Question

The Lorentz transformation for time is t = ϒ ( t’ + vx’/c² ). This is the time measured in O of an event that happened in O’ at x’, t’.

It contains two terms. The first is just time dilation, which is not hard to understand given the second postulate of SR. But the second term looks rather strange at first sight. It has the dimensions of time but doesn’t contain either t or t’. And it increases steadily with distance from the origin of O’. It represents a systematic de-synchronization of the clocks.

But why? In the parable of the angels, they all had identical clocks. Initially they were all at the origins of their coordinate systems. As the origin of O’ (x’ = 0) passed the origin of O (x = 0), all the angel (and angel’) clocks were set equal to zero. At that instant, all the clocks were indeed synchronized.

Then all the angels dispersed (as slowly as you like) to their appointed locations, and somehow, by the time they arrived, their clocks were no longer synchronized!

The challenge is to describe exactly what is happening and to derive the vx’/c² offset term in the Lorentz Transformation.

Answer 1

t = ϒ ( t’ + vx’/c2 ) in this equation we may say that time relative to other frame of reference is different but doesn't change for same frame of reference. The second term is in terms of velocity of different frame of reference which is relative to the speed of light.

We can understand by an example let we put a clock on Earth and we see it on Earth that is in normal time when we started to move away from it by relativistic speed then the light take some more time to come to us from watch hence clock will see slower if further we go with speed of light we see that light is in stop position as we are moving with the speed of light hence clock will appear to be stop or Time become stop relative to that frame but clock in your hand or in your frame of reference will show no time dialation.

I think I helped you.. this example is from Paul g Hewitt book.