11.3 Special Theory of Relativity

11.3 Special Theory of Relativity

The theory of relativity deals with how observers in different states of relative motion describe physical phenomena. The special theory of relativity addresses problems involving inertial (non-accelerating) frames of reference. There is another theory, called the general theory of relativity, that deals with problems involving frames of reference that are accelerating relative to one another. The special theory of relativity is based on two postulates, which can be stated as follows:

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1. The laws of physics are the same in all inertial frames (Principle of Relativity).

2. The speed of light in free space has the same value for all observers, regardless of the state of motion of the source or the observer (Principle of Constancy of Light).

The first postulate generalizes the fact that all physical laws are the same in frames of reference moving with uniform velocity relative to one another. If the laws of Physics differed for observers in relative motion, those observers could determine which was stationary and which was moving. However, such a distinction does not exist, implying that there is no way to detect absolute uniform motion.

The second postulate states the experimental fact that the speed of light in free space is a universal constant, denoted as $c$ ($c = 3 \times 10^{8}\,\mathrm{m/s}$). Since $c$ is constant, space and time become relative. For example, if you are sitting in a train moving at the speed of light and you hold up a mirror in front of you at arm's length, you will still see your reflection in the mirror. This is because, according to the principle of relativity, no experiment can detect the constant motion of the train relative to the person inside it.

These simple postulates have far-reaching consequences. They include phenomena such as the slowing down of clocks and the contraction of lengths in moving reference frames as observed by a stationary observer. Some interesting results of the special theory of relativity can be summarized as follows, without going into their mathematical details.