# relativity, special theory

## relativity, special theory

The theory proposed by Albert Einstein in 1905. It is concerned with the laws of physics as viewed by observers moving relative to one another at constant velocity (i.e. with observers in inertial frames), and with how relative motion affects measurements made by these observers. At low relative velocities, special relativity (SR) predicts the same results as the classical Newtonian laws of mechanics. As the relative velocity increases beyond that encountered in everyday experience, the predictions of the two theories diverge. It is those of SR that have been conclusively verified by experiment. SR must therefore be used to describe the behavior of bodies, such as electrons, when they are moving at velocities close to the speed of light.

One of the basic principles of SR is that the speed of light is the same in any direction in free space, is the same for all observers, and is independent of the relative motion of the observer and the body emitting the light (or other electromagnetic radiation). This violates the classical concepts of relative motion but has been demonstrated experimentally.

Another basic principle is that all physical laws are the same for every inertial frame. Any law deduced in one inertial frame will be true in every other inertial frame. The values of the numerical constants appearing in these laws are also independent of the frame in which they are measured. The same does not, however, apply to certain variable quantities measured in different inertial frames.

Prior to SR it had been assumed that there was a universal ‘absolute’ time and ‘absolute’ space that were the same for all observers. Einstein showed that as a direct consequence of the invariance of the speed of light, time and space could not be considered as separate concepts, independent of each other and of the observer. Instead they must be regarded as a composite entity, called spacetime. Any event in an inertial frame must therefore be described in terms of four spacetime coordinates – three spatial and one time coordinate. The spacetime coordinates of the same event measured in two different frames will differ, but they can be interconverted by the Lorentz transformation.

As the relative velocity (v) between inertial frames approaches the speed of light (c ), very strange things are predicted. One is time dilation: two observers approaching at a relative velocity close to c will each see the clock of the other operating more slowly than their own. The time intervals will be dilated by a factor of 1/β where

β = √(1 – v 2/c 2)

Another prediction is the apparent contraction of a moving object that is observed, in the direction of motion of the object, by someone in a different inertial frame. The observed contraction, known as the Lorentz contraction, amounts to the factor β. The object also appears slightly rotated. No change in dimensions is observed in directions perpendicular to the direction of motion.

A further consequence of SR, when applied to the field of dynamics, is that the mass (m) of a body is not invariant but increases as the relative velocity between body and observer increases: m = m 0m 0 is the rest mass of the body and is an invariant property of matter. It follows that no object with mass can reach the speed of light; only a particle with zero rest mass (such as the photon) can travel at the speed of light. Einstein showed that the transfer of energy by any process entailed the transfer of mass, and concluded that the total energy E of any system of mass m is given by the equation E = mc 2.

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