Originally posted by Martin Miller
I have repeatedly asked for a step-by-step description of some
means of absolutely synchronizing two clocks; so far, none has
appeared. I am of course speaking of dead-on synchronization
for clocks located anywhere in space, and not just close (i.e.,
within nanoseconds) of closely-located clocks. I am also talking
about proper verification of the claimed absolute synchronization.
Martin, I do not understand why clock synchronization is so important to you, since actual clock readings fall out of the mathematical analysis. In SR all that matters is how the "amount of time of an event" in one inertial reference frame relates to the amount of time of the same event viewed in a different inertial frame. My point is fairly simple to understand:
1. Let us stipulate that we have two clocks of identical construction, and that the clocks are attached by a rigid rod.
2. Let it be stipulated that the clocks are in an inertial reference frame.
Therefore, the clocks will tick at the same rate.
Thus, if they are in sync then they remain in sync, and if they are out of sync, then the difference in their readings is constant.
For example, suppose that when one clock reads 4, the other clock simultaneously reads 7. Since the readings of the two clocks differ, the clocks aren't synchronized. The difference in readings is:
7-4=3
Thus, the clocks are not in sync by 3 units.
If the readings had been equivalent, then the two clocks would be truly synchronous.
So here is my point though. The difference in readings is constant, and falls out of the mathematical analysis. In other words, relativity talks about how an amount of time in one inertial system "transforms" into a different inertial system.
For example, suppose that some event lasts \Delta t seconds measured by clock A, which is in an inertial reference frame. Now, suppose that clock B is moving relative to clock A, at a constant speed of v. According to SR, the time of the event will not be \Delta t seconds, according to clock B. Instead, the time measured by clock B will be delta t times gamma.
My point is that it is the difference in readings that matters, not the actual readings themselves. So, I don't see why clock synchronization is an issue.
I think your real question isn't being addressed. The issue shouldn't be how do you make two clocks synchronous, I think the real issue is, how does one determine the absolute difference in clock readings.
For example, suppose that one clock reads X, and another clock simultaneously reads Y. The difference in clock readings is defined as follows:
X-Y
If X=Y then the clocks are synchronized.
if not (X=Y) then the clocks aren't synchronized.
I think the real question for you is, "can one empirically determine the value of X-Y?" You seem to be hung up on empirically determining that X-Y=0. Wouldn't it be just as good to empirically determine "X-Y"? For example, suppose you already determined that X-Y = 52. Thus, the reading of clock X always exceeds the reading of clock Y by 52 units. Thus, if you are stationed at clock Y, and your clock currently reads 733, then you know that clock X reads 733+52=785.
So I guess my question is, "why do you need us to show that two clocks cannot be brought into synchronization?"