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The Principle of Equivalence which is at the heart of the conceptual foundation of General theory of Relativity, says that, the physics in a local gravitational field cannot be distinguished from the physics in a suitably chosen non-inertial frame in a gravity-free space.

  1. Isn't the term spatially uniform or spatially constant gravitational field more accurate and sufficient than a using the term local gravitational field?

  2. When we say physics in the two situations are indistingusable, do we only refer to gravitational experiments or both gravitational and non-gravitational experiments?

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  1. Nope. The principle is trying to convey that only local experiments have indistinguishable results. Saying a uniform or spatially constant gravitational field means the field might be the same but the experiment might be elsewhere (say at a lower potential). Whereas a local gravitational field always looks uniform (for the same reason that local spacetime always appears flat).

  2. I think the weak equivalence principle specifies non-gravitational experiments, but the strong equivalence principle says all experiments. The idea expressed is that "the physics... cannot be distinguished". Saying the physics is indistinguishable means the results of ALL experiments are indistinguishable. After all, physics is more than just gravity.

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  • $\begingroup$ Dear @Jim Which kind of experiment(s) might enable one to distinguish these two such situations? $\endgroup$ – SRS Apr 21 '17 at 13:55
  • $\begingroup$ "the field might be the same but the experiment might be elsewhere (say at a lower potential)." When you say local experiments, don't you mean that you're doing experiments in a sufficiently small region of space so that the gravitational field is unique and constant? Let me explain with an example. $\endgroup$ – SRS Apr 21 '17 at 14:00
  • $\begingroup$ Suppose, Alice stands on the Earth's surface in a closed box. He's not allowed to look outside. He's subjected to the local gravitational field of the Earth $\textbf{g}$ which is spatially constant or uniform. His friend Bob is in a similar box which accelerates in outer space with an uniform acceleration $\textbf{g}$, driven by an artificial engine. He can't look outside either. Then just by performing experiments inside their respective boxes, neither of them can tell which of the two situations he or she is in. $\endgroup$ – SRS Apr 21 '17 at 14:01
  • $\begingroup$ For example, two identical balls each of mass $m$, when dropped from the same height at rest, both falls towards the ground with same acceleration as detected by both of them. This example seems to imply that a spatially uniform gravitational field throughout the boxes is enough. Isn't it so? $\endgroup$ – SRS Apr 21 '17 at 14:03
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    $\begingroup$ @SRS those are local experiments, yes. But a spatially uniform field could just be something equal in magnitude and direction in one place as well as 1000km lower. If you observe an experiment performed next to you and one performed 1000km lower in the gravity field, you'll observe different results because of gravitational time dilation (among other effects). This is non-local but spatially uniform. The same is not true in just non-inertial frames. Thus the distinction between spatially uniform and local $\endgroup$ – Jim Apr 21 '17 at 15:08

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