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Special Relativity: Kinematics

Introduction to Relativistic Kinematics

Table of Contents

Terms and Formulae

The study of Special Relativity begins with the concept of a reference frame. This is just a particular way of dividing up space and time. Imagine someone standing still on the surface of the earth. This person naturally divides up space by drawing coordinate axes, and divides up time by having a clock which ticks, say, once every second. Now imagine another person moving past on a train. The most convenient way of dividing up space for them is also by drawing coordinate axes in the train and having a ticking clock. However, the person on the ground sees the coordinate axes on the train flying past them at a certain speed. Thus the person on the ground and the person on the train divide up space in different ways; what appears stationary in the coordinates of the train will appear to be moving in the coordinates of the ground. The person on the ground and the person on the train are said to have different frames of reference. What is meant by the "reference frame of the earth," for example, is just the set of coordinate axes in which the earth is stationary.

In 1873 James Clerk Maxwell presented his unified theory of electricity and magnetism which predicted the velocity of an electromagnetic wave as being the same as that of light ( c = 3.0×108 m/s). Towards the end of the nineteenth century it became apparent that there was a problem with Maxwell's elegant theory: it predicted the same velocity for the speed of light irrespective of reference frame, whereas one would expect that the speed of a light pulse emitted in your direction on a train traveling directly towards you would have a speed c plus the speed of the train. The only possible way out of this was to imagine that the measured speed would actually differ from c , but that there was be some 'special' frame in which Maxwell's theory applied exactly (and hence the speed of light would be exactly c ). Nineteenth century physicists also believed that light had to travel in a medium (just as any other wave does), and they called this as-yet-undetected medium the 'ether.' The 'special' frame in which Maxwell's equations applied was then supposed to be the frame of reference of the ether. This meant that it should be possible to measure a variation in the speed of light depending on one's velocity (that is, direction) with respect to the ether. A series of clever and famous experiments were designed and performed in the 1880s by the American physicists A.A. Michelson and E.W. Morley. They used an interferometer to accurately determine the speed of light when the earth was on opposite sides of the sun, and hence traveling in opposite directions through the ether. To physicists great surprise and dismay, they could detect no difference. Physics had to wait for Einstein's 1905 theory to resolve the dilemma.

This SparkNote examines some of the basic effects of Special Relativity on time, space, and motion. The next SparkNote on special relativity and dynamics extends these ideas into an analysis of energy, momentum and force. The final SparkNote on special relativity examines some interesting problems and applications of Special Relativity such as the famous twin paradox.

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