Re: Einstein's math and physical objects
From: Harry (harald.vanlintel_at_epfl.ch)
Date: 01/13/05
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Date: Thu, 13 Jan 2005 12:18:31 +0100
"Tom Roberts" <tjroberts@lucent.com> wrote in message
news:cs3pjr$hdu@netnews.proxy.lucent.com...
[reinserted] dseppala@austin.rr.com wrote:
>> In the final reference frame, you say the wires never touch. Please
>> explain what keeps each of these wires from taking the shortest path
>> between the connection points on the two end disks.
> Harry wrote:
> > Let the discs decellerate equally and synchronously
> > (in the rest frame) from let's say 100 m/s circumferial speed until
stop,
> > thus conserving the "twist". I suppose that now you won't claim that the
> > wires remain in a spiral shape, but that they do touch. Right?
>
> No. See below.
I looked and I saw that you *inversed* the problem. Surely you agree that
two wires that are at first parallel between two stationary discs, will
touch each other in rest after one disc has been turned relative to the
other by 180 degrees. (If you don't, I can set it up for you in 5 minutes
and send you a picture). See further below.
> > Next do the exact inverse, synchronously accelerating them back up to
speed.
> > What would make the wires separate in this perfectly symmetrical case,
as
> > they were crossing in the middle?
> You are confused, and both you and the original poster keep complicating
> things needlessly.
>
> Imagine this physical situation: In inertial frame A: two disks of
> diameter D separated by distance L along their common axis, which is the
> X axis of frame A. With the disks at rest in frame A, two wires are
> attached tautly between the disks at Y=+D and Y=-D. In frame A start
> both disks and wires spinning at time T0, let them reach a steady-state
> spin at time T1, at time T2 have them both slow down their spin, and
> they both stop spinning at time T3. At all times the two disks are
> attached to a common axle along the X axis, so they always remain in the
> same orientation in Frame A, and the wires never have any twist in frame
> A. The wires are stiff/taut enough so their bulging at the center due to
> the rotation is negligible.
That's roughly the *inverse* problem of David.
Anyway, both are similar and should work out equally well, and therefore I
already considered both.
So now we have two examples of which we can compare the Lorentz transformed
situation with the situation as predicted from laws of nature.
In the "rest frame" A we can have side by side the following two systems:
1) Tom's discs which are spinning with two parallel wires "in A".
2) David's discs which are spinnning with two crossed wires that exactly
touch each other "in A"
> Now look at this from inertial frame B which is moving along the X axis
> relative to frame A. The two disks do not start spinning at the same
> time, and as they spin up the wires acquire a twist. But this twist is
> due to the difference in simultaneity between the two frames,
1) In inertial frame B the observers see your two discs acquire a phase
difference, and the wires are stretched.
However, I find it that situation too complex to give my opinion.
2) On the other hand, David's discs with touching wires in the rest frame I
find more easy to picture - that's where I became interested! They are just
crossed, barely touching in frame A, and they must therefore also barely
touch in the moving frame B. But I know of no law of nature that would make
them come together against the inertial force to just touch.
> so in
> frame B the wires follow a helical path (in frame A each wire is a
> distance D from the X axis all along its length, and so in frame B that
> still holds). The two disks reach steady-state at different times in
> frame B, and the twist remains.
1) Here you just proclaimed that the Lorentz transformations can't fail
because you believe what the Lorentz transformations tell you even when the
laws of nature seem to tell otherwise - that's a nice statement of faith,
but useless as scientific argument!
A sientific argument would make it plausible that in steady state the
stretched wires of your example will remain in a helical shape of exactly
the diameter of the discs that are in between them. But as I already said,
your example is a bit too complex for me.
2) More interesting I find the final example of David, in which the wires
touch according to A and therefore also should touch according to B.
I know of no law of nature according to which the wires can be balanced in a
strange twisted shape whereby they just keep touching each other. Our usual
expectation is that they would be parallel (or more precisely, slightly
bowed outward in opposite directions), as argumented from David's original
example where all of us reached exactly that conclusion from another
starting condition - the final equilibriums should be state conditions,
shouldn't they?!
This crossed wire example really bugs me, and it even may lean itself to
experimental verification.
> Later, when the disks cease their
> rotation, the twist will have precisely been cancelled as seen from
> frame B.
1) Of course.
2) Similarly, in rest the wires will cross "in B" just as "in A".
> Don't forget that in frame B the disks+wires+axle also have
> a large velocity along X in addition to their rotation: my
> discussion above ignores this -- the twist and helix
> mentioned above are observed by taking a snapshot of the
> disks+wires at a constant time in frame B.
>
> Yes, in frame B the wires will have a different value for tension than
> in frame A. And they will have a different total length in frame B than
> in frame A (of courseyou measure it at constant time in frame B) -- this
> is complicated by the length contraction along X but none along Y and Z
> and the fact that the wires are not parallel to any axis.
I assumed that they are always under tensile stress, to keep it simple.
> Instead of using a different frame B, one could accelerate the
> disks+wires+axle using Born rigid motion to another inertial frame C,
> and then look at them from frame A.
David also started with parallel wires but instead of an axle he used
equally accelerated discs - with an axle the twist occurs "in" frame B.
> In this case the view from frame A
> would be similar to that from frame B above (for the same reasons),
> except possibly for the handedness of the twist (which depends on the
> direction of motion between the frames). And if instead of Born rigid
> motion the disks+wires+axle were accelerated with the same acceleration
> relative to frame A (as the original poster did), then the axle and
> wires must stretch (in proper length), but things are otherwise the same
> as for Born rigid motion.
>
> > And why, ignoring inertial effects, would
> > the force equilibrium create a spiral shape with constant distance to
the
> > centre of rotation?
>
> Because such a helix is the Lorentz transform from A to B of the wires'
> positions. The wires never cross in frame A, and so cannot possibly do
> so in any other frame. <shrug>
That's just another statement about what the Lorentz transforms yield, it
doesn't explain anything.
> > That would be a spectacular relativistic low-speed effect!
>
> No, for any observable twist you'll need frames with a relative speed of
> an appreciable fraction of c.
No, in the discussed example the twist exists in the rest frame. To me it
would be spectacular if the wires that do cross at rest will separate to a
helix shape when the discs rotate.
Harald.
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