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- I am confused. I see it written that standard SR and Lorentz type theories with a preferred frame are equivalent, but...

SR interpreted as having no absolute frame of reference and an absolute frame type version of SR, where the speed of light is isotropic only in one undetectable frame are considered equivalent, since they use the same math.

But here is a scenario in which I don't see how the physical predictions could be the same. What am I getting wrong? How are the below scenarios equivalent?

1. Standard SR. A sphere is rotating at a very fast angular velocity (hypothetical scenario). An observer in the same frame who is not rotating will see it as shrunk. But it will keep its spherical form.

2. Non-standard SR (call it LR) with light speed being isotropic only in one absolute frame. The sphere rotates at angular velocity w. It is not located in the absolute frame, so some parts will have the speed v + w, others v - w. Thus, the sphere will have an egg shape, because the part moving at speed v + w momentarily will contract more than the one with v - w (iff we take the degree of contraction to be proportional to the speed, as Lorentz did).

Therefore, in a world where an alternative interpretation to that of Einstein is adopted the fast moving spheres will be seen egg-shaped in any frame other than the absolute one.

Couldn't not seeing such eggs be a proof of standard SR, excluding any absolute frame?

If SR and LR are not distinguishable even in principle, how is this possible?

Thanks.

But here is a scenario in which I don't see how the physical predictions could be the same. What am I getting wrong? How are the below scenarios equivalent?

1. Standard SR. A sphere is rotating at a very fast angular velocity (hypothetical scenario). An observer in the same frame who is not rotating will see it as shrunk. But it will keep its spherical form.

2. Non-standard SR (call it LR) with light speed being isotropic only in one absolute frame. The sphere rotates at angular velocity w. It is not located in the absolute frame, so some parts will have the speed v + w, others v - w. Thus, the sphere will have an egg shape, because the part moving at speed v + w momentarily will contract more than the one with v - w (iff we take the degree of contraction to be proportional to the speed, as Lorentz did).

Therefore, in a world where an alternative interpretation to that of Einstein is adopted the fast moving spheres will be seen egg-shaped in any frame other than the absolute one.

Couldn't not seeing such eggs be a proof of standard SR, excluding any absolute frame?

If SR and LR are not distinguishable even in principle, how is this possible?

Thanks.

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