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I started reading up on GR a couple of days ago, and I'm somewhat stuck on the concept of a free-falling IRF. I understand that an observer on a free-falling small spaceship would experience the laws of physics in a rather simple form, eliminating the need for a force of gravity in the model, and thus would call it an inertial frame of reference, as in all proper accelerations being zero.

What I don't get is how this can be reconciled with the traditional relation between IRFs, that if you have another reference frame moving with constant translational speed with respect to the first, then the second will be an IRF as well.

Let's imagine a celestial body with an associated uniform gravitational field at sufficiently large distances. Let's also impose that it should not be rotating nor translating around some other object, in order for an observer on its surface to be qualified as an IRF in the traditional sense. If you define a second IRF to be the one associated with a spaceship in free fall, then clearly the observer on the surface cannot be considered to also be an IRF. The two observers' law of physics differ in the inclusion or exclusion of a force associated with gravity. So which one is more fundamental?

I'm sorry if I'm not wording this correctly, but my main problem is that it seems that there are two conflicting definitions of what an IRF should be, based on whether you want to include the force of gravity in your model of physics or not.

Cheers

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# Confused about the Equivalence Principle and Inertial Reference Frames

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