But this dispute over relativistic/rest-mass only applies to fast moving objects. For normal slow velocities, there is no difference between the two masses. They are both equal to the total internal energy.Likebox (talk) 17:20, 15 June 2009 (UTC)


 * I would like to understand the reason this rubs people the wrong way. Here are some unambiguous questions, questions where all physicists agree on the correct answer, (these types of questions don't involve any definition disputes):


 * If you have a box of gas with mass M, and you add Q Joules of heat to it, what is the new mass of the box of gas?
 * If the gas pushes the piston, doing W Joules of work on the environment, what is the new mass of the box of gas?
 * If you have a spring with mass M, and you compress it so that it has V joules of potential energy, what is the new mass of the spring?
 * If you have an atom bomb weighing 3,000,245 grams, and it explodes and releases (1g)c^2 of energy into the environment, what is the mass of the cooled down remnants of the bomb?


 * The reason there is no dispute is because the examples are all not moving very fast, so the notion of mass is just the rest-mass.Likebox (talk) 17:30, 15 June 2009 (UTC)

Thanks for the support, -Crunchy Numbers. I am reinserting the change, and I request that it be allowed to stand until somebody comes up with a reliable source that says mass and energy are the same thing. If you can find anything by Einstein that says that, I will be quite amazed. Timb66 (talk) 09:37, 16 June 2009 (UTC)

I just found an interesting article on mass-energy equivalence in the Stanford Encyclopedia of Philosophy and also a quote attributed to Einstein. It would be worth including references to them, if somebody has the time. Timb66 (talk) 10:07, 16 June 2009 (UTC)


 * You were not reverting me, because I did not reinsert the same statement, I made a modification to the sentence to say something else. Someone else reinserted the original form.


 * The stanford encyclopedia of philosophy article is extremely unreliable. It is written by philosophers, not physicists. Please do not modify this section until you have answered the questions above, or at least explained your position.Likebox (talk) 14:30, 16 June 2009 (UTC)


 * I tried Einstein's original phrase "The mass of a body is a measure of it's energy content", which is the title of his paper. This should please you.Likebox (talk) 14:40, 16 June 2009 (UTC)

Yes, I think Einstein's original phrase is a good choice. By the way, I saw what you wrote and then deleted from this discussion page. Please be aware that just because someone doesn't agree with you, it doesn't necessarily mean they don't know what they are talking about. Timb66 (talk) 00:37, 17 June 2009 (UTC)


 * I erased it, because it was rude. But I am not sure where the dispute comes from. Tell me--- what's the difference between saying "the mass of a body is a measure of it's energy content", "the mass of a body is always equal to it's energy content" and "mass is the same thing as energy"? All three statements sound identical to my ears.


 * What's the definition of energy? One definition is "the capacity to do work". If we are in a lab frame, and an object has mass M, then we can do Mc^2 amount of work using this object, exactly, and no more. Conversely, once we do this work and place the energy in container C, the container will have exactly M units of mass more. I don't understand where the distinction comes.


 * The only real distinction is whether you include kinetic energy of overall motion, or whether you measure mass in the rest frame. Is that what this was about?Likebox (talk) 01:05, 17 June 2009 (UTC)

Speed of light when light is massive
If light is massive, but relativity is still correct, the parameter we call the "speed of light" would still be called "c", but it would not be the speed at which light moves. The parameter c is just a unit conversion factor. Relativity rotates space into time, and space is measured in meters, while time is measured in seconds. So to add them up you need a unit conversion factor which has units m/s. That's what "c" is, it allows any formula which adds up "delta x" and "delta t" to be consistent with units.

The best choice of units is to set c equal to 1. This means that the relativistic speed unit-conversion paremeter is equal to 1. If light turns out to be massive, it would move at a speed less than 1, but this has nothing to do with relativity. This is again confusing the geometric theory of special relativity with the physical theory of light propagation. The special theory is just the appropriate notion of geometry which is consistent with Maxwell's equations. If you modified Maxwell's equations you could make the photon massive without changing the underlying geometry at all, in particular "c" would be exactly the same.

The reason this is somewhat confusing is that Einstein and others were bootstrapping from their knowledge of the Maxwell's equations to figure out the appropriate notion of geometry. So in their arguments, they use light as an example of something that moves at speed c. Once they found the right geometry for time, Einstein declared that this was more primitive than the physical laws of light. The parameter "c" is in the geometry, not the laws of light. You could repeat all of Einstein's arguments with massive particles that move very very close to c, and they would be unaltered (but more annoying to formulate).

As for citations, I saw a paper once that adressed this particular issue. I am sure I could find something like it if pressed. Unfortunately, the world is so big that someone else could also find a citation to support something else. Since this stuff is objective, I think it is helpful to sort out the disputes on the talk page first, so that everyone agrees on the objective stuff. Then the correct wording should become self-evident.Likebox (talk) 17:18, 25 June 2009 (UTC)


 * The citation is to David Mermin. His parameter K is one over c squared, so c would just be one over the square root of K.Likebox (talk) 20:40, 25 June 2009 (UTC)

1 Why are people so rude to each other in this section? Surely everyone is trying to get the article to be as good as possible. Personal abuse doesn't help. 2. I think it would improve the article if somene could come up with a clearer explanation of just what the equation adds compared to an eqation which said "E is proportinal to m" or " E=m*k" where k is a constant. —Preceding unsigned comment added by 80.169.162.100 (talk) 11:44, 30 June 2009 (UTC)


 * Honesty == Rudeness.


 * Human beings are evolved to form social collectives in which collective action is possible without lengthy debate. So that when someone says "OONG! Tiger enter cave! Get out!" Oong won't respond "But CROOP, what is evidence for this assertion? I am not yet convinced", instead Oong will get out.


 * This means that an assertion from a person higher on the social pecking order must always be accepted as true, an assertion from a person lower on the social pecking order can be challenged as false. What defines the human social hierarchy is precisely who is allowed to challenge what statement.


 * This means that when a person who is not a child or a social outcast tells you something, like "A is B", then it is an act of social disobedience to say "no A is NOT B". But this act is absolutely necessary for science.


 * Note that there is no specific personal attack here. Not a single statement is about the person. It is the very fact that the statement "A is B" is questioned which is the personal attack. It is considered personal, because it is viewed as a challenge to their social position. These monkey-like instincts are insane, and they must be suppressed. It's hard work to suppress them.


 * Many people say "Yes, but it is possible to challenge ideas politely." These people are wrong. When you are polite, then you end up saying "You could be right, but I don't think so. Lets come to a compromise", and then you end up with statements which give away too much ground. In order to do science, you need to be able to say "You're totally wrong", and the other person has to not feel bad. They should be able to say "No, let me explain..." without feeling any social position has been gained or lost.Likebox (talk) 15:15, 3 July 2009 (UTC)

Mass-Velocity Relationship
Some infos for historical accuracy: In the section Mass–energy equivalence it is claimed (for example) that Einstein derived "relativistic momentum" and he "needed to think carefully about collisions" etc.. It seems that some discoveries of Einstein were mingled with those of others. For example it was Planck who defined relativistic momentum (see Planck 1906), and Lewis/Tolman were the first to use collisions for describing relativistic mass (see Lewis & Tolman 1909 and Lewis 1908). I would suggest to rewrite this section without using names - or the correct names should be used. --D.H (talk) 18:15, 2 July 2009 (UTC)


 * While you are right that a lot of these things got assigned credit for other people later, in the 1905 relativity paper, Einstein derives the modified Newton's law in the form d/dt of relativistic momentum = force. He uses this to work out the amount of energy aquired by a particle moving in a constant E field. He then notes that the kinetic energy formula is the one quoted in that section.


 * But he doesn't jump up and down and say "E=mc2" yet. He is very careful on this claim, because it is so spectacular. He first finds a completely intuitive picture where it is obvious that energy is carrying off mass, then he completes the theory by concluding that the total energy is the mass.


 * Once this is done, it is somewhat routine (but necessary) to systematize the method, derive it from a Lagrangian, give a good geometric interpretation, etc. This is done by Minkowski Planck and others. The main thread required of the argument for E=mc2 though w

provides a lot of detailed infos on Einstein's §10 and the further development of mass-energy-equivalence by Einstein, Planck, Laue, etc... --D.H (talk) 15:35, 3 July 2009 (UTC)


 * Did he make a mistake? I am confused--- I read the paper and I thought the experessions were all correct. There might have been an erratum, but if there was, it came a month or two later in 1905, way before any of the other work.


 * The expression for the transverse F=ma mass is m/sqrt{1-v^2), the longitudinal mass is m/(1-v^2)^(3/2). I think these are the equations given be Einstein at the end of the paper. The concepts of transverse and longitudinal mass were later rejected as not very useful, but the expressions in the paper are still correct (I think, it's been a while since I read it).


 * For the expression for the kinetic energy, it is derived correctly, but with a suboptimal formalism. Einstein integrates the force over distance and finds that


 * $$\Delta (m/\sqrt{1-v^2}) = Fd $$


 * Which is the correct relativistic work-energy theorem. This is the formula quoted in that section. I am not sure whether that section is a bastardization at all--- it follows the logic in Einstein 1905 very closely.Likebox (talk) 16:33, 3 July 2009 (UTC)

No, they were not correct (as explained by Miller etc.). The correct formulas as given by Lorentz are: $$m_{L}=\frac{\mu}{\sqrt{1-\frac{v^{2}}{c^{2}}}^{3}}$$ and $$m_{T}=\frac{\mu}{\sqrt{1-\frac{v^{2}}{c^{2}}}}$$

Now, Einstein got the correct expression for $$m_{L}$$, but he derived the incorrect expression $$m_{T}=\frac{\mu}{1-\frac{v^{2}}{c^{2}}}$$.

The reason for Einstein's error was his poor choice of forces on p. 919, where he transformed the (correct) equations (A, p. 918) into the incorrect ones:

$$\mu\beta^{3}\frac{d^{2}x}{dt^{2}}=\epsilon X=\epsilon X'$$,

$$\mu\beta^{2}\frac{d^{2}y}{dt^{2}}=\epsilon\beta\left(Y-\frac{v}{V}N\right)=\epsilon Y'$$,

$$\mu\beta^{2}\frac{d^{2}z}{dt^{2}}=\epsilon\beta\left(Z+\frac{v}{V}M\right)=\epsilon Z'$$,

(where &beta;=&gamma;). Now, the value for &epsilon;X is correct, but the values for the transverse directions (on the right hand side) contain the &beta; term which should be removed. From this he derived the wrong value for the transverse mass.... Planck corrected those equations and was able derive the correct expression for relativistic momentum and mass.... This is all well known to historians of science, so I don't know why you reverted my edits. PS: And as I said before: Einstein did not discuss collisions in his earlier papers, so also that statement in the article is simply wrong. I strongly recommend to delete all names in that section.... --D.H (talk) 17:20, 3 July 2009 (UTC)


 * Ok-- he has a mistake in the transverse mass. I think this mistake was corrected in later reprintings, right? It's a simple algebra error, after all. This mistake is in a quantity which is only of interest for predicting cyclotron frequencies. It has nothing to do with E=mc2.


 * Einstein did formulate the correct kinetic energy formula, and the error you are pointing out is only in differentiating the momentum equation. The kinetic energy formula is indeed crucial to the reasoning that led to the next paper on E=mc2, which is all about collisions. I reverted, because I also read Einstein's papers, and I thought I was being fair to the thought process in them. I don't see where the inaccuracy is. Please correct me if I am wrong.Likebox (talk) 17:54, 3 July 2009 (UTC)


 * I see why we are talking past each other! When I said "collisions", I am talking about the 1905 paper on E=mc2. This paper has two "pulses" of light emitted in opposite directions. Einstein is obviously thinking about two photon emission, but he can't use those words because his photon idea is not yet accepted. So he says two pulses. Emission of two pulses of light is a "collision process" where one particle emits two particles. The kinematics of the collision process leads to E=mc2. It is emission of energy, and also emission of particles, and this duality is central to Einstein's thinking in this period.


 * This is the reason why I said "collisions" and "particle emission" when discussing Einstein's thinking. I think it is accurate to describe the 1905 E=mc2 paper this way. For the relativity paper, the only formula I am quoting is the work-energy formula from the early parts of the paper, not the force formulas from the later parts.Likebox (talk) 18:00, 3 July 2009 (UTC)


 * Since we seem to be disagreeing, let me be very clear


 * Transverse mass is irrelevant, the section doesn't mention it
 * Relativistic Work-energy theorem is in the 1905 relativity paper, as is the correct kinetic energy formula with an arbitrary constant.
 * The constant is fixed in the 1905 E=mc2 paper by considering two photon emission or two photon absorption, both collision processes.


 * The reasoning reproduced in this section is therefore completely faithful to Einstein's, as far as I can see.Likebox (talk) 18:06, 3 July 2009 (UTC)


 * Hmmm...here are some points:
 * You ascribe the relativistic expression for kinetic energy to Einstein - ok, because Einstein's corresponding equation of motion for X (p. 918) was correct.
 * You ascribe the relativistic momentum and mass formula to Einstein - wrong. Einstein should have derived the correct expressions, but he did not because of his wrong transverse mass/force definition. And this is not irrelevant, because the form of your edit gives the wrong impression that Einstein first derived the correct expression for momentum and mass....
 * In respect to the collisions, the problem is settled.
 * I will not revert your edits anymore, but if you want to describe Einstein's 1905 reasoning (I mean what he actually wrote), please modify it in a way without ascribing the momentum/mass formulas (in the current form) to Einstein. I'm sure, you will find a reasonable way. ;-)
 * PS: As far as I know, the transverse mass error was not correct in the later editions (at least not the German one from 1913). For the English editions: in the Calcutta edition the error is corrected, while in the Methuen edition it is not. --D.H (talk) 19:07, 3 July 2009 (UTC)


 * Thank you for pointing this error out. I didn't know about it. But I know that Einstein derived the correct relativistic form for the energy. I also am pretty sure he also had the correct formula for relativistic momentum. This has nothing to do with the transverse mass business, it is entirely contained in the formula for d/dt (momentum) = force, which is correct in the paper.


 * The first analysis in the paper (I think) describes an electron in a constant electric field acquiring energy. He shows that the work done by the field is equal to the gain in kinetic energy, where the kinetic energy is the modern formula, but with an arbitrary constant. This is the formula I am using in the section you don't like. The mistake on transverse mass is both really trivial and completely irrelevant.Likebox (talk) 21:26, 3 July 2009 (UTC)