Special Relativity & Einstein's Equivalence Principle

[jeremyfiennes]

TL;DR

Relation between SR and the equivalence principle stated in a published paper, but that doesn't seem to make sense.

I was recommended a paper:
<https://digital.library.adelaide.edu.au/dspace/bitstream/2440/101285/3/hdl_101285.pdf>.
And in the opening sentence read: "The Einstein equivalence principle (EEP) is at the heart of special relativity."
To me this didn't make sense. Firstly because Einstein formulated the EEP in ~1909 when he heard of a man falling off the roof of a house, which this was four years after SR was published. And secondly, because the EEP involves acceleration, whereas SR specifically excludes it. But since the paper was accepted by two reputable journals, I am wondering if there is some aspect that I am not grasping.

 

[Vanadium 50]

he opening sentence read: "The Einstein equivalence principle (EEP) is at the heart of special relativity."

Jeremy, Jeremy, Jeremy,

That's not what the opening sentence read. It says "The Einstein equivalence principle (EEP) is at the nheart of special and general relativity [1] and a cornerstone of modern physics." (emphasis mine)

It is not very good form to misquote a paper an ask us to explain the misquote.

 

[jeremyfiennes]

It is obviously at the heart of GR. But not GR and SR, as they say. I quoted the bit I was concerned with.

 

[vanhees71]

It's an interesting question, whether one can formulate GR without before having established SR, because one way (for me the most clear way) to get GR is to make the spacetime symmetry of Minkowski space (special orthochronous Poincare group) local (and forget about spin such to have a torsion-free connection) [1]. That's the mathematical assumption which is implied what's in the usual heuristic approach is called "the equivalence principle", which finally boils down to precisely the idea to "gauge" global Poincare invariance.

[1] T. W. B. Kibble, Lorentz Invariance and the Gravitational
Field, Jour. Math. Phys. 2, 212 (1960),
https://doi.org/10.1063/1.1703702.

 

[jeremyfiennes]

Thanks. I completely go along with SR and the EEP together being the foundations of GR. It was their saying that EEP is also at the heart of SR that made me wonder whether there is something that I don't have straight in my own mind.

 

[Ibix]

It is obviously at the heart of GR. But not GR and SR, as they say. I quoted the bit I was concerned with.

In that case you should put in an ellipsis (...) to indicate that you missed out something and that it is your personal opinion that the bit you've missed out is not relevant. We may disagree with that sentiment.

The equivalence principle says that SR is accurate in small regions even in curved spacetime. In a sense, the fact the spacetime is locally Lorentzian is what makes SR a useful theory at all given GR exists. I'm not sure I'd phrase that quite the way the authors did, but I wouldn't quibble over it either.

 

[vanhees71]

Well, this sentence in the paper is a bit unfortunate, because indeed I don't need any equivalence principle for SR but I need it to (heuristically) argue for the need of an extension of the space-time model to a Lorentzian manifold with the pseudometric as a dynamical field rather than a "rigid" space-time as in SR. I'd just have said the EP is at the heart of GR.

 

[jeremyfiennes]

Vanahee71 said "I'd just have said the EP is at the heart of GR". Ok. This was the essence of my query. Thanks all. Question closed.

 

[PeterDonis]

Einstein formulated the EEP in ~1909 when he heard of a man falling off the roof of a house

Where are you getting this from? Einstein's own account tells of his having the "happiest thought of my life" in 1907, while writing a review article--see pp. 151-152 here:

https://einsteinpapers.press.princeton.edu/vol7-trans/151

 

[jeremyfiennes]

Thanks for the ref. My memory is of seeing two accounts. One that "while I was sitting in my office in Bern". From which I assumed that it was shortly before he left there for Zurich. Another that he had seen in a newspaper an account of a man who had fallen from a roof -- luckily onto a pile of soft rubbish because otherwise the could have bee no GR! -- recounting that he had experienced "a marvelous sensation of weightlessness". Einstein was not always too consistent in his accounts -- of the role that M&M played in SR, for instance.

 

[PeterDonis]

My memory is of seeing two accounts.

The only account I have seen, and the only one I have ever seen discussed in any of the literature I have read, is the account described in what I referenced. The "while I was sitting in my office in Bern" refers to the time when he was writing the review article in 1907; he didn't move to Zurich until 1909. Since he described the equivalence principle in the 1907 review article, he obviously couldn't have first formulated it in 1909.

Einstein was not always too consistent in his accounts

Which means that one should not have much confidence in informal statements made by him; one should look for more reliable information. The reference I gave is to a published article he wrote after the 1919 eclipse observations that (apparently at the time--we now know they weren't actually accurate enough) confirmed the GR prediction of bending of light by the Sun (see the introductory material on p. 113 of the reference). So one would expect it to be more reliable.

 

[jeremyfiennes]

Ok. But in any case after 1905, so it can't have been a consideration in the formulation of SR.

 

[PeterDonis]

it can't have been a consideration in the formulation of SR

Yes, agreed.