Re: The Rotating Disk

e_erpelding@xxxxxxxxx wrote:
The question is, Are there certain non-inertial reference frames such
that a bounded region of space is physically larger than as seen from
an inertial (at rest) frame.

I think that question is not well formed. For instance, on the surface of the rotating disk you seem to want to apply length contraction to the rotating circumference, and then claim that "the circumference is larger to the rotating observer than to the inertial observer for which the center of rotation is at rest." That claim is inappropriate, because to the rotating observer that circumference is not a constant-time slice of spacetime, and "size" really only applies to a constant-time region.

An analogy to illustrate this: consider a circle in Euclidean 3-d space. What is the area inside it? The simple answer is "pi r^2", because that is the area of a circle in a plane. But this is 3-d space, and one could have any 2-d surface whose edge is that circle but which does not remain in the plane of the circle; obviously the area of such a surface can be anything larger than pi r^2.

The way you stated your original question implies you are thinking of a constant-time spatial volume of spacetime. But different observers have different notions of "time", and can obtain different results. As soon as you open the door to non-inertial coordinates, you allow the possibility that the 3-d spatial surface can be convoluted (as in the analogy).


Tom Roberts
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