The Twin Paradox in a Universe with a Compact Dimension
Eugene Shubert
inertial reference frame that can be determined experimentally
by measuring deviations from the 1/r^2 force law.
http://arxiv.org/PS_cache/gr-qc/pdf/0503/0503070.pdf
Eugene Shubert
http://www.everythingimportant.org/relativity/
Ben Rudiak-Gould
> A spacetime with a compact spatial dimension has an absolute
> inertial reference frame that can be determined experimentally
> by measuring deviations from the 1/r^2 force law.
>
> http://arxiv.org/PS_cache/gr-qc/pdf/0503/0503070.pdf
This is a very poor paper, in my opinion. The authors point out (correctly)
that a compact dimension -- and the associated preferred frame -- can be
detected in principle by emitting a pulse of light and waiting for it to
return, but that the wait time is comparable to the size of the compact
dimension. They then claim (incorrectly and ludicrously) that an experiment
based on the 1/r^2 Coulomb force doesn't require a similar waiting time. Of
course it does, and for the same reason that the light-pulse experiment
does. They do finally admit this near the end of the paper ("Eq. (8) assumes
that the charge has been at rest for sufficiently long so that our
expression for the electrostatic field applies.") Worse, their experiment
won't work even in principle, because there's no way to distinguish the
effect of an image charge from the effect of an unrelated charged body that
happens to be the same distance away. The only way you could distinguish
them would be to accelerate the charge and wait to see if the alleged image
charge accelerates in the same way -- in other words, to generate a light
pulse and wait for it to return!
In practice, a much cleverer technique is used to look for nontrivial
large-scale topologies: checking for correlated circles in the cosmic
microwave background. astro-ph/0310233 has a succinct explanation of why it
works:
>But how can we tell that the essentially random pattern of hot and
>cold spots on the last scattering surface have been multiply imaged?
>First of all, the microwave photons seen by an observer have all been
>traveling at the same speed, for the same amount of time, so the
>surface of last scatter is 2-sphere centered on the observer. Each
>copy of the observer will come with a copy of the surface of last
>scatter, and if the copies are separated by a distance less than the
>diameter of the surface of last scatter, then the copies of the
>surface of last scatter will intersect. Since the intersection of two
>2-spheres defines a circle, the surfaces of last scatter will
>intersect along circles. These circles are visible by both copies of
>the observer, but from opposite sides. Of course the two copies are
>really one observer, so if space is sufficiently small, the cosmic
>microwave background radiation from the surface of last scatter will
>have patterns of hot and cold spots that match around circles.
-- Ben
Nick
clock goes slow. Only the one
that accelerated(experienced weight)
will see the other twin's clock blueshifted.
There are no reciprocal relativistic effects.
Why should there be?
Only one clock will slowdown.