# Postulates of Special Relativity

Dr Lim Zhi Han

Koh Zhi Yong

Gerald Kang Joon Kiat

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Published 2022-09-25

# 6.5 Posulates of Special Relativity

The special theory of relativity is based on the acceptance of the universality of the speed of light. In developing his special theory of relativity, Einstein proposed two postulates (assumptions that are taken to be true). The first postulates asserts the existence of many inertia frames, travelling at constant velocity relative to one another.

First postulate of special relativity: The laws of physics remain the same for observers in inertia frames that are in uniform motion (even at rest) with respect to one another.

Notice how the above is similar to the Galilean principle of relativity, with "laws of mechanics" replaced by "laws of physics". Einstein claimed that the principle of relativity applies to all laws of physics, the laws of electromagnetism inclusive! In other words, among all inertia frames, there is no preferred frame; the laws of physics single out no one inertia frame as being in any way special than any other inertia frame.

The second postulate specifies the fundamental law of electromagnetism that is universal in all inertia frames.

Second postulate of special relativity: The speed of light (in vacuum) has the same value c in every direction in all inertia frames.

This is, of course, the result from the Michelson-Morley experiment. To put it in another way, the speed of light is invariant in all inertial frames. Let's take this postulate to the extreme and consider light as a single photon (Figure 1).

Figure 1. Observer 1 is in a train moving at constant speed v with respect
to Observer 2. A photon was emitted in the train and hits a screen.
Both observer made measurements of the speed of the photon and reported
the same numerical value. — Figure 1. Observer 1 is in a train moving at constant speed v with respect to Observer 2. A photon was emitted in the train and hits a screen. Both observer made measurements of the speed of the photon and reported the same numerical value.

If the photon is replaced with any other object travelling at a speed much less than the speed of light, Observer 2 will have seen the object move faster than Observer 1 according to the classical velocity addition formula Eq. GR (3). This is however, not the case for light, even as a photon! Although the second postulate flies in the face of our everyday experiences, it is by now a firmly established experimental fact.

In the next few sections, we shall explore the bizarre and surprising consequences of Einstein's postulates, all of which seem to contradict our everyday experiences.