## Introduction to Relativity, Theory of

Relativity, Theory of, a description of space and time as determined by physical measurements. The origins of the theory date back to the principles of relative motion formulated by scientists in the 17th century. In its present form, however, the theory is largely the work of Albert Einstein (1879-1955). According to Einstein's theory, space and time are relative concepts, and measurements of space and time depend on the state of motion of the observer.

Einstein's theory consists of two parts: (1) the special, or restricted, theory, which concerns measurements made by observers moving at constant velocity with respect to each other; and (2) the general theory, which expands the special theory to include measurements by observers whose relative velocity is changing. The general theory applies the principles of relativity to gravitation. The special theory of relativity was published in 1905; the general theory, in 1916.

Einstein's theory of relativity has been of great importance in modern physics. For example, the special theory showed scientists that it is possible to unleash the energy contained in the nucleus of the atom. The theory has influenced all branches of physics dealing with electromagnetic radiation and high-speed particles. It has had a profound effect on astronomy and the related science of cosmology, which attempts to explain the origin and structure of the universe.

The body of scientific principles developed before Einstein's time is referred to as classical physics. When applied to everyday situations, these principles are still valid. The theory of relativity differs significantly from classical physics only when dealing with objects moving at extremely high speed, with objects having very strong gravitational fields, or with the universe on a broad scale.

## Background of the Theory

In 1687, Sir Isaac Newton (1642-1727) formulated the basic laws of classical physics used in mechanics, the study of forces and the motion they impart to bodies. The laws of classical mechanics conform to a principle of relative motion. According to this principle:

- The motions of bodies within a given frame of reference are the same relative to each other, whether the frame of reference is at rest or moves uniformly—that is, at a constant speed and in a straight line. Example: A passenger in a smooth-riding train cannot tell whether it is moving or how fast it is moving if he looks only at objects inside the train. This is because everything in the train, including the passenger, is moving at the same speed. Only by looking out the window at some fixed object can he detect motion. However, if the motion is not uniform—if the train is increasing or decreasing its speed or if it is going over a rough roadbed—the passenger can feel the motion. Similarly, he can feel motion when the train rounds a curve.
- The absolute velocity of an object cannot be determined by measuring the velocity from a place (such as the earth) that is itself moving. Only relative velocity can be measured. Example: The absolute velocity of a rocket launched from the earth depends both on the motion provided by its engine and the motion of the earth through space. Measuring the velocity of the rocket by determining the time it takes the rocket to travel from one position to another as observed from the earth gives only the velocity of the rocket in relation to the earth. Determining the absolute velocity of an object is possible only if it can be measured from some non-moving point.

Newton regarded space as stationary and immovable. He believed that it served as a fixed frame of reference from which all motions could be determined. For the next two centuries most scientists agreed that Newton's views were correct.

By the mid-19th century, there was strong evidence that light was made up of waves. To physicists, it seemed obvious that if light consisted of waves, the waves must be transmitted by some medium, just as sea waves are transmitted by water and the vibrations we call sound are transmitted by air. They thus assumed that all of space must be filled with an invisible substance through which light and other kinds of electromagnetic radiation travel. They called this substance the ether.

This theory provided an explanation of light that agreed with the laws of classical mechanics. It also provided the fixed frame of reference, the absolute and immovable space, that Newtonian physics and cosmology required. But the more physicists studied the hypothetical ether, the less real it became. They could find no way to detect it experimentally. It seemed to have no properties except the ability to transmit electromagnetic waves.

Scientists reasoned that if the earth moves through the ether, the speed of light should be different in different directions just as the speed of water waves measured from a moving ship is faster or slower depending on whether the waves are moving in the direction of the ship's motion or against it. In 1887 Albert A. Michelson and Edward W. Morley conducted an experiment with an instrument capable of measuring the predicted change in the speed of light resulting from the earth's motion in space, but no such change was detected.

Furthermore, other experiments seemed to indicate that the speed of light was independent of the motion of the light source, although common sense and classical physics said that light thrown off by a moving source should share the motion of the source. Einstein resolved the incompatibility of the behavior of light with the laws of classical mechanics by taking a new viewpoint.

## 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.

## The General Theory of Relativity

The special theory of relativity applies only to observers moving with uniform velocity in relation to each other. Einstein expanded this theory into a general theory that also applies to observers with nonuni-form, or accelerated, relative motion. The general theory of relativity has strongly influenced developments in advanced physics, geometry, and astronomy. The theory is of particular importance in cosmology.

As an essential part of the theory, Einstein developed a theory of gravitation fundamentally different from that developed by Newton. The concept of gravitation in the general theory of relativity is largely based on the principle of equivalence. According to this principle, it is not possible by experiment to distinguish between the effects caused by the acceleration of a system and those caused by gravitation—the effects are equivalent to each other.

For example, a person in an elevator that accelerates upward will sense that the floor is pushing up against him. This effect results from the tendency of the person's body to resist acceleration. However, the same effect would be produced if the elevator were stationary and the pull of gravity increasing—there is no way to distinguish between the two effects.

Einstein saw that this equivalence could be explained by relating gravitation to the geometrical properties of the space-time continuum. According to the general theory of relativity, space-time is distorted by the presence of matter: specifically, gravitating bodies bend the space-time continuum. As an object moves through the space-time continuum, it follows the curvature of space-time. The resulting motion of the object is interpreted in classical physics as gravitational attraction.

Einstein developed a set of equations to describe the manner in which space-time is distorted by matter. These equations make use of a geometry developed by the 19th-century German mathematician Georg F. B. Riemann. In Riemannian geometry there are no straight lines but only curves. Therefore, the space described by the general theory of relativity is a curved space without straight lines.

Einstein proposed three relativistic effects that could be measured to test the general theory. These effects were the bending of light by a gravitational field, the shifting of the planet Mercury's orbit around the sun, and the gravitational redshift of light (the change in the wavelength of light as it enters or leaves a gravitational field).

Measurements of each of these effects supported the general theory. The most famous test was conducted during the total eclipse of the sun in 1919. One of the most conclusive tests involves an effect called time delay—a slight delay in the passage of radio signals through a gravitational field. This delay was very accurately measured in the late 1970's by determining the time it took radio signals from spacecraft on Mars to reach the earth when Mars was on the opposite side of the sun.

During the time since the publication of the general theory of relativity, various new theories of gravitation have been proposed that also incorporate the principle of equivalence. These theories make use of a curved space-time, but they differ from Einstein's theory in the amount of curvature they predict. Various experiments conducted since the 1960's to measure the effects of the curvature of space-time have tended to support Einstein's theory over the others.

The general theory of relativity is used in studying the overall structure of the universe. With the theory, scientists have predicted the existence of a variety of exotic celestial objects and phenomena, including black holes and gravitational lenses.