Re: Einstein's math and physical objects
From: Todd (nope_at_nospam.com)
Date: 01/15/05
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Date: Sat, 15 Jan 2005 17:56:52 GMT
----- Original Message -----
From: "Todd" <nope@nospam.com>
Newsgroups: sci.physics.relativity
Sent: Friday, January 14, 2005 10:55 PM
Subject: Re: Einstein's math and physical objects
> "Tom Roberts" <tjroberts@lucent.com> wrote in message
> news:Zo_Fd.9184$Vj3.729@newssvr17.news.prodigy.com...
>
TR's first scenario:
>> 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).
..
>> 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[#].
TR's 2nd scenario:
>> 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[#].
TR's Exercise:
>> [#] 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.
>>
> Well, I don't think you could ever have N greater than the ratio of disk
> spacing in A to diameter of wire _in A_ unless you are defining 'diameter
> of wire in A' differently than I would. Frame A sees the wire wrapped
> around the cylinder and I would define the diameter of the wire in A as
> the diameter of a perpendicular cross-section of the wire according to
> measurements in frame A. That is, suppose you take a 'snapshot' of the
> cylinder 'at one instant of time' according to simultaneity in A. The
> wire will be wrapped around the cylinder and it's diameter in A will be
> contracted relative to the wire diameter in B. The diameter of the wire
> in A is inversely related to the number of wraps in A such a way that you
> can never succeed in making N greater than the ratio of disk spacing in A
> to diameter of wire in A.
>
Here, I should have referred to frame C rather than frame B as I thought
your exercise referred to your second scenario where the wires wrap around
the cylinder in A but not in C.
However, your exercise makes sense to me if you intended it to refer to your
first scenario where the wires wrap around the cylinder in B and don't wrap
around in A. Then N is the number of wraps in B and you are saying that N
can be greater than the ratio of disk separation in A to wire diameter in A.
I agree with that. N can be arbitrarily large without the wires ever
touching.
Sorry for the misinterpretation on my part.
Todd
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