Undergrad Understanding the Einstein Equivalence Principle

[Frank Castle]

The Einstein equivalence principle (EEP) states that

“The outcome of any local non-gravitational experiment in a freely falling laboratory is independent of the velocity of the laboratory and its position in spacetime.”

I’m trying to make sure I’ve understood this correctly. I’m I correct to say that the EEP implies that all forms of non-gravitational energy fall at the same rate in a gravitational field and consequently that all non-gravitational laws of physics hold in the presence of a gravitational field, in particular, locally they take on the form they have in special relativity?

 

[PAllen]

That’s not really a complete statement of the EEP. Better is e.g. from page 9 of:

https://link.springer.com/content/pdf/10.12942/lrr-2014-4.pdf

What you say in explanation is certainly true, as far as it goes. Note that the local position invariance aspect of EEP is not limited to free fall frames, and is what says a Pound Rebka type experiment yields the same result, locally, on the surface of the Earth or an accelerating rocket.

 

[itfitmewelltoo]

I hate to be a bother here but I'm not understanding "non-gravitational experiment in a freely falling". Isn't "free-falling" by definition gravitational?

 

[PAllen]

I hate to be a bother here but I'm not understanding "non-gravitational experiment in a freely falling". Isn't "free-falling" by definition gravitational?

In Newtonian physics it is, but not in GR. The sense of the statement is that a Cavendish type of experiment (measuring attraction of two balls) is excludeded. The SEP (strong equivalence principle ) generalizes to allow such gravitational experiments, and it is hypothesized but not proven that GR is the only metric theory that observes the SEP.

 

[Frank Castle]

That’s not really a complete statement of the EEP. Better is e.g. from page 9 of:

https://link.springer.com/content/pdf/10.12942/lrr-2014-4.pdf

Thanks for the link.

Note that the local position invariance aspect of EEP is not limited to free fall frames, and is what says a Pound Rebka type experiment yields the same result, locally, on the surface of the Earth or an accelerating rocket.

So is this the statement that the (non-gravitational) laws of physics are valid locally in all frames of reference, and in particular, for a sufficiently small neighbourhood around each spacetime point they reduce to their special relativistic form?

In the strong form of the equivalence principle this is extended to gravitational experiments, what exactly is meant by this? I get that it requires that gravitational energy should fall at the same rate as all other forms of energy in an external gravitational field, such that objects whose total mass has a significant contribution from its gravitational binding energy behave identically to other objects (with negligible gravitational binding energy with respect to their total mass) in an external gravitational field.