Re: Einstein's math and physical objects
dseppala_at_austin.rr.com
Date: 01/17/05
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Date: Mon, 17 Jan 2005 14:19:22 GMT
On Mon, 17 Jan 2005 12:50:10 +0100, "Harry" <harald.vanlintel@epfl.ch>
wrote:
>
>"Todd" <nope@nospam.com> wrote in message
>news:05wGd.9492$eT5.4591@attbi_s51...
>>
>> "harry" <harald.vanlintel@epfl.ch> wrote in message
>> news:1105888400.022235.231360@c13g2000cwb.googlegroups.com...
>> > [Tod]:
>> > "Let me avoid the acceleration by bringing about the final state in a
>> > somewhat different way. Imagine that the disks are at rest in frame B
>> > and
>> > the disks are not rotating. Diametrically opposite wires connect the
>> > disks
>> > as before. Frame B is moving in the positive x-direction relative to
>> > frame
>> > A. Thus, A sees the disks sliding in the positive x-direction, not
>> > rotating, and the wires parallel to the x-axis."
>> >
>> > Oh oh, I'm afraid you now messed up - for without rotation the wires
>> > are simply crossed for all observers.
>> > This isn't going to help...
>> >
>> > Harald
>>
>>
>> I still think I'm right! But maybe you can explain where I'm going wrong.
>
>I now see that I misread diametrically for diagonally! Sorry.
>
>> I'm not sure what you're referring to when you say 'without rotation'.
>> There is no rotation initially, but there is rotation in the final state.
>>
>> Again, the disks are initially sliding along the x-axis in frame A with no
>> rotation. The wires are strung between them parallel to the x-axis.
>Frame
>> B sees the disks and wires all at rest - no sliding and no rotation.
>
>OK, thus wires parallel along x and x'.
>
>> Now, we introduce the rotation. More precisely, we imagine that torques
>are
>> applied to the two disks _simultaneously in frame A_ so that the disks
>> obtain identical rotations simultaneously in frame A. No external torques
>> or forces are applied to the wires. The wires feel only their internal
>> stresses and the forces of attachment to the disks.
>>
>> Imagine what happens in frame B. Due to relativity of simultaneity, the
>> disk that has the greater x-coordinate starts rotating first. In this
>frame
>> the disks are not sliding. So, it's just like you where holding the disks
>> in front of you and turning one of the disks without turning the other.
>So,
>> in frame B the wires will assume a simple crossed configuration.
>
>Right.
>
>> Once the
>> other disk also begins to rotate in frame B, no further twisting of the
>> wires will occur and the wires and disks simply maintain their crossed
>> configuration while the whole thing rotates (from the point of view of B).
>
>Exactly. That is non-relativistic mechanics.
>
>> In frame A, the final configuration of the wires must be the Lorentz
>> transform of the configuration in B. If I'm not mistaken, this will be
>the
>> conical helix shape. Any points where the wires touch in B, they will
>also
>> touch in A.
>>
>> Todd
>
>OK I'm again with you! Indeed this is the same end condition as the original
>paradox.
>As mentioned before, the problem of the paradox is to identify the
>centripetal forces on the wires in frame A.
>
>Harald
>
>
Harald, can you please clarify the following. Let's assume the wires
are very long so we can examine things at non-relativistic speeds.
And lets assume the wires as measured in the final reference frame,
after the acceleration has stopped and the wries have reached a
steady-state condition, and the two disks have a relative rotation
angle of 180 degrees, and that the wires take the shortest path and
indeed cross. If you are in the first reference frame, and are at the
points where the wires cross, do you see the wires cross or merely
touch? By cross, let's say the final reference frame observer sees
the wires in the x-y plane over some small distance and he sees one
wire go from a positive y to a negative y coordinate over some small
distance, and he see's the other wire go from a negative y to a
positive y coordinate over the same span.
If you are in the original reference frame at that same position
and at that same time, what do you see? I don't see how you can
possibly see the wires merely touch, instead of cross. If they do
cross (one wire going from positive y to negative y while the other
wire goes from negative y to postive y), that means there is another
location where they must also cross as observed by this oberver (since
the disks have zero relative rotation angle for observers in the
original frame). We can do the observation of this point
experimentally. We simply assume the wires segment we are looking at
are 1 meter long, and the relative velocity between the two frames is
3 meters per second, and the rotation speed is say 120 revolutions per
second. I don't see how we would see anything substantially different.
Can you clarify?
Thanks,
David
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