Talk:Special relativity/Archive 20

Special relativity in accelerating frames
There seems to be some kind of dispute on this page over the question of applying special relativity to non-inertial frames. As I understand it, SR is only an approximation to GR when a is close to zero, so you can apply it, but strictly speaking it doesn't really apply. In particular the speed of light is not constant in non-inertial frames. Delaszk (talk) 08:52, 9 November 2008 (UTC)
 * No, SR applies to all accelerating frames, irrespective of magnitude of a. GR applies to gravity, which differs from acceleration in that the gravitational field induces a non-uniform acceleration. --Michael C. Price talk 09:58, 9 November 2008 (UTC)


 * No. SR perfectly applies to accelerated frames. See for instance "Differential aging from acceleration, an explicit formula" and . I also removed your nonsense statement: "Acceleration requires a component parallel to the existing velocity in addition to a component in the direction of the acceleration.". Furthermore, the locally measured speed of light is constant in all frames. DVdm (talk) 10:39, 9 November 2008 (UTC)


 * You say the phrase "Acceleration requires a component parallel to the existing velocity in addition to a component in the direction of the acceleration." is nonsense. What it should have said is that "Acceleration requires a force with a component parallel to the existing velocity ...". See Pages 80-81 of "Introducing Special Relativity" by W.S.C.Williams, published by Taylor and Francis. Delaszk (talk) 11:16, 9 November 2008 (UTC)


 * Also the The book "A Broader View of Relativity" by Hsu and Hsu repeatedly says that the speed of light as measured by an observer in a non-inertial frame is not constant.


 * The Lorentz transformations of SR do not apply to non-inertial frames whether the acceleration is uniform or not. According to the book - In 1943, Moller obtained a transform between an inertial frame and a frame moving with constant acceleration, based on Einstein's vacuum eq and a certain postulated time-independent metric tensor, although this transform is of limited applicabilty as it does not reduce to the Lorentz transform when a=0. Anyway this relies on extra postulates and so cannot be strictly called SR.


 * The book describes attempts throughout the 20th century to generalize the Lorentz transformations from inertial frames to non-inertial frames with uniform acceleration. It says these efforts failed to produce satisfactory results that are both consistent with 4-dimensional symmetry and smoothly reduce to the Lorentz transformations in the limit as accl tends to zero. The authors then claim that they have finally come up with suitable transformations for constant linear acceleration (uniform acceleration). They call these transformations: Generalized Moller-Wu-Lee Transformations. They also say: "But such a generalization turns out not to be unique from a theoretical viewpoint and there are infinitely many generalizations. So far, no established theoretical principle leads to a simple and unique generalization." Delaszk (talk) 11:06, 9 November 2008 (UTC)


 * See Can Special Relativity handle accelerations? --80.104.235.169 (talk) 11:13, 9 November 2008 (UTC)

There are several references in the article to the effect that SR only applies to inertial frames, whereas infact SR applies to accelerating frames as well. For example an analysis of Bremsstrahlung does not require general relativity, only SR. GR is required for a general coordinate transformations, which can describe acceleration which varies in space and time. --Michael C. Price talk 15:30, 9 November 2008 (UTC)


 * The confusion here results from trying to describe three different things with just two labels. The three things are:
 * A description of physics without gravity using just "inertial frames", i.e. non-accelerating Cartesian coordinate systems. These coordinate systems are all related to each other by the linear Lorentz transformations. The physical laws may be described more simply in these frames than in the others. This is "special relativity" as usually understood.
 * A description of physics without gravity using arbitrary curvilinear coordinates. This is non-gravitational physics plus general covariance. Here one sets the Riemann-Christoffel tensor to zero instead of using the Einstein field equations. This is the sense in which "special relativity" can handle accelerated frames.
 * A description of physics including gravity governed by the Einstein field equations, i.e. full general relativity.
 * I hope this clears things up. JRSpriggs (talk) 19:26, 9 November 2008 (UTC)
 * So you are agreeing or disagreeing with my statement? --Michael C. Price talk 19:48, 9 November 2008 (UTC)
 * To MichaelCPrice: No. You seem to be defining SR as something in between my first two theories. I do not believe that there is any coherent theory in between them. JRSpriggs (talk) 19:58, 9 November 2008 (UTC)
 * But you can use SR for analysing the hyperbolic path of an accelerating particle (with constant local acceleration), so SR can obviously be used for more than just inertial frames. --Michael C. Price talk 20:19, 9 November 2008 (UTC)
 * I think the key point is that you can use special relativity to describe all kinds of accelerated phenomena, and also to predict the measurements made by an accelerated observer who's confined to making measurements at one specific location only. If you try to build a complete frame for such an observer, one that is meant to cover all of spacetime, you'll run into difficulties (there'll be a horizon, for one). Markus Poessel (talk) 22:33, 9 November 2008 (UTC)
 * So, again, we seem to be saying that -- contrary to what the article says -- SR applies to more than just inertial frames, although it obviously can't describe frames in general. --Michael C. Price talk 06:27, 10 November 2008 (UTC)
 * Sure. Just trying to make that statement more precise. Markus Poessel (talk) 08:48, 10 November 2008 (UTC)

I changed the sentence about aceleration. The problem is that you cannot derive from the postulates of special relativity that an acceleration will not have a non-trivial effect. E.g. in case of the twin paradox, we know that you can compute the correct answer of the age difference of the twins simply by integrating the formula for time dilation along the trajectory of the travelling twin. This means that one assumes that at any instant, the twin on its trajectory can be replaced by an inertial observer that is moving at the same velocity of the twin. This gives the correct answer, as long as we are computing effects that are local to the travelling twin.

The fact that the acceleration that distinguishes the local inertial rest frame of the twin and the true frame of the twin does not have any additional effect follows from general relativity (it has, of course, been verified eperimentally).

Note that the discusion of the twin paradox on its own wiki page involves a twin undergoing an infinite acceleration from moving away from the Earth at a uniform velocity to toward the earth at a unifirm velocity. Then, the acceleration does cause an effect, but that's simply due the fact that you have to change inertial frames. Count Iblis (talk) 15:10, 10 November 2008 (UTC)


 * I have taken everyone's comments in this discussion and used them to create a section called Curvilinear coordinates and non-inertial frames in the article:Special relativity (alternative formulations). Delaszk (talk) 20:36, 10 November 2008 (UTC)

The paragraph in the lead was altered successively to indicate that SR applied to only inertial frames and locally around only geodesics. Neither of these statements is true (SR applies to some accelerating frames; SR is locally valid around any trajectory), so I reverted the paragraph --Michael C. Price talk 11:00, 7 February 2009 (UTC)


 * To MichaelCPrice: To apply SR to anything other than inertial frames, it must be made generally covariant. The theory described in this article is not generally covariant. While it is true that a generally covariant theory exists which is physically equivalent to what is described here, it is not what is described here. So you should revert to my version of the lead which is the correct version. JRSpriggs (talk) 20:58, 8 February 2009 (UTC)


 * It is not true that theories have to be generally covariant. Aside from that general point, the specific statements you want to revert to are incorrect.  Are you disputing that SR is locally valid around any trajectory / worldline (as the article now states), or do you insist that SR holds locally only around geodesics (as previously stated)?  Remember, as DVdm reminds us, to distinguish between the application of the principle of relativity and the application of SR itself.--Michael C. Price talk 23:11, 8 February 2009 (UTC)


 * I think that you have misunderstood my previous message. I did not say (and do not believe) that theories have to be generally covariant (although there are advantages (and disadvantages) to casting them into that form). I was saying that the version of SR described at length in this article is NOT generally covariant; most of the equations in the article are given in forms which can only be true in an inertial frame. Thus SR as described in this article does not apply to accelerating reference frames such as that described at Rindler coordinates. Thus in the presence of gravity, SR is only applicable to free falling reference frames, and then only to the first order in deviations of the position from the geodesic. JRSpriggs (talk) 06:35, 13 February 2009 (UTC)
 * Then the solution is not to remove the statement(s) that SR is applicable to non-gravitational situations, but to improve the article to make it clear that SR does apply to non-gravitational setups. i.e. that it applies to more than just inertial frames or locally around geodesics.--Michael C. Price talk 12:59, 13 February 2009 (UTC)

Why special?
There seems to be some disagreement as to why the theory is called special and what SR includes. That maybe because historically SR was restricted to inertial frames but now it is generally taken to be all of relativity except gravitation ie the physics of Minkowski spacetime. Perhaps we could formulate something to say along these lines. Martin Hogbin (talk) 11:26, 7 February 2009 (UTC)
 * Yes. I think you're probably right that the scope of SR has extended with time -- it is now basically non-gravitational mechanics / dynamics. --Michael C. Price talk 12:31, 7 February 2009 (UTC)

I rather think there is confusion between (1) why the theory is called special, and (2) what SR includes. In the former case a principle is applied to frames. In the latter a theory is applied to physical situations. Even if a principle is applied to a special kind of frames only, the resulting theory can still be applied'' in other frames. And I have removed the bizarre phrase "... or acceleration is constant with time and uniform in space." again. - DVdm (talk) 16:49, 7 February 2009 (UTC)
 * Yes I agree. The theory was originally called special because it was restricted to inertial frames but,as the article makes clear later on, it is now used to mean all of relativity except where there is significant gravitation.  This is what we should say. Martin Hogbin (talk) 17:24, 7 February 2009 (UTC)


 * I agree with the changes; but why was the link to inertial frames removed? Any objection to it going back in?
 * Also, if we're agreed with Martin's summary, that SR "is now used to mean all of relativity except where there is significant gravitation." then the article should say just this, since not knowing this is a constant source of confusion for newbies. --Michael C. Price talk 18:13, 7 February 2009 (UTC)


 * I left out the link to inertial frames since they are not mentioned as such in Einstein's book. The reference talks about uniform relative motion. I think inertial frames are mentioned and linked to sufficiently higher up in the intro. DVdm (talk) 18:34, 7 February 2009 (UTC)
 * The link to inertial frames would be helpful. Anyway, what about Martin's suggestion? --Michael C. Price talk 19:59, 7 February 2009 (UTC)


 * The link (inertial frames of reference) is present in the first line of the (i.m.o. already overlinked) introduction.
 * What about Martin's suggestion? "This is what we should say", is exactly what the 3rd paragraph says. So we clearly already say what we should say. I think this was just a factual remark, rather than a suggestion to make a change. DVdm (talk) 09:47, 8 February 2009 (UTC)
 * Actually the 3rd paragraph does not say that, but at least we seem agreed that it should say that. BTW, not overlinked IMO. --Michael C. Price talk 10:22, 8 February 2009 (UTC)
 * Clarified 3rd paragraph on both points. See edit comment. --Michael C. Price talk 10:42, 8 February 2009 (UTC)

The terms special and general relativity are derived from the principles of special and general covariance which give guidelines for the form of the laws of physics for tensor fields. The principle of special covariance implies the invariance of these tensor fields under isometric coordinate trasformations which is a special group of transformations as compared to general coordinate transformations. See "General Relativity" by Robert M. Wald, pg 59. —Preceding unsigned comment added by 99.237.29.67 (talk) 06:02, 27 February 2009 (UTC)

Mass–energy equivalence
The last paragraph in this section is wrong on a number of points. This paragraph if fixed does not supply any new information that is not contained elsewhere therefore I suggest it just be deleted. First of all, there is no such thing as conservation of invariant mass, only conservation of energy. The easiest counterexample is the annihilation of matter and antimatter since the resultant photons do not have rest mass. Also, there is nothing wrong with saying that matter and energy are convertible as is the case in matter/antimatter annihilation.

Somebody please fix this!


 * I agree. But I have a more radical suggestion.  Delete 99% of the whole section, which is just meant to be a resume of the the article Mass–energy equivalence. --Michael C. Price talk 00:58, 28 February 2009 (UTC)
 * PS Please sign your posts! --Michael C. Price talk 00:58, 28 February 2009 (UTC)


 * Especially sign your posts if you're wrong, which you are! Invariant mass, relativistic mass, energy, and momentum are all separately conserved in closed systems for single observers, in SR. Invariant mass is of course conserved in closed systems, and a pair of photons (so long as they aren't moving in precisely the same direction) has an invariant mass. In fact the two 511 kev photons from an electron-positron anihiliation AS A SYSTEM have an invariant mass, and it is 1.022 MeV-- the same as that of a system of a motionless electron and positron. As expected, since the anihilation conserves mass, energy and momentum. Yes, each photon has no rest mass as a separate object, but nobody claimed that the mass of a system can be calculated by adding up rest masses of its parts. That isn't even true for a system of moving massive objects (a container of hot gas) and it's not true for a container of photons, either. Photons add mass to systems, even if they don't have it themselves. It's all there in m2 = E2 - p2. Apply this to a single photon and E = p, thus m= zero. Apply it to two photons going in opposite directions and p=zero and thus m=E. The system has mass! As to whether or not the section should be condensed and summarized and redirected to mass-energy equivalence, it was expanded at the request of somebody who wanted a further explanation. Since the explanation as contained and carefully laid out is not understood by at least one reader (see above), perhaps it should be mostly left. I will leave it to others to explain how the invariant mass of systems is conserved via the energy-momentum equation, if you condense this.  S  B Harris 01:59, 28 February 2009 (UTC)
 * The unsigned poster is not wrong. For example, a statement such as Thus, the invariant mass of systems of particles is a calculated constant for all observers is highly misleading.  1st, I have no idea what the merit of "calculated" is here; 2nd, invariant mass is invariant under a Lorentz transformation but is not a constant with time (as the annihilation example shows) which is implied.  I say delete the whole goddam sorry mess and pray that it is explained more clearly at mass-energy equivalence. --Michael C. Price talk 06:17, 28 February 2009 (UTC)
 * "Calculated" was put in because invariant mass cannot be directly measured in many systems. In a bound system you simply weigh or measure the mass or something. But the concept also applies to unbound systems, and then it must be calculated. Yes, it's invariant, which means the same for all observers. And it's conserved in closed systems. Which means constant over time. The annihilation example shows this quite well. Mass of electron and positron is M before annihilation, and after annihilation, invariant mass of the system of two photons flying in opposite directions, is STILL M. If you disagree, let's see your math. (But I already put everything you need just above). S  B Harris 23:54, 3 March 2009 (UTC)
 * Explanation accepted. But the problem with the article is that it uses the term "mass" loosely.  Sometimes it means "rest mass", other times it means "relativistic mass".  "Invariant mass" is the catch-all, but that is often sloppily just called "mass". --Michael C. Price talk 00:40, 5 March 2009 (UTC)
 * Yes, there's a whole Mass in special relativity article due to these confusions. But all three types of mass are conserved in closed systems over time (in a given frame, which means for a single observer), so there's never any "conversion" of energy to mass, and mass never "disappears"-- unless you "let it out" ! The "conversion of mass to energy" is a popular misconception, which I've tried to kill, but it's a hydra. I don't know of very many wrong physics "facts" which are taught so widely. Sigh. As to the types of mass, relativistic mass is just total energy/c^2, so most people prefer total energy. It's obviously conserved. Rest mass is the same as invariant mass for single particles so the concept is easy. Invariant mass is the generalization of the "rest mass" idea to systems of moving particles. Again it's easy if the system is bound: it's just the system mass in the COM frame, where you could "weigh" it (like a container of hot gas). It's the rest mass of a bound system which has parts not at rest. It's conserved, obviously: the weight stays the same so long as you don't let any energy or mass out (I use the example of a nuclear bomb in a really strong box on a scale: blow it up and no change in weight. But it's very much hotter in the box). Only for unbound systems is "invariant mass" something "non-physical" and not something that isn't directly associated with common experience. S  B Harris 02:10, 5 March 2009 (UTC)
 * I share you angst over the mass - energy "conversion" misconception, but it's going to take a long, long time before people forget E=Mc^2. I assume you meant to say that "rest mass" isn't conserved, whilst "relativistic mass" and "invariant mass" are, since rest mass does vanish in (say) electron-positron annihilation whilst invariant and total relativistic mass (effectively total energy) don't change.--Michael C. Price talk 02:32, 5 March 2009 (UTC)
 * Rest mass of closed systems doesn't vanish so long as you keep one observer through the process. The rest mass of systems is called invariant mass. Since places where "rest mass" is said to disappear always end up being systems (either at both start or finish, or at least at the finish), it's more or less true that rest mass is conserved also-- at least in bound systems where "rest" has a physical meaning. Example, a single (π0) has a rest mass. When it decays to two photons, neither has a rest mass, but the two photon system has an invariant mass, and if you trap it in a bottle (photons bouncing around), a "rest mass" also (it would add weight to a container on scales). This system rest mass is conserved for any observer who starts out at the beginning of the reaction and follows it over time. Now, it is true that the sum of rest masses of things in a system isn't conserved ("rest mass" as measured by many observers, each at rest with the things in question, and reporting zero when they can't do it). But you can't measure the individual rest masses without changing frames multiple times, so this violates the "single frame" or "single observer" rule. There's no reason why the sums of rest masses that many observers measure, SHOULD be conserved. Conservation laws may allow any observer from start-to-finish of a process, but they don't allow you to change observers while the process is underway, or otherwise many conservation laws would not work! (only invariant ones would remain-- but conservation of energy and momentum as separate entities would have to go). As for E = mc^2, when written like that it only means that energy HAS mass (and vice versa). When it's written ΔE = Δm c^2 it means that somebody let some energy or mass out of the control volume, and thus the other went with it (usually energy is let out, and mass inside is now found to be smaller, as is the case when binding energy is released). It doesn't mean m was converted to E! The E let out took the m with it!  S  B Harris 01:00, 6 March 2009 (UTC)
 * Our disagreement is only over definitions and phraseology. I would say that the "rest mass" of a collection of particles is simply the sum of their rest masses.  Not conserved with time and different observers may disagree since they may not agree about the number of particles present at a particular time.  Better to reserve the term "invariant mass" for the conserved quantity.
 * I agree with your interpretation of E=mc^2 as I previously indicated. --Michael C. Price talk 08:28, 6 March 2009 (UTC)
 * Well, I don't know what the term "rest mass" of an unbound system of particles would be. However, the rest mass of a bound system doesn't agree with your definition, since it's defined as what mass we measure when the system is at rest (not necessarily the particles). So there's a rest mass of a proton or a C-12 atom, both of which are composites (collections of particles). And these rest masses by measurement are not the sum of rest masses of their components. This is the system invariant mass when defined that way (system mass when system p=0). So it has the virtue of being invariant and (of course) conserved. We have the need to talk of the rest masses of bound systems, because those are usually the masses that we're measuring. What else would we call them? Would you suggest that we cannot use "rest mass" as a term for the mass we measure for hadrons and atoms and baseballs and such? S  B Harris 01:15, 8 March 2009 (UTC)
 * maybe some mention of longitudinal and transverse mass would be appropriate. just-emery (talk) 10:00, 13 May 2009 (UTC)
 * To Em3ryguy: See the end of subsection Special relativity. JRSpriggs (talk) 23:46, 13 May 2009 (UTC)

Relativistic Speeds Linking To SR
Whenever I click a link talking about relativistic speeds, it always links to the special relativity page. The article, however, makes little to no mention about what relativistic speeds or velocities actually are. I suggest adding a sentence to the intro, adding a redirect sentence to the top, or adding a stub article about relativistic speeds. As it stands right now, there is no real way for a person to learn what the many references to relativistic speeds mean without consulting an outside source. Serge (talk) 07:18, 6 April 2009 (UTC)


 * Alternatively, the article on Relativistic speed could be enhanced. A speed is considered relativistic, if it is fast enough that relativistic effects become important, i.e. if $$\frac{v^2}{c^2}\,$$ is not negligible. However, the difficulty is that this is a judgment call depending on what you think is important. JRSpriggs (talk) 07:50, 6 April 2009 (UTC)

Einstein's 1905 derivation
It is obviously, self evidently, correct, as anyone who reads it can see. There were a few papers claiming that it is wrong over the years, but these papers are ridiculous.Likebox (talk) 17:29, 12 May 2009 (UTC)

Request
Would it be possible to more concisely define the term "relativistic velocity" somewhere in this article? The term "relativistic velocities" is used in the "Relativistic mechanics" section without explanation, and the term appears in other articles (such as in Containment field, Lorentz group and Gamma-ray burst emission mechanisms) as well. Perhaps some examples would be sufficient, giving the velocity where relativistic effects cause a 1% and 50% Lorentz contraction? Thank you.&mdash;RJH (talk) 19:30, 14 May 2009 (UTC)
 * See Talk:Special relativity. JRSpriggs (talk) 00:18, 15 May 2009 (UTC)

A.A. Ungar's gyration operator
Is this for real? Martin Hogbin (talk) 11:53, 19 July 2009 (UTC)


 * You are referring to the mention at the end of Special relativity to Gyrovector space. I have not seen it before, so I cannot be sure. However, it is plausible to me because I know that the future-pointing unit-vectors in Minkowski space form a hyperbolic (constant negative curvature) three dimensional space. JRSpriggs (talk) 18:18, 19 July 2009 (UTC)


 * Yes, I am referring to Gyrovector space. It just looks a bit suspect to me.  If you start following links most of them lead back to Ungar.  My maths knowledge is not good enough for me to decide but there is something about it that screams crackpot maths to me.  Try following some links and see what you think. Martin Hogbin (talk) 21:30, 19 July 2009 (UTC)


 * I've put the definition of the gyr operator into the article. So now, you can check yourself that the formula is correct by plugging in numerical values. Charvest (talk) 15:33, 3 September 2009 (UTC)

relativistic rocket and general relativity
A discussion of a relativistic rocket accelerating past a line of evenly spaced stationary synchronized clocks would be an obvious way to lead into general relativity without getting too technical. Since, from the point of view of the rocket, the clocks are becoming more and more out of sych, while at the same time the entire line is shrinking and  moving past the rocket, there is a point behind the rocket where the clocks 'pile up' and time slows to a halt. A kind of 'black hole'. I know of no simpler way of explaining the principles of special or general relativity. Lemmiwinks2 (talk) 22:31, 30 August 2009 (UTC)


 * See Rindler coordinates. JRSpriggs (talk) 15:21, 1 September 2009 (UTC)

Wrong citation of postulate
Starting with a reminder, Einstein's second postulate is as follows (both his formulations):

(*stets = every time; omitted in the other translation)
 * "light is always* propagated in empty space with a definite velocity c which is independent of the state of motion of the emitting body"


 * "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"

This light principle is "apparently irreconcilable" with the Principle of Relativity. Halfway in his derivations from these postulates, 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; 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.".

That makes sense as his light postulate does not pretend that light is propagated with the same velocity c in more than one system. Now, check that with the rendering in this article:

The Principle of Invariant Light Speed – Light in vacuum propagates with the speed c (a fixed constant) in terms of any system of inertial coordinates, regardless of the state of motion of the light source. (emphasis mine)

Do I need to point out that this article both wrongly describes and wrongly cites the second postulate? Note also that it does not make sense to prove a postulate. And who of you pretends that a "principle of invariant light speed" is "apparently irreconcilable" with the Principle of Relativity?!

Moreover, the theory concerns "the electrodynamics of moving bodies based on Maxwell's theory for stationary bodies ". I wonder if anyone else recognizes Maxwell's theory in either of Wikipedia's postulates.

Apparently it is a widespread error as it is also mentioned in the literature, see for example http://bjps.oxfordjournals.org/cgi/content/abstract/44/3/381 :

"It is still perhaps not widely appreciated that in 1905 Einstein used his postulate concerning the ‘constancy’ of the light-speed in the ‘resting’ frame, in conjunction with the principle of relativity, to derive numerical light-speed invariance".

Am I really the only one who noticed that the wrong citation produced a big misrepresentation?

Harald88 (talk) 03:03, 2 December 2009 (UTC)


 * That's a fair comment. For another published article on this subject, see Baierlein, Ralph (March 2006) "Two myths about special relativity", American Journal of Physics 74(3), pp. 193-195, section III. --  Dr Greg   talk  18:54, 2 December 2009 (UTC)


 * Thanks for the additional reference. As I'm rarely involved in editing anymore I'll just give here a constructive suggestion for what to put instead of the erroneous citation:


 * Light is propagated in empty space with a definite speed c which is independent of the state of motion of the emitting body [+ add a few additional references as cited here above].
 * [then add:]
 * From these two postulates follows that the speed of light must be invariant.
 * Harald88 (talk) 11:02, 5 December 2009 (UTC)

STR?
Is special relativity really alternatively known as 'STR'? I have never heard it called this... For stylistic reasons I find it very unsightly, as it is almost a disrespectful (though I am sure this was not the intention) way to open an article on one of the greatest and most beautiful theories ever developed by mankind.Spinachwrangler (talk) 06:04, 18 December 2009 (UTC)

Misstatements in Status section
The Status section had some historical misstatements, which I've fixed. It claimed that the Trouton-Noble and Michelson-Morley experiments led to special relativity, but in fact Einstein was unaware of them before 1905. It listed the Fizeau experiment as being an after-the-fact confirmation, but Einstein was aware of it before 1905. History of special relativity gives what I think is a correct and uncontroversial statement of the historical facts, and Special relativity contradicted it on these points. I've corrected the mistakes.--207.233.87.95 (talk) 20:26, 14 April 2009 (UTC)


 * The statement you make here above related to Michelson-Morley is untrue according to Pais. Harald88 (talk) 03:07, 2 December 2009 (UTC)


 * It is correct according to Polanyi who asked Einstein about it And also according to A P French IIRC. --Michael C. Price talk 12:02, 5 December 2009 (UTC)


 * Maybe so; Pais gave strong evidence to the fact that it is untrue (do you really believe that everything people say is true?!). It is safe to say that that claim by Einstein is disputed and therefore it should not be stated as fact (nor should indeed the contrary be stated as fact; thus I agree with removing such strong claims). Harald88 (talk) 07:52, 18 January 2010 (UTC)

Undid changes to section on time dilation and length contraction
I have reverted StradivariusTV's edits to the section for the following reasons:
 * The opening sentence is entirely wrong:
 * "Consider two events A and B which occur at rest in a certain reference frame S. Special relativity predicts that the time difference between A and B as measured in another reference frame S′ will be greater than that measured in S—an effect known as time dilation. Additionally, the distance between A and B as measured in S′ will be less than that measured in S; this is known as length contraction."
 * Remarks:
 * Events do not "occur at rest in some frame". Events just occur.
 * Special relativity predicts that the time difference between two colocal events (i.e. occurring at the same place in some frame S), as measured in another reference frame S' will be greater than that measured in S.
 * The above statement requires two events at the same place in frame S (i.e. Dx = 0), and therefore the distance between these events is zero, so these events cannot be used in the classical example of length contraction. The statement on length contraction requiring simultaneity in S' (Dt' = 0) would be reduced to the trivial 0 = 0. In fact, every quantity would be zero: Dx = Dx' = Dt = Dt' = 0. We wouldn't even have two distinct events A and B.
 * In short, there is no way you can use one single pair of events to explain both the standard time dilation and length contraction examples in one swoop.

I have kept the referenced muon example. DVdm (talk) 13:30, 1 January 2010 (UTC)
 * The original explanation provided an operational view, i.e. it worked with physical clocks and rods and it took great care to separate the pairs of events needed to apply the Lorentz transformation.

Some rephrasing/reorganization
The article clearly isn't in good shape; it's too long, too verbose at times, and confusing at other places. I've attempted a rewrite and reorganization of some sections, moving some (rather dubious, IMHO) material to Consequences of special relativity. Please comment. —Preceding unsigned comment added by 171.66.105.155 (talk) 07:39, 8 January 2010 (UTC)


 * That was a pretty wp:BOLD action. For easy reference, you made this edit to the current article, and this edit to Consequences of special relativity.
 * In order to put this article in better shape, you turned another article, which already was in a horrible shape, in an even worse shape (in your opinion) by sending "rather dubious (IYHO) material" to it. I had a look at that material and it doesn't look dubious to me. On the contrary, it's all standard and highly relevant in this article, and it has been living here for quite a long time under general consensus.
 * I propose we do the following:
 * Discuss what you find dubious about the material so we can remove any doubts by providing sources and/or removing what is considered dubious by consensus.
 * Restore some (or all) of the material to this article.
 * Revert Consequences of special relativity to its original state.
 * Discuss whether we need a separate article for Consequences of special relativity in the first place, i.o.w. whether we can perhaps move some of its remaining material in here, or just file for deletion.
 * Alternative proposal:
 * Revert both articles to their original state and discuss the changes you have in mind on the talk page before you actually implement them.
 * Discuss what we do about the article Consequences of special relativity.
 * Also, please sign up for a username and sign your talk page messages with four tildes ( ~ )? Thanks.
 * DVdm (talk) 09:44, 8 January 2010 (UTC)


 * I agree such a rewrite of this article is unnecessary. The changes so far seem largely to have made matters worse, where they've made a difference. The introduction in particular seems a lot worse, as do many of the changes to headings. And in what universe does c -> ∞ ?


 * I would support rolling back to the last version before this re-write was initiated. There are just too many changes to un-pick them otherwise. Then look at addressing individual concerns here first and reach some sort of consensus before making any more changes like this.-- John Blackburne (words ‡ deeds) 11:04, 8 January 2010 (UTC)


 * I'm the guy who made the edit (different IP, yes). I apologise about the anonymity, but I'm rather reluctant about such account (for personal reasons). Yes, I've been rather wp:BOLD. Now, I'm not particular about letting my edit as it was written stand, but about making the article better.


 * Let's summarise the changes I've made. I've rewrote (rather, paraphrased) the intro; reorganised the material into kinematics (Minkowski space, Lorentz transform, etc.), dynamics (momenta, Minkowski force, etc.), electrodynamics (Maxwell in covariant notation), and status (history, domain of validity, experiments), and cut out some material into Consequences of Special Relativity.


 * Now, I agree that Consequences of Special Relativity is very badly organized. I would be for removing/reorganizing the material somehow. I was not responsible for creating it; I just removed the material there because I didn't see anywhere better for it to be there.


 * The article as it stood before my edit was very haphazard:
 * Postulates
 * Lack of an absolute reference frame
 * Consequences
 * Reference frames, coordinates and the Lorentz transformation
 * Simultaneity
 * Time dilation and length contraction
 * Causality and prohibition of motion faster than light
 * Composition of velocities
 * Relativistic mechanics
 * The geometry of space-time
 * Physics in spacetime
 * Relativity and unifying electromagnetism
 * Status
 * I don't know about you, but I couldn't make sense of it, and I think I'm pretty qualified to judge that. For instance velocity composition is in "Consequences", "Composition of velocities", and "Physics in spacetime" ("we can turn the awkward looking law about composition of velocities into ..."). And there is a separate article on Velocity-addition formula (as ought to). I claim that an organization into kinetics and dynamics (as is conventially done for all physical theories) is more lucid.


 * Now, whether my rewritten text is clearer is an open question (I hope it is). And doubtless there was a lot of clear material in the original article. It was just very badly organized/mixed with less-than-clear material/overly detailed and needed to be cut into its own article.


 * For the record, I am biased in terms of abstract formalisms and theoretical physics. So my characterization of Minkowski space as "four-dimensional Euclidean space with a certain non-positive-definite metric" may not be as clear to those not as acquainted with mathematics. (But hey, I didn't write "flat pseudo-Riemannian manifold"...)


 * And, for the record, as to $$c\to\infty$$: yes, it's slightly misleading; of course Einstein's constant doesn't change. What it means, effectively, is you set terms involving 1/c^k as zero. This yields the classical limit of a relativistic formula. For instance if you Taylor-expand &gamma;mc^2, subtract off the constant mc^2, and keep only the leading-order term (i.e., discard negative powers of c), you get the nonrelativistic kinetic energy formula. This sort of trick is reasonably common in higher physics/math, like sending $$\hbar\to0$$ to obtain a (semi)-classical approximation of a quantum formula. Quickly Googling for "c to infty" gives me "non-relativistic limit c->infty" in Terry Tao's blog (you surely know Terry goddamn Tao, right?) and "The k->oo ~ c->oo limit is generally thought to correspond to classical geometry" (arXiv:hep-th/9310098). There are doubtless more. This bit is indisputably correct. —Preceding unsigned comment added by 171.66.105.135 (talk) 08:51, 9 January 2010 (UTC)


 * I fixed the indentation of your reply. You say you are reluctant about about an account (for personal reasons), but note that your IP-adress tells a lot more about you than some string like for example "DoeJohn", which you can choose freely, and which effectively hides your address for everyone. I have no problem with the c -> infinity. Let's wait for futher input from others. Please sign your messages with the four tildes ( ~ )? Thanks. - DVdm (talk) 13:57, 9 January 2010 (UTC)


 * Thanks for fixing my poor MediaWiki markup. And thanks about letting me know about the hazards of IPs. I'm refraining from further editing until we reach consensus. 128.12.66.182 (talk) 18:47, 9 January 2010 (UTC)

My own thoughts are the article in its previous state is much better. The main reasons are the order is better. By first laying out the principles and consequences, then starting on the mathematics at a gentle pace, it allows even a reader with only limited mathematics to appreciate what is involved. It proceeds at a steady pace so in theory you could work through it and pick up the subject.

Now the key information on reference frames, i.e. the principle of relativity is gone, as are the consequences which the reader might be familiar with. The first maths are some rather scary partial differential equations and the spacetime metric, with lots of fairly specialised vocabulary, content that is much better placed towards the end.

And the choice of headings seems a bit odd. Kinematics is not a widely used and certainly in special relativity which is mostly not a mechanics topic it seems misplaced, and as noted above means the order of the theory is rather odd. Putting the "Domain of validity" (the what ?) so high up is a bit odd too, it should be near the end.

Special Relativity need not be an advanced topic: it was a first term first year topic when I was at university, i.e. taught using high school maths. The article before this rewrite is much more suitable for a general audience, without skimping on the more advanced stuff. -- JohnBlackburne wordsdeeds 19:14, 9 January 2010 (UTC)


 * The usual approach to addressing this issue is to either have a "mathematical derivation" or "formal description" section later in the article (having trouble finding a sample article offhand), or to link to a "mathematics of X" article from a shorter "mathematical derivation" section in the main article (as with general relativity). Taking either content approach exclusively tends to result in a poor article (an article aimed at laymen tends to either make inappropriate approximations or miss important details, and an article aimed at being accurate tends to be inaccessible to most readers). --Christopher Thomas (talk) 21:45, 9 January 2010 (UTC)


 * SR is primarily a kinematic theory: most of its interesting consequences are from the Lorentz transformation. Special relativitic kinematics differs sharply from Galilean/Newtonian kinematics. Recall that kinematics is simply motion in the absence of forces (dynamics). This includes spacetime, its symmetries, and motion of particles in the absence of force (Newton's 1st law/geodesics). In Newtonian mechanics, spacetime has Galilean symmetry; SR replaces this wholesale by the Lorentz/Poincaré group, which is completely different (topologically and as Lie groups). Relativistic dynamics differs somewhat from Newtonian dynamics (2nd law), primarily because the kinematics has become radically different (everything becomes four-vectorized, etc.). But this is mostly cosmetic; Newton's second law still holds, suitably relativised. A quick Googling yields this page from lecture notes for an intro SR class, which clarifies that SR is primarily a kinematic theory.
 * The previous version of the article was divided into noncovariant notation versus covariant (four-vector) notation. I claim that notation is not a good way to conceptually organize a topic. Perhaps it's better pedagogy, but it ends up treating everything twice. There are many possible formalisms for SR: besides three/four-vectors, you can use quaternions, Clifford/geometric algebra, hyperbolic quaternions, gyrovectors, etc. to describe SR. arXiv:math-ph probably contains dozens more. As Feynman once said, any physicist worth his salt knows many different formalisms for the same physics. I do not advocate presenting only the high-level formalism. Certainly the three-vector formalism is useful. (For instance thinking of mass as a tensor, i.e., longitudinal/transverse mass, can be helpful in SR mechanics.) The topic needs to be presented in a coherent and non-dumbed-down fashion (unlike Intro to SR), presenting a reasonable subset of the gamut of possible formalisms, perhaps supplemented by Introduction to special relativity, Mathematics of special relativity, Quaternions in special relativity, etc.
 * I fully agree that SR can be understood in an elementary way. (I learnt it in 10th grade, FYI.) That, however, does not mean it's that elementary. (You still learn a lot about representations of the Poincaré group in your 2nd-year graduate QFT class.)
 * About domain of validity, etc.: I wasn't sure where to put all the non-mathematical/heuristic bits (history, consequences, experiments, etc.), so I just grouped them under a big Status section. And I figured that since this stuff is more elementary (less mathematical), it ought to come before the harder stuff. I'm not particular about this, though.
 * About any stuff that was (inadvertently) deleted: I have nothing whatsoever against reintegrating material from previous versions of the article. Removal of material was not my primary intention; I apologise if this is a big problem. 171.66.109.132 (talk) 16:12, 10 January 2010 (UTC)

My edit has been repeatedly reverted, not so surprising since I'm an IP user. I've been un-reverting them. To clarify, if consensus turns against me I have no problems with my edit being reverted. That, however, is not the case at the moment. 171.66.108.136 (talk) 21:53, 10 January 2010 (UTC)


 * I've replied to your post on my talk page with a few pointers about ways of getting articles revised. I respect your intent, and look forward to your contributions to the encyclopedia; however, as you're in the process of finding, it's easy to step on peoples' toes when making large-scale changes. My recomendation to you is that you voluntarily roll back the article to the state it was in before your edits as a show of good faith, as they have generated a considerable amount of controversy, and then make arguments on this page for specific changes (per the detailed advice in my reply). The result will be an article closer to what you want, that the other editors here will be more likely to accept as well. What's happening now is that you're acting with the best of intentions, but managing to step on a lot of toes, and a couple of rules as well. --Christopher Thomas (talk) 23:21, 10 January 2010 (UTC)
 * Yes. Pick out a username (it doesn't hurt), and then make edits a paragraph at a time. Don't just delete a whole section and say "wups, feel free to re-integrate it," and then take offense when somebody restores it. If you can't be bothered to say why you blanked out many sections, I surely can't be bothered not to start at the beginning and expect you to "reintegrate" the differential stuff you put in which didn't involve blanking.  S  B Harris 23:51, 10 January 2010 (UTC)


 * Just getting back to the topic, the varying IP from Stanford wrote "Perhaps it's better pedagogy...", and if that is the case (I've never taught SR so cannot say) the pre-rewrite version is perhaps more accessible too, which was my point. It is better for the average first-time reader, who is probably in high school or has a high school science education. Most will not get as far as the more advanced mathematics, or at least will take a long time getting to it. More experienced and expert readers who know a little of the subject or maths can skip over the first sections and go straight to the more advanced maths, or use the wikilinks to get to other more appropriate articles. They have no problems in either case, but the rewrite poorly serves the general reader.-- JohnBlackburne wordsdeeds 00:02, 11 January 2010 (UTC)

Before I reverted him, I skimmed over the IP's version to see whether there was any possibility that he might have actually improved the article. I found this in his version:
 * For example, in special relativity, the conserved momentum must be modified as

\mathbf p=m\frac{d(\gamma\mathbf x)}{dt} = \gamma^3m\frac{d\mathbf x_\parallel}{dt} + \gamma m\frac{d\mathbf x_\perp}{dt}. $$ This is a patently false and indeed ridiculous formula. JRSpriggs (talk) 09:02, 12 January 2010 (UTC)

Division of content
I do not understand the rationale for dividing this article into two different articles; this current article which presupposes knowledge of physics, and another introductory article for the general public. Wikipedia is for the general public, what's the use of an article which is basically a collection of formulæ? (Sorry if you've had this discussion before, couldn't find it) Sandman888 (talk) 17:01, 3 March 2010 (UTC)


 * Both articles are rather long, so it is best to separate them. As far as I am concerned, this article is introductory and the other one is trivial. Wikipedia is not just for joe-sixpack, it is also for enlightened people. JRSpriggs (talk) 20:30, 4 March 2010 (UTC)

Lead
Also, the current lead is terrible, this lead http://en.wikipedia.org/w/index.php?title=Special_relativity&oldid=83782793 is much better as it immediately draws the reader into the subject. Just a thought. Sandman888 (talk) 17:07, 3 March 2010 (UTC)


 * It's curious that for years the bizarre assertion that special relativity is "the physical theory of measurement in inertial frames of reference" has remained as the defining statement of the subject. Tim Shuba (talk) 16:19, 6 March 2010 (UTC)
 * Why is that so bizarre? Einstein got to SR by asking himself what had to be done to make Maxwell's equations the same for moving observers (moving interial frames). The answer turned out to be the Lorentz transformations for space and time. Now Einstein had the epiphany that perhaps this would need to be necessary for all laws of physics, not just Maxwell's equations: they're all the same in all inertial frames. As is (necessarily) the speed of light. Which means there are no privileged inertial observers. This requires the general application of the Lorentz transformations between frames and observers, and these transformations are not mere math tricks to get Maxwell's equations back, but ACTUAL statements about how the flow and start-point of timekeeping changes between frames, and how spacial measurements change, too. And that's it.  S  B Harris 19:10, 6 March 2010 (UTC)
 * It's bizarre to define relativity as simply a branch of metrology. It would be far better to define it as a theory of invariance of physical law, or perhaps say something like "space, time, and invariance..." as an initial definition. Regarding inertial frames, a clock can be taken on an arbitrary non-inertial path in flat spacetime between two events to measure a time difference ∆τ. I guess this idea is outside the domain of special relativity according to wikipedia. Tim Shuba (talk) 22:51, 6 March 2010 (UTC)
 * Ummm, I don't think it's "inside" the domain of SR according to anybody. Two non-colocal events (ie, spacially separated) don't HAVE a ∆τ that everybody agrees on. Any more than they have a spacial separation ∆x that everybody agrees on. The only thing (measure) that all observers agree on, is a combination of these two things, the space-time interval I, the square of which is given by (∆x)2 - (∆τ)2. (Using units where c =1). And no, I don't think SR is defined as "merely" a branch of metrology. It tells how changing intertial viewpoint, changes time and space. It's a philosphical question to say that it tells how measurement of time and space is changed. What's the difference between the measurement of the thing and the thing itself? Does space contract or just yardsticks? Does time go slower, or just clocks? Ultimately, it doesn't matter. All you have to tell you about these things are measuring tools (including your brain's time-sense and the length of your arms). So it doesn't really matter. S  B Harris 00:58, 7 March 2010 (UTC)
 * Two events on the trajectory of a clock can certainly be non-colocal, and of course the separation of these events will be timelike. Just take a stopwatch, move around arbitrarily until you are at a different place, and note the elapsed time ∆τ. Or calculate the lifetime (in its own non-inertial frame) of a charged particle moving in a magnetic field from creation until anihilation. Not part of special relativity? Seriously? As far as special relativity being a theory of measurement, what does that mean? Which theories in physics are not theories of measurement? If the answer is "none", then what is this meaningless fluff doing in the first sentence of the article? I've been astonished at this first sentence for some time, wondering if anyone making a critical analysis would possibly agree with it. Tim Shuba (talk) 02:12, 7 March 2010 (UTC)

Seriously, it's not part of relativity that there's some kind of "real" ∆τ between events. That ∆τ depends on who measures it. You can look at a stopwatch that moves from event P1 to event P2, and note the elapsed time on the watch, but there's nothing "special" or real about that time. Some other watch in another frame, if started when the first watch crossed P1, and stopped when the first watch crossed P2, could easily measure a different time-interval between the two events. And of course an observer in a different frame would see a different space-interval also. An example is the muon. They have a half-life of 2.2 μsec in their rest frame. Let's pretend they all live exactly that long-- this would allow them to travel no more than 660 m = .66 km at the speed of light. But muons made in the upper atmosphere travel 10 times that far, or more (often far more). So let's let the muon be the stopwatch, and P1 be its creation from a pion (created by a cosmic ray proton hitting an air atom), and P2 the destruction/decay of the muon, to an electron + 2 neutrinos. In the muon frame, the stopwatch between creation and decay reads 2.2 μsec, but there's nothing more "real" about that time. In the Earth's frame, assuming a muon speed with a tau factor of 10, the time is 22 μsec from creation to destruction, and the distance traveled is 6.6 km. For the muon, the distance is only 0.66 km, but it has no problem making it to the ground from its own viewpoint, because for the muon, the Earth's atmosphere is relativistically compressed/shortened, and is far thinner. What the Earthlings see as 6.6 km flight, the muon sees as only a 0.66 km flight, but since it sees a 10x compressed atmosphere, all is well. The space-time interval in both frames is the same, and it is the only "real" thing thing that everybody agrees on. Not the distance or the time, but a combo of the two. S B Harris 03:10, 7 March 2010 (UTC)
 * Debate about the "reality" of particular quantities is a road to metaphysical mush, so I'll try to avoid that, but you are incorrect in some of your statements. The invariant proper time τ should not be confused with a coordinate time t. For constant velocity (inertial motion) of a clock, any two ticks define timelike separated events with a negative spacetime interval s²=−(∆τ)² with elapsed proper time given by ∆τ=√((∆t)²−(∆x)²) which is invariant. In the rest frame of the clock, ∆x is zero so ∆τ=∆t in that frame. The elapsed time for any moving object is related to the spacetime interval in the very same way way: the elapsed time is invariant and is the square root of negative of the spacetime interval (assuming appropriate conventions). For an arbitrarily moving clock, the previous sentence is still true but the formula becomes a path integral along the path followed by the clock: ∆τ=∫√((dt)²−(dx)²) which is likewise invariant with ∆τ=∆t in the non-inertial frame of the clock, because the origin of the clock in its own frame is fixed at x=0. For your case of the muon, you have two frames, the muon rest frame where ∆τ=∆t and the earth frame where the muon is moving, in which ∆x≠0 so ∆τ=√((∆t)²−(∆x)²). Both frames here will measure/calculate the same ∆τ, the proper time from the muon creation to its destruction. I think we've been talking past each other a lot, and while much of what you've written is okay, none of it actually addresses the problems I see with the first part of the first sentence. Perhaps someone else will chime in with an opinion about that. If you wish to believe that an elapsed time on an arbitrarily moving clock is not a valid relativistic invariant, go ahead, but that is very, very wrong according to my understanding. Tim Shuba (talk) 08:15, 7 March 2010 (UTC)


 * Also, look at the next phrase "considerable and independent contributions". Why does it say "independent"? It seems to suggest that Einstein did not make use of the previous contributions. But everyone agrees that he did make use of some of them. Roger (talk) 02:40, 7 March 2010 (UTC)
 * It doesn't strike me that way at all. Previous contributions were independent in that Einstein was not a collaborator, regardless of what he did or did not make use of. As you know, giving credit to the work of Einstein is a bugaboo over at conservapedia, and it just looks silly to beat that drum. I checked the special relativity article over there, and I will say the defining sentence "...is a generalization of classical mechanics" is considerably better than the bizarre assertion I was complaining about above. Quite aside from the specific content, the first sentence here is extremely poorly written, with two unwieldy parenthetical phrases and a generally disjointed presentation. It sets the stage for a rather dreadful article, which is too bad because there actually is some useful information to be found within. Here are a couple other issues, outside the lead.
 * There are two separate sections entitled Mass-energy equivalence, one of which is inexplicably placed in the Postulates section. I can't really understand putting it under Relativistic mechanics either, but that's at least slightly more sane.
 * There's a hilarious and eye-catching section that contains eleven citations run together. It is a mystery why so much detail about cyclotron equations appears in this article, and these equations are largely missing from where they should be.
 * Tim Shuba (talk) 22:07, 8 March 2010 (UTC)


 * So it says "independent" to mean that the earlier work did not depend on the later work? Isn't that obvious? It would be simpler and better to just say that Lorentz and Poincare also made contributions. There are discussions elsewhere about what depended on what. Roger (talk) 00:03, 9 March 2010 (UTC)


 * Offhand, I think the entire parenthetical phrase may have been inelegantly bolted on to the initial sentence due to bickering about who ought to get top billing for developing the theory. Having a separate sentence in the intro mentioning important figures in the nascent days of relativity would be better, and yes, interested readers are already directed to the history article for further details. The word independent doesn't seem to add much and could certainly be left out as far as I'm concerned. Tim Shuba (talk) 14:43, 9 March 2010 (UTC)


 * I agree that the parenthetical remark makes the lead's flow awkward. Poincaré and Lorentz are properly credited with their important contributions in the body of the article. I think the lead would be improved by removing the parenthetical remark. Every innovation is based on the works of people who came before; to omit such detail in the lead of any article is perfectly appropriate. CosineKitty (talk) 16:03, 9 March 2010 (UTC)

Free falling or arbitrary acceleration?
In the last line of the lead, it said "From the theory of general relativity it follows that special relativity will still apply locally (i.e., to first order) to observers moving on arbitrary trajectories, ..." (emphasis added). This is wrong. I corrected it to say "From the theory of general relativity it follows that special relativity will still apply locally (i.e., to first order) to observers on any free falling trajectory, ...". If the observer is not free falling (e.g. a scientist in his laboratory siting on the surface of the Earth), then there is an effect of time dilation due to gravity. This gravitational redshift is proportional to the first power of the elevation of the test clock relative to the reference clock. Thus it is a first order effect. In other words, special relativity fails in the first order to predict the rate at which time passes. JRSpriggs (talk) 08:29, 11 March 2010 (UTC)
 * As I understand GTR, spacetime is locally Lorentzian, i.e., at any event, a coordinate system can be found for which the metric components are that of STR to first order. I'm not sure the former or the later version of the last lead line correctly captures this idea.  After all, in the context of spacetime, local means (infinitesimally) nearby in space and in time.
 * OTOH, if by local we're only referring to space (as implied by the talk of "moving along a trajectory"), then isn't it the case that STR applies equally well to the scientist sitting in his (infinitesimal) laboratory on the surface of the Earth as to a free fall observer? IOW, how in principle would curvature be detected locally? Alfred Centauri (talk) 15:13, 11 March 2010 (UTC)
 * JRSpriggs' version seems good to me. We are talking about a spacetime trajectory, i.e. trajectory is linked to world line. It's true that local flat coordinates can be chosen at any event, but any "infinetesimal" measurement of gravitational time dilation in the lab frame still results in first order dependence, whereas for a freely-falling local frame the dependence is of higher order. Tim Shuba (talk) 19:43, 11 March 2010 (UTC)
 * Tim and JR, is it not true that locally, the lab sitting on the surface of the Earth is indistinguishable from a uniformly accelerated lab within the context of STR? If so, then is it not true that, locally, STR will still apply to the lab even though the worldline of the lab is not a geodesic?  Alfred Centauri (talk) 21:05, 11 March 2010 (UTC)
 * Here's how I think about it, which admittedly may not be quite right. Mathematically, the local flat frame at any event in a curved manifold contains in general only that event (of the manifold that is, the rest of the tangent plane is in a tangent space). The tangent space is perfectly SR, but it isn't a physically realizable thing that can be probed with clocks and rods. For either case of local lab frame or local free-falling frame, there will be corrections to SR, called tidal forces, which indicate the presence of curvature. However the local lab frame has corrections to first order, while these first order terms disappear for sufficiently "small" (in space and time) measurements in the free-falling frame. There is no way in general to remove the higher order terms, so the local free-falling frame is the closest thing to a special relativistic inertial frame and is therefore considered the analog to it in general relativity. For any single event in the lab frame, the equivalence with a uniformly accelerated frame is strictly valid at just that one event, and there is obviously no way to perform actual experiments without some extent in spacetime. Tim Shuba (talk) 23:46, 11 March 2010 (UTC)
 * I understand what you are saying Tim but what I'm getting at is that the gravitational red shift JR uses as an example of a first order effect is not related to tidal forces AKA curvature. As I understand it, curvature shows up as 2nd order terms in the metric which cannot be transformed away.  If I understand all this correctly, the first order terms in JR's example indicate an accelerated coordinate system, not curvature.  Take a look at  this and  this where we find:


 * This was precisely Einstein's conclusion in 1911. He considered an accelerating box, and noted that according to the special theory of relativity, the clock rate at the bottom of the box was slower than the clock rate at the top. Nowadays, this can be easily shown in accelerated coordinates. The metric tensor in units where the speed of light is one is:



ds^2 = - r^2 dt^2 + dr^2 \,$$


 * Correct me if I'm wrong, but, to first order, this is the line element of the spacetime of the lab sitting on the surface of the earth, i.e., the line element of an uniformly accelerated coordinate system in the flat spacetime of STR. Alfred Centauri (talk) 00:44, 12 March 2010 (UTC)

To the first order the metric at the surface of the Earth is like that of Minkowski space in Rindler coordinates as Alfred Centauri observes. However, the observer in Rindler coordinates knows that he is accelerating and can transform the metric from an inertial frame to his accelerating frame. A scientist ignorant of general relativity would presume that since the center of the Earth is the center of an inertial frame (ignoring its rotation about its axis and revolution about the Sun etc.), then he must also be in an inertial frame. But it is the free falling frames which are like inertial frames to the first order. "how in principle would curvature be detected locally?": It cannot be in the first order, that is why we have to focus on which frames are nearly inertial and which are not. Otherwise, what is the difference between SR and GR? A physicist trying to work with SR and Newtonian gravity would have no reason to expect that the laboratory siting on the surface of the Earth is not inertial, no reason to predict the gravitational redshift. So when he saw it, he would have to conclude that SR is wrong. The only other possibility is that the whole Earth is accelerating, but measurements at the antipode would show that it is "accelerating" in the opposite direction. Alfred is unconsciously bringing GR type reasoning into SR to try to save it from this problem. That is cheating. JRSpriggs (talk) 05:17, 12 March 2010 (UTC)
 * I don't see anything wrong with bringing GR reasoning into a sentence that begins with "From the theory of general relativity it follows that...". Actually I just was about to reply that I am convinced of the validity of Alfred's point and I now think it's best to leave mention of trajectories completely out of that sentence, like this: From the theory of general relativity it follows that special relativity will still apply locally (i.e., to first order) to observers on any free falling trajectory[8], and hence to any relativistic situation where gravity is not a significant factor. Tim Shuba (talk) 05:45, 12 March 2010 (UTC)


 * OK, I rewrote it again to say "From the theory of general relativity it follows that special relativity will still apply locally (i.e., to first order), and hence to any relativistic situation where gravity is not a significant factor. Inertial frames should be identified with non-rotating Cartesian coordinate systems constructed around any free falling trajectory as a time axis.". Do you-all agree with that? JRSpriggs (talk) 17:34, 12 March 2010 (UTC)
 * Agreed. That avoids the objection and still mentions the important role of freely-falling frames. Tim Shuba (talk) 04:55, 13 March 2010 (UTC)

No speed or velocity can exceed c
I disagree (a bit) with UncleBubba's revert and with part of the edit summary (" ... unsigned/unexplained change from "velocity" to "speed" ..."). The fact that a change is unsigned/unexplained is not sufficient to undo it, specially if the change was (at least slightly) more correct than the original. I added the "slightly more"-clause because I think that both formulations sound awkward. I propose we replace the current phrase with "no object or signal can go faster than light". DVdm (talk) 21:35, 20 April 2010 (UTC)
 * Your formulation sounds fine to me. And avoids the problems with trying to explain FTL (faster than light) wavefunction collapse, FTL virtual particle speed, and so on. Those things can't carry information (in the sense of Morse code, etc), so cannot be "signals." But there are all kinds of wacky FTL effects that still are possible even so-- like the EPR-effect correlation "speed," and the fact that the direction of static E and B and G fields all point exactly at their moving sources a distance x away (so long as the sources are not accelerating), and not back at the time-retarded position x/c of the sources (really, they do; there is no light-time correction needed, so long as the source doesn't accelerate). Light-time correction in position is needed only for light, not static fields. And static E and B and G fields can "escape" black holes, since they're STATIC fields composed of virtual particles, so they can go FTL. It's only signals carried on those fields (disturbances in the force!) that can't get out. S  B Harris 21:45, 20 April 2010 (UTC)


 * My reasoning for reverting "speed" to "velocity" was--more or less--one of specificity: While "speed" can refer to many things, distance traveled per unit of time, film sensitivity, a transmission gear ratio, light-gathering ability of an optical system, or a popular drug, "velocity" (to the best of my knowledge) is always used to describe the amount of something--usually distance--over time. Therefore, "velocity" seemed the more specific and accurate of the two terms.


 * A quick census of the text, though, shows "speed" used 51 times, while "velocity" was written 33 times. (Nowhere, BTW, did I find the phrase "magnitude of velocity", although it's a great construct that would work very well in a few places.)


 * While an unsigned, IP-address-only edit is certainly not, per se, grounds for reversion, dumbing-down a technical article is. The fact that the editor did not enter an Edit Summary or use a registered account just made me look a little more closely at his/her actions.


 * Personally, I think the whole sentence is pretty awkward and should be rewritten. I would suggest something like this:


 * "One of the implications of special relativity (if causality is to be preserved) is that no information or material object can travel faster than light. Some think special relativity says 'no velocity can exceed c', which is not true. On the other hand, in general relativity the logical situation is not as clear; whether is contains some fundamental principle that preserves causality (and therefore prohibits motion faster than light) is an open question."


 * Of course, there is only so much that can be done to make this subject easily understandable. This is an off-the-cuff shot at it; I'd love to see what y'all can do with it, especially since it sounds like y'all understand the underlying mathematics far better than do I. UncleBubba (Talk) 01:19, 21 April 2010 (UTC)


 * An example would be nice, such as "The location where the beam of a search light hits the bottom of a cloud can move faster than light when the search light is turned rapidly.". JRSpriggs (talk) 01:29, 21 April 2010 (UTC)

I think UncleBubba's suggestion is ok, but I'd like to insist (a bit) that we still replace "no velocity can exceed c" with "no object or signal can go faster than light" - after all, velocity is a vector and vectors just don't exceed numbers. Their magnitude does. I think that the fact that the remainder of the article is sloppy in this regard, does not warrant this statement to be sloppy as well. DVdm (talk) 07:30, 21 April 2010 (UTC)
 * I agree, c is a scalar, we should not be comparing it with a vector. Martin Hogbin (talk) 09:03, 21 April 2010 (UTC)
 * Ok, I went ahead and changed it. DVdm (talk) 09:45, 21 April 2010 (UTC)


 * To DVdm: Your edit seemed to ignore the context giving "... no object or signal can go faster than light ... is not true". This is false and directly contradicts the previous sentence of the article. So I rewrote that paragraph again. I also removed a content-free sentence on general relativity. JRSpriggs (talk) 14:13, 21 April 2010 (UTC)
 * The context was that the phrase in question is a consequence of SR, as opposed to a principle of it. But never mind. The text is better without the remark to begin with. If anyone thinks the remark does belong there, feel free to re-insert (but preferably without comparing vectors with numbers). JR, your added sentence is not really related to the (causality) context of the section, and I think it doesn't belong there, but, ah, whatever. Do note however that you left a typo in "somethings". DVdm (talk) 14:27, 21 April 2010 (UTC)

It is the binomial theorem
Classical limit Notice that γ can be expanded into a Taylor series for, obtaining:

and consequently

For velocities much smaller than that of light, one can neglect the terms with c2 and higher in the denominator. These formulas then reduce to the standard definitions of Newtonian kinetic energy and momentum. This is as it should be, for special relativity must agree with Newtonian mechanics at low velocities.

I just say, the article is wrong for the discription of "Taylor series ". Instead of the Binomial theorem! —Preceding unsigned comment added by 140.123.72.3 (talk) 10:30, 23 April 2010 (UTC)


 * Neglecting terms is precisely what a Taylor series (or in this case a McLaurin series) does. I notice that the binomial series is present since this edit dd. May, 2009. I had reverted your edit because you had confused a "theorem" with a "series". I have added the standard expression for gamma now, and referred to both the Taylor and the binomial series. Cheers, DVdm (talk) 12:47, 23 April 2010 (UTC)

Note: I think the expression of the binomial series (sum of products) is not relevant in the context of the article. After all, this is not a math aticle. I propose we remove it. Any seconds? DVdm (talk) 15:36, 23 April 2010 (UTC)


 * No. I think that the section is useful because it shows the relationship between classical physics and relativistic physics. How special relativity can be arrived at by adding a series of ever finer corrections to classical physics. And having the actual series is useful since some users may not be able to calculate it or may easily be mistaken when trying to calculate it. In practical use, adding one or two additional terms of the series would involve less computation than calculating &gamma;. JRSpriggs (talk) 22:22, 23 April 2010 (UTC)


 * JR, of course the section is useful. I was merely talking about removing the expression of the binomial series (the sum of products). I.o.w. I propose to replace
 * $$\gamma = \frac{1}{\sqrt{1 - \frac{v^2}{c^2}}} = \sum_{n=0}^{\infty} \prod_{k=1}^n \frac{(2k - 1)}{2k} \frac{v^2}{c^2} = 1 + \frac{1}{2} \frac{v^2}{c^2} + \frac{3}{8} \frac{v^4}{c^4} + \frac{5}{16} \frac{v^6}{c^6} + \ldots$$
 * with
 * $$\gamma = \frac{1}{\sqrt{1 - \frac{v^2}{c^2}}} = 1 + \frac{1}{2} \frac{v^2}{c^2} + \frac{3}{8} \frac{v^4}{c^4} + \frac{5}{16} \frac{v^6}{c^6} + \ldots$$
 * DVdm (talk) 09:12, 24 April 2010 (UTC)

Actually, I think that the correct derivation of the classical limit is far more subtle than doing a trivial series expansion of the energy in powers of v/c. The fact that c already appears in the equations is not ok. i.m.o., as it already tells you how to appoach the correct scaling limit in which special relativity will tend to classical mechanics.

A non-trivial physics argument should start from equations in which c has been put to 1. One then decides to study the physics of slowly moving, very massive objects. To study this, one can derive an approximate theory by rescaling the relevant variables in a carefully chosen way, so that you approach the limit of infinitely slow and infinitely massive objects, but such that the equations don't all get singular. Compare this with e.g. singular perturbation theory where you have to rescale your variables in a careful way to make boundary layer phenomena visible.

The approximation is then that a situation involving very slow and very massive objects is approximated using equations valid in the infinite scaling limit. In this limit some relations do become singular and are lost. This then means that you need to introduce a new variables that would not be needed in the original theory. In this case you need to introduce a properly rescaled rest energy as a new variable. In the scaling limit this will be rescaled by an infinite factor. Count Iblis (talk) 00:05, 24 April 2010 (UTC)


 * Actually, I think the idea that c=1 is the proper way to do physics is mistaken. The processes which we use to measure length and duration are significantly different, so a conversion factor is necessary in any case. This is not just a matter of using a meter rod instead of a foot rod. JRSpriggs (talk) 00:22, 24 April 2010 (UTC)


 * Well, you should change your vote and vote for the zero constants party :) .Count Iblis (talk) 00:38, 24 April 2010 (UTC)

To DVdm: How about
 * $$\gamma = \frac{1}{\sqrt{1 - \frac{v^2}{c^2}}} = 1 + \frac{1}{2} \frac{v^2}{c^2} \left( 1 + \frac{3}{4} \frac{v^2}{c^2} \left( 1 + \frac{5}{6} \frac{v^2}{c^2} \left( 1 + \ldots \right) \right) \right) = 1 + \frac{1}{2} \frac{v^2}{c^2} + \frac{3}{8} \frac{v^4}{c^4} + \frac{5}{16} \frac{v^6}{c^6} + \ldots$$

which makes it clear how to calculate additional terms of the series? JRSpriggs (talk) 22:56, 24 April 2010 (UTC)


 * Yes, this is very nice as well, but in the context of a physics article I still think we don't need it. Who would ever have a practical (or even theoretical) reason to calculate terms beyond (v/c)^4, let alone beyond (v/c)^6? DVdm (talk) 08:38, 25 April 2010 (UTC)
 * I might want to look at in the future to remind myself how to calculate it, and to make it easier to verify that this is the right series. I do not know who else might want it. But I see no harm in leaving it in. So why prejudge the situation by taking it out?
 * It also helps to get an upper bound on the tail of the series (multiply the last retained term by $$\frac{1}{1 - \frac{v^2}{c^2}} \,$$) so that one knows if one has gone far enough to achieve the desired accuracy. JRSpriggs (talk) 17:35, 25 April 2010 (UTC)


 * I don't think that these days anyone uses the approximation to make an actual calculation. It is only interesting to demonstrate how the low speed limit is obtained from the relativistic equations. I just find the binomial expression, specially in a physics article, irrelevant and perhaps even a bit distracting. Have you ever seen it mentioned or spelled out in that form in a physics journal or textbook? DVdm (talk) 17:49, 25 April 2010 (UTC)


 * I am sure that I did not think of the idea of the series myself. However, it has been so long since I first saw it that I do not remember where it was. Perhaps it was in a Schaum's Outlines or some such practically oriented book. JRSpriggs (talk) 19:04, 25 April 2010 (UTC)


 * Ah... good old Schaum's... a bit messy, but always a joy to browse through :-) DVdm (talk) 19:08, 25 April 2010 (UTC)

Correct derivation of the classical limit
See here. It also explains in the last section why c is (wrongly) considered to be a fundamental constant, why it is dimensionful, and why it is numerically large when expressed in conventional units. Sadly, because most sources explain this in completely the wrong way, my explanation is probably OR. Count Iblis (talk) 00:04, 4 August 2010 (UTC)

Speed with respect to what
New qestion moved to bottom

The intro says the speed of light is always the same irrespective of the motion of the source - but what does this ambiguous statement mean ? Speed with respect to what ?

Does it mean with respect to the source, in which case it will vary according to the observer in relative motion. Or does it mean the same with respect to some fixed spatial reference frame ? —Preceding unsigned comment added by 195.194.10.178 (talk) 14:29, 11 September 2010 (UTC)


 * Please post new messages at the bottom of the page and sign your talk page messages with four tildes ( ~ )? Thanks.
 * The text says that the speed "is the same for all inertial observers", implicitly meaning that the speed is measured with respect to any inertial observer making the measurement. DVdm (talk) 14:38, 11 September 2010 (UTC)


 * In that case shouldn't it say "two way average speed" as it only applies to to-and-fro measurements ? What I'm getting at is that to just say "the speed of light" is the same etc.etc. gives a misleading impression that the one-way speed is implied, but of course this will be C+V or C-V depending on the relative motion of source and observer.
 * Quite apart from the red & blue Doppler shift of spectral lines showing speeds of C-V or C+V, the derivation of the Lorentz length contraction depends essentially on speeds of C-V & C+V to-and-fro together with SQRT(C^2-V^2) laterally in order to arrive at the special relativistic formula.- Mike Greene 212.85.28.88 (talk) 14:28, 15 September 2010 (UTC)


 * replying to this: "The intro says the speed of light is always the same irrespective of the motion of the source - but what does this ambiguous statement mean ? Speed with respect to what ?"
 * It means relative to the observer, i.e. with respect to the observer. If you have a way to measure lightspeed, and do so while in a stationary room then on a train going at 100mph you will get the same speed each time. Of course "stationary" is also relative, and we are all moving as the Earth rotates, orbits the sun and the sun orbits the galaxy. But none of these motions can be detected in the speed of light: it is the same whenever measured, to the limit of the accuracy of the measuring technique.
 * There is a practical problem that it's only possible to measure light going two ways, or in a round trip, as it's impossible to synchronise clocks with the remote station you'd need at the other end of your experiment. So in theory the one-way speed could vary - be different going there and coming back - and we'd never know as we can't detect it. But this would both go against intuition and against common understanding of the laws of physics (though both could be wrong as they have been in the past). There's more on this at One-way speed of light.-- JohnBlackburne wordsdeeds 15:17, 15 September 2010 (UTC)


 * If all clocks used are synchronized at a central location and moved slowly to their final positions, then one get the same result for one-way speed of light in a vacuum : it is a constant. JRSpriggs (talk) 21:27, 15 September 2010 (UTC)


 * In reply to Mr.Blackburne, I'd agree that the two way speed could be different each way, and if it were not for Lorentz length contraction, this would be detectable by a Michelson-Morley setup. So the assumption of length contraction depends precisely upon the to and fro speeds being C+V and C-V. I don't agree that it goes "against intuition and against common understanding of the laws of physics". In fact, intuition and common understanding of laws of physics would lead us to expect different speeds to and fro. It is special relativity that counter-intuitively introduces length contraction in such a way as to make any speed differential undetectable in a round trip.
 * Einstein's 1905 S.R. paper specifically assumes speeds of C-V and C+V for the to and fro speeds of light emitted from a moving source in order to derive the Lorentz transformations.


 * In reply to JR Spriggs the technique of slowly moving synchronised clocks apart, even assuming it worked in the sense of maintaining "absolute" synchronisation at distance, could not be assumed to always give the same one-way speed of light. Again, as above, if it were possible hypothetically to achieve absolute synchronisation between two positions, then unless they were both stationary the speeds would be C+V or C-V.

-Mike Greene 195.194.10.178 (talk) 15:59, 16 September 2010 (UTC)
 * This is a misconception. Speed of light is a relativistic invariant. It is always the same in any inertial frame of reference and in any direction. It simply can not be otherwise because it would imply existence of a privileged frame of reference. Ruslik_ Zero 16:23, 16 September 2010 (UTC)
 * Yes, by "common understanding of the laws of physics" I mean special relativity, which has as an postulate that light speed is invariant, and is perhaps the most widely accepted theory of modern physics. Once you accept this and understand the maths behind it it's also very intuitive that the speed of light is uniform, both in time and space. It's not only well supported by experiment but incorporated into real-world systems such as GPS. If the speed of light were not constant it would be a leap into the unknown, as so much of our theory would need to be torn up and re-written.-- JohnBlackburne wordsdeeds 16:53, 16 September 2010 (UTC)
 * To clarify things further, the two-way speed of light can be shown experimentally to be the same in any inertial frame. The one-way speed is dependent on the clock synchronisation scheme used.  It can, however, be shown experimentally that the one-way speed of light is independent of the motion, inertial or otherwise, of the source.  This is explained in more detail at the One-way speed of light article. Martin Hogbin (talk) 17:28, 16 September 2010 (UTC)

Mike Greene obviously has closing speeds (c+v and c-v) in mind, but I think this is not the place to discuss or explain this. Perhaps Mike can use the science referece desk for this. This is where we discuss the article, not the subject. DVdm (talk) 18:41, 16 September 2010 (UTC)


 * No. What I'm saying is not controversial. It's perfectly correct. Special relativity only says that the two-way there-and-back speed of light is a constant - not the one way speed. Nothing in SR says the one-way speed is a constant and nor is there any experimental evidence that it is. Ruslik, Blackburne and Hogbin I'm afraid, all seem to have misunderstood a fundamental feature of special relativity.


 * Let me prove the point with three separate items which any gainsayer must address rather than just saying "no, you're wrong, it is constant" which is futile and devoid of logic.


 * (A) Two observers in high enough relative motion will detect opposite red or blue shifts in spectral lines from a distant star. Similarly a binary star system shows alternating red & blue shifts which are clear indications of light being received at C-v or C+v.


 * (B) The fundamental Lorentz transformation formulae of SR are specifically derived from assuming that the speed of light with respect to a moving source is C+v or C-v in direction of motion, and SQRT(C^2-v^2) laterally. Not only is this explicit in Einstein's 1905 paper (look it up in Dover), but the Michelson-Morley experiment is regarded as definitive confirmation of it. The derived SR length contraction is needed purely to compensate for the C+v and C-v journey otherwise taking longer than the lateral reflection.


 * (C) Relativity of Simultaneity is utterly dependant on differential one way speeds of light. The classic setup is two clocks at each end of a (sufficiently rapidly) moving train. When they are synchronised on board by sending light signals between them, the observer on the platform finds the forward train clock to be set "behind" (ie. lagging) the rear train clock. This happens precisely because the light takes longer to go from rear to front than to go from front to rear. Thus if say, the round trip is 4 nanoseconds then a signal from the rear arrives at the front a little over 2 nanoseconds later, taking slightly less to come back. So when the front clock is set to half-way between times of transmission & reception, it will be set slightly behind the rear clock because the rear has gone slightly past 2 nano secs when reflection occurs.


 * Let someone who thinks one-way speed is constant try and explain Doppler shift, length contraction and relative simultaneity as above ! - Mike Greene 212.85.28.88 (talk) 10:58, 18 September 2010 (UTC)
 * No, the speed of light is a constant, c, whichever direction is measured. At least that is what special relativity says. The one way speed of light is a practical and philosophical problem: out theory says c is a constant, we can confirm this and relativity in many different ways and it explains the large-scale universe remarkably well. But we cannot measure the one way speed as accurately as the two way speed. So while we know c to a high degree of accuracy that's using two-way measurements: in theory there could greater uncertainty in the one way speed, but as that would invalidate relativity and probably show up in experiments in some way it's not something that gives many people sleepless nights. In any case it is bound a small effect, and your examples are all incorrect: the speed of light is c in all cases (or a little less not in a vacuum) to all observers up to a high degree of accuracy.-- JohnBlackburne wordsdeeds 11:41, 18 September 2010 (UTC)


 * To Mike Greene: How would you determine the value of V? The principle of relativity and the isotropy of space indicate that there is no way to find it. So your distinction between one-way and two-way velocities of light becomes a mere metaphysical fantasy. JRSpriggs (talk) 17:13, 18 September 2010 (UTC)


 * To respond to the three items mentioned by Mike Green:


 * (A) This is NOT a clear indication of light being received at C-v or C+v. Red and blue are frequency measures. It is only a clear indication that the frequencies of the light received are different. Frequency ($$\nu$$), speed of light (C) and wavelength  ($$\lambda$$) are related by $$\lambda \nu = C$$. If the frequency changes, then either the wavelength or the speed of light has changed in such a way that the above relationship is maintained. To say that it is a clear indication that the speed of light is changing to C+v or C-v is to assume that the wavelength is unchanged, which, according to the theory of relativity, is incorrect. The theory of relativity says that, in fact, the speed of light is unchanged and the wavelength is Lorentz contracted. This will yield the relativistic Doppler equation.


 * (B) I have not read the paper carefully, but I cannot imagine that Einstein said that the forward and backward speeds of light are C+v and C-v respectively, while a major point of his paper was that C is constant. Anyway, the question is not "how did Einstein derive the equations" but rather "what is the present interpretation of these equations".


 * (C) In this example, you have assumed a synchronization method. You say "the observer on the platform finds the forward train clock to be set "behind" (ie. lagging) the rear train clock". You must ouline exactly how is this observation made. This observation cannot be made without making assumptions about the forward and backward speed of light, or assuming that slowly bringing the clocks together will hardly affect their time readouts. If you assume the forward and backward speeds are different, then fine, you can come up with a consistent theory which will imply a preferred inertial frame. If you assume they are the same, as Einstein did, then again, you come up with a consistent theory in which there is no preferred inertial frame. Einstein's postulate that all inertial frames of reference are physically equivalent means that the preferred frame that is constructed by assuming different back and forth speeds can never be physically detected. So far, this has held up. Lets use Occam's razor and pick the simplest assumption, as Einstein did, rather than invent undetectable preferred reference frames.


 * In this regard, JRSpriggs question stands - how do you detect the difference in the forward and backward velocities? Answer: you cannot without making arbitrary assumptions which pre-determine the answer. Thats what Einstein did, and he chose the simplest, assumption which does not involve fantasy reference frames. PAR (talk) 17:23, 18 September 2010 (UTC)