Prior to Einstein it was assumed that identical clocks of any two observers could be synchronized so that they would always agree. In terms of equations it was expected that:
With regard to spatial coordinates, it is clear that if two frames of reference are moving relative to each other, they will measure different coordinates on their respective meter sticks for the same event, and also different velocities for the same object. For example, if the frames in Fig.11.1 were exactly lined up at t = t' = 0, then the coordinate of the explosion in frame O would be equal to the coordinate x' as measured by O' plus the distance that the frames had moved relative to each other in that time interval:
Eqs[11.1] and [11.2] constitute the so-called Galilean transformations relating coordinates as measured in two
different frames. Common sense tells us that they must be
correct. It was therefore a complete shock to the scientific
community when Einstein realized that they contradicted the speed of
postulate, and suggested that they were, in fact, incorrect. To see
where they fail, we need to look at what they imply for the addition
of velocities. Suppose that just as the frames O and O' coincide, their
clocks are synchronized to read t = t' = 0. At precisely this instant
the observer in O' throws the ball to
the right with a velocity of u' = 3 cm/s relative to his frame.
(See Fig. 11.2 below).
We now have to extend our discussion to a situation which is easy to imagine, but rather difficult to realize in nature. Such situations are called gedanken or thought experiments. Suppose that O' is moving relative to O, at three quarters of the speed of light, instead of 2 cm/s. Moreover, instead of throwing a ball forward O' points a flashlight in the forward direction and turns it off and on quickly. This sends out a pulse of light moving at 300 million meters/second as measured relative to O'. How fast would O' see the pulse of light moving relative to his frame? In order to save writing, we will henceforth use the symbol c to denote the speed of light. Everytime you see this letter, you should think ``300 million meters per second''. According to the above discussion the speed of the pulse relative to O' would be c + 3c/4 = 7c/4, or about 500 million meters/second. This contradicts the speed of light postulate, which says that the speed of light should be the same in every frame of reference.
So what has gone wrong? The easiest conclusion to draw is that the speed of light postulate is incorrect. However, Einstein realized that one cannot give up this postulate without giving up either Maxwell's wave theory, or the postulate of uniform motion, and he was willing to give up neither. He therefore made a brilliant intuitive leap and concluded that our common sense is wrong. Einstein's faith in the speed of light postulate turned out to be well founded. Its strange consequences have since been verified experimentally. We will now discuss them in turn.