Re: Relativity

[David Bowman <dbowman@tiger.gtc.georgetown.ky.us>]

Leigh wrote:
> Deep down I suspect that there must be some fallacy in the hypothesis that
> such a system can be constructed. Perhaps the rim must deform elastically
> under the tension necessary to balance the centrifugal force, and of course
> we know that the requirement that the speed of sound be less than c
> constrains the rigidity of the material, given its density. Does anyone
> know a good solution to this simpler problem?

Leigh's suspicion above is essentially correct.  Imagine starting the disk
from a nonrotating state and then continuously spinning it up to the
relativistic rim speed that he considers.  As the disk spins up its radius
*grows* due to it yielding to the centrifugal tension present.  This process
cannot be postulated away by assuming that the disk is rigid since the
concept of rigidity is not allowed in relativistic problems (rigidity
*contradicts* the relativistic requirement of no instantaneous action at a
distance).  As the disk spins up it stretchs radially *and circumferentially*
by an amount which dwarfs any incipient Lorentz contraction of the
circumference.  At an angular velocity *much* lower than that necessary for
the rim speed to become significantly relativistic, the disk will fly apart.
This requirement that the disk must fail well before relativistic rotational
speeds are reached is a consequence that the (negative) cohesive energy
holding the particles of the disk together must be a small fraction of the
disk's rest energy, and this requirement of a small cohesive energy
(potential energy of interparticle interaction) is a consequence of the
requirement that the internal fields in the system must be small enough so
that the system is stable against spontaneous runaway pair creation via
tunnelling between "positive" and "negative" energy particle-antiparticle
states.

David Bowman
dbowman@gtc.georgetown.ky.us