Undergrad Acceleration vs Gravity in General Relativity

[bgq]

Hi,

It is usually claimed that a person in an accelerating elevator with an acceleration equals to the gravity of the earth; this person cannot make any experiment that makes him know whether he is in the elevator or on the surface of earth.

However, if this person project two light beams vertically downward and perform extremely accurate measurements, then he can predict whether he is on the Earth or in an accelerating elevator as follows:

If the light beams converge a little bit, then he is on the surface of the earth. If they don't converge then he is in an accelerating elevator. Consequently, the two situations are not identical.

I totally understand that the strength of general relativity is because it passes a lot of other tests, but what surprised me is that this example is always presented although it looks to me as not accurate.

Am I missing something?

Thanks in advance.

 

[Ibix]

Am I missing something?

No. You are correct that the equivalence principle is only true locally. See, for example, the diagrams on pages 98 and 99 in Carroll's GR lecture notes (the second and third pages of this PDF: https://preposterousuniverse.com/wp-content/uploads/grnotes-four.pdf) which illustrate pretty much the example you are talking about.

The definition of "local" in this case is a small enough region of spacetime that you don't notice this kind of effect (with whatever degree of precision you are measuring).

 

[bgq]

No. You are correct that the equivalence principle is only true locally. See, for example, the diagrams on pages 98 and 99 in Carroll's GR lecture notes (the second and third pages of this PDF: https://preposterousuniverse.com/wp-content/uploads/grnotes-four.pdf) which illustrate pretty much the example you are talking about.

The definition of "local" in this case is a small enough region of spacetime that you don't notice this kind of effect (with whatever degree of precision you are measuring).

Thank you very much.