Was Einstein's Proof of E=MC^2 Flawed?

[bhobba]

Hi All

I am reading the following interesting book:
https://www.amazon.com/dp/0393337685/?tag=pfamazon01-20

In it he makes the claim Einsteins proof of E=MC^2 had errors. They were fixed (not by Einstein - but by Von-Lau in 1911 using Minkowski's tensor formalism) - but, he claims, even now correct proofs are not usually given.

I am scratching my head about that one.

The proof I know comes from Landau and is almost trivial - you write down the only reasonable relativistic Lagrangian for a free particle ∫m*dt where t is the proper time. You then apply Noether - its simple.

So what gives - is there something wrong with the above or is that dead simple proof not often given? If not - its a shame - its so easy and beautiful - and you would have to ask - why?

Thanksa
Bill

 

[PAllen]

SR is often presented when students have not yet mastered (or in some cases even seen) Lagrangians, and don’t know Noether’s theorem. Even von Lau couldn’t have used this approach because Noether’s theorem was not yet known.

 

[vanhees71]

I've no clue what the book means. Where is the original paper on $E=mc^2$ (which was a short addition to the famous paper "On electrodyamics of moving bodies") flawed, according to this author? To the contrary I find it to be one of the few early sources which get it right! Usually books with such title are written by people who haven't understood Einstein. There are many books claiming Einstein hadn't understood QT either, which for sure is not true. He had, of course, understood QT very well from the very beginning. He only considered it as "incomplete", which is of course as well true (because there's no quantum theory of gravity yet) as it is wrong (because QT has survived all tests, including the inseparability, which was the main point of Einstein's criticism on the formalism, but this has been discovered with the work by Bell and experiments related with it and was very much triggered by this famous debate between Einstein and Bohr concerning the EPR paper). He was very right in his criticism against the Copenhagen collapse interpretation, which is indeed flawed.

 

[bhobba]

I've no clue what the book means.

He claims Einstein made unwarranted assumptions about slow moving particles being the same for fast moving ones, but doesn't detail anything.

Ohanian has a bit of a penchant for claiming flaws with Einsteins work.

His book on GR was the first serious book on the subject I read and claims a number of errors by Einstein. One is Kretschmann's well known objection to general covarience:
https://en.wikipedia.org/wiki/Erich_Kretschmann

I think Einstein agreed with that one and these days we have the principle of general invariance instead.

But the other one leaves me scratching my head. He attacks the principle of equivalence by saying tidal forces is the dead give away. I never really got that one - if you are near a large slab of mass its constant.

And you are right about QM - Einstein understood it very well and after his final attack on Bohr using his box and Bohr's solution using Einsteins own equivalence principle he never questioned it's validity again. He accepted it as correct - just incomplete. He championed the Ensemble interpretation precisely because it bypassed the objections (which I actually concur with) he had against Copenhagen.

Even some current physicists don't seem to get it, publicly anyway. Saw Brian Cox on a popular program the other night. When he was asked what science can teach politicians he said complementary. Quantum objects sometimes are particles and sometimes waves - the views are complementary. Politicians should forge the same between left and right views on politics. I too am not that happy with dogmatic left and right views in politics, but to link it to complementarity, which I have never understood anyway - maybe I have a block or something I don't know - others seem to get it - via the highly dubious wave-particle duality just leaves me shaking my head - he really should know better. I think he does - but does take liberties with lay audiences, but I am not sure that's a good way to discuss political philosophy.

Thanks
Bill

 

[vanhees71]

"Complementary" is the most superfluous notion about QT. Maybe it's adequate for politics, who knows ;-)).

 

[Mister T]

I am scratching my head about that one.

It all depends on what you mean by proof. In the strictest sense a proof shows that a conclusion follows from a set of premises. In that sense the conclusion contains nothing that is not already present in premises. Induction, on the other hand, produces something not present in the premises. I don't think Einstein ever claimed that he had proven that rest energy is equivalent to mass. Rather, he demonstrated that in some cases rest energy contributes to the mass of a body.

 

[vanhees71]

Yes, indeed, and that's the correct interpretation of $E=m c^2$, which is perhaps the most famous formula of physics, even part of pop culture. At the same time it's the most misunderstood formula ever, and it's hard sometimes to convince even physicists that mass is not energy. The best one can say from a modern point of view is that mass terms are parts of the Hamiltonian of a dynamical system.

That there is a fundamental difference between mass and energy (despite the trivial factor $c^2$ which is just a unit-conversion factor, because for practical reasons we meausure times and distances in different units) is obvious from the mathematical structure underlying all relativistic physics. In SR it's Minkowski space, and there total energy and momentum of a closed system build a (conserved) four-vector, while mass (squared) is the corresponding invariant square of this four-momentum or, if the mass is not vanishing, the energy (squared) in the center-of-mass frame (up to appropriate unit-conversion factors in terms of powers of $c$).

Einstein got it right, even without Minkowski's math, and this once more proves his amazing physical intuition. I still don't know what the claim in the book mentioned in #4 might be!

 

[bhobba]

I still don't know what the claim in the book mentioned in #4 might be!

Found the following:
https://arxiv.org/ftp/arxiv/papers/0805/0805.1400.pdf

Had a quick scan.

The whole thing looks much more complicated than needed from our modern perspective and Noether. Don't know if it's still valid or just of historical interest.

It speaks of proofs by Einstein in 1921 - Noether was known by then so beats me what the fuss is - Einstein knew very well about Noether - it came about because defining energy in GR is problematical and Noether sorted it out - it's still problematical - but she found out why.

Thanks
Bill