General Relativity

Type of physical science: Relativity

Field of study: General relativity

The general theory of relativity is a theory describing the effects of acceleration and gravity on bodies, as well as the structure of space and time. Developed by Albert Einstein in 1915, it is the basic theory of gravity on which astronomers, cosmologists, and theoretical physicists base their study of the universe.

Overview

The general theory of relativity is a model of how gravity works. Considering the large-scale structure of the universe, gravity is the governing force. Gravity is what holds the solar system together and what dominates the interactions between stars and galaxies. It also dictates theories of the past and future of the universe as a whole. Any model of the universe, then, must have its basis in a theory of gravity. The general theory of relativity has stood the test of time and experimentation to become the basis of modern cosmological theory.

The motivation of Albert Einstein (1879-1955) in working out the principles of relativity was the belief that it is impossible to detect motion relative to any fixed point in space and that, therefore, there is no absolute motion. The general theory is the second of two stages of a larger picture of relativity theory. The first stage is special relativity, which deals with the laws of physics as seen by observers in uniform, or unaccelerated, motion. The general theory goes beyond the special theory to deal with accelerated motion and gravity.

General relativity describes the universe in the terms of four dimensions: three dimensions in space and the fourth in time. This concept becomes clear when one thinks about the relationship between time and space. Since light travels at a finite pace, the objects that humans can see in the night sky are not seen as they are now, but as they were when their light originally left them. Light from the closest star to Earth has taken about four years to reach this planet, while the light from the nearest galaxy has taken more than 2 million years. From frames of reference located elsewhere in the universe, the relative positions of the stars and galaxies change, as does their relative distance in time. Therefore, space cannot be referred to without reference to time. In general relativity, the fabric of the universe is referred to as space-time.

A fundamental concept in the general theory of relativity is the principle of equivalence. Einstein showed that the effects of acceleration and the effects of gravity are indistinguishable. This principle is often demonstrated with the use of a "thought experiment."

Imagine that a man is in an elevator which has no windows. Now imagine that the elevator is in deep space where there is no gravitational effect. As long as the elevator is in constant motion, he floats around freely inside, experiencing weightlessness. If a constant force is applied to the bottom of the elevator, then it accelerates at a uniform pace and the contents of the elevator (the man) are pushed against the floor. This accelerating force can be adjusted to exactly match the downward pull that he would experience if the elevator were on the surface of the earth. Without a window to determine the motion relative to the outside world, it would be impossible to tell if the force that he felt was attributable to gravity or to the acceleration of the elevator. From this type of thought experiment, Einstein concluded that gravity and acceleration were equivalent.

Following from the principle of equivalence, Einstein proposed that the idea of gravity as the force that attracts separate masses is entirely unnecessary. Instead, he described a more accurate way of looking at gravity by showing that the presence of mass changes the nature of space-time. Gravity changes the very geometry of space by curving, or warping, it. In the absence of matter, then, the shape or curvature of space-time is flat. Near massive objects, however, space-time is strongly warped. The larger is the amount of matter at any location, the greater is the curvature of space-time at that location. The extent of the curvature is greatest near the massive object, and the curvature becomes progressively less with increasing distance.

Effectively, then, the curvature of space-time around massive objects determines the path of bodies traveling through space. In other words, the curvature of space causes objects to follow curved paths. The earth, therefore, orbits the sun not because of the gravitational force of the sun, but because the mass of the sun curves the space immediately around it.

Another thought experiment is useful to picture the curvature of space. Imagine a pool table whose surface is not rigid but is made of a thin rubber sheet. When a large weight is placed on such a pool table, the normally flat sheet would stretch, curving around the weight. The heavier is the weight, the more curved is the surface of the pool table. Attempting to play pool with this weight distorting the surface of the table, one finds that balls passing near the weight are deflected from their straight paths. This is a two-dimensional analogy describing how radiation, light, and material objects are deflected by the curvature of space-time around massive objects. When the universe is taken as a whole, the size, shape, structure, and dynamics of the whole is determined by the net effect of curvature caused by every massive object it contains.

While the basic principles of general relativity are straightforward, some of the implications of the theory defy common sense and ordinary experience. Einstein found that the laws that are used to describe the behavior of objects in most circumstances do not hold when very strong gravitational fields are involved or when velocities approach the speed of light. In special relativity, one finds that uniform motion at speeds approaching that of light affects the measurements of the length of objects or the time that it takes for events to occur. In an accelerated frame of reference, or a gravitational field, similar effects take place. Time actually slows as a result of acceleration, and experiments have repeatedly shown this effect to be true.

An atomic clock positioned near a massive object will run slower than a clock farther away.

Researchers also have found, for example, that clocks in Boulder, Colorado, a mile above sea level, gained about fifteen-billionths of a second per day as compared with clocks near sea level.

The difference is attributed to Boulder's greater distance from the earth's center of gravity.

There is another unusual prediction arising from the general theory of relativity which surprised and disturbed even Einstein. One of the early solutions of the complex sets of equations Einstein created indicated that, if an object were sufficiently compressed, then its gravitational field would be so strong that not even light could escape it. The equations of the theory of general relativity also allowed for mass to be squeezed into an infinitely small space. The implications of this curiosity would wait almost fifty years to be realized. It then became the basis for the fascinating theory of black holes.

Another result predicted by general relativity is that the wavelength or color of a light will be affected by gravity. For example, if blue light is emitted from the surface of a very massive star, then the theory predicts that its wavelength will be lengthened and the color of the light will move toward the red end of the visual spectrum. Experiments using light emitted by the sun, light emitted by white dwarf stars, and measured γ rays have succeeded in confirming that this shift actually does take place.

There have been many experimental tests of the validity of the general theory of relativity. In one experiment, the curved path of light near the edge of the sun was measured during a solar eclipse. The stars near the edge of the sun were photographed near the edge of the darkened sun during the eclipse, and their positions were compared with their positions under normal conditions away from the sun. It has been found that the apparent positions of the stars are shifted by an amount which is consistent with the predictions of general relativity. During the eclipse, the stars appear to shift because the path of their light is warped as it passes the massive body of the sun. Other variations of this test have been performed and also have confirmed the predictions of general relativity.

Another test is related to the motion of the planet Mercury. Based on the traditional theory of gravity, when all gravitational influences on the planet are taken into account, the observed path of Mercury still fails to correspond to the predicted path. According to general relativity, however, another factor is brought into the equation: Because of the distortion of space around the sun, Mercury's orbit will not always be the same, but the whole orbit will slowly revolve around the sun. A comparison of the predicted amount of this added motion with observations of the actual motion of Mercury agree nearly precisely.

While it may be impossible to prove that the general theory of relativity is correct, the experiments that have been used to test it so far have failed to disprove it. It remains the most accurate theory by which to measure and predict the effects of gravity.

Applications

The importance of the general theory of relativity lies not so much in the ability to measure and predict with accuracy, but in the way in which humans think about the universe.

The theory is of fundamental importance to astronomy because it alters views about space, time, and matter. In particular, the theory has surprising and profound implications when applied to very massive compact stars and when used to understand the large-scale structure of the universe.

Massive compact stars are objects like neutron stars and white dwarf stars. A neutron star is a very dense body composed of tightly packed neutrons. It is thought to be one possible end result of a supernova. A neutron star represents a mass greater than that of the sun compressed into a sphere only 16 kilometers wide. A white dwarf star is an old, extremely dense star about as large as the earth but with a mass as great as the sun. It is the final result of a star that has used all its fuel. At the extreme end of density lies a black hole, whose intense gravity has compressed it into a singularity (a mass that has been compressed into an infinitely small point). A singularity was one of the early solutions of the general relativity equations. Because the results defied common sense, the idea that objects such as these might actually exist was rejected by Einstein himself and by most scientists as aberrations of the theory. With new techniques in astronomy, however, amazing new observations began to be made which required explanations using these aspects of relativity theory. Extremely dense objects powered by gravitational fields are universally accepted. Although they have not yet been observed directly, even black holes are commonly considered to be bonafide members of the cosmic family--bizarre objects that even Einstein himself could not imagine but that were predicted by his theory of general relativity.

Einstein believed that the universe was static. Although the equations that he worked with did not indicate a static universe, his belief caused him to introduce changes in his equations which would keep it as a steady state model. It is now known that the universe is not static, that the galaxies and all the matter in the universe are rushing outward as part of the expansion of the universe. Armed with this knowledge and a working theory of gravity--the general theory of relativity--a new cosmology was created.

Since gravity is the force that governs the large-scale dynamics of the universe, general relativity has been used to create models of the universe that roughly fit observations. It helps to describe how the universe might have expanded from a singularity (in which all the matter in the universe was compressed into a single, infinitely small point) to form galaxies, stars, and planets.

It allows scientists to formulate answers to the biggest questions of all: How did the universe begin? Will it end? and if so, how?

All models begin with the assumption that the universe is expanding, having its origin in the cosmic explosion known as the big bang. Although this theory has been contested, no other theory has yet become as widely accepted. According to modern models of the universe, its fate ultimately depends on the average density of matter in the universe. This density determines whether gravity will act to stop the expansion of the universe.

If the average density of the universe is below a critical value, then the universe is considered to be "open." In this case, gravitation cannot act to stop expansion and the universe will continue to expand forever, its atoms spreading farther and farther apart until it is nearly energyless. If the average density is above the critical value, then gravity will eventually cause the universe to halt its expansion and to begin contracting until it eventually is returned to the state of a singularity. If the average density of the universe is equal to the critical value, then gravity will slow the expansion of the universe but will never quite be able to stop it. For all these models, quite different geometries prevail. Ultimately, it is mass which determines the shape and therefore the geometry of the universe, as explained by Einstein's theories. Direct observation reveals about ten times less than the critical density value of matter to close the universe, but scientists suspect that the reason humans do not see more matter in the universe is that it radiates in a form which cannot yet be detected. These questions lie on the frontiers of modern astronomy.

Context

The theory of relativity emerged as a logical step forward in the understanding of space and time and the relationship of the earth to the rest of the universe. It arose out of the inability of Newton's laws of gravity and motion to describe the observed universe in certain circumstances.

At very high velocities or in the presence of very strong magnetic fields, Newton's laws of gravity break down.

The general theory of relativity arose out of Einstein's earlier special theory of relativity. The concept of relativity was extremely important for the development of theories about the universe because it described two fundamental truths: All motion is relative, and there is no preferred frame of reference in which space and time are defined absolutely. Einstein wrote his first paper on relativity in 1905. He was motivated by the conviction that it is fundamentally impossible to detect motion relative to absolute space. Relativity also abolishes the commonsense notion of a basic universal time.

Although the importance of relativity theory was recognized from the start, it lay mostly dormant for nearly forty years. Theoretical work was being done, but little experimental work. In the early 1960's, when increased technology allowed for the discovery of unexpected types of astronomical objects, relativity theory went through a renaissance. Explanations of the behavior of distant objects could only be explained on the basis of Einstein's theories.

Einstein's goal was to develop a unified theory of the universe. He spent the last years of his life searching for the universal force that would link gravitation to electromagnetic and subatomic forces. This remains a major goal of physics, although it has become even more complex since Einstein's day. At the end of the twentieth century, the attempt was to merge the general theory of relativity with quantum mechanics, the theory that describes how subatomic particles interact. The goal was also to develop a theory which encompasses the forces and all the elementary particles of nature (the fundamental, irreducible components that make up all the matter in the universe).

Relativity has stood the test of time and experimentation to become the foundation of modern cosmology and physics. It is a cornerstone of the attempts to create a unified theory of the universe. Much of the focus of future study centers on the predictions and consequences of general relativity. It is one more tool in the continuing efforts to describe and predict events in the world and, if possible, to understand the nature of the universe.

Principal terms

ABSOLUTE SPACE, ABSOLUTE TIME: the idea that there is an overlying stationary structure in space and time which never changes, and against which all events and objects can be measured

ACCELERATION: a change in velocity; also, a change in the direction of motion when speed remains constant

BLACK HOLE: a theoretical body which is so compact and has such great gravitational force that no radiation can escape from it

COSMOLOGY: the study of the large-scale structure of the universe and its movements, origin, evolution, and ultimate fate

DENSITY: the amount of matter that is contained within a given volume of space

FORCE: a physical phenomenon capable of changing the momentum of an object; the four fundamental forces in the universe are gravity, electromagnetism, the strong nuclear force, and the weak nuclear force

FRAME OF REFERENCE: a particular position, moving or stationary, from which objects and events are observed

GEOMETRY: a set of rules which describes the structure of a region of space; traditional geometries described space as flat, while relativistic geometries describe it as curved

GRAVITY: the force that is responsible for the mutual attraction of separate masses

PRINCIPLE OF EQUIVALENCE: the rule that, in a limited region of space-time, the effects of the acceleration of a given frame of reference are not distinguishable from those of a gravitional field

SINGULARITY: a state of matter in which it is compressed into an infinitely small space

Bibliography

Calder, Nigel. EINSTEIN'S UNIVERSE. New York: Viking Press, 1979. A well-written book directed toward a general audience. Details the principles of special and general relativity in reference to Einstein's life and a general philosophy of the universe. Useful analogies and popular language make a difficult subject more easily understandable.

Chaisson, Eric. RELATIVELY SPEAKING. New York: W. W. Norton, 1988. A highly readable book giving an overview of Einstein's work on special and general relativity and how it relates to modern astronomical and cosmological questions. Gives a nonmathematical analysis of cosmology and singularity theory.

Hawking, Stephen. A BRIEF HISTORY OF TIME. New York: Bantam Books, 1988. An excellent overview of relativity theory as it applies to modern cosmological inquiry. An excellent resource for the reader who has an interest in the theories but does not have a strong background in science. Written by one of the foremost researchers of cosmological theory of the twentieth century.

Parker, Barry. EINSTEIN'S DREAM. New York: Plenum Press, 1986. A perspective of relativity theory related to Einstein's ultimate goal of a unified theory of the universe. Gives a good historical analysis of relativity and unification theory. Devotes chapters to the origin of the universe, the ultimate fate of the universe, black holes, and quantum theory. Nonmathematical, but recommended for the reader with a background in physics.

Schwartz, Joseph, and Michael McGuinness. EINSTEIN FOR BEGINNERS. New York: Pantheon Books, 1979. A delightful introductory book for those intimidated by the usual presentations of scientific theory. Written in simple language with comic book style drawings, it gives a basic overview of Einstein's life, the political and social environment from which he emerged, and the basic principles of his work.

Time-Life Books editors. THE COSMOS. Alexandria, Va.: Time-Life Books, 1988. Part of the Voyage Through the Universe series, which examines the universe from the big bang theory to space exploration. A richly illustrated volume that explores the study of the large-scale structure of the universe from a historical perspective. Does a very good job of presenting a complete picture of the subject, although the language and concepts are advanced for the general reader.

Grand Unification Theories and Supersymmetry

Space-Time Distortion by Gravity

The Evolution of the Universe

The Expansion of the Universe

Large-Scale Structure in the Universe