Re: Einstein's math and physical objects

From: Harry (harald.vanlintel_at_epfl.ch)
Date: 01/10/05 

Date: Mon, 10 Jan 2005 12:47:14 +0100

<dseppala@austin.rr.com> wrote in message
news:41e048bb.200022594@news-server.austin.rr.com...
> On Thu, 06 Jan 2005 02:55:59 GMT, "Todd" <nope@nospam.com> wrote:
>
> >
> >"Todd" <nope@nospam.com> wrote in message
> >news:j3WCd.282655$5K2.75608@attbi_s03...
> >>
> >> Now imagine that somehow the cylinder is accelerated along the x-axis
such
> >> that each point of the cylinder has identical acceleration relative to
the
> >> earth frame for the same amount of time (relative to the earth frame).
> >> This will cause tensile stress to build up in the cylinder, .....
> >
> >Not just tensile stress, but also *torsional* stress. After all, the
> >cylinder will now be 'twisted' (as well as stretched) in its own rest
frame.
> >
> >That's kind of neat - a twisted version of the Bell spaceship 'paradox'!
> >
> >Todd
> >
> If we are in a frame that has zero velocity wrt to the disks and the
> wires are attached and stretched as described in my original post ,
> you must agree if the disks aren't rotating that the wires will cross
> (touch) if the relative rotation angle of the two disks is 180
> degrees. Its real easy to do this experiment with short wires or
> rubber bands. Furthermore, if the disks are rotating, and the disks
> develop a relative rotation angle of 180 degrees or more, the two
> wires will cross just as they did in the case where the disks are not
> rotating.

That looks correct to me; however, that doesn't reply my question to show
that this can happen. For example, you should show that while the speed of
the wire is less than c, such a relative rotation angle can be reached in
principle. Thus, to check if there really is a paradox, you would need to
produce a calculation example (either with equations or numbers).

Harald

> This too can be confirmed by experiment. The wires cross
> because if they are stretched, they try to follow the shortest
> connection path between the two disks. This steady-state condition
> may take awhile to achieve if the wires are long, but each wire will
> eventually take the shortest path connecting its two attachment
> points. When this occurs the wires will cross. And for each 180
> degrees of relative rotation angle between the disks, the wires will
> wrap around each other.
>
> In the problem I posted, the situation that I just described in the
> previous paragraph is the situation that occurs when the acceleration
> of the disks has stopped. The two disks have a relative rotation
> angle greater than 180 degrees, and the wires are stretched between
> the two disks. Therefore, as we know from experiments, the two wires
> must cross when a steady-state condition is achieved. But observers
> in the original reference frame never observe these wires crossing
> each other and wrapping around each other as they must do in the final
> reference frame. The only way the wires get "braided" is by having
> the relative rotation angle 180 degrees or greater. This never occurs
> in the original reference frame. Einstein's notions of space and time
> seem to lead to a physically impossible situation.
>
> Several people who posted a response think that the wires remain as if
> they were on the surface of a cylinder before, during and after the
> acceleration as viewed by observers in the final reference frame.
> This cannot be because Einstein's theory actually requires a physical
> stretching of the wires during the acceleration because the two disks
> are accelerated in an identical fashion as measured in the original
> reference frame.
> David

Relevant Pages

  • Re: Einsteins math and physical objects
    ... >> earth frame for the same amount of time. ... If we are in a frame that has zero velocity wrt to the disks and the ... you must agree if the disks aren't rotating that the wires will cross ... develop a relative rotation angle of 180 degrees or more, ...
    (sci.physics.relativity)
  • Re: Einsteins math and physical objects
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  • Re: Einsteins math and physical objects
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  • Re: Einsteins math and physical objects
    ... >> In the final reference frame, you say the wires never touch. ... >> between the connection points on the two end disks. ... two wires that are at first parallel between two stationary discs, ...
    (sci.physics.relativity)
  • Re: Einsteins math and physical objects
    ... > If we are in a frame that has zero velocity wrt to the disks and the ... > you must agree if the disks aren't rotating that the wires will cross ... ends of the rope. ...
    (sci.physics.relativity)
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