Clock synchonization in relativity

In summary, the concept of relativity involves a transformation formula for time between two moving systems. According to the transformation, synchronized clocks in one system will be delayed as their distance along the direction of motion increases. However, this leads to the question of when simultaneous events in one system occur in the other system. The Lorentz transformation shows that moving clocks, initially synchronized, will become desynchronized by a factor of Dv/c^2, where D is the distance between the clocks along the direction of motion.
  • #1
Demian^^
8
0
I'm a bit confused about a statement in my course on relativity. I have a system S' that is moving with a direction v (in the x'-direction) compared to the system S, so the following transformation formula holds:
t = gamma*(t'+vx'/c^2)
The textbook now goes on to say (translated from dutch.. possibly poorly):
"Clocks that are synchronized in S (t=constant) will be delayed more (t'=smaller) as their distance along the x' axis increases."
Indeed, I agree that t' will be smaller, as x' increases. However, I was wondering the following. If at a time t in S all the clocks give a short lightflash or something, to show for instance that it's twelve o'clock, then in the S' system this flash will be seen at a time t' at a location x'. Now, in S' the lightflash will be seen sooner (t' smaller) as x' increases, so an observer in S' will conclude that as x' increases the clock actually runs more and more ahead, knowing that the flash means '12 o'clock' and that that '12 o'clock'-signal happens first for larger x'.
Is the statement in my course-book therefore wrong or am I messing something up? (probably the second, but I've thought this through a number of times now and I can't seem to figure it out)
 
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  • #2
The question really is: For events that occur simultaneously in S (the S clocks all strike 12 noon, for example) when do they occur according to S'?

Start with the appropriate Lorentz transformation:
[tex]\Delta t' = \gamma(\Delta t - v\Delta x/c^2)[/tex]

Since [itex]\Delta t = 0[/itex], this tells you that according to S' a clock at position x (x > 0) in S will strike noon before a clock at the origin (x = 0). ([itex]\Delta t'[/itex] will be negative.)

A way to summarize the clock desynchronization effect is: Moving clocks, synchronized in their rest frame but separated by a distance D along their direction of motion, are not synchronized in the stationary frame; The front clock lags the rear clock by an amount:
[tex]T = Dv/c^2[/tex].
 

1. What is clock synchronization in relativity?

Clock synchronization in relativity refers to the process of ensuring that clocks in different reference frames are accurately synchronized, taking into account the effects of time dilation and length contraction predicted by the theory of relativity.

2. Why is clock synchronization important in relativity?

Clock synchronization is important in relativity because it allows for accurate measurements of time and distance between different reference frames. Without proper synchronization, measurements would be affected by the differences in time and space predicted by relativity.

3. How is clock synchronization achieved in relativity?

Clock synchronization in relativity is achieved through the use of Einstein's synchronization procedure, which involves sending a light signal from one clock to another and adjusting the time based on the speed of light and the relative motion of the two clocks.

4. What are some real-world applications of clock synchronization in relativity?

Clock synchronization in relativity has practical applications in fields such as global positioning systems (GPS), where accurate time measurements are essential for precise location tracking. It is also important in the synchronization of clocks in different satellites and for accurate communication across vast distances.

5. Is clock synchronization in relativity always perfect?

No, clock synchronization in relativity is not always perfect due to factors such as gravitational time dilation and the limitations of technology. However, it can be made accurate enough for practical purposes, and any discrepancies can be accounted for through the use of correction factors and adjustments.

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