Re: Einstein's math and physical objects

From: Tom Roberts (tjroberts_at_lucent.com)
Date: 01/15/05 

Date: Sat, 15 Jan 2005 01:32:41 GMT

dseppala@austin.rr.com wrote: [...]
Harry wrote: [...]
Todd wrote: [...]

You guys are all confused.

In its initial inertial frame A, start the disks and wires spinning
(together). So at any instant in time in this frame the wires remain
parallel to the X axis and do not touch or cross. Note I stipulate stiff
wires that do not bend outward due to their rotation, and that the disks
remain rotating synchronously in this frame (e.g. mounted on a common axle).

If you don't agree with that, then that's the problem -- you don't
understand the physical situation.

Given that, look at it from another inertial frame B moving along the X
axis relative to frame A. In this frame, due to the difference in
simultaneity, at any instant in time the wires will not be straight, but
will be a helix wrapped around the surface of the cylinder with the same
radius as the disks. How much wrapping there is depends on the spacing
of the disks in frame A, their rotation rate, and the relative speed of
frame B wrt frame A. In particular, no matter how much wrapping there
is, the wires never touch or cross[#].

If you don't agree with that, then that's the problem -- you don't
understand SR.

        Yes, Harry, I have indeed "inversed" the original situation
        here. Because this is simpler to describe and understand.
        So back to the original situation:

Instead of the previous situation, accelerate the spinning disks using
Born rigid motion until their speed wrt frame A is the same as that of
frame B above, but in the opposite direction; call this frame C. Now
looking at the wires from frame A, they appear EXACTLY the same as when
in the previous situation we looked from frame B at the spinning system
at rest in frame A. In particular, no matter how much wrapping there is,
the wires never touch or cross[#].

If you don't agree with that, then that's the problem -- you don't
understand acceleration via Born rigid motion.

        [#] Exercise for the reader: prove they do not touch or cross
            even if the rotation rate and/or relative velocity are so
            large that there are N full-turn wraps, with N greater
            than the ratio of disk spacing in frame A to wire diameter
            in frame A (i.e. if one wrapped such wire smoothly and
            tightly around the cylinder one could not put N turns
            in a single layer because the wire is too thick).
            Hint: This is a very easy proof.

        [This is getting too repetitive, so I probably won't respond
         further.]

Tom Roberts tjroberts@lucent.com

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