Talk:Special relativity/Archive 5

Priority, ad nauseum
An anonymous editor using IP address 68.0.143.223 has changed this article and General relativity to stress prior contributions of Lorentz, Hilbert, and Poincare. Please be aware that exactly how to briefly describe the development of gtr and str is contentious. That is, there is substantial agreement among historians of science on the basis issues, but some cranky claims that Einstein "stole" from Hilbert, or his first wife Mileva, or whomever, have currency among certain individuals. For this reason, editors should not make such changes without discussion on the appropriate talk pages.---CH 05:35, 23 December 2005 (UTC)


 * CV is very right about how contentious it is, and he/she demonstrates it perfectly by trying to suggest that the view of some historians is that of "certain" "cranky" "individuals" -- a tendentious, POV approach. However, the Wikipedia policy can prevent problems: just stick to reliable sources, without ignoring notable differing opinions. Harald88 14:57, 2 January 2006 (UTC)


 * Related to this, what do you think of this edit by an anonymous contributor, suggesting "that the work of Carathéodory help shape some of Albert Einstein's theories". It has enough details to make me think that the fact are probably correct (though I didn't check anything). -- Jitse Niesen (talk) 16:48, 3 January 2006 (UTC)


 * It is out of character with the rest of the article, and reads "possible hoax" to me. My temptation is to move it to the talk page and call for citations backing the claim up. --EMS | Talk 02:51, 8 January 2006 (UTC)

Two way "calculating" velocities?
Why do we elismate(changed to "estimate"--HydrogenSu 12:02, 30 January 2006 (UTC)) phase velocity by $$\mathcal E=mc^2 $$,and elismate group velocity by $$E=\sqrt{P^2C^2+m_0^2C^4}$$?

Any differences?

I think that reasons may be a group velocity can represent a true body when it moves.(which might need to considerate both of rest-mass and move-mass $$\mathcal (P^2C^2) $$ effect) But a phase velocity is just a S.H.O. vibrating.(which doesn't need to considerate of rest-mass effect) &mdash;The preceding unsigned comment was added by HydrogenSu (talk &bull; contribs) 18:41, 26 January 2006.


 * ??? elismating? What is that supposed to mean?  First of all, this business of phase and group velocities is matter for quantum mechanics, as relativity is a classical theory isntead of a quantum one.  Secondly, you are not even looking at the right equations for determining the energy and momentum of an object.  $$\mathcal E=mc^2 $$ is for the rest energy of an object (meaning that it is good only when v=0), while $$\mathcal E=\sqrt{P^2C^2+m_0^2C^4}$$ is the relativistic energy-momentum relationship and is good at any velocity. --EMS | Talk 04:41, 27 January 2006 (UTC)
 * Maybe I spelt the word wrong. I thank you. (I'm a Taiwanese.)
 * I was then wondering of that question above. It's started on my book when I read. It said:
 * Find a relativistic particle's $$\mathcal Vg $$ and its $$\mathcal Vp $$.
 * My book solved them by those:

$$\mathcal V_p=\frac{\omega}{k}=\frac{E}{p}=\frac{mc^2}{mv}=\frac{c^2}{v}$$ which is possible greater than speed of light. $$\mathcal V_g=\frac{d\omega}{dk}=\frac{dE}{dp}=\frac{d\sqrt{P^2C^2+m_0^2C^4}}{dP}=v $$ which is impossible equal to speed of light,even greater than that.
 * My trouble is in their physical picture.I'm not quite sure still. --HydrogenSu 11:19, 27 January 2006 (UTC)


 * I still don't know what word you are trying for. The current version is reminiscent of "eliminating", but velocity is eliminated when something stops!  As for the details:  Yes, that is a standard quantum mechanical calculation.  ( However, you have your labels reversed as of 1/17/06.  It is the first equation that gives superliminal values, not the second. Actually, the labels are correct but just plain confusing.  "cannot" would work better than "possible" [parenthtical remarks revised by EMS | Talk 00:03, 28 January 2006 (UTC)]) In essense, the waves within an object are always superluminal, the the group (which defines the object) travels with the object (and it had better do so).  Since the object/wave group itself cannot travel at c or greater, relativity is not violated by this. --EMS | Talk 17:58, 27 January 2006 (UTC)


 * "Eslimating" is not an english word either. "Estimating" perhaps?  However that implies inaccuracy in the result, and there is none in classical equations.  I strongly advise finding other words to use.  Either that or use |the Chinese version of this article  --EMS | Talk 00:03, 28 January 2006 (UTC)


 * Bingo! The word that you are after is "calculate"!  Now your question makes sense. However, the answer is as I stated above:  This involves quantum mechanics, and not special relativity in particular.  You need to look in category:quantum mechanics for the overall answer.  Remember that you are dealing with wave velocities here, and not just the particles. --EMS | Talk 00:10, 28 January 2006 (UTC)
 * Thank you. That truely was not my fault. (Beacause that word "Estimate" something about math-or-physics was taught by my professors to me and maybe misunderstand from we Taiwanese textbooks from America. (HHHeer...be humorous a monment...^^)
 * About everything about those questions of S.R.,I need to think alone for a long time. I've been learning Einstein.
 * (We Chinese cultures do not actually clarify "Calcualte" and "Estimate". Sorry but that makes you confused.><")By the way,thx
 * --HydrogenSu 08:20, 28 January 2006 (UTC)

In a few days,I proposed my new opinions as the followings.


 * The "phase" velocity means that particles as sets of waves(Q.M.'s wave-pocket) and vibrates in Y axis (represnts as heights) only. The famous English physist,P.A.M. Dirac,truely said on his book named of P.Q.M. :Waves with harmonic oscillators,and that of the opposite either. But he had never said this kind of concept already violated Special Theory of Relativity. Because of : the physical action which something vibrates in Y axis,it cannot represent as "the speed of wave-pocket travelling in X axis". Hence,alough my previous formulas proposed in a few days before which were got by $$\mathcal E=mc^2 $$ so that phase velocities can be greater than those of light but still not violate S.R. And speaking another,I feel we don't need to use Q.M. to think about this question with a good acient Chinese words:"Killing smaller animals within worse weapons;killing gohsts within a pices of paper-golden-money". How do you think?.....

--HydrogenSu 13:15, 29 January 2006 (UTC)

To HydrogenSu - These questions should be asked at Reference desk, not on the talk page of an article. PAR 20:36, 29 January 2006 (UTC)
 * All right. Thanks for reminding.


 * About previous talking of "velocities which eliminate each others" by EMS,I would say is we might consider two objects' some other phisical properties.
 * Like masses,accerelations,...etc. I just take the simplest for instance. If two particles' velocities eliminate exactly,that doesn't represent as "stopping". 'Cause the masses are not must the same exactly. If we use "Vector Methods" to analyse,it gives
 * $$\mathcal ,m_{a} v_{a}+m_{b} v_{b}=0, $$ when wanting objects "both" stop.
 * Only if the masses are the same value and the velocities are too,can they both stop. If not,there exists some momentum exchanging each others remainly.--HydrogenSu 12:34, 30 January 2006 (UTC)
 * Your conclusion is mistaken even in classical mechanics, and I see no good reason to clarify it here. You have wasted enough bandwidth on this business.  This page is to discuss issues related to the article, not to educate someone in relativity.  --EMS | Talk 01:13, 1 February 2006 (UTC)
 * Could you please tell me why my question need to be sloved by quantum mechanics but not relativity? I keep memory of an inserted question copied from my book's exercise that is:
 * "Find a relativistic particle's $$\mathcal Vg $$ and its'' $$\mathcal Vp $$."
 * Had already said of "a relativistic particle's...". By the way,I know that I truely made something about talking polite and was rude too much. I apology now. :) In fact,I'm glad to discuss with you. Wanting to read your again reply. (I didn't educate someone but expressed my opinions about phase and group velocities.)--HydrogenSu 20:52, 1 February 2006 (UTC)

Criticism of Relativity Theory
I'm not sure about this. I left the section in, because it seems there's a real NPOV here- there really are quite a lot of people who don't understand relativity and make honest but usually ignorant criticism of the theory. Perhaps we should move it into a separate article? (Having said this, I am quite reluctant to do this, but generally the experience in the wikipedia of this kind of thing has not been too bad at all, but nevertherless I am still a bit nervous.)WolfKeeper 01:26, 2 February 2006 (UTC)

The phrase "His 'proof' that Relativity theory is inconsistent has not been in any way supported by other scientists or experimental evidence." is incorrect, but it's a bit subtle. I plan to write a part about Dingle and reactions in twin paradox (that's what he focussed on), but I haven't come around doing that yet. Now I correct that phrase to "special relativity" and I turned the phrase around, as proof of absence is hard to give. That should make it quite correct IMO, and keeps it with the subject matter of this article. Harald88 11:45, 2 February 2006 (UTC)


 * The section that starts "The German scientist group g.o.mueller..." in the current revision is very odd indeed. It's also pretty incoherent. It looks like it's been machine translated from German (or possibly Italian) without any editing at all. It appears to be a POV rather than a serious attempt to add to a critical analysis of the issues; the suggested search for a link (and why not the link itelf?) at times out, so I can't do a better analysis of this. The Google cache of this page is most peculiar.  --Alex 21:20, 2 February 2006 (UTC)

Lorentz Transformations
Quote from this article:

Then the Lorentz transformation specifies that these coordinates are related in the following way:
 * $$t' = \gamma \left(t - \frac{v x}{c^{2}} \right)$$


 * Good day.I cannot be cleared for this formula. More details:why does $$(t - \frac{v x}{c^{2}})$$ (Especially in term $$(\frac{v x}{c^{2}})$$.) Is it about the speed of light,messages transported?


 * I am going to go my professor's class about S.R. But he puts some important part near the end of the Modern Physics class. Hope someone can tell me that yo. (Yo is a Chinese pronunciation for using of expressing stronger,not "I" in Spanish.) --HydrogenSu 18:19, 2 February 2006 (UTC)


 * Picture two coordinate systems, one moving in the x-direction relative to the other. The two origins overlap at time t=t'=0.
 * Let's imagine that there's an observer at the origin of the unprimed frame and a clock that emits a flash of light every second at the origin of the primed frame. As the primed frame moves away from the unprimed origin, not only does it's clock appear to tick slower (the spacing between the flashes is larger because the clock is moving away), but it's time is also delayed because the flashes take a nonzero amount of time to travel from the clock to the observer.  The first term accounts for the first effect, and the second term for the latter.
 * It's hard to describe well without diagrams, but try drawing it yourself with some sample clock-flash wavefronts. In fact, I found when studying this that it's impossible to understand without drawing a diagram at every important event.  &mdash; Laura Scudder &#9742; 18:36, 2 February 2006 (UTC)


 * The term that bugs you creates an effect called the relativity of simultaneity. Imagine a light clock:   |<>|.  At rest, the light will go back and forth between the bar characters (which act as mirrors in this discussion) in a time of d/c in each direction where c is the speed of light and d is the distance between the mirrors.  Now let's put this light clock in motion:  |<--->| --->.  In our frame of reference, when the light moves to the left, it goes between the mirrors in $$d/(c + v)$$ (where v is the speed of the clock) since the clock is moving towards the light.  Then when the light is going to the right, it goes between the mirrors in a time of $$d'/(c - v)$$.  So the "tick" is not consistent, but instead alternates faster and slower.  The difference in perception of how the clock operates is explained by "at the same time" being different in co-moving frames of reference.  BTW, because of the Lorentz contraction, $$d' = d / \sqrt{1 - v^2/c^2}$$ $$d' = d \sqrt{1 - v^2/c^2}$$, and this makes it so that the moving light clock ticks at the same average rate (for a given speed) no matter how it is oriented. --EMS | Talk 21:43, 6 February 2006 (UTC)


 * No, the above is not correct. The error is in saying that the velocities add as c+v or c-v. Velocities do not add in this way. (See the article). All clocks keep steady time, with the same time between ticks, although that time may vary (to you) depending on the speed of the frame (with respect to you). PAR 02:22, 7 February 2006 (UTC)


 * Oh yes it is correct. Within a given frame of reference, velocities add linearly even in relativity.  As seen in the observer's frame, the setup is moving at v.  Within that same frame of reference, the light is moving at c (as it always must).  So of course the time for the light to go between mirrors must be $$d' / (c \pm v)$$.  Now if you want to know the speed of the light with respect to the mirrors in the frame of reference of the mirrors, then you use the relativistic addition of velocities (which you refer to), and as expected will get c in either case.  The unsteady tick (based on each tick being when the light is reflected) is a very real phenomenon, and the $$c \pm v$$ business also appears in the relativity of simultaneity article.  The point is that the midtime between reflections of the same mirror is not simultaneous with the reflection off of the other mirror when the setup is in motion.  I advise you to think about that. --EMS | Talk 04:40, 7 February 2006 (UTC)


 * Ok, yes, you are correct, except for the statement $$d'=d\gamma$$. It should be $$d=d'\gamma$$, but I expect thats just a typo. I didn't account for the reflections correctly. I agree, the clock will have two different periods between ticks when viewed from the observer frame. Also, in your answer, saying that the velocities add linearly within a given frame of reference is not correct. The v+c term (for example) does enter into the calculation, but there is no physical object travelling with velocity v+c. PAR 02:50, 8 February 2006 (UTC)


 * As Einstein and others put it, their relative velocity is c-v (note that this is subtraction). Nowadays more commonly the jargon "closing speed" is used for that same concept. Harald88 18:49, 8 February 2006 (UTC)

Time Dilation
The sentence is not correct:
 * "Similarly, in the equation for time t', t is multiplied by gamma in the second non comoving frame. This may be interpreted as time proceeding more slowly when an object is moving relative to another frame of reference."

because then, it has to be a time "shortening" because 1 sec in rest frame would be more than 1 sec in moving frame.


 * That's exactly what time dilation is. Let's say that in my frame it takes 3 minutes to boil an egg, and x=0. From the point of view of a moving frame with a gamma of two; the elapsed time is 6 minutes. Hence time dilation. It's as simple as that.WolfKeeper 22:23, 30 March 2006 (UTC)
 * No: t' is the time-coordinate of the moving frame. t is yours. you are in t. t' is another frame in which you are not. In your picture a person in t' would have cooked two eggs, in 6 minutes (one after the other) while you have only time for one in 3 minutes. You can only compare the rest frame with the moving frame by using the equation. you cannot use the equation to go from t' to t by inverting it.


 * So if the moving frame thinks that it takes six minutes to boil your egg, then does the moving frame think your water is colder, or that the fundamental properties of eggs have changed? --Carnildo 05:32, 31 March 2006 (UTC)
 * Frame's don't think. People think. People think that time is dilated :-), but also the mass of the molecules in the egg will be higher; so in a sense the fundamental properties of eggs have changed. The temperature has gone down from the point of view of the moving frame though.WolfKeeper 13:52, 31 March 2006 (UTC)
 * It`s not possible to argue like that, because not the speed of particles defines their temperature but their momentum. It is very dangerous to argue in words.

the correct calculation would be:
 * $$ t' = \gamma (t- \frac{vx}{c^2}) $$
 * $$ t' = \gamma (t- \frac{v\cdot vt}{c^2}) $$
 * $$ t' = \gamma (1-\beta^2)t $$
 * $$ t' = \sqrt{1-\beta^2} t $$
 * $$ t' = \frac{1}{\gamma} t $$

The point is to express x in terms of v*t, then the equation contains not gamma but 1/gamma, so 1 sec in rest-frame is less than 1 sec in moving frame. --84.152.247.197 17:19, 14 February 2006 (UTC)

I think you've swapped around what t and t' refer to. Your maths looks correct to me from a quick glance at it; it's just more complex than it needs to be.

Thank you for your answer. You cannot swap around t and t' to go to the inverse transformation. You have to go from v -> -v for the inverse transformation. You are always in the rest frame t and the moving frame is always t'. So from every point of view you see the time running more slowly in the other frame. the only thing that I like to say is that you cannot "read" the equation for the time as the equation for x, because then you would make the wrong conclusions (when you watch the moving frame, then there time seems to go faster). You have first to use the insertion above.

SR, mass and E=MC2
I recently enjoyed actually reading Einstein's fourth 1905 paper ("does the inertia of a body depend upon its energy content?" from ). In that paper, Einstein says "If a body gives off the energy L in the form of radiation, its mass diminishes by L/c2. The fact that the energy withdrawn from the body becomes energy of radiation evidently makes no difference, so that we are led to the more general conclusion that The mass of a body is a measure of its energy-content; if the energy changes by L, the mass changes in the same sense by L/9 × 1020, the energy being measured in ergs, and the mass in grammes." (emphasis mine).

This - the idea that mass and energy are the same thing - has always seemed to me to be one of the key and unique insights of special relativity - but the article here, and other articles on the subject, seem to talk only about the "mass change of radiation" when discussing E=mc2 - the "consequences" section of this article doesn't mention it at all.

Is there a reason that I don't see why this generalized equivalence shouldn't be more strongly featured in the articles talking about special relativity? --Alvestrand 09:21, 18 February 2006 (UTC)


 * First of all, mass and energy are according to Einstein not exactly the same thing, and I agree. Energy and mass are different concepts, but mass = energy/c^2. When normalizing to c=1 they become numerically equal.
 * Secondly, that equation is not SRT; Einstein showed that SRT can be used to derive it. I have also seen derivations without SRT. Thus it looks appropriate to me that in this article it's not much discussed.
 * However, I saw somewhere the suggestion to write a separate page about the history of E=mc2. That would be a very good idea, IMO.
 * Cheers, Harald88 07:27, 2 March 2006 (UTC)

Redunant (sic) second postulate - edits by EnormousDude
This article is not a place to state a personal opinion. Not everyone agrees that the second postulate follows from the first. A separate section discussing the fact that some believe the 2nd postulate to be redundant is more appropriate than stating an opinion as fact. Alfred Centauri 02:52, 16 March 2006 (UTC)


 * On the other hand, the second postulate is frequently misstated. I edited the "Postulates of special relativity" after reading this article on PhysOrg.com
 * http://www.physorg.com/news11829.html
 * One of the points that Baierlein makes, is that relativity is generally taught using a version of the second postulate which is far less intuitively plausible than the second postulate as originally formulated by Einstein. I hence replaced the second postulate text with an exact quote and added comments.
 * Minor Crank 12:42, 25 March 2006 (UTC) (aka 67.163.106.133 before I created a user name)

The exact quote you contributed comes from the introduction. Later, Einstein writes "These two principles we deﬁne as follows: -" and "2. Any ray of light moves in the “stationary” system of co-ordinates with the determined velocity c, whether the ray be emitted by a stationary or by a moving body." Contrast this with his earlier statement that "light is always propagated in empty space with a definite velocity c which is independent of the state of motion of the emitting body". See the difference? In the former, he refers to a co-ordinate system and a determined speed while in the later, he refers to empty space and a definite speed.

Earlier, Einstein writes "Let us take a system of co-ordinates in which the equations of Newtonian mechanics hold good. In order to render our presentation more precise and to distinguish this system of co-ordinates verbally from others which will be introduced hereafter, we call it the stationary system."

IMHO, Einstein here identifies 'stationary system' with what we now call an 'inertial system'. Taken together with his 2nd principle, as he defined it above, Einstein does appear to assume that the measured speed of light in an inertial system of co-ordinates is c.

I referred to and  for the quotations. Alfred Centauri 16:25, 25 March 2006 (UTC)


 * The actual demonstration of the fact that the measured speed of light in the "moving" system of coordinates is c does not take place until Section 3, "Theory of the Transformation of Co-ordinates and Times from a Stationary System to another System in Uniform Motion of Translation Relatively to the Former", where Einstein writes: "We now have to prove that any ray of light, measured in the moving system, is propagated with the velocity c, if, as we have assumed, this is the case in the stationary system; for we have not as yet furnished the proof that the principle of the constancy of the velocity of light is compatible with the principle of relativity."
 * Einstein follows this statement with a demonstration that a spherical wave emitted in the "stationary" system with velocity c at time t = τ = 0, when the origins of the two coordinate systems coincide, appears also to be a spherical wave with velocity c in the "moving" system.
 * Clearly, Einstein did not include invariance of the velocity of light as measured by any inertial observer as part of his starting assumptions.
 * Minor Crank 00:58, 26 March 2006 (UTC)

Please re-read the very quote you have provided. Einstein assumed that the 2 principles were true but had yet to prove that they were not contradictory. That is, it is not at all clear at the outset that there is a co-ordinate transformation that is compatible with the two principles that he defined earlier. I quote from section 3: "With the help of this result we easily determine the quantities $$\xi, \eta, \zeta$$ by expressing in equations that light (as required by the principle of the constancy of the velocity of light, in combination with the principle of relativity) is also propagated with velocity c when measured in the moving system" (emphasis is mine). Einstein states quite clearly here that the notion that light is progagated at the velocity of c in the moving system is required by the combination of the 2 principles. Thus, IMHO, section 3 proves only that there is a transformation that is compatible with the 2 principles. Alfred Centauri 06:20, 26 March 2006 (UTC)


 * Let us look at Einstein's use of the second postulate.
 * 1) We are agreed that the introductory statement did not include any mention of invariance of c as measured by the "moving" observer.
 * 2) In Section 2, Einstein re-states what he regards to be the principle of the constancy of the velocity of light: "Any ray of light moves in the “stationary” system of co-ordinates with the determined velocity c, whether the ray be emitted by a stationary or by a moving body." His arguments in this section use only this principle.
 * 3) In Section 3, he continues using only this limited assumption: "...by inserting the arguments of the function tau and applying the principle of the constancy of the velocity of light in the stationary system" (italics mine). He does not assume correctness of the principle in the moving system.
 * 4) Continuing in Section 3, Einstein writes, "With the help of this result we easily determine the quantities xi, eta, zeta by expressing in equations that light (as required by the principle of the constancy of the velocity of light, in combination with the principle of relativity) is also propagated with velocity c when measured in the moving system." Einstein continues carefully to distinguish what he terms the "principle of the constancy of the velocity of light" from the more general notion that light might be propagated at c in the moving system. Rather, he states that the following paragraphs must establish that fact.
 * 5) Einstein states: "We now have to prove that any ray of light, measured in the moving system, is propagated with the velocity c, if, as we have assumed, this is the case in the stationary system..." Einstein repeats that his starting assumptions included only constancy of c in the stationary system. Einstein proposes to show that if c is constant in the stationary system, then c must be constant in the moving system.
 * 6) "...for we have not as yet furnished the proof that the principle of the constancy of the velocity of light is compatible with the principle of relativity." Einstein continues to use the term "principle of the constancy of the velocity of light" in exactly the sense in which he expressed it in the introduction.
 * 7) Einstein shows that
 * x^2 + y^2 + z^2 = (c^2)(t^2)
 * transforms to
 * xi^2 + eta^2 + zeta^2 = (c^2)(tau^2)
 * 8) The demonstration that light travels at c in the moving system "...shows that our two fundamental principles are compatible", by which Einstein means the principle of relativity and the principle of the constancy of the velocity of light, still referring to the second principle in the original sense in which he stated it.
 * 9) Concerning Section 3, you wrote: "Einstein states quite clearly here that the notion that light is progagated at the velocity of c in the moving system is required by the combination of the 2 principles." I agree perfectly, the two starting principles being the principle of relativity and the principle of the constancy of the speed of light in the stationary system. The notion that light is propagated at the velocity of c in the moving system is derived from the combination of the two starting principles.
 * Minor Crank 10:46, 26 March 2006 (UTC)


 * 10) You wrote: "IMHO, Einstein here identifies 'stationary system' with what we now call an 'inertial system'."
 * I disagree. Einstein very deliberately chose as his definition of 'stationary system' one with which any of his (almost universally aetherist) contemporaries would be comfortable, namely "a system of co-ordinates in which the equations of Newtonian mechanics hold good."
 * Obviously, a 'moving system' would be one in which the equations of Newtonian mechanics might possibly be violated. To an aetherist, such a scenario would make perfect sense, and many experiments at the time were directed towards detecting such violations. On the other hand, if you are at rest with respect to the aether, no motion of an emitter body could possibly alter your measurement of the velocity of light being radiated. Einstein's statement of the second law was carefully worded to be completely acceptable to his aetherist contemporaries.
 * Minor Crank 16:15, 26 March 2006 (UTC)

If, as you claim, Einstein derived the result that light is propagated at the velocity of c in the moving system, then the assumption that this result holds cannot be used in the derivation of this result, right? Yet, in section 3, immediately after establishing the form of the transformation for the time coordinate &tau; in the moving system, Einstein writes "For a ray of light emitted at the time &tau; =0 in the direction of the increasing &xi;


 * $$\xi = c \tau$$..."

Let's summarize step by step where we are at this point:

(a) Einstein assumes that the ray of light is emitted from the origin of the moving system of coordinates (&tau;, &xi;, &eta;, &zeta;)

(b) By applying the 2nd principle only, that the speed of the light ray is c in the stationary system of coordinates (x, y, z, t), he derives the form of the transformation &tau;(x',y,z,t).

(c) By applying the 1st principle only to (b), that the speed of the light ray must also be c in the moving system of coordinates, he derives the transformations for &xi; &eta; and &zeta.

So, at this point, Einstein has established the form of the transformations from the coordinates of the stationary system to the coordinates of the moving system based on the assumption that a ray of light emitted by a stationary object in the moving system propagates at c in both systems. I suppose one could say that this assumption is derived from the 2 principles but, IMHO, that is a stretch. Look at it this way, this is a simple case of "If A AND B THEN C" - if the 1st principle is true and if the 2nd principle is true then then the speed of light is c in the stationary and moving coordinate systems. Case closed - nothing else needs to be said. The result has been 'derived' and no further proof is needed as long as one assumes that the 2 very reasonable principles are true. So what is the rest of the paper for?

Clearly, Einstein needs to show that the the two principles are not contradictory. To show this, he first assumes the 'derived' result that the speed of light is c in both coordinate systems. Thus, contrary to your point (8) above, he cannot show this result as he assumes it to be true from the outset. Instead, what he shows is that the coordinate transformation derived from this assumption is consistent thus establishing that the 2 principles are compatible.

Once again, I think it is quite clear that Einstein assumed the constancy of the speed of light in both systems in order to derive the coordinate transformations which he then showed to be consistent proving that the two principles are compatible. On the other hand, time dilation, length contraction, etc. are quite clearly derived results. That is, there were no starting assumptions with respect to these results. Alfred Centauri 18:05, 26 March 2006 (UTC)


 * We seem to be in some danger of arguing in circles here...
 * I've just emailed Prof. Baierlein, who was the subject of the article in PhysOrg that I cited above http://www.physorg.com/news11829.html
 * His email address (slightly modified to deter spambots) is Ralph.Baierlein AT nau.edu
 * If we BOTH write him, maybe Prof. Baierlein would step in and offer his insights, at least on a private basis. Could you do so? Thanks!
 * If I have a chance, I'll try to get to the university library to obtain a copy of Prof. Baierlein's article in AJP, and I'll figure some way of getting you a copy.
 * This is what I wrote:
 * Dear Dr. Baierlein:
 * Are you familiar with Wikipedia, the online freely editable community encyclopedia?
 * Please refer to the Wikipedia article on special relativity:
 * http://en.wikipedia.org/w/index.php?title=Special_relativity
 * In response to your article in AJP, I changed the discussion of the second postulate in the above article from
 * Second postulate (invariance of c): Light is always propagated in empty space with a definite velocity c that is independent of the state of motion of the emitting body or on the state of motion of observer measuring it.
 * In other words: The speed of light in vacuum, commonly denoted c, is the same to all inertial observers, and does not depend on the velocity of the object emitting the light. An observer attempting to measure the speed of light's propagation will get the same answer no matter how the observer or the system's components are moving.
 * to
 * Second postulate (invariance of c): Light is always propagated in empty space with a definite velocity c that is independent of the state of motion of the emitting body.
 * Most current textbooks mistakenly include a major derived result, that the speed of light is independent of the state of motion of the observer measuring it, as part of the second postulate. A careful reading of Einstein's 1905 paper on this subject shows that, in fact, he made no such assumption. The power of Einstein's argument stems from the manner in which he derived startling and seemingly implausible results from two simple and completely reasonable starting assumptions.
 * One of the most highly counterintuitive of these results (and, as stated above, commonly included in statements of the second postulate), is that the speed of light in vacuum, commonly denoted c, is the same to all inertial observers. An observer attempting to measure the speed of light's propagation will get the same answer no matter how the observer or the system's components are moving.
 * As "Minor Crank", I am currently engaged in debate with another member of the Wikipedia user community, "Alfred Centauri", over whether my change was a proper edit. We are reading the same 1905 article and coming to opposing conclusions.
 * I was wondering if you could spare a few minutes to enter the discussion and offer your insights? "Alfred Centauri" and I are currently engaged in discussion topic 36.
 * Thank you very much!
 * Minor Crank 18:31, 26 March 2006 (UTC)
 * Minor Crank 18:31, 26 March 2006 (UTC)

One e-mail should be sufficient. If not, I will e-mail him also.

BTW, I don't really consider this a debate over whether your edit is appropriate. If I truly thought it to be inappropriate, I would have reverted your edit first and then explained why on the talk page. In any event, the historical wording versus the modern wording of the 2nd postulate is certainly an appropriate topic for this article.

Where we disagree appears to me to be with the use of the word 'derive' and what constitues a 'startling' result. If we assume that the speed of light is c in a coordinate system in which Newtonian mechanics hold regardless of the state of motion of the emitting body AND if we assume that in uniformly moving coordinate systems, Newtonian mechanics hold, it follows that the speed of light is c in uniformly moving coordinate systems. This is an immediate and purely logical conclusion - and not a particularly startling one, IMHO.

I suppose the reason I'm pushing back here is that I associate the word 'derive' (in this context) with some mathematical process as in the way the transformation equations are derived. Thus, I would prefer that the entry on the 2nd postulate say something more along the lines of "That the speed of light is measured to be c by all inertial observers is a logical consequence of the combination of the principle of relativity and the principle of the constancy of the velocity of light". Alfred Centauri 19:26, 26 March 2006 (UTC)


 * From your modern perspective, I don't doubt that the constancy of the speed of light in moving coordinate systems seems immediate and obvious. Historically, however, this was not so, and many experiments were conducted in an attempt to detect the consequences of movement through the aether, by Roentgen, Eichenwald, Bradley, Wilson, Arago, Fizeau, Airy, Michelson and Morley, Trouton and Noble, etc.
 * The conviction that there should be measurable consequences of movement through an aether was great, and Einstein was careful to frame his starting postulates in such a way that his paper would not suffer immediate rejection. Little by little, through inexorable logic, Einstein leads the reader to an abyss, either to accept or reject his conclusions. To early 20th century physicists, the constancy of c in all inertial frames as a logical consequence of seemingly innocuous starting assumptions was indeed one of many startling results in Einstein's paper.
 * However, it has been over a century since Einstein's seminal publication. To what extent should we retain the historical perspective? From a modern standpoint, Einstein's approach is very "clunky". Several alternative derivations of far greater elegance exist.
 * For example, starting from the first postulate alone, and understanding that any reasonable set of transformations must form a group, then one finds that there exist only two sets of transformation laws that satisfy the principle of relativity. These are the Galilean and Lorentz groups. If the universe follows Galilean relativity, then there is no upper speed limit to the universe. If the universe follows Lorentzian relativity, then there must exist an upper speed limit. Experimentally, we observe that an upper speed limit exists; therefore the universe must follow Lorentzian relativity. The role of the second law is extremely limited in this development of SR. Basically, the second law exists only to establish the value of the upper speed limit. SR is purely a geometric theory in this development, and light has no special role in its derivation. The velocity of light is observed to correspond rather closely with the upper speed limit, but that's merely a consequence of photons' being either massless or very nearly so.
 * So, should we abandon Einstein's primitive, clunky derivation in favor of one of the modern approaches? Perhaps I am being a Luddite, but I don't think so...
 * Minor Crank 22:54, 26 March 2006 (UTC)

Good points that you make here. This is an interesting read. I found this particularly interesting:


 * "Thus they [Poincare and Lorentz] believed that the speed of light was actually isotropic only with respect to one single inertial frame of reference, and it merely appeared to be isotropic with respect to all the others. Of course, Poincare realized full well (and indeed was the first to point out) that the Lorentz transformations form a group, and the symmetry of this group makes it impossible, even in principle, to single out one particular frame of reference as the true absolute frame (in which light actually does propagate isotropically). Nevertheless, he and Lorentz both argued that there was value in maintaining the belief in a true absolute rest frame, and this point of view has continued to find adherents down to the present day."

Yes, it is hard to shed long held notions. Alfred Centauri 00:15, 27 March 2006 (UTC)


 * I received two emails from Prof. Baierlein including a pdf of a proof version of his AJP article. However, he was very explicit in stating that I should not redistribute the pdf because of copyright restrictions (Sorry). I've uploaded the two emails that he sent me to my daughter's web site http://rosemarysgallery.home.comcast.net . Scroll down four inches below the list of images, and you will see two underscores "_ _". Each of these is a link to one of Prof. Baierlein's emails. After you've accessed the emails, let me know so I can delete the links.
 * It is evident from the AJP article that Prof. Baierlein would say that I had an incorrect emphasis in my wiki edit. The second postulate as commonly stated today is not wrong; rather, it has shifted in meaning since Einstein's day.
 * I believe I should be able to quote a few paragraphs of the AJP article without violating the bounds of fair use:
 * Today, the primary meaning of the phrase is that, given a specific burst of light, the burst's speed is measured to have the same numerical value in all inertial frames. That is, the speed is constant with respect to changes in the reference frame in which it is observed.
 * A secondary meaning also exists: in any given frame, bursts of light from sources with different velocities all have the same speed. That is, the speed of light is constant with respect to changes in the source’s velocity.
 * When the typical contemporary textbook uses the phrase, "the constancy of the speed of light," it intends that both the primary and the secondary meaning apply.
 * In the years immediately preceding 1905 and in Einstein's seminal paper, the phrase, "the constancy of the speed of light," meant only that the speed of light is independent of the source's velocity.
 * To derive the Lorentz transformation, Einstein used only the principle that the speed of light is independent of the state of motion of the emitting (or reflecting) body and the relativity principle (the laws of physics are the same in all inertial frames).
 * To take as a postulate that the speed of light is constant relative to changes in reference frame is to assume an apparent absurdity. . . . No wonder, thinks a student, that we can derive other absurdities, such as time dilation and length contraction, from the premises. Far better to start much closer to where Einstein started and to derive the logical consequence that the speed of any given light pulse has the same value in all inertial frames.
 * It's a bit late right now for me to make changes to reflect Prof. Baierlein's critique, but maybe tomorrow I'll have time to revise my edit, and you can check it over? Thanks!
 * Minor Crank 05:56, 28 March 2006 (UTC)
 * It's a bit late right now for me to make changes to reflect Prof. Baierlein's critique, but maybe tomorrow I'll have time to revise my edit, and you can check it over? Thanks!
 * Minor Crank 05:56, 28 March 2006 (UTC)


 * BTW, the MathPages indeed have some of the most thoughtful commentary on relativity available on the internet. The author of the MathPages is an executive of a major corporation and prizes his anonymity. Back a few years ago, when I was helping Don Koks find a backup editor for the Usenet Physics FAQ http://math.ucr.edu/home/baez/physics/, I was able to do a whois on the site to identify the owner, and unsuccessfully tried to recruit him for FAQ duties. Shortly afterwards, it no longer was possible to get any useful whois information...
 * Minor Crank 06:13, 28 March 2006 (UTC)


 * The pdf that Prof. Baierlein sent me is watermarked, and if his proof copy "got out into the wild" there would be absolutely no doubt that he was the source. But if I make a pdf from a photocopy, that should protect him from any liability.
 * Minor Crank 12:24, 28 March 2006 (UTC)

Thanks! I've saved the e-mails and will now take a look at them. Alfred Centauri 14:30, 28 March 2006 (UTC)

OK, I downloaded Prof. Baierleins' paper. Having reflected on our previous discussions and then quickly reading this paper, I believe I can better summarize my position on this. I agree that Einstein phrased the 2nd postulate in a way that is more restricted than the modern phrasing. And, I agree that the modern phrasing of the postulate is actually is a logical consequence of the original 1st and 2nd postulates.

However, I would like to point out that the following statement in Prof. Baierleins' paper:

"Second, Einstein wrote, 'Now, we have to prove [my italics] that, measured in the moving system, every light ray propagates with the speed V [we would write c]...'".

cannot be used as a evidence that Einstein was here proving the modern form of the 2nd postulate. As I have pointed out above, it is my opinion that here, Einstein is showing that the derived transformation equations are consistent. That is, in deriving the transformation equations, he writes:


 * $$\xi = c \tau$$..."

Recall that these are the coordinates of the moving system. Thus, Einstein is explicitly saying that the propagation velocity of light is c in both the stationary and moving coordinate systems. Since this is 'built in' to the transformation equations, why would he later need to prove this?

In any event, there is no need to 'prove' the modern form of the 2nd postulate in his paper at all as it is an immediate and logical consequence of the original 1st and 2nd postulates. Instead, Einstein needs to show that these postulates are not contradictory by demonstrating that there is a non-trivial transformation between the coordinate systems that is consistent with the postulates. Do you see my point? Alfred Centauri 15:23, 28 March 2006 (UTC)