Re: Einstein's math and physical objects

From: Todd (nope_at_nospam.com)
Date: 01/16/05 

Date: Sun, 16 Jan 2005 14:43:04 GMT

"Tom Roberts" <tjroberts@lucent.com> wrote in message
news:CumGd.9732$Vj3.8326@newssvr17.news.prodigy.com...
> Todd wrote:
>> I'll venture to speak for Harry and say we both agree. But, again, this
>> is not the situation we find intriguing. We want to consider David's
>> original situation where the disks and wires are NOT Born accelerated.
>> In David's situation the disks are accelerated in identical manners
>> relative to A (reminiscent of the Bell spaceship paradox).
>
>
> It's essentially the same as for Born rigid motion, as should be obvious
> if the disks are mounted on a common axle. The only difference is that the
> disks are pulled further apart, so the axle and wires must stretch.
>
> The helix is caused by the different in simultaneity, not any details of
> the acceleration.
>

The case we're looking at is not Born rigid motion. In our case, a common
axle connecting the disks would develop twisting stresses which indicates
that we are not dealing with Born rigid motion.

Let me avoid the acceleration by bringing about the final state in a
somewhat different way. Imagine that the disks are at rest in frame B and
the disks are not rotating. Diametrically opposite wires connect the disks
as before. Frame B is moving in the positive x-direction relative to frame
A. Thus, A sees the disks sliding in the positive x-direction, not
rotating, and the wires parallel to the x-axis.

Now suppose that the disks begin to rotate simultaneously _according to A_.
Describe the appearance of the wires in A once the wires have achieved a
steady state motion where all elastic waves in the wires have dissipated and
we can neglect distortions of the shapes of the wires due to 'centrifugal'
forces.

I think the wires will assume a _conical_ helix shape in A. If so, then
observers in frame A see something fairly 'odd' which begs for a _dynamical_
description in terms of forces as measured in frame A. After all, A is an
inertial frame and the SR laws of dynamics must account for the contortion
of the wires into the conical helix shape.

If the disks were not sliding along in frame A and they started rotating
simultaneously in A, then the wires would of course remain parallel to the
x-axis. It is interesting that just adding the uniform sliding motion in
frame A makes the wires assume such a different shape.

Todd

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