Re: A Clock for Einstein - can anyone explain local time
- From: Tom Roberts <tjroberts@xxxxxxxxxx>
- Date: Thu, 06 Apr 2006 03:40:14 GMT
David wrote:
In an inertial reference frame I have a wall that is at rest. At
equal local time intervals a flash appears at some location, not
necessarily the same location, on this wall. Let's say these flashes
occur at one second intervals, and let's say each flash is numbered
consecutively starting at zero. That's my clock.
That is not a clock. That is a wall on which flashes of light are projected.
The basic problem is that to be a clock this wall requires a clock at each place where a flash will be produced, and those clocks must all be synchronized in the rest frame of the wall. And the clocks and flash generators must be pre-programmed or communicating so that no two of them fire together.
In your case below that clock is in the rest frame of the laser, not in the wall; and since there is but a single "flash generator" no pre-programming is necessary to ensure just one flash occurs at a time.
Here's the problem. Let's say I have two inertial reference frames,
Frame A and Frame B. Let the relative velocity be V =0.866c. Let
each of these frames have an identical "wall clock" as described
above. Now let there be a third frame which I'll call the rest
frame. Let Frame A and Frame B move with equal and opposite
velocities parallel to the x-axis relative to this rest frame. Let
Wall Clock A be at y=1 and Clock B be at y=-1. In the rest frame I
have a laser that is pointed parallel to the y-axis. I use this laser
to generate the clock pulses seen on the wall in Frame A and in Frame
B. When the laser fires, it sends the same numbered pulse in both the
positive and negative y directions.
Note the relative motion is parallel to the walls, which remain parallel and a fixed distance "2" apart; the walls are parallel to the x-z plane.
Now both Frame A and Frame B see the pulses occur at one second
intervals as measured in their respective frames (due to the symmetry
of the problem).
OK. But to measure this each observer must have a number of assistants, each with a clock synchronized to the observer's clock in the observer's frame, and prepositioned where the flashes will occur. Note also that in the rest frame of the laser the flashes must be emitted 0.5 seconds apart.
That is Frame A observers say that pulse N+1
appeared on the wall in their frame one second later than pulse N.
Frame B observers say the same thing. Frame A and Frame B and the
rest frame observers all agree that each pulse hitting the respective
walls occurs simultaneously. In other words all three of these frames
agree that pulse N hit both walls simultaneously as is true for every
pulse. I don't see how it's logical for Frame A observers to
conclude that Clock B is running at half the rate Clock A is when they
can observe the same number at the same time on both walls for every
single "tick" of their clock.
These are flashes on a wall that is moving at high speed. This is not a set of two clocks, this is a set of 2N clocks, where N is the number of flashes observed.
Can someone explain why this "wall clock" is not allowed with
Einstein's theory? Exactly what are the rules for measuring "local
time"?
This is not a clock. In SR, and indeed in all of physics, a clock is located at a specific place and is treated as a pointlike object. Your "wall" is not at all like that.
Basically you have constructed a situation in which the time dilation between frames A and B is canceled by the difference in simultaneity between them.
Tom Roberts tjroberts@xxxxxxxxxx
.
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