The Special Theory of Relativity

Einstein formulated his special theory of relativity on two basic assumptions:

  • The laws of physics are the same for all observers moving with a uniform motion relative to each other.
  • The speed of light in a vacuum is a universal constant, the same for all observers regardless of their relative motion or the motion of the light source.

The first statement incorporates the relativity principle of classical mechanics, but is more comprehensive. Einstein was thinking not only of mechanical laws but also of the laws governing light and other electromagnetic phenomena.

The second statement means that it is futile for an experimenter to try to determine his velocity through space by using a beam of light as a gauge. It is futile because regardless of the speed of the observer, his measurement of the speed of light will always give the same value. This statement implies that nature offers no absolute reference system for the comparison of time or distance. The movements of the stars and of all the galaxies can be described only with respect to each other, for in space there are no fixed directions and no boundaries. Space is not a substance but is merely the order or relation of things with respect to each other. Without things occupying it, space is nothing.

As part of the special theory, Einstein developed mathematical equations to be applied to mechanical and electromagnetic problems. These equations modified the Newtonian laws of mechanics and formed the framework for relativistic mechanics which has been of great importance in nuclear and elementary-particle physics. Some of the principles deduced from the equations can be stated as follows:

  • A clock moving at a uniform velocity with respect to an observer keeps time at a slower rate than a clock at rest.
  • Length changes with velocity. Specifically a measuring rod, or any other object, moving with respect to an observer shrinks in the direction of its motion.
  • The energy content of an object increases as its velocity increases. It is not possible to accelerate a body to the speed of light, because an infinitely large amount of energy would have to be supplied as the body reached the speed of light.
  • Mass and energy are equivalent. Matter can be converted into energy and energy can be converted into matter.

The statement that mass and energy an equivalent came from the important equation:

E = mc²

The equation states that the energy (E) contained in any particle of matter is equal to the mass (m) of the particle multiplied by the square of the velocity of light (c). The equation provided the answer for such long standing problems in physics as how the sun and stars can go on radiating light and heat for billions of years, and how radioactive substances such as radium are able to emit particles with very high energy.

In Newtonian physics, space and time are considered as separate things; in relativistic physics, on the other hand, space and time are closely connected. The Russian mathematician Hermann Minkowski (1864-1909) simplified the method of solving many types of problems in special relativity by developing a geometry of four dimensions in which time is related to length, width, and depth—the three dimensions of space in classical physics. The resulting four-dimensional space is called the space-time continuum, or simply space-time. Einstein further developed the idea of space-time in the general theory of relativity.

Numerous experiments and observations have supported the validity of the theory of special relativity. For example, the increase of the energy of bodies moving at high speed is basic to the design of particle accelerators (atom smashers), in which atomic particles have attained velocities greater than 99.9995 per cent of the speed of light. Time dilation (the slowing down of time) for fast-moving objects has been observed in subatomic particles called muons. These particles are commonly created when cosmic rays from outer space strike atoms high in the atmosphere. Muons are extremely unstable and decay into other particles so quickly that, without time dilation, they would all decay a short distance into the atmosphere. However, because of time dilation, muons are observed to reach the earth's surface.