Re: Einstein's math and physical objects
From: Harry (harald.vanlintel_at_epfl.ch)
Date: 01/12/05
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Date: Wed, 12 Jan 2005 16:20:29 +0100
"jem" <xxx@xxx.xxx> wrote in message news:7U9Fd.2$do.0@fed1read06...
> dseppala@austin.rr.com wrote:
>
> > On Mon, 10 Jan 2005 09:01:49 -0500, jem <xxx@xxx.xxx> wrote:
> >
> >>dseppala@austin.rr.com wrote:
SNIP
> >>>>>>>When I don't accelerate the disks from one frame into the other, I
> >>>>>>>follow you are saying. However, if I were to go into a lab here on
> >>>>>>>earth where the disk has zero velocity along the x-axis (as in the
> >>>>>>>final reference frame of the problem I posted), it is physically
> >>>>>>>impossible for me to have the two disks more than 180 degrees out
of
> >>>>>>>phase without the wires crossing (touching). There is no way to
make
> >>>>>>>that happen. If I'm observing the wires from a reference frame
that
> >>>>>>>has zero relative velocity wrt to the x-axis in this problem, the
> >>>>>>>wires must cross (touch) if the disks have 180 or more degrees of
> >>>>>>>phase difference - that is what physically happens when we do the
> >>>>>>>experiment here on earth.
> >>>>>>
> >>>>>>This is a different experiment than the original. One difference is
> >>>>>>that in this formulation (where the wires touch), the wires also
> >>>>>>stretch, whereas no stretching occurred in the original formulation.
> >>>>>
> >>>>>During the acceleration, since the two disks are accelerated in an
> >>>>>identical fashion as measured in the original reference frame, the
> >>>>>wires do indeed stretch in the experiment of my original post. This
> >>>>>is per Einstein's equations.
> >>>>
> >>>>OK, I mis-recalled the specification, but the manner in which the
disks
> >>>>are accelerated isn't important, the description you gave here (where
> >>>>the wires touch) is still different than the original.
> >>>>
> >>>>At any rate, you should have paid more attention to the second
paragraph
> >>>>than the first. The nature of coordinate transformations makes it
> >>>>impossible for one observer to see the wires touch when another
doesn't.
> >>>>
> >>>
> >>>Yes I agree that's what should occur, but the wires must cross in the
> >>>final reference frame when a steady-state condition is achieved. This
> >>>is a physical condition, so therefore we must get the math to agree.
> >>>Or can you show me how to attach non-accelerated wires to the same
> >>>points on the disks in the final reference frame in a manner that they
> >>>will not cross. I don't see how that is physically possible. Paul
> >>>seems to think that the wires that are accelerated lie on the surface
> >>>of a hypothetical cylinder even after the acceleration has stopped,
> >>>but he has not yet posted why these accelerated wires behave
> >>>differently then wires attached to the same points of the disks in the
> >>>final reference which haven't been accelerated.
> >>> Unless you can explain that, there seems to be two choices left.
> >>>Either the wires cross while the disks and wires are accelerating, or
> >>>the analysis is wrong.
> >>
> >>The only thing that's wrong is your insistence that if the disks are
> >>measured to be more than 180 degrees out of phase then the wires must
> >>touch. That's only true when the disks are "stationary" wrt the
measurer.
> >
> > As they are as measured by observers in the final reference frame.
> > That is what I don't understand. Why do you think the two disks do
> > not have 180 degrees or more of relative rotation angle between them
> > as measured in the final reference frame, after the acceleration
> > stops?
>
> They very well might "have 180 degrees or more of relative rotation
> angle between them as measured in the final reference frame", but the
> disks weren't "stationary" in this frame while the rotation was
> occurring, so the fact that the wires don't touch shouldn't be surprising.
I find your assumption very surprising - it's a perfectly symmetrical
situation in the frame in which the rotational axes are resting. I don't see
how the wires can't touch, from symmetry they must do so according to the
laws of nature.
The situation isn't symmetrical in the frame in which the whole set-up is in
translation - but I can't think of what would make the wires come together
in that frame, and misaligned on top of that...
> You can specify what it is that actually happens - the disks rotate such
> that the wires don't touch or they rotate such that they do touch. In
> either case when the transformation equations for observers in motion
> wrt the apparatus are applied, you'll find that all observers reach the
> same conclusion re. touching.
I am afraid you didn't understand the problem, for we all know that the
transformation equations only change the mapping. If I understood it well,
the question was if in this case that mapping is conform the laws of nature,
as is always claimed.
Cheers,
Harald
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