Talk:Mass–energy equivalence/Archive 4

Can we explain this better?
The lead now says "Mass–energy equivalence does not imply that mass may be "converted" to energy, but it allows for matter to be converted to energy if mass remains conserved."

But if you look at the rest mass of the matter involved, that is mass; if the rest mass of the particles out of a reaction is less, then some of that original mass has been "converted" to energy. Yes, total mass is conserved, because that energy has mass. Still this is the usual notion of converting mass to energy. What is the purpose of denying it in the lead? If the purpose is to be as clear and correct as possible, I think it fails on that. Can someone find a better way to explain it? Maybe even a sourced way? Dicklyon (talk) 16:58, 23 October 2011 (UTC)


 * No, if the rest mass out of the reaction is less, you have slowed your particles down (cooled them and removed their kinetic energy), so of course the mass is less-- the kinetic energy had mass and you trickily removed it before you did your observation! Mass is not conserved if you remove mass first, and let it go someplace else where you don't pay attention to it. Nor is it converted to anything. Kinetic energy has mass. Example: after fission the two particles have the same mass they did before fission, as long as they are moving. Only when you stop them do they have less mass. But the mass of their kinetic energy is now heat, and you're not weighing that because you let it escape. Hot products conserve mass. Cooled products don't but only because heat has mass and it got away. S  B Harris 18:24, 23 October 2011 (UTC)

Maybe we need to resort to converting the mass associated with matter to the mass associated with energy. Converting "matter" as it says now is not so good, since we don't say how matter is quantified. If it's quantified as mass, then does it mean rest mass? Or mass of just the matter involved (e.g. after we let the photons out of the box)? Dicklyon (talk) 17:01, 23 October 2011 (UTC)


 * Some of your questions will be answered if you read the rest of article again. The part you removed from the lede said that the term "matter" is hard to quantify and not well-defined, and yet it is only matter that is "converted" to anything (as when electrons and positrons are converted to photons or kinetic energy). Mass is never converted because it is conserved (sums of rest masses are not conserved, but you can't get a sum of rest masses for moving particles without changing observers in order to look at each mass). Mass is not conserved in systems when you remove some energy (like allowing a gamma ray out, after binding nucleons) but (as a general rule) mass is not conserved in systems anytime you let mass out of the system. It's not conserved if you pour water out of a glass and forget the water. Of course mass is not conserved in open systems. The gamma ray adds mass to the system whenever it is in it (or counted as part of it), and when it is let out (or not counted or otherwise ignored), that mass leaves with it, or is not counted with it. Invariant mass (of a particle or a system) is not only conserved, but even Lorentz-invariant, unlike energy and momentum. So it is observer independent, unlike energy, momentum and relativistic energy. Because relativistic energy is connected to relativistic mass, it is not invariant, either. But all these quantities (invariant mass, relativistic mass, momentum, energy) are conserved through time in closed systems, as seen by any ONE observer. However, for the non-invariant quantities, that one observer will disagree with a second observer in relative motion, as to what the absolute value of the conserved quantity is. For rest mass and invariant mass, that is not the case. As the article notes, there are two kinds of energy in SR and two kinds of mass. E=mc^2 is true any time momentum is zero. It is also valid as long as the mass and energy are both relativistic OR it is valid so long as both the energy and mass are invariant (system minimal energy, and rest or invariant mass). However, E=mc^2 is not valid when momentum is nonzero, for one type of mass and the other type of energy. For that, you need m^2 + p^2 = E^2.  S  B Harris 18:22, 23 October 2011 (UTC)


 * Let's be clear: I didn't remove anything from the lead (except the word "special" that some random threw in).  I'm just saying that it's not clear.  I understand the concepts well enough, I think, and I agree with your details above.  Nonetheless, conversion of mass to energy is a widely known concept for which explanation might be better than denial, even when we all agree that mass and energy are equivalent and are conserved.  There must be a better way to explain it in the lead, no?  The current approach of explaining in the negative with "Mass–energy equivalence does not imply that mass may be 'converted' to energy, but it allows for matter to be converted to energy if mass remains conserved." is rather unsatisfying, even with the scare quotes.   Dicklyon (talk) 18:43, 23 October 2011 (UTC)
 * Okay, somebody else recently removed some clarifying material from the lede-- take a look. The best "explanation" I can think of (you are welcome to try one of your own) for the fact that mass is NOT converted to energy and the equation doesn't say that it is, is that it is actually matter that may sometimes be converted to energy (while mass is conserved in the process). The problem is in confusing mass and matter. Going farther than that requires explaing the difference between mass and matter. When an electron and positron anihilate to two gammas, the mass of this system does not change. But matter (fermions) converts to energy (photons) and if the photons are absorbed by two floating objects, you've even converted matter to kinetic energy (as the objects will recoil). And so on. There's a limit to how much you can do in a lede. Truth and brevity (or maybe clarity) are conjugates. A lede can only be so long, and so if it is to remain true, it can only be so clear. S  B Harris 18:54, 23 October 2011 (UTC)


 * I don't think the "matter" approach helps much. If you take the bomb-in-a-box example that you put on my talk page, exploding the bomb doesn't change the mass of the box, but then opening the box does.  This opening doesn't involve conversion of matter to energy, but does reduce the mass of the box and give off energy, which is the usual notion of conversion of mass to energy. Dicklyon (talk) 19:06, 23 October 2011 (UTC)
 * Yes, but the point is that the mass of the box decreases AND the mass moves someplace else. That's not all that profound. It would happen the same way with a bag of sugar. The profound part is that the energy you let out STILL HAS MASS. S  B Harris 19:35, 23 October 2011 (UTC)
 * We could look at how physics books handle it:, , , , etc. I'm not endorsing any of these, and I'm sure they're not as precise on on-the-point as SBHarris wants, but they do illustrate some attempts to explain the concept.  One snippet (page I can't get to) says "In general, if a body gives off energy E in the form of radiation, E its mass..." in which the "gives off" is the key to the conversion concept.  You have to let the energy out to have a reduced mass, and it's this "given off" energy that can be said to have been converted from mass.  If we can find one of more sources that has a correct but positive way to explain the common concept of conversion of mass to energy, and summarize it in the lead instead of saying there's no such thing, we would be doing the reader a service, I think.  Saying "it allows for matter to be converted to energy if mass remains conserved" is particularly puzzling, since "if mass remains conserved" suggests situations where mass might not be conserved; what's that about?  Dicklyon (talk) 19:06, 23 October 2011 (UTC)

I certainly agree that the "if mass is conserved" language is confusing and must be fixed, since there is no "if." But I don't like the idea that if a body gives off energy E that anything has been "converted." That energy E has mass. You haven't converted the mass, but merely moved it somewhere else. "If a system has some mass and you take a little mass and move it someplace else, then it will have less mass." Sure, but it's not very profound. The profundity is that you removed mass along with the energy, which of course you do, since mass is conserved. Mass is conserved, period. You can move it, but you can't convert it. Mass is a property, not a "thing." Matter is a "thing." Mass is a property of energy, and vice versa. S B Harris 19:33, 23 October 2011 (UTC)
 * I wrote this to try to make the intro easier to understand: User:Zojj/e%3Dmc2. I won't just dump it into the article.  Sorry for my earlier rant. =/ --Zojj tc 04:39, 25 October 2011 (UTC)
 * Well, it's a pretty strained analogy. And it still fails to acknowledge what many reliable sources say, which is that mass can be converted to energy.  In some sense, they are right.  Why must we totally deny that sense, in favor of the sense in which they are wrong?  Dicklyon (talk) 04:49, 25 October 2011 (UTC)
 * That sentence is in the current article and I left it alone. But it wouldn't bother me to remove it! Can you think of a better analogy?  I'd rather get the point across and be 90% correct in the intro, than be 100.00000% correct and unintelligible. --Zojj tc 05:01, 25 October 2011 (UTC)
 * Well, what point are you trying to get across? Dicklyon (talk) 05:27, 25 October 2011 (UTC)

There was this other camp, incompatible with yours if I understand correctly, the said that in physics, the term "mass" is now reserved for "rest mass", because otherwise it's a pointless term, no different from energy. In that camp, the photons that get away are massless particles, and you can't treat their mass as e/c^2 because that's "relativistic mass", a concept they abhor. Am I correct to interpret that these two camps are incompatible? If so, why not admit that "mass" is used in two different ways by two different camps, and that in one way it can actually be converted to energy (because the sums of the rest masses change)? Or do you think that other camp hasn't a leg to stand on? Dicklyon (talk) 03:09, 25 October 2011 (UTC)

Perhaps my recollection of it as a "camp" is wrong. Maybe it was just User:Edgerck. See most of Talk:Photon/Archive_3. Dicklyon (talk) 03:22, 25 October 2011 (UTC)


 * Here's a book that discusses conversion of mass to energy rather carefully, in terms of the rest masses of the parts. I think we agree that they've got the physics right, so why can't we acknowledge the "conversion" concept?


 * This book uses the phrase "in some sense" in discussing the notion of conversion of energy to mass; it's perhaps not quite as careful, but not wrong. Dicklyon (talk) 05:01, 25 October 2011 (UTC)


 * This one, on the other hand, is much less careful; sloppy even; I wouldn't recommend going that way.


 * Dicklyon (talk) 05:01, 25 October 2011 (UTC)


 * Here is a long and scholarly review of the mass-energy "conversion" debate, without going down to the level of college texts: F. Fernflores. The Equivalence of Mass and Energy. Stanford Encyclopedia if Philosophy. BTW, looking at how physics texts define anything including weight, "mass" and whether or not "relativistic mass" is a proper concept, gets us down a long and nasty road, which you can view on the mass talk page. Suffice to say that if you insist (with Einstein) that the concept "rest mass" is the only one we should use for "mass" then you need to accept the analogue to rest mass for systems (for example a bottle of gas on a scale, or a solid at any temperature on a scale) which is invariant mass. Second, I want to emphasize that there is NO sense in which mass is "converted" to energy in physics. Going to each moving particle after a reaction and looking at their rest masses and adding them up, amounts to changing inertial observers umpteen times, and that causes conservations laws of all types to be violated: energy, momentum, etc. It's not a question of definition so much as improper procedure, since no conservation law "works" if you change inertial observers over time AND look at only parts of systems with each observer. A simple example of this, is to look at an unchanging bottle of gas, sitting on a scale. It has a rest mass which you can weigh with a scale, which is the invariant mass of this system. But if you THEN look at all the rest masses of the parts individually (each gas atom plus the bottle) these do not add up to what you weigh on the scale, because in each case you miss the kinetic energy of the particles, which adds mass and weight to the system, but not to each individual molecule in its own frame (though of course it does in the scale frame-- albeit relativistic mass). Relativistic mass is the same as invariant or system mass, in systems like this where total momentum is zero. But you can't add up all the individual masses and claim that mass has been "converted" to energy, just because you can no longer "see" the mass at the molecule scale. After all, it's the same bottle of gas as it was before--so when did this so-called mass-energy "conversion" happen? The mass is still there in the system as seen by an observer in the scale/lab frame, and never went anywhere, or was "converted" to anything. You were always weighing the kinetic (thermal) energy in the lab frame. That is the only sense in which mass is "converted" to kinetic energy after a reaction, if you suddenly start paying attention only to mass of individual parts in their own frames AFTER the reaction, whereas you didn't before the reaction (but only looked in the single lab frame). You'll lose "mass" this way by changing your point of view, but that happens even BEFORE a reaction, as we just saw with the unchanging bottle. This hasn't a thing to do with any "conversion" but rather has to do with you getting a different number because you changed your method of collecting data. That's hardly fair.  S  B Harris 15:03, 25 October 2011 (UTC)


 * You're right, it's not fair. But when you take the position that "there is NO sense," you are being rather radical, not giving any weight to the hundreds of reliable sources that discuss the conversion of mass to energy.  How can we fix that?  By trying to re-educate the world?  I don't think that's WP's job.  Better to acknowledge and explain the sense in which mass is converted to energy.  Dicklyon (talk) 01:46, 31 October 2011 (UTC)


 * What sense is that? The only "sense" I see that there is any "conversion" is that you convert something to a form or place where you no longer pay attention to it, or measure it, and then CALL that a "conversion." It's converted to a place or form where you now ignore it. Wow, "converted" to a state of ostracism. I think we explained that. This is a bit like the alchemists missing conservation of weight and mass, because they ignored the weight and mass of gases (which exist and are real). If you take a glass of water and wait for it to evaporate, its weight and mass go down. Does this mean mass is converted to masslessness, and weight is converted to weightlessness? No. It means you merely moved water off your scale! Weight and mass are instead conserved in this process (the same thing happens in burning a log, which caused early alchemists no end of problems). Are there a lot of textbook writers that would laugh at the idea that mass is "lost" in water evaporation, but would still insist that mass is "lost" in nuclear fission? Yes. Should we educate the world that these people still don't "get it"?  Yes. We have plenty of reliable texts that say otherwise, and the more scholarly they are (Wheeler and Thorne on relativity) the more they agree with me. If some college introductory physics text written by somebody who hasn't thought much about it disagrees with the specialists, that's too bad for them. This is one of those urban myths in science that it's time we helped stamp out. Finally, is it Wikipedia's job to stamp out urban myths in science and other places? Hell, yes. There is a list of them in List of common misconceptions from horns on Viking helmets to George Washington's wooden teeth. If the public believes that microwaves cause mutations and destroy all nutrients in foods, and that microwave ovens don't tolerate metal in them, and that they heat food from the "inside out", then it's Wikipedia's job to educate them otherwise. The same with physics. At worst, the textbook writers are confusing "matter" (in the sense of atoms and fermions generally) with "energy" (kinetic energy, and also massless particles, like photons), and saying that matter can be converted to light, or energy of motion (which it can). But that's not at all the same thing as saying mass is converted to energy. Loosely equating "matter" (a poorly defined word) with "mass" (a better-defined word) causes no end of trouble in beginning physics courses. We should help students by reminding them of the traps that lurk in use of the word "matter." This will all be to their benefit later.  S  B Harris 20:17, 16 December 2011 (UTC)

Mistake
I think there is a issue with what is said in about attractive fields contributing negatively to mass as it is described here:

For things made up of many parts, like a nucleus, planet, or star, the relativistic mass is the sum of the relativistic masses of the parts, because energy adds up. In some cases, however, the parts include fields of force, and if the fields are attractive, they contribute a negative amount to the mass-energy. For example, the mass of an atomic nucleus is less than the total mass of the protons and neutrons that make it up. The amount by which it is smaller is the energy required to break up the nucleus into individual protons and neutrons. Similarly, the mass of the solar system is slightly less than the masses of sun and planets individually, since the gravitational field is attractive.

First off, this isn't really the effect that is going on in nuclei and if you're going to talk about the mass defect in nuclei you should really reference binding energy.

Secondly, I've have never heard of in general relativity a gravitational gradient lowering the "mass energy" of a system, in fact the presence of a gravitational gradient with objects moving through it, as in the solar system, should produce gravitational radiation; in which case an instantaneous measurement of the solar system would show that it is more massive than its constituent parts.

In any case, even if I am wrong, these effects are very poorly described in this article and are possibly more advanced than this article warrants, the proposed solar system mass defect deserves an article on its own, assuming that it exists. For simplicity sake, and because I think the section is fundamentally wrong, I think it should be removed. I'll wait a couple of days and see if anyone objects and then remove it.

Smittycity42 (talk) 03:00, 3 July 2009 (UTC)smittycity42


 * These topics are neither difficult nor advanced, you are just learning something new. That's what this article is for. The fact that you learned something new means that others will learn something new too.Likebox (talk) 14:43, 3 July 2009 (UTC)


 * Let me be more explicit: I object. Don't remove these things. You are wrong that they are confusing or "advanced", they are simple and obvious. You just never heard them before. Likebox (talk) 14:47, 3 July 2009 (UTC)

Apparently I will need to be more blunt if I want to improve this page. I am NOT learning something new thank you very much, I wouldn't get very far if every time I look at something I took it as truth and decided that I learned something new. Based on what I know I am claiming that there are errors, please prove me wrong by citing sources rather than simply claiming I am wrong.

1) The notion that all attractive forces decrease the mass of the system they are in is wrong. If you disagree please do not simply say I am wrong, cite something that claims otherwise. Do not simply sight an example of this happening, I know there are examples, I want to see justification for what is in the article which claims that attractive forces always contribute negatively to the mass of a system.

2) I'm glad you think that the method through which the strong force for binds nuclei together and also make nuclei less massive is simple, good for you. What I am saying is that a novice does not need a one line vague description of a complicated physical process dealing with elementary nuclear physics to understand mass energy equivalency and it is better for be deleted than remain in its current state. If you want to talk about binding energy in this article than do it justice.

3) The notion that the Solar System is less massive due the the gravitational gradients that exist in it is wrong. If you disagree, prove me wrong, cite something displaying this mass defect, or better yet, do the general relativity treatment your self and post it. Actually don't do that, that could potential violate the no original research rule. In any case even if there is a Solar System mass defect of the nature that is described, this effect would be so negligibly small that it would probably be offset by the dust in the Solar System, not to mention the aforementioned gravitational radiation flux.

Summery-- Citations: Show them to me. Smittycity42 (talk) 20:05, 3 July 2009 (UTC)smittycity42


 * I don't like citing sources for stuff that everybody knows, because usually sources are very bad when talking about elementary stuff, and there is no real disagreement between knowledgable people. I think I understand the source of your confusion. You are pointing out that field gradient energy is always positive, and therefore the contribution of any field, attractive or repulsive, is positive. That's not the right thing to compute, because you have to compare the configuration when the parts are far apart to the configuration where the parts are close together. Both configurations have fields and sources, the difference in energy is in how the fields are spread around.


 * By the way, the mass defect in the solar system is approximately equal to:


 * $$ {GM_s M_j \over 2R c^2} \approx 5 10^{17}{\mathrm kg}$$


 * Where G is Newton's constant, M_s is the mass of the sun, and M_j is the mass of jupiter. This is the Newtonian binding energy of jupiter divided by c^2, since I think that Jupiter pretty much dominates this. The factor of 2 on the bottom is because in a circular Kepler orbit the total binding energy is half the potential energy, and R is the radius of Jupiter's orbit.


 * The total mass defect is then the mass of jupiter times the ratio of the schwartschild radius of the sun to the radius of jupiter's orbit. That's 10^18 kg, or one millionth the mass of the Earth, which is negligible compared to the total mass of the solar system, but probably bigger than the mass of the dust in the solar system.


 * The way to do this, and it works almost the exact same way in General Relativity, in EM, and in classical Newtonian gravity reformulated as a relativistic scalar field, is to imagine pulling apart the system into its parts. As you do this, you have to do work, which goes into making new field between the parts. When the parts are far apart, you have free particles, but you did work, so these free particles are more massive than the bound particles. It's really not controversial.Likebox (talk) 21:12, 3 July 2009 (UTC)


 * Regarding your other points, you are right that outgoing gravitational radiation decreases the mass of the solar system, but it does so not by making Jupiter less massive, but by moving Jupiter closer to the sun. That lowers the total energy by increasing the gravitational binding energy, and decreases the mass of the solar system infinitesimally. This effect is negligible compared to the binding energy in the solar system, otherwise Jupiter would be spiraling in quickly. The effect is not negligible for inspiraling black holes or neutron stars.


 * You are right that the nuclear forces are complicated, but their energetics are simple: the forces are attractive so nuclei are always less massive than the same number and kind of free nucleons. The mass of the nucleus is the mass of the nucleons minus the binding energy over c^2.Likebox (talk) 21:20, 3 July 2009 (UTC)


 * Yes. The total gravitational wave energy radiated by Jupiter and all the rest of the solar system (but mostly from Jupiter) is on the order of 1 kilowatt. That's pretty small compared with the mass-equivalent of 10^18 kg for the binding energy of Jupiter, which I check you on (I get 1.2e18 kg). A key fact in all this is emphasized in the article, which is that binding energy causes NO mass loss from closed systems. That is because all types of mass and energy are conserved across time for single observers, in closed systems. So binding energy needs to be radiated away to cause mass-defect. In a nucleus or the solar system. So per se it has nothing to do with field strength changes, whether attractive or EM or grav or whatever. These fields may change as potential energies are traded for some other kind, but as the fields disappear or are created, the energy stays in the system as something else, until it's got rid off by radiating it out. If it stays as heat, the system mass does not change. Some kinds of fields contain positive energy. EM fields have mass/volume and have positive energy. They gravitate. So if allow a proton and electron to slam together, without removing any energy, the field strength (total) decreases (as you see from outside as the effective system “charge” decreases) and the decrease in field is a decrease in energy in the field, but it goes into kinetic energy of the electrons, so the mass of the system does not change. The energy from the EM has to go somewhere (a 13.6 eV photon or whatever, radiated from the H atom). Gravitational fields are odd, inasmuch as they don't clearly contain energy/volume themselves like EM fields. G fields are a marker for energy that has been removed (though this energy deficit is in the system someplace not in a volume of the field-- it can't be localized). What this really means is that remove any of the energy in a system (including gravitational potential energy) the G field of the system seen from outside decreases. But after all, you’ve removed mass from the system (the binding energy) so why shouldn’t it? So as you let Jupiter move in from outside the solar system, as it heads toward the sun and picks up speed, the mass of the whole system goesn’t change and therefore neither does its G field as seen from far away-- energy goes from graviational potential to kinetic energy but they equally gravitate. BUT you cannot bind Jupiter unless you let it do work on you to let it bind to the sun (you have to slow it down to cut its kinetic energy in half for a circular orbit). As it does work on you, energy leaves the system, and thus its energy decreases, mass decreases, and G field (as seen from far away) decreases. As the work is removed, the total gravitational field (Sun+Jupiter) decreases (just as would be the case for the binding field if this were an electromagnetic binding). The difference is that EM fields have mass, so you can point to where the decrease in G field comes from there: it’s merely compensated by an increased G field somewhere else in the system until the energy of binding is removed (the kinetic energy of that electron gravitates until it is slowed and bound). so again the G field of the atom doesn’t decrease until the photon is removed (nor does its mass decrease). In gravitationally bound objects the missing mass is not necessarily “from” the field before binding-- it's hard to say where it was—unlike the case with other forces, the energy just comes out of the gravitational potential without coming out of the field itself. The field decreases because the mass decreases and the mass decreases because you’ve removed the binding energy somehow, and that carried away the missing mass (and has its own field, of course). The 10^18 kg mass is missing from the system because you removed it, but it didn’t come out of the G field per se even though that does decrease; it came out of the whole system and just shows up as a smaller G field by the amount of G field that 10^18 kg would generate. In the end I’m not sure why G fields are said to have negative energy, positive energy, or what. G fields are associated with the positive energy of mass-energy. If energy is removed from such systems, the G field decreases. If energy is not removed, it doesn’t. But I can’t assign energy to the G field itself, because what the G field is depends on the observer (if I fall toward a system with a G field, the field disappears and then where did its energy go, either positive or negative?). Probably the question doesn’t have an answer unless the observer is carefully defined and held far away and stationary. In that case the G field is just a marker for total system energy, and has none of its own (necessarily). Even G waves radiating through space have the same problem in GR—they certainly have positive energy, but there’s no place in them you can point to and say “there it is.” S  B Harris 00:19, 4 July 2009 (UTC)

The axiom or truth when figuring Einstein is the equation in base. the actual equation should be formed as E=m^3*C^4 so you're looking at actual mass and an infinite constant. signed Robert G Cazier Jr. a.k.a misnomer piles — Preceding unsigned comment added by 216.201.66.242 (talk) 16:14, 27 January 2012 (UTC)

E2 = m2c4?
Somewhere I read the above equation, which resolves to E = ± mc2, allowing for antimatter. Could anybody confirm or deny? Rbakels (talk) 06:38, 21 March 2012 (UTC)

E = mc³
I have been told, in the past, and can easily see that E = mc³ can be directly extrapolated from the formula for the volume of a sphere, V = 4/3 pi r³.

Launching an atomic bomb into empty space so are to be free of gravity and atmosphere which leads to a mushroom cloud on the Earth, the bomb is exploded in a theoretically perfect spherical expansion from a point source, the light from the explosion following the radii of the sphere in all directions where 'c' then follows 'r'.

Hence the quantity 'Q' of energy 'E' is defined as a volume 'V' the mass 'm' setting the size of Q, E and V where Q = E = V for all practical purposes.

Q. E. V. ? (Quite Easily Verified?)or Q.E.D. ? (Quite Easily Detonated?)

Anon 178.116.241.108 (talk) 13:34, 29 March 2012 (UTC)


 * Take it step by step and you'll see your error. The units are wrong for E = mc^3. If you explode an antimatter bomb in space where all matter is converted to radiation, you still have the same mass (please read the opening paragraph of the article). After that, this mass/ (or energy) is diluted by volume, as the light disipates. What you finally have is E/V = mc^2/V = constant determined by your bomb energy and initial volume. Then V(t) = 4/3pi R = 4/3pi (ct)^3. But you can't get much of interest by playing with those equations.  S  B Harris 19:25, 29 March 2012 (UTC)

Who wrote the exact formula "E=mc²", when, and where?
If Einstein did not write the exact formulation of E=mc² in his 1905 papers, then who did it for the first time? When and where was it first published? Any clue on this? sentausa (talk) 07:44, 16 April 2012 (UTC)

I have tried to answer it in the section "Nomenclature", but the section was removed with the recommendation to place it on the talk page. I understand that the aim of this recommendation is to perfect the section, especially provide it with sources. I must say that I had lived up to the age of 47 being sure that Einstein wrote E=mc² in 1905 until I discovered that I had been wrong. I wrote an essay "Quantum Archaeology" in 1995 and tried to get it published but no one was interested. Anyway, hardly anyone had access to the Internet at that time and it was definitely a pre-Wiki era. So, here it goes, the section to be enriched by sources - see below :) --C. Trifle (talk) 08:03, 27 June 2012 (UTC)

c2
If e = mc2 and c = movement of approximately 2.98 x 108 meters for every second, then mass is converted to energy when mass is accelerated to movement of 8.88 x 1016 square meters for every square second. Does this sound right? Lestrade (talk) 16:13, 12 August 2009 (UTC)Lestrade
 * No, totally wrong. This equation has nothing to do with acceleration. S  B Harris 03:51, 14 August 2009 (UTC)

m2/sec2 means a change of distance for every second, occurring every second. That is acceleration. According to the Acceleration wiki–article, acceleration is measured in metres per second squared (m/s2).Lestrade (talk) 01:57, 15 August 2009 (UTC)Lestrade
 * Yes, but m2/sec2 is not the same as m/s2. Notice there's an extra "meter" in c^2. So it's distance times acceleration. Add the mass and now you have mass times distance times acceleration. Like mhg or mgh. Mass times acceleration gives you a force. Force times distance gives you energy. S  B Harris 09:51, 16 August 2009 (UTC)

Plain text read, the formula is contradictious in itself. Because due to the core definition of its c, c (as a natural constant) can never get a factor greater then 1. Here it is c x c ! That antinomy should be remarked to the reader for better understanding and avoiding error. —Preceding unsigned comment added by Tripod-vie (talk • contribs) 01:24, 26 August 2009 (UTC)
 * While understandable, your comment is incorrect because c2 is not using the same units as c. The universal "speed limit," if you will, is c, but m2/s2 is not a speed. This is Madness 300  04:57, 29 June 2012 (UTC)

NOTICE "Nomenclature"
The aim of editing the section "Nomenclature" below is to provide it with sources before it can be included into the article. --C. Trifle (talk) 08:15, 27 June 2012 (UTC)


 * The first half, about Einstein, remains unsourced. I tagged it in the article.  And it's not clear the section should be called "Nomenclature", or why it's not included as a subsection of the History section instead of as first main section; it is not providing nomenclature for the article, not historical notes on different points of view and nomenclatures.  Dicklyon (talk) 15:50, 6 July 2012 (UTC)

Nomenclature
In Does the inertia of a body depend upon its energy-content? Einstein used V to mean the speed of light in a vacuum and L to mean the energy lost by a body in the form of radiation. Consequently, the equation E = mc2 was not originally written as a formula but as a sentence in German that meant if a body gives off the energy L in the form of radiation, its mass diminishes by L/V2. A remark placed above it informed that the equation was approximate because the conclusion was only justified if one neglected "magnitudes of fourth and higher orders" of a series expansion. In 1907, the einsteinian mass-energy relationship was written as M0 = E0/c2 by Max Planck and, subsequently, was given a quantum interpretation by Johannes Stark, who assumed its validity and correctness (Gūltigkeit). However, Stark wrote the equation as e0=m0 c2 which meant the energy bound in the mass of an alectron at rest and still was not the present popular version of the equation. In 1924, Louis de Broglie assumed the correctness of the relationship "énergie=masse c2" on page 31 in his Research on the Theory of the Quanta (published in 1925) but he did not write E = mc2. However, Einstein returned to the topic once again after the World War Two and this time he wrote E = mc2 in the title of his article intended as an explanation  for a general reader by analogy

"Practical" examples
Removed the final part from "practical examples", because it was quite urelated to the section's topic (quantitative examples), in addition of being quite un-organized and unclear. The general problem is that the relation between mass-energy equivalence and gravity is not well explained in the article. Additional issues follow:
 * Note further that in accordance with Einstein's strong equivalence principle (SEP), all forms of mass and energy produce a gravitational field in the same way.Earth's gravitational self-energy is 4.6 × 10^-10 that of Earth's total mass, or 2.7 trillion metric tons. Citation: 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.). So all radiated and transmitted energy retains'' its mass. Not only does the matter comprising Earth create gravity, but the gravitational field itself has mass, and that mass contributes to the field too. This effect is accounted for in ultra-precise laser ranging to the Moon as the Earth orbits the Sun when testing Einstein's general theory of relativity.

The reference to the Strong Equivalence Principle (SEP) is quite vague and not fully correct in the present context. The Weak Equivalence Principle (WEP) -- i.e. equivalence of gravitational and inertial mass -- plus mass-energy equivalence is sufficient to deduce that all energies produce a gravitational field. The SEP is a strictly stronger statement. A better explanation of the issue, perhaps in a different section, seems to be required if the paragraph is to be restored.


 * According to E=mc2, no closed system (any system treated and observed as a whole) ever loses mass, even when rest mass is converted to energy.

This was already stated few lines above in the same section.


 * All types of energy contribute to mass, including potential energies. In relativity, interaction potentials are always due to local fields, not to direct nonlocal interactions, because signals cannot travel faster than light. The field energy is stored in field gradients or, in some cases (for massive fields), where the field has a nonzero value. The mass associated with the potential energy is the mass–energy of the field energy. The mass associated with field energy can be detected, in principle, by gravitational experiments, by checking how the field attracts other objects gravitationally.There is usually more than one possible way to define a field energy, because any field can be made to couple to gravity in many different ways. By general scaling arguments, the correct answer at everyday distances, which are long compared to the quantum gravity scale, should be minimal coupling, which means that no powers of the curvature tensor appear. Any non-minimal couplings, along with other higher order terms, are presumably only determined by a theory of quantum gravity, and within string theory, they only start to contribute to experiments at the string scale.

This doesn't really seem to be related with "practical examples". What precisely is the point of this discussion? In particular, the note referring to the renormalization group, quantum gravity, and string theory is absolutely obscure. Such details should be discussed separately, otherwise they only generated confusion.


 * The energy in the gravitational field itself has some differences from other energies. There are several consistent ways to define the location of the energy in a gravitational field, all of which agree on the total energy when space is mostly flat and empty. But because the gravitational field can be made to vanish locally at any point by choosing a free-falling frame, the precise location of the energy becomes dependent on the observer's frame of reference, and thus has no exact location, even though it exists somewhere for any given observer. In the limit for low field strengths, this gravitational field energy is the familiar Newtonian gravitational potential energy.

This goes into quite specific topics of general relativity, diverging from the topic of the article and with no relation with the subsection's topic ("practical examples"). The article Mass in general relativity is perhaps a better place to discuss these issues. (A reference to that article could fit in the present, but definitely in a differenct section). --131.130.45.12 (talk) 11:42, 11 September 2012 (UTC)

Replacement for E=mc2-explication.jpg
I created a SVG image to replace E=mc2-explication.jpg. I'm not sure how to make the replacement so if you know, please do so. — Preceding unsigned comment added by JTBarnabas (talk • contribs) 11:59, 15 March 2013 (UTC)


 * ✅. See . - DVdm (talk) 12:22, 15 March 2013 (UTC)

Nomenclature- the latest editions of April 2013
I appreciate the latest editions by User: D.H. It is important to learn about important writers who worked on mass-energy equivalence in the years 1907-1918. Still not all have been mentioned. However, I think the loss of de Broglie from this section was not necessary as his usage of mass-energy equivalence made possible his "phase waves" and the wave-particle duality as the new field of physics. The fact that he used the equation was important for history of science even if you don't agree with that approach. Do you think it would be good to bring him back to the section? Another thing - do you like the use of those big dots? I'm not sure if I can propose anything better, though. --C. Trifle (talk) 21:59, 29 April 2013 (UTC)

typography
I removed the "superscript 2" character ² since it is too small to read clearly/easily and depreciated anyway by WP:MOSMATH. M&and;Ŝc2ħεИτlk 10:12, 19 May 2013 (UTC)

ability to "convert matter to energy" is still misleading terminology (or at least easily misinterpreted)
"Converting X to Y" may be interpreted as a process in which you end up with less X than before, and correspondingly more Y than before.

"Converting matter to energy" is misleading because, while you do end up with less matter, you don't end up with more energy than before!

Of course matter can be converted to non-matter, but the "new" non-matter (along with anything that escapes) has exactly the same energy (and thus mass) as the "old" matter did.

Do variations on either of the following provide a suitable alternative (in order to avoid talking about conversion between matter and energy)?
 * 1) Matter has some amount of energy (and thus mass) in some form(s) (such as binding energies and rest masses of its constituent particles). Matter may be transformed to some other substance, but none of its original energy (and thus none of its original mass) will be destroyed;  all of its energy will remain or be released in some combination of electromagnetic, kinetic, and other forms.
 * 2) Some forms of energy are considered matter; a matter form of energy may be converted to (or from) a non-matter form, with the total amount of energy (and thus the total amount of mass) staying the same.

I think we should completely avoid talking about converting anything either "from energy" or "to energy" as these seem to suggest that the amount of energy can change.

DavRosen (talk) 20:20, 5 June 2013 (UTC)


 * You have a good point, of course. I shouldn't have said anything about converting matter to energy when I really meant something along the lines of converting "material energy" to "non-material energy." With "material energy" being the "matter" that is the subject of the matter article (and poorly defined it is, too), and "non-material energy" being everything else that is energy but that nobody even thinks of calling matter (photons, kinetic energy, static EM and other fields except gravity, etc). Of course the astronomers have not helped, as they now differentiate between "dark energy" and "dark matter" which both have mass-energy, but only one of which is matter. So dark matter is really "dark material energy," according to what we're trying to say. Dark matter and dark energy both have positive energy (gravitational fields have negative energy). But dark matter has mass in the usual rest-mass way that curves space-time in the usual way, whereas dark energy must curve space-time in opposition to gravity, but without the rest-mass. Normally systems that contain energy and curve space also have invariant mass, but nowhere have I seen a discussion of the invariant mass of dark energy. If all mass is energy, does not dark energy have associated with it a type of invariant mass? Or perhaps this falls outside special relativity, which is the only place E=mc^2 is guaranteed. Anyway, I support your clarification of this article in any way that makes it clear that matter can appear and disappear within systems (in at least some definitions of matter), but that neither the total mass nor energy of systems can do so (as both of these are fixed). At least in the flat space of special relativity. Thanks for pointing out this problem.
 * S B Harris 01:33, 8 June 2013 (UTC)


 * What I'm still struggling with is whether to say matter is a form of energy, or whether it has energy among its properties. I'm leaning toward the latter.  Focusing on just a particle for the moment, we shouldn't say a particle is energy any more than it is spin or other conserved attributes. I don't want to fall into the trap of saying that light is (a form of) energy while atomic matter (for example) merely has energy.  But what can we say energy is a property of, most generally?  A property of "substances", or does that sound too much like matter?  A property of "anything"?  "Stuff"?  "Elementary particles and everything composed of them"?  There's always "energy of a physical system", but that gets awkward, e.g. "matter and other systems can have energy".


 * Also, should we consider simply saying that mass is a (universal) property of energy, rather than saying mass is a property of what ever energy is a property of? Per Einstein, inertia is a measure of the energy.  Inertia or mass is a much more specific concept than energy.  There are specific ways to (directly) do a mass measurement, which form a small subset of the ways we can measure energy.


 * Another problem is that when we refer to the Mass, Matter, and Energy articles... well, they seem to have even more problems in these areas.
 * DavRosen (talk) 02:59, 12 June 2013 (UTC)


 * Elaborating further: The whole emphasis on the idea that mass is conserved but matter isn't is questionable and confusing (and unsourced) at best. Matter is a category, not a quantity.  Conservation laws refer to a quantity (e.g. of energy or mass).  A category can't be "converted" into a quantity.  Also, it isn't accurate to say that a photon (for example) is energy; rather a photon has an amount of energy as one of its properties.   How about:
 * Rest energy (thus rest mass) of a system or body can be converted to other forms of energy (thus mass).
 * For example, an electron and a positron can "annihilate" one another, which doesn't destroy any energy, but rather their rest energy (thus rest mass) is converted into another form of energy (thus of mass) carried by the photons produced, since photons have no rest energy (rest mass).
 * DavRosen (talk) 17:49, 19 June 2013 (UTC)

Intro should go further on basic fact of m-E equivalence itself before bringing in relativity at all.
Reader should be able to understand the most basic concept and a a couple of concrete examples immediately without having to read anything about relativity per se.

First paragraph of article is almost this way already, except that it unnecessarily mentions special & general relativity in the first sentence. m-E equiv arises even when one is not learning anything [else] about relativity, even though historically, relativity is the context in which it was first proposed.

Before we go into "there are different ways to define mass", let's give a concrete example of a familiar system to which we add some amount of energy, and the "surprising" fact that this also increases its mass, as can (in principle) be measured with a scale/balance (or F=ma measurement if we want to completely sidestep gravitation). Then show numerically how small this mass increase is, and therefore often difficult to measure.

And that we can't change or or convert mass to energy, but rather they always both occur together the same proportion.

(Of course the proportionality factor in the commonly-used systems of units "turns out" to involve the speed of light, but this isn't the most important part of the concept and the reason for this can be deferred.)

And that the energy (and thus mass) of a system go down when some of the energy (and thus mass) escapes from it, rather than any energy being converted to mass or vice-versa.

The average reader should know, even if they stop reading when they get to [other] relativistic concepts, that, e.g., raising the temperature of water makes it "heavier" (I know we're trying not to conflate weight with mass but that's a subtlety that can be addressed later; the lay usage of "heavy" does not distinguish or refer exclusively to gravitation as opposed to inertia; if you have trouble pushing a car you say it's "heavy", meaning in this case that it is difficult to accelerate, even when gravity plays no role at all.)

Even the example of the mass of the elements vs. the mass of their separate constituents. E.g. this comes up in chem 101 in that the elements' masses aren't quite proportional to their atomic nummbers; this fact and the corresponding energy equivalence can be taught without knowing what a reference frame is or anything about the motion of objects in relativity, or even the speed that light travels (except optionally as an interpretation of the c in c2).

That goes along with concept of nuclear reactions (with bomb examples) that change those elements into other ones and the energy released.

That can all be done before adding terms like momentum (even classically), rest or invariant mass, relativistic, etc.

Of course, everything above is already addressed later in the article -- I just think we should introduce them at the most basic level right away even though they will be expanded on later.

Of course relativity has an essential relationship to m-E equiv and this should be addressed within the intro (before the TOC), but it needn't be mixed in until the basic concepts are stated without explicitly-relativistic terminology.

DavRosen (talk) 19:05, 18 June 2013 (UTC)


 * This approach is okay with me, but remember that this article is the redirect from E=mc2 and was originally as much about this equation as mass-energy equivalence. So the original idea was to introduce relativity early. As to whether mass should be considered a property of energy (thus making energy primary) or energy should be regarded as a property of mass (thus in a sense doing the reverse) has been a subject of great debate among physics teachers. There is no consensus. It's even worse when we come to matter, which has various definitions. You can say: "matter is a category, not a quantity," but not everybody agrees with you. For some, matter is the quantity of rest mass in systems. A particle can lose a fractional amount (quantity) of its matter, as when a proton binds to a deuteron and some gammas are given off. The He-3 weighs less than the two particles (D,p) that went into it. No particles are destroyed-- it's just a fractional loss of matter. We can't assign the loss to any of the three baryons that make up a He-3, but nevertheless in this process a bit of the matter (in the sense of "ponderable stuff" the world and baryons are made of) has been converted into gamma rays (which aren't that kind of stuff). In that sense, a bit of matter is destroyed to make photons, even without matter particles being destroyed (as happens in the matter-antimatter reaction). While, all the while, mass and energy remain the same. S  B Harris 00:55, 20 June 2013 (UTC)


 * I don't think what I said is less so whether the article is primarily about E=mc2 or not; to me, E=mc2 is primarily about m-E equiv :-). This equation isn't foundational for special relativity originally; rather the latter implied E=mc2 for certain forms of energy in a certain context, but not necessarily for energy in all possible forms.  There are other articles where the theory of relativity itself is more primary. If there are different opinions about what's a property of what, let's say so -- do you have any citations we could use for the differing views?  So long as we point that out, I think it's okay to adopt one of those terminologies and try to use it consistently throughout the article to avoid flip-flopping.  To me, E being a property of m is more confusing because there should be simple and general way to measure a property, which there is for m but not for E.  What ever forms of energy (btw do you really want me to say "what ever forms of mass"?) a system may have, its mass can in principle be measured in the same way, say via an inertia measurement.  If we say mass takes on many forms such as that of light and atoms, we gain nothing by saying such mass has a universal property called Energy, since there's no universal way to measure that energy.  I'm okay with either saying m is a property of E, or saying both have co-equal status as two distinct properties (which are always proportional to one another) of a system, or even saying they are one and the same property expressed in different units.  In the latter case we could say energy (i.e. mass) exhibits a property or phenomenon called inertia whose measurement is made more convenient in mass units than in other energy units. But if they're co-equal properties or identical properties then the terms kinetic mass, potential mass, etc., are just as good as the terms potential energy, etc.  I'd rather use one as the primary term so we aren't always wondering which one to use.  Using mass as primary mangles more of our familiar terminology so we start saying "kinetic and potential mass have a property called energy" -- does that really help the reader's understanding?  If energy is primary then we can say "rest energy", which is already a recognized alternative term to "rest mass".  As for matter, how can we say so much about it without saying which definition the statements apply to?  If we want to define matter as simply rest mass, that's fine -- we can mention this once and then use only the term rest mass since we are already using it and it's less ambiguous than matter in case someone didn't read our definition. But then when we hear that there is "more matter than antimatter" in the universe, do we want to say that this means there is "more rest mass than anti-rest-mass"?  If matter is indeed a quantity, it appears to be a signed one (a particle with an antiparticle together have "zero net matter", both before and after annihilation?), whereas mass is unsigned.  I don't think this is the appropriate article in which to address the pro's and cons of various definitions of matter (and of anti-matter). DavRosen (talk) 06:16, 20 June 2013 (UTC)

De Pretto
Hi. It's quite obvious that De Pretto equated mass and energy before Einstein. Why is this not stated? 218.152.128.52 (talk) 12:21, 6 October 2013 (UTC)

"But this deduction leads us to unexpected consequences and incredible. One kilogram of the subject, launched with the speed of light, would represent a sum of such energy that it is no nor even conceive.

The formula mv 2 gives us the living force and the formula gives us, expressed in calories, such energy.

Since, therefore, m = 1 and v equal to three hundred thousand kilometers per second, that is, 300 million meters, which would be the speed of light, also permitted for the ether, everyone will see that you get a quantity of calories represented by 10794 followed by 9 zeros, ie more than ten million million.

A frightening as a result there has never led our reasoning? No one will readily admit that stored and latent state, in one kilogram of matter whatsoever, completely hidden to all our investigations, lies such an amount of energy equivalent to the amount that can be held by millions and millions of pounds of coal; the idea will certainly be judged insane." 218.152.128.52 (talk) 12:29, 6 October 2013 (UTC)


 * For ease of reference, the OP seems to be referring to Olinto De Pretto. This is mentioned extensively in the artocle, so I am not sure what point the OP is making. — Quondum 16:05, 6 October 2013 (UTC)


 * @IP: Well, many people (even before De Pretto) stated some form of energy-mass-equivalence before Einstein (see history section), but Einstein was the first to formulate it correctly in a coherent theory. Since this article is about the modern concept of equivalence, Einstein has the priority, as you can read in literally thousands of primary, secondary, and tertiary sources. See (WP:Sources, WP:OR, WP:Undue)... --D.H (talk) 20:09, 6 October 2013 (UTC)
 * Agreed, I removed this from the lede again. It is already mentioned in the body of the article, where it belongs. VQuakr (talk) 03:57, 7 October 2013 (UTC)
 * Agree. This edit was clearly inappropriate per wp:UNDUE. - DVdm (talk) 10:17, 7 October 2013 (UTC)

Misinterpretation
The formula E = mc^2 was started from special relativity. It means that a particle of mass m has the energy content of mc^2. However, it does not mean that any type of energy is equivalent to a mass m = E/c^2. In fact, it has been proven that the electromagnetic energy alone is not equivalent to mass [1]. This misinterpretation was initiated by Einstein although he failed to prove that any energy has a mass equivalent for many years (1905-1909)[2]. This misinterpretation is responsible to overlooking the charge-mass interaction from the Reissner-Nordstrom Metric. This static repulsive force is crucial for the unification between gravitation and electromagnetism [1].

References: 1. C. Y. Lo, The Question of E = mc2 and Rectification of Einstein’s General Relativity, GJSFR Vol. 14, Issue 2, Version 1.0 (2014). 2. "Einstein's Miraculous Year" edited and introduced by John Stachel, Princeton Univ. Press (1998), p. 118. — Preceding unsigned comment added by ChungYLo (talk • contribs) 23:46, 25 April 2014 (UTC)


 * I have added a section header for your message. Please sign you talk page messages with four tildes ( ~ ). Thanks.
 * Note that Wikipedia is not a place to promote our own work—see wp:PROMO and wp:FORUM. We can only add such content if our publications are covered and cited in the literature—see wp:Secondary sources. I can't find anything with Google Scholar and Google Books. Perhaps a few years from now. - DVdm (talk) 06:51, 26 April 2014 (UTC)

Coversion confusion
The following two claims appear in the Efficiency paragraph: "mass cannot be converted to energy" and "the mass is not destroyed, but simply removed from the system. in the form of heat and light from the reaction"

Maybe it's just me, but it seems as though if it is first mass, and then heat and light, wasn't there a conversion? Maybe the article should just stay away from the word "convert" if the basic idea is that they are equivalent.192.249.47.204 (talk) 19:43, 30 October 2014 (UTC)


 * You're right, that paragraph is definitely confusing. It should distinguish between rest mass (of the matter particles) and the total mass (inertia--gravitation) of the system (including that of any light or other forms of energy).  Just as you wouldn't say "light can be converted to energy", you can't say "rest mass can be converted to energy"; it already is energy (namely in a form called rest energy).  Rest mass can be converted to *other* forms of energy (light, etc.).    From another point of view, the system as a whole exhibits its total mass (via inertia and gravitation phenomena) and this mass depends only on the total energy of the system; thus, because the total energy can't change, this overall system's mass can't change either.  In other words the light or other forms of energy contribute exactly the same amount of mass to the system as did the matter they replaced. DavRosen (talk) 22:05, 30 October 2014 (UTC)

En-dash or hyphen?
Mass-energy should be connected with a hyphen, not an en dash, I think, per WP:HYPHEN. "Mass-energy" is a compound modifier of equivalence, and mass and energy are related terms in this context. Any objection to a move?

This was briefly discussed in 2009. —Alex (ASHill &#124; talk &#124; contribs) 19:42, 17 February 2015 (UTC)
 * Actually, I guess since mass and energy are reversible (ie could be energy–mass and have the same meaning), the MOS says that en dash is marginally preferred. —Alex (ASHill &#124; talk &#124; contribs) 19:52, 17 February 2015 (UTC)
 * Yes, when the terms are linked rather than one modifying the other, usually in a balanced context, the en-dash should be used. The reversibility is a good indicator of this.  Here the linkage is between alternatives, meaning that mass and energy are equivalent in the context: either would do, but the linkage emphasizes the equivalence.  So I'm against a move. —Quondum 20:01, 17 February 2015 (UTC)

Coding: mc² or mc2?
Square power is denoted by superscript 2. There are two ways of presenting this character: either use of standard Unicode character "Superscript Two" (U+00B2): mc², or forcing the normal digit 2 to be raised to superscript using HTML coding:, resulting in mc2. From typographical point of view, the former is more correct and consequently looks better in many typefaces (including in the heading above).

Are there any WP policies on using either of two? 31.185.130.54 (talk) 13:53, 12 September 2015 (UTC)


 * Yes, WP:MOSMATH. It is much easier and uniform to use, which works for any superscript, not just the power 2 or "square". Using specialized characters is not always good since they are often untypeable   it is, not  . M&and;Ŝc2ħεИτlk 14:48, 12 September 2015 (UTC)

"even though no matter has been added."
Is this strictly correct? Given that this is the lead statement on an extremely important topic, this needs to be scrupulously phrased. According to its WP page Matter deosn't have a universal definition in modern Physics so it should either be defined in this context or reworded. The question is: if mass and energy are equivalent then does it make sense to distinguish adding energy from adding matter? Btljs (talk) 07:27, 23 September 2015 (UTC)

Weight/mass confusion
A spinning ball will weigh more than a ball that is not spinning.

Shouldn't this say "will have greater mass" ? The article deals with increased masses at different energies, introducing the term weight merely causes confusion. — Preceding unsigned comment added by 86.156.95.255 (talk) 13:25, 21 October 2015 (UTC)

c^2 value is wrong
In the explication the c^2 value is wrong and should be c^2 = 89875517873681764. Dr. Morbius (talk) 21:20, 14 November 2015 (UTC)
 * The section Mass–energy equivalence says:
 * So what's the problem? - DVdm (talk) 22:06, 14 November 2015 (UTC)
 * So what's the problem? - DVdm (talk) 22:06, 14 November 2015 (UTC)

Way too technical in the lede
This is already a taxing article for the layman; the lede at least should be kept accessible.

I also think that a section on popular cultural references would be useful, if not an entire new article on "E=mc2" in its own right. Btljs (talk) 15:17, 11 October 2015 (UTC)
 * Agree. Also wish there were Wiki editors who understand these concepts to have this page on their Watchlist. I do not trust the editor Undolie, the change they made here changed the entire concept of the article. The page has also been a target of vandalism by a ip hopping vandal. Dave Dial (talk) 15:39, 11 October 2015 (UTC)
 * This is a vital level article and as such it should be exemplary. I was actually quite surprised to be redirected to such dense scientific language from "E=mc2". I don't know what I expected, but there are books out there which have made this subject accessible so it is possible. Btljs (talk) 15:49, 11 October 2015 (UTC)
 * It seems as if the editor is just vandalizing the article. As I was removing their edits and making sure to keep the tag you put into the article, another editor removed the edits made by Undolie as 'nonsense'. Thanks to Dr Greg for that. Dave Dial (talk) 15:57, 11 October 2015 (UTC)
 * I thanked someone - don't know if it was you or them! I actually prefer this lede from 2009 in terms of style. Also there should be a discussion of how famous the equation itself is (celebrity status). Btljs (talk) 16:03, 11 October 2015 (UTC)
 * I'd say the 2009 version of the article is altogether better than the current version. The current text tries to put rest-mass/rest-energy and relativistic mass/total energy on an equal footing throughout the article.  This makes it difficult to follow and also doesn't match the usual meanings of "mass" and "energy" in physics.  The result is that readers who come to this article to help them understand what they've read somewhere else in the encyclopedia end up more confused than before.  --Amble (talk) 22:58, 11 October 2015 (UTC)
 * I agree. I largely restored the 2009 version of the lede (though I kept a few tweaks from the newer version). I kept the technical tag; if someone else could take a look and see whether it's enough less technical to justify removing the tag, I'd appreciate it. (Don't want to make that judgement myself.) I think that everything that was in the lede was in the article, so I don't think I threw out any useful detail that was only in the lede, but I may be wrong. I didn't look much at the article beyond the lede. —Alex (Ashill &#124; talk &#124; contribs) 15:29, 12 October 2015 (UTC)

As a frequent user of Wikipedia (and a financial sponsor), I am concerned that making articles "accessible to the layperson" will dumb-down Wikipedia and make it no more reliable than a blog. For my purposes, Wiki serves as a bridge to further reading in peer-reviewed publications that report the results of original research. I hope I'm making this comment in the proper form. Dbbotkin (talk) 18:12, 27 December 2015 (UTC)
 * Your comment is a general one and may be better dealt with in WP:Villagepump or similar; however, a couple of points with respect to this particular subject: first, I was talking about clarity and accessibility in the lead paragraph, not the whole article; someone who wants more details can read further, while someone who wants a quick overview should be able to get this from the lede. Second, reliability has nothing to do with detail, but is maintained by making sure we use reliable sources (the same ones which you want to 'bridge' to, hopefully). Personally, I don't like the phrase 'dumbed down' as it implies, incorrectly, that intelligence is linked to being able to absorb information in a specific form - there is nothing dumb about simplicity. "If you can't explain it simply, you don't understand it well enough." Now who said that? Btljs (talk) 08:17, 28 December 2015 (UTC)

A simpler entry for the layman.
What we have here is an article that makes heads spin with equations. It requires over a 12th grade reading and math level to understand. This equation is not that difficult, the concept is not that difficult. What I see is a bunch of people trying to get it mathematically correct and not many people trying to make it understandable. Writing on a lower reading level will absolutely not express things as clearly as the math (to a math-savvy mind), the aversion to that sort of explanation is why the average person thinks math is some sort of holier-than-thou sorcery.

I put up the following, and got reverted. The reversion reason said "unsourced and a lot is simply wrong", with no statement as to what was wrong. (I'm not saying I was right, and I don't mind critique.) There are parts that are correct - why weren't they left in?


 * The equation $E / m =$ ("energy is equal to the mass times the speed of light squared") is common in popular culture due to its simplicity and relation to Einstein. Because of this, most people are at least familiar with the equation even if they themselves do not understand it.


 * Essentially matter (everything you can see and touch), and energy (like electricity and motion) are the same thing. One can be changed into the other. Because one side of the equation multiplies matter by the speed of light squared, it means:




 * Actually converting matter to energy (and energy to matter) still remains in the realm of science fiction. A real world example would be the difference in size between a Nuclear weapon and the enormous explosion is produces, however despite the huge explosion a nuclear weapon still only converts a small amount of its matter into energy.


 * It is because matter is energy that that a person traveling at the full speed of light experiences strange effects that even experts have trouble wrapping their minds around, and is probably impossible. Movement is a form of energy, and the thing being accelerated is matter (another kind of energy), so you have energy becoming energy.

The thing is, we do need a less technical explanation, simply undoing the edit is giving up. Could we change this so it better reflects the topic? How?--Varkman (talk) 15:39, 12 February 2016 (UTC)


 * We could leave everything out that is unsourced (or wrong), and then we would be left with what's already in the article. If you like to know what exactly is wrong, a good exercise would be to look for sources for what you have written, or, if you can't find any, to ask at the wp:reference desk/science. Note that, per wp:talk page guidelines, article talk pages are not for explanations why unsourced content is wrong. Good luck! - DVdm (talk) 16:32, 12 February 2016 (UTC)

Completely rewriting the lede
The presentation in this PBS SpaceTime video: https://www.youtube.com/watch?v=Xo232kyTsO0 is much clearer than the current language here, and gives (to me) a much better and informative explanation. I hesitate to make such a large change without checking first, especially since there's the possibility of simply being reverted/downvoted out of existence. But if the consensus agrees, I'd be happy to take a first shot at writing something up along these lines. Geoff Canyon (talk) 05:14, 20 November 2015 (UTC)


 * (New section, moved to bottom.)
 * Perhaps, but as this is not a reliable source in the Wikipedia sense, provided nothing from it is taken that differs from (or adds to) what is in the body of the article. - DVdm (talk) 07:42, 20 November 2015 (UTC)


 * This seems like a reliable source to me. From wp:rs: "However, audio, video, and multimedia materials that have been recorded then broadcast, distributed, or archived by a reputable party may also meet the necessary criteria to be considered reliable sources." PBS qualifies as reputable, and the host is a physicist. The contents of the video are (mostly) aligned with what is currently presented in the article, it's just that the emphasis and presentation are different and more straightforward, which is exactly what the discussion above says needs to happen with the lede here. Geoff Canyon (talk) 16:44, 20 November 2015 (UTC)

In the Reiki System of Healing, discovered by Japanese doctor Usui, it gives reference that every manifestation [mass] has two components (1) Aura [Energy] (2) Vibrations [corresponds to c^2 ]

Dr. Usui discovered this mass-energy equivalence after studying Vedic Sanskrit texts. 23 Jan 2016 Sudhirkulkarni29 (talk) 15:47, 23 January 2016 (UTC)


 * Energy (esotericism) and Energy (Physics) are not the same thing. Physics Energy has been proven through scientific method.  Esoteric energy is subjective and has not been proven as a universal fact.  Hence you can't really apply Reiki energy to physics without some proof that it exists.--Varkman (talk) 15:43, 12 February 2016 (UTC)

I would not trust PBS, usually wrong. Get a good book by a well known professor. But rewrite. I am not really dead (talk) 15:33, 16 February 2016 (UTC)

Confusion is not relative
What permeates these series of Wikipedia articles on relativistic mass and energy is a cosmic invariant called confusion. Each one makes a different assumption about relative, rest and invariant mass, confuses issues about single particles and compounds, etc.

Interestingly, the page refers to Hecht's paper "How Einstein confirmed E0=mc2" but does not refer to his paper "There is no rally good definition of mass". Hecht is a lightweight in the field, but if you are going to use him, look at the other one too. I could not help but laugh at the fellow above who talked about Reiki. That was obviously dumb of course, but there is serious confusion about rest, invariance and relative as applied to mass in this article, and in fairness, among practitioners in the field.

To clean it up, please read John Roche "What is mass" European Journal of Physics 2005 pp 225. A google search will get you a pdf. Roche knows what he is talking about and has consulted with serious physicists above Hecht's class. I am not really dead (talk) 15:51, 16 February 2016 (UTC)

Invalidity for Tachyonic Field Theory
I was wondering if somebody would like to help write this new section? The premise is that for superluminal speeds, there is even more energy contained in the atom. This is the basis of the paper I am publishing. — Preceding unsigned comment added by 8SEAL9 (talk • contribs) 21:30, 8 April 2016 (UTC)


 * Please sign all your talk page messages with four tildes ( ~ ). Thanks.
 * alas, Wikipedia doesn't allow new research—see wp:NOR. Your paper must be peer reviewed, and published, and sufficiently widely mentioned/cited/quoted in the relevant literature—see wp:secondary sources and wp:UNDUE. Give it at least 5 years or so... - DVdm (talk) 08:44, 9 April 2016 (UTC)

Gravitational waves
Two observations of merging black holes have now been confirmed. In each case, vast amounts of matter have been turned into energy which was radiated away via gravitational waves. Is there an expert here who can add a bit about this to the article? It's mind-blowing to think that the mass of our Sun could be turned into pure energy by this process. Tayste (edits) 22:16, 5 July 2016 (UTC)
 * Is there something in the literature that makes the connection between mass–energy equivalence and energy radiated away via gravitational waves? - DVdm (talk) 07:14, 6 July 2016 (UTC)

Provable formula?
Is this equation E=mc2 a provable one? The article is not clear about the derivation of the formula (whether it is a derivable one or it has axiomatic status), the steps of the proof. It lacks a section called Proof. Thoughts?--213.233.84.188 (talk) 19:52, 23 July 2016 (UTC)


 * As Einstein did, one can start with a set of axioms about motion in special relativity that necessarily lead to E=mc2. The section Mass–energy equivalence actually sort of alludes to how this would go.  However, the axioms of special relativity, though well supported by experiment, would probably seem a bit weird to the novice reader if one attempted to illustrate a proof using that starting point.  Dragons flight (talk) 20:08, 23 July 2016 (UTC)


 * So it is indeed a provable formula. I think a great improvement to article is to insert a fully developed proof with the set of axioms about motion explicitly stated and other assumptions as well, if appearing.--213.233.84.208 (talk) 10:02, 24 July 2016 (UTC)

Link to RefDesk Math discussion on this topic: Reference_desk/Archives/Mathematics/2016_August_12.--213.233.84.230 (talk) 23:51, 8 September 2016 (UTC)

formatting
I think the fonts used for variables do not look good in this article. I think this would be much better:

It expresses the law of equivalence of energy and mass using the formula$$E=mc^2,$$where $$E$$ is the energy of a physical system,$$m$$ is the mass of the system, and $$c$$...

That way all formulae would be renderd using the same fonts. Any objections to that? --Physikerwelt (talk) 17:30, 11 October 2016 (UTC)