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How can moving frame explain this experiment in SR



 
 
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Old April 10th 06 posted to sci.physics.relativity
David
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Posts: 326
Default How can moving frame explain this experiment in SR

I haven't been able to understand how this is explained from the point
of view of a moving observer. I asked a similar question before but
did not get a clear answer.

Here's the problem.

I have a rotating cylinder whose longitudinal axis is aligned along
the x axis. This rotating cylinder is in the rest frame. Let this
cylinder rotate at 100 revolutions per second as measured in the rest
frame, and let the diameter of this rotating cylinder be 10 meters.

I have a second inertial frame moving with velocity V along the x
axis. I'll call this frame the moving frame. At time t0 as measured
in the moving frame a straight line is drawn by the moving frame
observer along the top of the cylinder. Let the length of the
cylinder be such that the simultaneous events at each end of the
cylinder as measured in the moving frame is measured as a 1 second
interval in the rest frame. This means the cylinder rotated 100 times
as the line was drawn. As viewed in the moving frame this straight
line is always parallel to the x-axis. As viewed in the rest frame,
this line spirals around the cylinder 100 times. Now along this line
we attach a steel rod. It spirals along the surface of the cylinder
following the identical path as the line we drew. Observers in the
moving frame measure this rod to be a straight line.

Now at time t1 as measured in the moving frame all of points
connecting the steel rod to the cylinder are simultaneously
disconnected. Let's say we do this by removing the rotating cylinder
without affecting the attached steel rod. With the rotating cylinder
removed and only the steel rod remaining, observers in the moving
frame measure that this straight steel rod has an unusual property.
An observer in the moving frame would expect a straight rod to fly off
parallel to the x-axis. But instead of this occuring, this straight
steel rod continues to rotate length-wise around the x-axis at the 10
meter diameter as if the original rotating cylinder that it had been
attached to was still there. It does this eventhough no force is being
applied to it to cause this motion.

Don't the moving frame observers who conducted this experiment have to
conclude that this is not a straight steel rod?

The moving frame observers do some additional experiments. They find
they can create the identical situation if they accelerate a spiral
rod to V and set it spinning. Or set a spiral rod spinning and then
accelerate it. These experimenters also try to simultaneously attach
all points of various straight rods of different materials to a
rotating cylinder. They find that if the straight rod and the
rotating cylinder have zero relative velocity and also are at rest
with respect to experimenters ( the moving frame) all rods they try to
attach can be attached to the rotating cylinder without breaking the
rod. They find that if they try to attach one end first and then
the other end some of these rods break, others stretch and twist.
These same experimenters find that if the straight rods and the
rotating cylinder have zero relative velocity but they are moving
along the x-axis relative to the experimenters frame, then some rods
break when all points are simultaneously attached. When these broken
rods are examined these experimenters find that the rods are broken
due to stretching and twisting just as they would have been if they
were attached in the rotating cylinder at different times in the
experimenters frame if the rod and cylinder had zero velocity with
respect to the experimenters. These same experimenters can conduct
various other related experiments. In the original experiment for
example,after the cylinder has been removed, the experimenters can
slow either the rotation rate of the "straight rod" or they can slow
the velocity of the rod along the x-axis. In either case they find
that the rod becomes a 10 meter diameter spiral - just as it would
have been if the two ends were not attached to the rotating cylinder
at the same time. With each experiment, the experimenters must
conclude that the stretching and twisting was due to the rods not
being attached to the two end points of the cylinder at the same time.
I don't see what possible explanations exist for the shape of the rod
if the moving frame observers measure that the rod on the rotating
cylinder is indeed "straight". What possible explanation is there
for a "straight rod" rotating lengthwise in a 10 meter diameter about
the x-axis with no force acting on it to change its direction?
This all seems non-sensical to me. Please give the relativity
explanation.
Thanks,
David Seppala

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