Tests Of General Relativity

Type of physical science: Relativity

Field of study: General relativity

Tests of general relativity have been performed since 1919 and are ongoing. They are difficult to perform locally because the effects in the solar system are very small.

Overview

When Albert Einstein published his general theory of relativity in early 1916, ten years after his remarkable special theory of relativity, he was not even forty years old. He was not yet known beyond the scientific world, although physicists knew of his papers in many branches of physics, including atomic theory and the photoelectric effect. In 1916, however, while World War I raged, his new theory predicted three (by now well-known) effects: the bending of light near the sun, the advance of the orbits of the innermost planets (most notably Mercury), and the gravitational redshift.

None of these effects has a place in Newtonian, or what is called classical, physics. In Sir Isaac Newton's theory, it was held that light was without any weight and should therefore travel in straight lines, even in gravitational fields. Also, light does not change wavelength in a gravitational field. As for the motions of the planets around the sun, Newtonian physics, which does allow for perturbations in the orbits of planets, does not allow that the orbits might advance because of "curvature." (Curvature is a measure of the strength of a gravitational field, and in Einstein's theory, space becomes curved, rather than flat, as in Newton's work.)

Einstein, working in Berlin in 1916, had no direct way to test his general theory. He was, however, supremely confident that his predictions would turn out to be correct, because of the beauty of his theory. It is interesting that there was, at that time, a paucity of evidence for the results of his 1905 special theory of relativity, which included the famous result that energy is equal to mass times the velocity of light squared: E = mc². This equation became verifiable only in the 1930's. One of Einstein's general theory predictions would, however, prove to be verifiable by 1919, and as a result Einstein would in that year become a world-famous figure--a second Newton.

The three well-known effects that Einstein predicted--listed above--are strictly applications of the theory and are described below in "Applications." Not so well known are some other effects, which have been investigated by experimental physicists since the 1940's; in fact, Einstein's theory continues to be tested as the accuracy of measuring instruments improves.

Because Einstein's general theory of relativity provides a theory of gravitational fields (a theory that supplants Newton's when dealing with very strong fields but agrees with it otherwise), and because it predicts how massive bodies distort space and time, scientists expect general relativity to be concerned with measurements of lengths and times, or quantities related to lengths and times, such as speeds.

Accurate tests on lengths and times are extremely difficult to conduct in Earth's solar system, because gravity, even near the sun, is not sufficiently strong. It is certainly strong enough to hold the planets in their orbits, but what comes into the equations of general relativity, when describing experimental effects in the solar system, is always a term M/R, where M is the mass of the sun and R is the sun's radius. This ratio, for the sun, is not large enough to make predicted effects detectable. If the solar system were to possess a neighboring black hole (a star which has collapsed on itself and whose gravitational field is so great that no matter can escape) or a neutron star (a star whose gravitational field is also immensely strong), with a large mass and a very small radius, tests of general relativity might be considerably easier, because such bodies are needed in order to display Einstein's predicted distortions of times and distances.

While it is not easy to find local bodies with such an appropriate mass:radius ratio, it is possible to make extremely accurate measurements of time. Such accurate time measurements have enabled scientists to verify the slowing down of the speed of light near the sun.

Einstein's theory also predicts the existence of gravitational radiation from large accelerating masses. Although such radiation has never been detected on Earth, astronomers believe that it has been detected in binary systems in the galaxy.

Applications

The effects of general relativity have been, and are being, examined and tested experimentally and are integral to the work of physicists, astronomers, and cosmologists.

First, whenever any electromagnetic radiation--light waves, radio waves, infrared radiation, ultraviolet radiation, X rays, and/or γ rays--passes through a strong gravitational field, the usual straight-line (or geodesic) path tends to be bent similar to the way that a beam of light is bent under refraction. This effect results from the slowing of the speed of light in a gravitational field. Unlike refraction, however, this slowing is independent of the wavelength, and so in general relativity all radiation is bent near the sun by the same amount. A light beam coming straight toward us from a star far behind the sun will not come past the edge of the sun in the expected straight line, but will apparently fall toward the sun a little as it passes.

In 1919, Sir Arthur Eddington was the first to measure the bending of starlight as it passed close to the sun (during an eclipse of the sun). He measured 1.98 seconds of arc (plus or minus 0.16 second of arc), which agreed reasonably well with Einstein's predictions of 1.75 seconds of arc. Since that time, many other measurements have been made: 1.82 seconds of arc (plus or minus 0.51) in 1922 at Lick Observatory; 2.01 seconds of arc (plus or minus 0.27) in 1947 at Yerkes Observatory; 1.70 seconds of arc (plus or minus 0.10) in 1952, again at Yerkes Observatory; 1.82 seconds of arc (plus or minus 0.14) at the Mullard Radio Astronomy Observatory in Cambridge; and 1.73 seconds of arc (plus or minus 0.05) in 1974 at the Haystack and National Radio Astronomy Observatory. It is predicted that, in the vicinity of a black hole, the bending of light would become so intense that photons could actually orbit the black hole.

Since the 1980's, astronomers have suspected that light from distant quasars (or quasi-stellar objects, bodies that emit immense amounts of electromagnetic radiation and are suspected of having black holes at their centers) is sometimes bent around an intervening huge mass--such as a galaxy or cluster of galaxies--forming two or more images of the quasar. This phenomenon has been dubbed the "gravitational lens effect" and is physically the same bending phenomenon that has been described here.

General relativity predicts that the major axis of the elliptical orbit of a planet revolving around a heavy star advances slightly. It has been known since before Einstein's time that the perihelion of Mercury (the innermost planet and therefore located in the strongest part of the sun's gravitational field) advances by an unexplained amount of 43.11 seconds of arc (plus or minus 0.45) per century. Newtonian physics had been unable to explain this phenomenon, but general relativity predicts it: When the orbital motion is calculated by Einsteinian gravity, there is a prediction of an extra 43.03 seconds of arc, which very satisfactorily explains the discrepancy.

For Venus, the second-innermost planet, an advance of 8.4 seconds of arc (plus or minus 4.8) per century has been observed; Einstein's prediction was 8.6 seconds of arc. For Earth, the third-innermost planet, 5.0 seconds of arc (plus or minus 1.2) has been observed, and Einstein's prediction was 3.8.

General relativity predicts that light escaping from near a massive object will be "redshifted" (that is, the electromagnetic radiation will appear to have longer wavelengths as it moves father away from its source, similar to the way that a horn sounded by a passing train will seem to sound lower as the train speeds off into the distance), whereas light falling toward a massive object will be "blueshifted" (the opposite effect). Observations of the spectra from white dwarf stars (dying stars with small radii) show such shifting. Interestingly, the effect has even been shown on Earth, a result of Earth's gravitational field. In an experiment first performed by R. V. Pound and G. A. Rebka in 1959, and repeated by Pound and J. L. Snider in 1964, the wavelength of γ rays leaving the ground floor of the Jefferson Physics Laboratory at Harvard University was found to be shifted to a slightly longer wavelength at the top of the building (or to shorter wavelengths at the bottom of the building). Such minuscule differences in wavelength were actually possible to detect by use of the Mossbauer effect.

The three tests discussed above are those most often quoted in the years in which Einstein's theory was new. In the 1960's, there was a resurgence of ways in which general relativity could be tested. It was known that Einstein's theory predicted a slowing of the speed of light in a gravitational field. In the 1960's and 1970's, radio signals from both the Arecibo and Haystack radio telescopes were bounced off the inner planets Mercury and Venus, in experiments by I. I. Shapiro as well as others. (Radio signals were also bounced off the Mariner 6 and 7 spacecraft.) The delaying of signals as they passed near the sun has been observed; the reflected signals have arrived back slightly late when compared to the time calculated from Newtonian physics.

In 1972, J. C. Hafele and R. E. Keating made a direct measurement of how "clocks run slow" in a gravitational field. As it happens, both the special and the general theories predict distortions in time measurements, and it was these that Hafele and Keating managed to measure.

(They also managed to separate out the effects from the two theories so that there would be no confusion.) Very accurate cesium clocks were placed in regular round-the-world jumbo jets, while comparison clocks were monitored at the U.S. Naval Observatory in Washington, D.C.

Because a clock at a higher altitude is in a weaker gravitational field, it runs slightly faster than a clock on the ground--just as in the Pound-Rebka frequency experiment described above.

The clock in the jumbo jet gained time very close to that predicted by the general theory of relativity: 177 nanoseconds (plus or minus 12 nanoseconds), as compared with the predicted 179 nanoseconds (plus or minus 18 nanoseconds). In another flight, a gain of 125 (plus or minus 21) nanoseconds was observed, as compared with the predicted 144 (plus or minus 14) nanoseconds.

Another, more recent, test is the "gyroscope test" (also called the "geodesic effect" test). This experiment was meant to have been sent into orbit around Earth in the 1980's, but it unfortunately encountered numerous and ongoing delays. The idea is very simple: In Newtonian physics, a gyroscope continues to spin in its original direction unless it is acted upon by a twisting force, or torque. Thus, a perfectly balanced gyroscope will show no precession (or wandering away from the original motion), and, if set spinning in (say) the direction of a star, it will point forever toward that distant star even if carried up hill and down dale. (In this discussion, a small effect called Thomas precession, which arises in special relativity, is not taken into account.)

In Einstein's theory, however, when a gyroscope orbits Earth, following its natural "geodesic," Einstein's equations predict that it will wander away slightly from its original orientation. This happens every orbit; consequently, the effect is cumulative, amounting to about 8 seconds of arc per year (for a near-Earth orbit). Such an angle is measurable, and astronomers await eagerly the performance of the gyroscope. The gyroscope has been designed with almost frictionless gimbals; it is expected to spin freely for more than one hundred years. In the experiment, it is to be pointed to a particular background of stars; then, as it orbits, it will deviate systematically from the original position and begin pointing toward neighboring stars.

Finally, another test is the "binary pulsar" PSR 1913+16, in which scientists are investigating the possibility of gravitational radiation. In 1975, R. A. Hulse and J. H. Taylor, of the University of Massachusetts and Princeton University, respectively, found two massive stars in the Milky Way, orbiting each other with an extremely short common orbital period of 7.75 hours. This interesting pair has been carefully monitored since that time, using the 305-meter radio telescope at Arecibo, Puerto Rico. In 1989, Taylor and J. M. Weisberg reported that the heavier mass (1.44 solar masses) was a neutron star spinning extremely fast on its axis--about seventeen times per second--and that its companion was in all likelihood another neutron star (of 1.39 solar masses; previously it had been thought that the companion was a white dwarf star). Over a period of fourteen years, they had learned that the orbit was decaying exactly as predicted by Einstein's theory because of the gravitational radiation loss from two accelerating masses. This orbital energy loss agreed over the fourteen-year period to within 1 percent of the predictions. Moreover, the predictions were based on the full nonlinear theory; all of the former experimental results outlined above have been for weak gravitational fields, using the approximate linearized Einstein equations.

A spinning neutron star, or pulsar, is usually detectable because it gives off clearly defined radio "ticks" or pulses as it spins. Such pulses are easily detected by radio telescopes. In the PSR 1913+16 pair, only the 1.44-solar-mass star can be "heard"--it has a period of 59.029997929 milliseconds--and it is thus like an orbiting alarm clock, sounding a higher frequency as it comes toward us and a lower frequency as it goes away. The diameter of each star is about the size of a large city, about 15 kilometers across. Here, nature has provided a wonderful laboratory, far away in space, in which astronomers and physicists may study general relativity safely. The binary stars have an eccentric orbit with common eccentricity of 0.6; their orbit also slowly advances as predicted by general relativity. Between 1975 and 1989, the orbit advanced through 60 degrees of arc--a much better example than the tiny advance of the orbit of Mercury around the sun. Interestingly, the orbital speeds reach 400 kilometers per second, which is about 0.1 percent of the speed of light.

Another binary pulsar, PSR 1855+09, is being studied by astronomers looking for applications of the results of general relativity. This pair of stars has a period of twelve days; the neutron star (1.4 solar masses) has a millisecond period, and its companion (0.2 solar mass) is probably a white dwarf. This orbit is also being observed for the decay associated with gravitational radiation.

Such pulsars have provided the first-ever experimental opportunities to see the effects of gravity in conditions where they are appreciable. All the observed properties appear to be described correctly by Einstein's general theory of relativity.

Context

Scientists' present-day understanding of the physical world was to a large extent provided by Sir Isaac Newton (1642-1727), and Newtonian physics continues to apply to everyday phenomena, including those of mechanical and civil engineering and even, to a large extent, space technology. If, however, the human race had emerged as a society in a different part of the universe, where gravity were much stronger, Newtonian mechanics might never have developed; instead, a different model would have had to be articulated to describe common phenomena. That model, scientists believe, is best expressed in Albert Einstein's general theory of relativity. Einstein's more profound study of nature's laws opened a deeper, and more astonishing, view of the physical universe: Newton would have been surprised that the rate of flow of time was not the same for everyone, or that mass was a relative concept, or that distances depended on who was doing the measuring.

It is worth noting that Einstein arrived at his views of the universe--especially in regions where masses are much larger than in the solar system--by pure thought. He had no idea that neutron stars existed or that light was actually bent; he only theorized these things.

Einstein often stated that the important parts of a physical theory were simplicity and beauty, but his theories (of special as well as general relativity) predict such surprising results to the common observer that it has been imperative to sort out whether he was right or wrong through empirical evidence. So far, the general theory relativity, as stated by Einstein, is being borne out by experiment.

Principal terms

APHELION: the farthest position of a planet from the sun

GEODESIC: the path taken by a particle moving freely in a gravitational field

PERIHELION: the closest position of a planet to the sun

PULSAR: a rapidly spinning neutron star that emits radio pulses

REDSHIFT: a lengthening of the wavelength of light

Bibliography

Bergmann, Peter G. THE RIDDLE OF GRAVITATION. New York: Charles Scribner's Sons, 1987. An easy-to-read, nonmathematical treatment of Einstein's ideas. The author was a coworker with Einstein in the 1940's and is an expert in general relativity. The book contains many photographs and diagrams, and discusses the basic applications described in this article.

Foster, J., and J. D. Nightingale. A SHORT COURSE IN GENERAL RELATIVITY. New York: Longman, 1986. A short introduction to Einstein's theories, suitable for advanced undergraduates and graduate students. Its chapter 4 deals with the experimental results described in this article.

Gardner, Martin. THE RELATIVITY EXPLOSION. New York: Vintage Books, 1976. This book is by the editor of the Mathematical Games Department of SCIENTIFIC AMERICAN and makes very easy reading, with no equations and with diagrams by the artist Anthony Ravielli. It has a nice discussion of time effects, including the Hafele and Keating experiment (on page 139).

Misner, C. W., K. S. Thorne, and J. A. Wheeler. GRAVITATION. San Francisco: W. H. Freeman, 1973. This twelve-hundred-page paperback textbook for graduate students and scientists in all fields is regarded as the bible by many people interested in relativity. It has a comprehensive list of references to papers, experiments, and to other texts.

Narlikar, Jayant B. THE LIGHTER SIDE OF GRAVITY. San Francisco: W. H. Freeman, 1982. Chapter 5 deals with the results of Einstein's theory that is discussed in this article, and the whole book (by a well-known physicist-astronomer) is directed to the nontechnical reader, with humorous anecdotes, illustrations, and diagrams.

Ohanian, Hans C. GRAVITATION AND SPACETIME. New York: W. W. Norton, 1976. This well-written book is a text for advanced undergraduates and graduate students, but it has many diagrams and explanations that are accessible to the general reader as well. The topics of this article are treated in chapters 3, 4, and 5. Ohanian has also written a popular textbook for introductory physics students, PHYSICS, published by Norton in 1989, and there is a brief account in that book of the effects discussed in this article.

Pais, Abraham. "SUBTLE IS THE LORD...": THE SCIENCE AND THE LIFE OF ALBERT EINSTEIN. New York: Oxford University Press, 1982. An authoritative, nontechnical, and beautifully written history of Einstein's work. At the end, there is a detailed chronology of Einstein's life. The book does contain equations, but they are easy to understand. Discusses the tests of general relativity and comments on war, Einstein's relatives, philosophy, and all branches of physics. Witty and wide-ranging.

Schwinger, Julian. EINSTEIN'S LEGACY: THE UNITY OF SPACE AND TIME. New York: Scientific American Library, 1986. Another popular work written for the nonscientifically trained reader, by an eminent scientist. Chapter 4, with photographs and diagrams, deals with the bending of light, the gravitational redshift, and other Einsteinian effects such as gravitational radiation.