From: pcm@cs.brown.edu (Peter C. McCluskey)
Subject: Re: Simultaneous events and frames of reference?
Keywords: relativity
Organization: The Ergosphere Colonization Society
Date: Sun, 16 Aug 1992 17:02:34 GMT

In article <1992Aug12.211935.17309@bert.eecs.uic.edu>, artn@bert.eecs.uic.edu (Ellyn Sandor) writes:
|> 1) The twin paradox.  Twin O (old) stays home and twin Y (young) goes
|> for a ride.  Fine, time slows down for the person accelerating .  But wait!
|> Motion, acceleration, etc. is relative, right?  So, relative to twin Y,
|> twin O is moving. Or is it purely acceleration (which is relative over
|> time to ones last frame of reference) which causes time dilation. Or
|> something like that. Anyway, my point is, if relativity means there are no
|> privelaged (sp?) reference frames, why does the twin who goes away get to
|> stay younger? 

Relativity means that all reference frames provide equally valid descriptions
of the universe. Frames with different accelerations will use somewhat different
rules which reflect those differences in acceleration. It is not obvious
whether the idea of "zero acceleration" is an absolute or is defined relative
to the total mass of the universe.

|> 2) If you have a disk with a circumference of one light year, and rotate
|> it at the rate of one revolution per year, does it shrink?  I suspect the
|> answer to that has something to do with points moving in a circle being
|> in constant acceleration, so if neccessary, modify the question so that 
|> a point on the edge has a tangential speed close to that of light.  It
|> seems that the disk should shrink, since relativity doesn't really care
|> whether you end up in the same place, and if a point on the disk is moving
|> at the speed of light, that would be an impossibility, so the disk must
|> contract in order to prevent it (which is also a length contraction
|> tangentially)

Assuming the disk is sufficiently rigid, attempting to accelerate it to
1 rev per year will cause the mass of the disk to go to infinity as the
speed of the edge approaches c. So let's assume it can be accelerated to
1/4 rev per year. This gives an edge point speed of PI/4 ~ .8c, and an
acceleration ~ 6g, so there is nothing absurd about the conditions.
Attempting to apply special relativity to it yields the conclusion that
the circumference must shrink to less than 2*PI*r, i.e. that space in
this region becomes positively curved. This contradicts an assumption
of special relativity, and suggests that general relativity is needed
to reach a trustworthy result.
The closest I have seen to a treatment of this problem using GR is the
Tipler cylinder. If a cylinder of infinite length and existing for an
infinite time has enough rotation (I think the surface speed has to be
> .25c), Tipler demonstrated that time travel is possible in its vicinity.
Poul Anderson's book, "The Avatar", has references to the original articles
on this subject. I don't think he was able to get an exact solution for
finite length cylinders, which is presumable how the disk should be analyzed.
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