Re: A Clock for Einstein - can anyone explain local time
- From: David <dseppala@xxxxxxxxxxxxx>
- Date: Sat, 08 Apr 2006 03:55:11 GMT
On Thu, 06 Apr 2006 03:40:14 GMT, Tom Roberts <tjroberts@xxxxxxxxxx>
wrote:
David wrote:I do not understand your phrasing. " You said, "to be a clock this
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
wall requires a clock ..."
each place where a flash will be produced, and those clocks must all beLet's say I do that. I have N pairs of wires, each one light-second
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.
longer than the next. And I have a flash-bulb at the end of each set
of wires. The flash-bulbs are placed at random (x,y,z) locations in my
inertial reference frame but the other end of each pair of wires are
at the same coordinate. I now attach a battery across the wires.
The bulbs flash at one second intervals as measured in this inertial
reference frame. Every other frame measures that the bulbs do not
flash at a constant rate. And I can accelerate this 3 dimensional
structure into any other inertial frame and the bulbs flash at a one
second rate in whatever inertial reference frame I end up in. Is
this structure allowed as a "clock" since the flashes occur at a
constant rate and it can be used in any inertial reference frame to
measure how many seconds have elapsed, yet no other inertial reference
frame will agree that the flashes occur at constant intervals?
Or do all the flash-bulbs have to be at the same point in space to
be considered a clock in relativity?
Actually the emitter rate isn't 0.5 seconds apart since the relative
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.
velocity between the rest frame and Frame A or Frame B is not 0.866c
(that's the relative rate between Frame A and Frame B).
Okay. But please put your answer next to my answer so I can see where
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.
we agree or disagree.
1. Do both Frame A and Frame B agree that each pulse hits both walls
simultaneously? My answer is Yes. This is because the y measurement
from laser to wall is the same for both wall A and wall B, and the two
pulses share the same x coordinate when they hit the wall, and the two
pulses started at the same point in space and time.
2. Does each pulse hit wall A at one second intervals as measured in
Frame A? My answer is Yes - this is the given info. When pulse 10
hits wall A, the synchronized clock at that flash position reads 10
seconds. When pulse 22 hits wall A, the synchronized clock at that
position reads 22 seconds.
3. Does each pulse hit wall B at one second intervals as measured in
Frame B? My answer is Yes, using the same reasoning as for answer 2.
4. Do the frame A observers agree that the number of pulses that hit
wall A equals the number of pulses that hit wall B during any interval
of time? My answer is Yes based on the answer to question 1 whenever
a pulse hits wall A a pulse hits wall B simultaneously.
5. Do the frame A observers agree that the number of pulses that hit
wall A match the number of seconds shown on every clock in Frame A?
My answer is Yes - the pulses hit at one second intervals.
6. Are the answers to questions 4 and 5 analogous for Frame B? My
answer is Yes - the logic and symmetry is the same.
7. If the same synchronization procedure used in Frame A is used in
Frame B, do the frame A observers agree that the Frame B clocks are
synchronized within the Frame B frame? My answer is Yes. Einstein's
answer appears to be no.
8. If 7 is Yes, and both frames agree that the number of flashes
hitting wall A matches the number of seconds elapsed on the A clocks,
and the number of flashes hitting wall B matches the number of seconds
elapsed on the B clocks, and the same number of flashes hitting wall A
equals the number of flashes hitting wall B, then both frames must
agree that the number of seconds elapsed on the A clocks equal the
number of seconds elapsed on the B clocks. My answer is yes.
Einstein's answer is no because of answer 7. Einstein's theory
seems to indicate that even when the same synchronization procedure is
used in both frames the same logic cannot be applied to the problem as
a whole. Is that correct?
Thanks,
David
.
Tom Roberts tjroberts@xxxxxxxxxx
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- A Clock for Einstein - can anyone explain local time
- From: David
- Re: A Clock for Einstein - can anyone explain local time
- From: Tom Roberts
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