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The Postulates of Special Relativity

As discussed in Chapter 1, the laws of physics are generally assumed to be invariant under displacements in time and space, as well as rotations about any axis. Einstein went one step further and advocated the following additional symmetry for the laws of physics.

\fbox{\parbox{4.5in}{\vspace*{7pt}{\bf Fundamental Postulate:}\\
The laws of physics should be the same for
all observers in uniform motion.\vspace*{7pt}}}

Given this symmetry postulate and Newton's first law (that all objects persist in their state of uniform motion unless acted on by external forces), Einstein came to what we will call the postulate of relative motion.

\fbox{\parbox{4.5in}{\vspace*{7pt}All {\bf uniform} motion is relative.\vspace*{7pt}}}

To understand the meaning of this postulate, consider the following situation. You are sitting in a train that is stopped at a railway station, with another train facing the opposite direction on the track directly beside you. At ten minutes before your train is due to leave, you look out the window at the other train, and see that it is slowly starting to move relative to yours. Your first reaction would probably be one of surprise: your train was leaving early! After the other train has passed from in front of your window, you might notice that the station was still there, and conclude that it was the other train that was moving.

To take this example further, suppose that your train is now moving at a constant speed of 100 km/hr. As long as the track is straight, you can pour beverages, juggle, play cards or doing anything else without taking into account the fact that you are moving. The postulate of relative motion takes this to its logical conclusion and states that if the motion is truly uniform, and you are sheltered from effects of the matter outside the train, there is no experiment that can be performed that will tell you whether your train is in motion or standing still. The best you can do is measure its relative motion compared to some other object.

You will have noticed that the uniformity of the motion plays an important role in the above analysis. This too is consistent with our experience. Suppose that the engineer of your train spots a cow blocking the tracks, and hits the breaks, causing the train to decelerate rapidly. You immediately detect this change in motion: if you are walking, you get thrown forward, or if you are holding a drink, the liquid suddenly sloshes out. If you are sitting in a seat facing the back of the train, you feel yourself pressed hard against the back of the seat. Even if you happen to look out the window and see the change in relative motion between you and the neighbouring train, you would not be tempted to conclude that the other train was accelerating. It is your drink that is spilling, while the people on the other train are completely unperturbed. Thus your intuition forces you to interpret the strange effects as a sudden change it in your train's motion.

This seems to contradict something one sometimes hears about Relativity, namely that ``all motion is relative''. If this were true, why would accelerating observers be different from those in uniform motion. The answer to this can be found in Newton's first law: there can be no acceleration without force. The many effects that you feel as your train decelerates are ultimately due to the forces causing your train to slow down. Although uniform motion is relative, there are big differences between observers moving at constant velocity and those that are accelerating.

Einstein needed to make on other assumption in order to arrive at the Special Theory of relativity.

behaviour of light is correctly described by Maxwell's\\
Theory of

As discussed in Chapter 10 Maxwell's theory describes light as a wave whose velocity in vacuum is determined by fundamental constants of nature. Consequently, for this theory to look the same to all observers, it must be true that:  

\fbox{\parbox{4.5in}{\vspace*{7pt}The speed of light is the same for all observers in uniform motion.\vspace*{7pt}}}

Since we will refer to it frequently in the following, we will call this the speed of light postulate. From this somewhat innocuous-sounding statement all the bizarre and counter-intuitive consequences of Special Relativity can be derived. This will be the goal of the next few sections.

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