SR clock sync problem

In solutions to various problems (as in the twin's paradox) clocks
appear to get reset when frames are changed. And the change in time
is a function of the distance of events, although in any given
reference frame distances between clocks have nothing to do with clock
rates and resynchronization. I don't understand what physically
causes this to happen, so I setup a simple SR clock problem. I don't
see how to explain the result of this simple problem using Einstein's
notions of time and space.

There are two reference frames that have a relative velocity V=0.866c
along the x-axis. I use that value so that its simple to talk about
the clock rates. Einstein really didn't detail how to synchronize
clocks so I am using a simple method. At time t0 = 0, a light pulse is
emitted from a point on the x-axis. In their respective inertial
frames, the distance from each clock to this point is measured. When
the light pulse arrives at a clock, the clock is set to the time equal
to this distance divided by c. Now all clocks in their respective
frames run at the same rate and are set to the same time.

Here's the problem. Let one frame be called the rest frame and the
other frame be called the moving frame. With the relative velocity
between the two frames at 0.866c, each frame measures that clocks in
the other frame run at half the rate of clocks in their own frame. So
let's say observers in the moving frame want to place a clock in the
rest frame that runs at the same rate as all of their clocks in the
moving frame. Since "time" in the rest frame runs half as fast as in
their own frame, they modify the oscillator frequency of the clock by
doubling it. I'll call this clock Cd (d for double the rate of ideal
clocks). So now the moving observers have a clock in the rest frame
that runs at the same rate as all of their clocks. They place it in
the rest frame at time t=0 at the point where the pulse of light used
to synchronize all clocks originated.

The rest frame observers say that this clock is not setup correctly.
They say clocks in the moving frame run at half the rate of the rest
frame clocks, so they say that instead of doubling the oscillator
frequency, the clock in the rest frame that runs at the same rate as
all the moving frame clocks should have its oscillator refrequency cut
in half instaed of doubled. So the rest frame observers modify a
clock so that it runs at half the rate of an ideal clock. I'll call
this clock Ch (h for half the rate of ideal clocks). This clock is
also placed in the rest frame at time t=0 at the point where the pulse
of light used to synchronize all clocks originated.

Now let two clocks in the moving frame be separated by 866
light-seconds. I'll call these clock A and Clock B. And let clock A
be at the point of origin of the light pulse used to synchronize all
clocks. Let the moving frame be moving in the negative x-direction
relative to the rest frame. Clocks Cd and Ch will take 1000 seconds
(as measured in the moving frame) to reach clock B. Now we can apply
Einstein's equations, and find that the rest frame observers say that
the separation between these two moving frame clocks is 433
light-seconds and the second moving frame clock will be at the same
point in space as clocks Cd and Ch in only 500 seconds. So we find
that when the clocks meet, clock B reads 1000 seconds, clock Cd reads
1000 seconds (it is running at twice the rate as other rest frame
clocks), but clock Ch only reads 250 seconds (it is running at half
the rate as other rest frame clocks). So clock Ch is not synchronized
with all of the moving frame clocks as thought by the rest frame
observers.

I don't see how to resolve this problem. According to the rest frame
observers, clock Ch is running at the same rate as every moving frame
clock. Clock Ch got set to zero at the same time as Clock A in the
moving frame and Clock Cd were set to zero. According to the rest
frame observers, Clock Ch is running at the same rate as Clock A and
Clock B, so therefore this must have been some problem with the
initialization of Clock B. But I could not determine how the rest
frame observers say the initialization of Clock B should have been
done.

Can anyone explain how the rest frame observers resolve the
discrepancy between clock Ch reading 250 and clock B reading 1000 when
they meet?
Thanks,
Dave Seppala
.

Relevant Pages

  • Re: SR clock sync problem
    ... clock Ch is running at the same rate as every moving frame ... moving frame and Clock Cd were set to zero. ... do not read the same time simultaneously according to the rest frame. ...
    (sci.physics.relativity)
  • Re: SR clock sync problem
    ... clock Ch is running at the same rate as every moving frame ... moving frame and Clock Cd were set to zero. ... do not read the same time simultaneously according to the rest frame. ...
    (sci.physics.relativity)
  • Re: SR clock sync problem
    ... clock Ch is running at the same rate as every moving frame ... moving frame and Clock Cd were set to zero. ... moving clocks that are strung along the x axis of the moving frame and synchronized according to the moving frame are _not synchronized_ according to the rest frame. ...
    (sci.physics.relativity)
  • Re: SR clock sync problem
    ... so I setup a simple SR clock problem. ... Let one frame be called the rest frame and the ... other frame be called the moving frame. ...
    (sci.physics.relativity)
  • Re: Clocks in circular motion - math logic help please
    ... Call one frame the rest frame and the other ... Let a clock K' in the moving frame ... Let the clock K" in this circular path (the non-inertial ...
    (sci.physics.relativity)