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See The Principle of Relativity here: The Principles of Mathematical Physics. This was written by Poincaré in 1904, a year before Einstein published his theory of relativity.

It appears from this and other writings of Poincaré that Poincaré discovered the theory of special relativity before Einstein. So why does Einstein get the credit?

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Also, it is worth pointing out that Lorentz contraction is called Lorentz contraction for a reason. Lorentz did some good work on this aspect of relativity, but did not understand the result. It was Einstein that gave these finding physical meaning/enterpretation and this was recognised by Lorentz. @RonMaimon is 100% right with what he is saying here... –  Killercam Aug 29 '12 at 13:04
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@Killercam: But Poincare differed from Lorentz in this regard, in that Poincare really believed the contraction was of no physical significance, and that any two frames are truly equivalent in every respect. In this sense he certainly knew the principle of relativity. His screw-ups are in the details of mechanics and electromagnetism, and the only real one I found is not formulating E=mc^2, something he fixes after Einstein's work. –  Ron Maimon Aug 29 '12 at 13:17
    
I find no fault in anything you are saying. You know your stuff... All the best. –  Killercam Aug 29 '12 at 13:23
    
I would like to give someone credit for having the "right" answer, but unfortunately, I'm not an expert on this subject, so I wouldn't know who is correct. But I thank everyone for their answers. –  Craig Feinstein Aug 30 '12 at 13:43
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6 Answers

Poincaré was confused on several points. (See the discussion on Wikipedia regarding "mass energy equivalence".) He could never get the mechanical relations straight, since he could not figure out that $E=mc^2$. Einstein followed Poincaré closely in 1905, he was aware of Poincaré's work, but he derived the theory simply as a geometric symmetry, and made a complete system.

Einstein did share the credit with Lorentz and Poincaré for special relativity for a while, probably one reason his Nobel prize did not mention relativity. Pauli in the Encyclopædia Britannica article famously credits Einstein alone for formulating the relativity principle, as did Lorentz. Poincaré was less accomodating. He would say "Einstein just assumed that which we were all trying to prove" (namely the principle of relativity). (I could not find a reference for this, and I might be misquoting. It is important, because it shows whether Poincaré was still trying to get relativity from Maxwell's equations, rather than making a new postulate—I don't know.)

Special relativity was ripe for discovery in 1905, and Einstein wasn't the only one who could have done it, although he did do it best, and only he got the $E=mc^2$ without which nothing makes sense. Poincaré and Lorentz deserve at least 50% of the credit (as Einstein himself accepted), and Poincaré has most of the modern theory, so Einstein's sole completely original contribution is $E=mc^2$.

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I'd say he showed that the Lorentz force equation comes from Maxwell's equations, rather than having to be added on. $E =mc^2$ wasn't proved adequately in his first paper, hence the title in the form of a question: "Does the Inertia of a Body Depend upon its Energy-Content?" –  Larry Harson Aug 28 '12 at 14:57
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I just wanted to add some detail about Lorentz in particular. I've read that he actually misinterpreted his own transformations as applying to the Ether (in fact I think he derived them purposely to describe how the ether "reacts" in such a way as to be in accord with experiments (Michelson-Morley?). So Einstein at the very least gets credit for being the first to correctly interpret the equations and do away with the Ether concept. –  tachyonicbrane Aug 28 '12 at 15:44
    
Actually it was Lorentz who said that Einstein just postulated what had previously been proved. Everyone agrees that Poincare formulated and published the relativity principle well before Einstein. –  Roger Aug 28 '12 at 18:55
    
@Roger: I remember that Poincare said it negatively, perhaps Lorentz said it positively. The problem with Poincare's work is his renounciation that energy carries inertia from emitter to absorber, and the resulting rest frame that the separation "mass" and "energy" entails. This appears in 1904, while not in earlier 1900 work (he probably wasn't confident at either point) and this gets sorted out by Einstein. The issue is important, Poincare did a center of mass theorem that fails (as he noted) if radiation doesn't carry inertia between emitter and absorber. –  Ron Maimon Aug 28 '12 at 19:03
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@tachyonicbrane: I agree for Lorentz, not so much for Poincare. Poincare wanted a manifestly invariant formulation, he just stumbled on some details. It is perhaps for this reason that Lorentz accepts Einstein as the founder of relativity, while Poincare is less accomodating of the upstart. Also, Einstein read Poincare, not Lorentz, of this we can be sure, because he goes through the work "breathlessly" (his words, at least in German) in his private correspondence of 1904. –  Ron Maimon Aug 28 '12 at 19:08
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I think the quote Maimon gives of Poincare, "Einstein just assumes that which we were all trying to prove." highlights exactly why Poincare did not discover anything like special relativity. Poincare was looking for a "mechanical" explanation of why the speed of light "appeared" constant in all reference frames. In other words, Poincare did not even believe in relativity in the Einsteinian sense. He believed that there was a preferred frame at a fundamental level.

What Einstein did was to raise the "problem" of the speed of light appearing constant in all reference frames to the level of a postulate. This is what Poincare means when he says "Einstein just assumes that which we were all trying to prove". I think Poincare didn't really understand what Einstein had done -- space and time were fundamentally woven together in Einstein's theory. In Poincare-Lorentz's theory, space and time are separate, but only appear to be woven together -- there is a preferred frame where simultaneity of spacially separated events is absolute.

I would also like to add -- and this part is just speculation -- that I believe we would still not have special relativity today if it hadn't been for Einstein. I believe we would still be working in the framework of Lorentz-Poincare, where Lorentz Invariance is achieved at an observational level, but fundamentally the theory has a preferred reference frame.

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Does it really matter if his theory has a preferred reference time, as long as the theory works (makes correct predictions)? –  Craig Feinstein Aug 28 '12 at 17:11
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@CraigFeinstein Does it really matter if burning materials give off phlogiston, and it's buildup suppresses combustion as long as it correctly predicts that a burning splint placed inside a small sealed container will rapidly be extinguished? –  Dan Neely Aug 28 '12 at 18:11
    
Well, your question was why did Einstein get credit for relativity. Relativity says there are no preferred frames. Einstein removed the preferred frame from the theories of Lorentz and Poincare, so he is credited with relativity. You are right that Lorentz's theory had the same equations -- they are called the Lorentz transformations for a reason, however it is not a theory of relativity. –  user7348 Aug 28 '12 at 18:16
    
It is also of interest to mention now that the theory of Lorentz and Poincare is very much akin to the current formulation of quantum mechanics. In quantum mechanics there is a fundamental preferred frame in which one can describe the causal sequence in entanglement, however the theory is completely Lorentz invariant at an observational level. The fact that almost no serious physicists realize this is precisely why I believe nobody would have ever discovered relativity without Einstein. –  user7348 Aug 28 '12 at 18:19
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@user7348: this is not 100% accurate--- you can formulate quantum mechanics as a path integral (or as S-matrix) and either way allows a Lorentz invariant formulation. Field theory is Lorentz invariant in path integral, and string theory is Lorentz invariant in S-matrix sense (and in worldsheet path-integral sense, at least in the appropriate formalism). –  Ron Maimon Aug 28 '12 at 19:06
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Poincare introduced in 1905 the spacetime geometry as we know it today. I say this because (1) he combined space and time into a 4-dimensional spacetime, (2) he defined the metric, now known as the Minkowski metric, (3) he formulated the Lorentz group (and not any Galilean group) as the symmetries of spacetime, (4) his relativity was a spacetime theory that was applicable to electromagnetism as well as any other forces, and (5) he proved that the electromagnetism equations were covariant with respect to the spacetime geometry. These 5 concepts form the core of what modern textbooks teach as relativistic geometry. Poincare had them all in 1905, and Einstein had none of them.

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That's not true--- Einstein had the electrodynamic transformations in 1905, and the correct energy density and momentum density expressions, and the right relation between mass and energy. Poicare had all but the last, and this got him confused on several important points. –  Ron Maimon Aug 28 '12 at 19:07
    
Yes, Einstein had the electrodynamic transformations in 1905. So did Lorentz in 1904. But they did not have those 5 points that summarize the spacetime geometry. –  Roger Aug 28 '12 at 21:50
    
I meant Einstein had all 5 points, minus the Minkowski metric, but he had the interval relation somewhere in his paper. Poincare was annoyingly wrong on several points, but he and Lorentz certainly deserve 50% of the credit, just Einstein deserves the other 50%. –  Ron Maimon Aug 29 '12 at 0:39
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It is important to note that Poincaré did not have spacetime geometry before Minkowski because: A) he did not define it through non-galilean relativity, B) Poincaré did not express particle motion in terms of a worldline, or define proper time as a worldline parameter. So inasmuch as spacetime geometry includes worldlines and proper time, Poincaré did not discover spacetime geometry.

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This is not right--- Poincare had worldlines (as did everybody), and he defined "proper time" at least along a moving observer's axis, and it's no stretch from this to worldline proper time. Poincare deserves 50% of the credit for SR, it's just that he didn't finish it. –  Ron Maimon Aug 29 '12 at 11:48
    
Actually, in 1905 and prior, his work on space-time vectors showed no expression at all of motion with regards to wordline nor proper time as a worldline parameter. He might have included it more formally after -07, albeit in his lectures (his famous London lecture for instance) he noted that Minkowski spacetime was the new one and his was merely galilean space and time with an added 4-d vector. Naturally the formulation of 4-d vectors are interesting but for the meat of SR not strictly necessary. Poincaré deserves at least 50% credit for SR, I agree.´ –  Jonoleth Svarttörn Aug 30 '12 at 7:56
    
Also, in the above mentioned lecture, as a curiosa; Poincaré noted a preference against using Minkowski spacetime. Another curiosa, Moskowzki sat in the audience at his Berlin lecture where Poincaré had talked about Einstein's work both in the positive and negative. The speech-transcript does not include any explicit mention of Einstein by name though, so we are left to assume he did a bit of adlib when talking about Einstein specifically. From Moskowzkis impression, it seems Poincaré did indeed regard Einstein's work as not only different to his but... too revolutionary and daring. –  Jonoleth Svarttörn Aug 30 '12 at 8:00
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Looking at comments on what Einstein had that Poincaré didn't have, beyond the mass-equivalence stroke; where Einstein argued that a light pulse which is spherical in one inertial frame, is spherical in every inertial frame. According to Poincaré, a light pulse that is spherical in the above mentioned privileged frame is an elongated ellipsoid in every other inertial frame. The difference in description is due to that fact that Einstein recognized the relativity of spatio-temporal coordinates, when Poincaré did not. And, the aberration constant, Poincaré didn't derive it, Einstein did. –  Jonoleth Svarttörn Aug 30 '12 at 8:08
    
It is possible to be a little less charitable when reading historical works. I don't dispute what you say, and this is why Einstein deserves the other 50% of the credit, but it is possible that Poincare was just following convention and describing things in one reference frame for mathematical convenience, not because he actually believed there was a preferred frame. I am not sure. –  Ron Maimon Aug 30 '12 at 19:12
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An historical confection reposted from MathOverflow … was young Albert Einstein a sci-fi reader? :)


I ran across the following (to me startling) example in Robert Cromie 1895 techno-thriller The Crack of Doom (reprinted in The End of the World: Classic Tales of Apocalyptic Science Fiction, Michael Kelehan, ed.)

Page 102: "If you consult a common text-book on the physics of the aether, you will find that one grain of matter, contains sufficient energy, if etherised, to raise a hundred thousand tons nearly two miles."

Here "grain" is a standard unit of jewelers (one gram = 15.4 grains). Then it is easy to verify, that within ±2% error, Cromie's "etherised" mass-energy relation is $E = m c^2/2$.

Einstein was 16 years old when Cromie's book appeared (published by a European publishing house) ... a very impressionable age, needless to say. Yet despite the clue that Cromie so generously provided to science fiction fans in Europe, ten years passed before Einstein got the factor of two right! :)

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This form of E=mc^2 was not due to Cromie, but it was standard lore that the field energy of the electron was comparable to the rest mass, and so people expected that E is a small constant times mc^2. Einstein showed that the coefficient is 1, he wasn't the first to suggest that there is a proportionality, but the unit coefficient is important, it makes relativity work. You can look at Tolver and DePretto for other E=mc^2 ideas floating at the end of the 19th century, to see where they come from, how different they are from Einstein's and why they fail. –  Ron Maimon Aug 29 '12 at 0:37
    
@RonMaimon +1 for the references. –  Igäria Mnagarka Aug 29 '12 at 4:01
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From what I've been told by my mentors there were a few things that happened.

  • Poincare was extremely generous person, he routinely attributed his contributions to others left and right. For instance, he contributed the transformations to Lorentz, while Lorentz himself admitted he didn't do them in the form in which Poincare presented them, and didn't see their value at the time. That was one factor why Poincare did not insist on attribution to his work from Einsten.
  • Einstein was told by his mentor Minkowsky about Poincare's work, which included pretty much everything on special and general relativity, including $mc^2$ which was derived by Poincare. Minkowsky was friends with Poincare, and theyt had a lot of private communication with stuff which was not published. Einstein took everything that Poincare did, and did not refer to him until way-way later, many years later. He then pretended that he forgot. Yes, of course. Rightfully, he did not get Nobel for relativity work, because at the time everyone knew what was going. Minkowsky spoke with Poincare on the subject, and the latter did not want to complain.
  • There was some anymosity between German and French, and also physicists vs. mathematicians kind. So Planck and other German dudes kept promoting EInstein's work, and consistently ignored Poincare's. For instance, there are myths that somehow Poincare did not do general relativity (false), or that he wanted ether (false) etc. It sort of worked, the general population thinks Einstein did it all, but all physicist know that something's not right with this business.

You can find a few historical researches on the subject out there, like this one.

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