aachenmann said:
Einstein's second postulate states that the speed of light is constant as viewed from any frame of reference. Most of the books on relativity that I have been reading usually ask the reader to accept that fact because proving it is behind the scope of the book. Can anyone help me understand the actual reason behind the second postulate?
thanks...
The reasoning behind this has some subtle complexity that is not always appreciated. The short answer is that the speed of light is constant because we
define distance and time in such a way that it is automatically true.
If you are a beginner in relativity, it might help to just accept the short answer and come back to this later when you have learned more.
Now for the longer answer.
To measure the speed of something, you need to measure the distance it travels from A to B, the time when it passes A and the time when it passes B. To measure times we need two clocks that are stationary in the frame of reference, one at A and one at B. The reason we can't use a single clock that moves from A to B is that we already know, from the
twin paradox, that motion affects clocks (or to be more precise, relative motion between clocks affects their synchronisation).
The problem arises, how do you synchronise the two clocks at A and B? You can't do it by transporting a clock from A to B, as already mentioned. The convention is, we use light signals sent from A to B and reflected back to A. Assuming the speed of light is the same in both directions, we can set the time at B to be half-way between the transmission and reception times at A.
However, as we have now used the constancy of the speed of light to sync the two clocks, if we now use those two clocks to measure the speed of light, it is inevitable that they will measure the same speed in both directions.
If we then combine this fact with the experimentally-verified fact of the constancy of the so-called "two-way speed of light" (its
average speed when reflected A-B-A as above, and timed using a single clock at A) then we must conclude that the "one-way" (A-B) speed of light is constant in all reference frames.
Note that all of this depends on our choice of clock-synchronisation convention. In special relativity it is assumed that the "
Einstein synchronisation convention", which I described above, is always used. It is possible to use other methods of synchronisation, and then the speed of light wouldn't be constant
measured in those non-standard coordinates.
I have already said you can't sync two clocks by transporting a clock from A to B. But in fact, you can consider what happens as the transported clock moves slower and slower. If you extrapolate the results as the speed of the clock tends to zero (relative to our frame of reference), it can be proved that this "ultra slow clock transport" sync gives exactly the same result (in the limit) as the "Einstein sync" I described above. This lends credence to the proposition that "Einstein sync" is the natural way to sync, and thus that the speed of light should be constant.
