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I have a question regarding Einstein's theory of relativity.

Einstein's equivalence principle states that locally it's not possible to tell if you're accelerating or being stationary in a gravitational field.

Nevertheless apparently a precise experiment will be able to distinguish between gravitation and acceleration according to this stackexchange post:

Tidal force in equivalence principle

a sufficiently precise experiment will be able to distinguish gravity from acceleration. The reason behind it is that the two effect are undistinguishable at a point, but the experiment will happen across a bunch of points.

One could argue now that Einstein added "locally" into the definition and this principle applies only locally and as far as I understood it only a mathematical abstraction like a point would be absolutely local? As soon as something exists it can't be absolutely local since it has a size but it could be treated as such since it's small (local) enough.

Does this mean that Einstein's theory of relativity has been violated and it is indeed possible to tell if you're moving or standing still with a precise enough instrument (as the linked post states)?

The following video from Eugene Khutoryansky's youtube channel tried to explain that Einsteins theory of relativity hasn't been violated.

https://www.youtube.com/watch?v=1ENkP0h8nAg&t=548

According to the aforementioned stackexchange post Tidal force in equivalence principle shouldn't the balls closer to the gravitational field therefore accelerate faster than the balls further away from it? Additionally shouldn't the balls have equal acceleration (along the axis at which they're falling) if it were acceleration instead of a gravitational field?

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  • $\begingroup$ Not an answer, but you seem to conflate "motion"/"movement" with acceleration in your question. Things can move relative to other things while having zero acceleration. $\endgroup$
    – Marius Ladegård Meyer
    Commented May 18 at 13:23
  • $\begingroup$ What I meant was that if something accelerates it has to be moving. Something can't stay still after or during acceleration and therefore knowing that something has accelerated or is accelerating I can most certainly state that this has to be moving therefore I know its not standing still @MariusLadegårdMeyer $\endgroup$
    – Ethan Brown
    Commented May 18 at 14:39
  • $\begingroup$ No...? If I am inside a car and the car is accelerating, it is still at rest with respect to me. From my (non-inertial) reference frame the car is at rest. It is not moving. $\endgroup$
    – Marius Ladegård Meyer
    Commented May 18 at 14:56
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    $\begingroup$ To understand relativity, the first step is to stop saying "is is at rest" or "it is moving" and such things. You have to specify with respect to what is something stationary/moving/accelerating. $\endgroup$
    – Marius Ladegård Meyer
    Commented May 18 at 14:59
  • $\begingroup$ Leonard Susskind published a series of video lectures called the Theoretical Minimum. They are aimed at physics enthusiasts with some algebra/calculus background and no teacher. The idea is to provide just enough material and rigor to form a complete introduction to each topic. The series on General Relativity covers tidal forces. $\endgroup$
    – mmesser314
    Commented May 18 at 15:57

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