Time Dilation: Is Distance a Factor?

[Moose352]

Someone told me that the normal time dilation formula $$\Delta t = \gamma t_{0}$$ is not correct and that the time dilation also depends on the distance (I'm not entirely sure of what). Is this true?

 

[DW]

Someone told me that the normal time dilation formula $$\Delta t = \gamma t_{0}$$ is not correct and that the time dilation also depends on the distance (I'm not entirely sure of what). Is this true?

He was probably referring to an accelerated frame observer. It is correct for calculating the time dilation of something with respect to an inertial frame.

 

[quantumdude]

Your friend could also have been referring to the Lorentz transformed time interval in a frame S' for which two events in S do not occur at the same location. In that case:

Δt'=γ(Δt-vΔx/c²)

In that case, the time interval in S' depends on the spatial interval between the events in S. Of course, it would be a misnomer to call that "time dilation".

However, in an inertial frame, for which Δx=0, the formula you state is correct.