Summary of Special Relativity

The theory of special relativity is the combination of two ideas and their seemingly weird consequences.

  1. The laws of physics take the same form in in each inertial frame – a reference frame in uniform motion. For example, Newton's 2 nd Law of Motion might take the formandin two inertial frames, whereandare for example, the accelerations in the two frames, but both Laws 'look' the same, so take the same form. This means that an experiment carried out in a moving train will give the same results as when it is performed in a lab. Furthermore, if there were no windows on the train and it was moving at a constant speed, there is no experiment that you could do to see whether or not it was actually moving. You may have experienced the feeling of sitting in a train, seeing the train next to you moving relative to you and not knowing whether it is your train or that train that is actually in motion. There is no such thing as absolute motion. All motion is relative.

  1. The speed of light has the same value in all inertial frames. Intuition leads us to add and subtract the speeds of bodies in uniform relative motion. We may be able to do this with ordinary objects moving slowly, but we cannot do this with light. The speed of light always has the same speed relative to us, and if we measure the speed of light emitted from a body moving relative to us we will find it has the same constant speed.

The first of these is called the principle of relativity, and it has survived in one form or another since being introduced by Galileo. The second one was Einstein's own insight. Evidence in favour of it had been gathering for some time. The Michelson – Morley experiment failed to find any difference in the speed of light, no matter how light travelled relative to the Earth's motion around the Sun, if it travelled in the direction of the Earth's motion, at right angles to it, or in the opposite direction.

The only way that the laws of physics and the speed of light can always be the same is for the nature of space and time to change. Prior to the theory of special relativity, space and time were thought to be fixed and rigid concepts. There were three dimensions of space, all at right angles, permeated by time, which it was thought, moved at a constant rate for all observers, as if the Universe's time were kept on some great cosmic clock. Special Relativity unified space and time into a single unified spacetime concept, in such a way that the faster you travelled through space, the slower you travelled through time, until for anything travelling at the speed of light, time ceased to pass. Space and time became partially interchangeable, with space becoming a fourth dimension in addition to the three space dimensions. Time remains distinct from the three space dimensions, and we may need a fully unified theory of all the forces to fully understand the stricture of space and time.

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