From: *Jason Resch* <jasonre...@gmail.com <mailto:jasonre...@gmail.com>>
Clock desycnhronization is a different phenomenon and has a different
cause and explanation than time dilation.
Because of the relativity of simultaneity in SR, clock synchronization
is not a global phenomenon -- it depends on the way in which the clocks
are synchronized. So clocks synchronized by one method in one frame will
not necessarily be synchronized in different frames. The time read on
such clocks is local only, so will they will not necessarily agree when
they are brought together.
The effects of time dilation are dependent on relative speed. But
whether I bring the clocks together moving one of them at either 1
meter/second or 1 mm per year, they will still appear synchronized to
the person on the ground. You can calculate the time dilation effects
of moving at 1 meter per second over the ship's length of 100 meters,
it won't account for the 266.85 nanoseconds of clock descynrhonization
that the observer on the ground sees.
The effect is more related to length contraction than anything. If you
see a length contracted object, you are simultaneously seeing "older"
and "newer" parts of that object, the rear part of the object will be
newer in time, while the forward part of the object will be the older
part of the object. Consider the observer on the ground watching the
rocket gradually slow. The entire part of the rocket is slowing at
the exact same rate, but by the time it stops both clocks will again
be perfectly synchronized. This resynchronization cannot be explained
in terms of time dilation or different relative velocities.
There are no "older" or "newer" parts of an object, because there is no
such thing as an absolute time. Time is a purely local phenomenon:
apparent clock rates are affected by relative motions.
Because of general relativistic effects, slowing the rocket will cause
the clock rates at the front and rear of the rocket to be different, so
they will not remain synchronized, even if that concept made any sense
in the first place.
However, it can be explained in terms of objects in spacetime being
4-dimensional, and viewing acceleration or deceleration as the
rotation of those 4-dimensional objects. (which also explains the
phenomenon of length contraction)
4-dimensional space-time is a construct that sometimes has heuristic
value, but it cannot be said to be the 'explanation' for anything. The
only explanations that SR gives are in terms of the effects of Lorentz
transformations. When we introduce general relativity, we see that
Lorentz symmetry is only ever a local effect, so 4-dim space-time
becomes insignificant.
Bruce
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