Gravitation, acceleration, and inertial reference frames

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I have a 3-pack of related relativity musings I was hoping someone(s) could enlighten me on:

1) Since the reach of gravity is infinite and the universe is homogeneous and isotropic with regards to the distribution of matter, is it fair to say that no object, even those in deep interstellar or intergalactic space, is truly in an inertial reference frame? It would seem as if every object would always be accelerating all the time to some sort of degree, and thus always be in a non-inertial frame.

2) The only thing we know has a constant velocity is light. Could we consider light (photons) to be in an inertial frame, or is the fact that it is massless, etc. put it in a special category so we don't think of light as defining an inertial frame?

3) If I put an accelerometer on my kitchen table, would it read 9.8 m/s^2? Which direction would it read that it was accelerating in, up or down?

Thanks in advance for your consideration :approve:
 

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Orodruin
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1) Since the reach of gravity is infinite and the universe is homogeneous and isotropic with regards to the distribution of matter, is it fair to say that no object, even those in deep interstellar or intergalactic space, is truly in an inertial reference frame? It would seem as if every object would always be accelerating all the time to some sort of degree, and thus always be in a non-inertial frame.
Gravity is not a force per se in the general relativistic framework. If there are no forces (e.g., electromagnetic) acting on an object, it will feel no proper acceleration and be in a local inertial frame (assuming it is small enough not to notice tidal effects). This is essentially why many situations are well described by special relativity.

Could we consider light (photons) to be in an inertial frame, or is the fact that it is massless, etc. put it in a special category so we don't think of light as defining an inertial frame?
There are no inertial frames that are moving with the speed of light relative to other inertial frames, so the photons do not have a rest-frame. This is indeed due to photons being massless.

If I put an accelerometer on my kitchen table, would it read 9.8 m/s^2? Which direction would it read that it was accelerating in, up or down?
Yes, it will read 9.8 m/s^2. The acceleration is in the up direction (away from the Earth's center).
 

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