Let me write one more reply since I think my first one wasn’t entirely clear.
Let’s put all this into a thought experiment like this: Universe A contains only a light observer with a round bottle half full of water. Universe B contains all that, and moreover a lot of uniformly isotropically distributed distant massive stars. In both universes the spacetime region around the observer can be described by Minkowski metric. At the beginning, the observer sees that the water is spread near the walls of the bottle with a round vacuum bubble in the middle; this minimises the energy due to surface tension. Now, the observer gives the bottle some spin. Will the observation in universe A be different from that in universe B?
If GR is right, then no, it wouldn’t. In both, the observers will see the water concentrated in regions most distant from a specific straight line, which is reasonable to call the axis of rotation. To see that, it is enough to realise that the distant stars influence the bottle only by means of the gravitational field, and it remains almost the same in both cases—approximately Minkowskian, assumed that the bottle and the observer aren’t of black hole proportions.
Of course one can then change the coordinates to those in which the bottle is static. With respect to these coordinates, the stars in universe B would rotate, and in universe A, well, nothing much can be said. But in both universes, we will find a gravitational field which creates precisely the effects of the rotation of the now static bottle. The stars are there only to distract the attention.
We can almost do the coordinate change in the Newtonian framework: it amounts to use of centrifugal force, which can be thought of as a gravitational force (it is universal in the same way as the gravitational force; of course, this is the equivalence principle). There are only two “minor” problems in Newtonian physics: first, orthodox Newtonianism recognises only gravitational force emanating from massive objects in the way described by Newton’s gravitational law, which is why the centrifugal force has to be treated differently, and second, there is the damned velocity dependent Coriolis force.
Okay, I give up. I don’t know the math well enough to speak confidently on this issue. I was just taking the Machian principles in the article I linked and extrapolating them to the scenario I envisioned, using some familiarity with frame-dragging effects.
Still, I think it’s an interesting exercise in finding the implications of a universe without the background mass, and not as easy to answer as some initially assumed.
Yes, it’s interesting, I was confused for quite a while, still the answer is simpler than what I initially assumed, which makes it a good brain teaser.
Let me write one more reply since I think my first one wasn’t entirely clear.
Let’s put all this into a thought experiment like this: Universe A contains only a light observer with a round bottle half full of water. Universe B contains all that, and moreover a lot of uniformly isotropically distributed distant massive stars. In both universes the spacetime region around the observer can be described by Minkowski metric. At the beginning, the observer sees that the water is spread near the walls of the bottle with a round vacuum bubble in the middle; this minimises the energy due to surface tension. Now, the observer gives the bottle some spin. Will the observation in universe A be different from that in universe B?
If GR is right, then no, it wouldn’t. In both, the observers will see the water concentrated in regions most distant from a specific straight line, which is reasonable to call the axis of rotation. To see that, it is enough to realise that the distant stars influence the bottle only by means of the gravitational field, and it remains almost the same in both cases—approximately Minkowskian, assumed that the bottle and the observer aren’t of black hole proportions.
Of course one can then change the coordinates to those in which the bottle is static. With respect to these coordinates, the stars in universe B would rotate, and in universe A, well, nothing much can be said. But in both universes, we will find a gravitational field which creates precisely the effects of the rotation of the now static bottle. The stars are there only to distract the attention.
We can almost do the coordinate change in the Newtonian framework: it amounts to use of centrifugal force, which can be thought of as a gravitational force (it is universal in the same way as the gravitational force; of course, this is the equivalence principle). There are only two “minor” problems in Newtonian physics: first, orthodox Newtonianism recognises only gravitational force emanating from massive objects in the way described by Newton’s gravitational law, which is why the centrifugal force has to be treated differently, and second, there is the damned velocity dependent Coriolis force.
Edit: some formulations changed
Okay, I give up. I don’t know the math well enough to speak confidently on this issue. I was just taking the Machian principles in the article I linked and extrapolating them to the scenario I envisioned, using some familiarity with frame-dragging effects.
Still, I think it’s an interesting exercise in finding the implications of a universe without the background mass, and not as easy to answer as some initially assumed.
Yes, it’s interesting, I was confused for quite a while, still the answer is simpler than what I initially assumed, which makes it a good brain teaser.