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A Radical in Tweeds: Robert H. Dicke and the General Theory of Relativity  

Mercury, July/August 1994 Table of Contents

Jack Zirker, National Solar Observatory

(c) 1994 Astronomical Society of the Pacific

Could Einstein be wrong? Only a crank or a very self-confident physicist could ask such a question seriously in the middle of the 20th century. Robert H. Dicke, professor of physics at Princeton University, is by no means a crank, but one of the foremost experimentalists of his time, and by the mid-1950s he had become very skeptical about the empirical evidence for Einstein's General Theory of Relativity. He set out to test the Theory rigorously and to explore alternative theories.

The General Theory has been hailed as the greatest single achievement in physics of this century and possibly of all time. It leads to an explanation of gravity very different from Isaac Newton's. In Newton's picture, space is "flat" (the sum of the angles in a triangle adds to precisely 180 degrees) and time unfolds at the same rate everywhere, no matter how fast you and your clock may be moving. Heavy bodies attract each other with a gravitational force proportional to each body's "mass," (the amount of matter they contain) and accelerate at a rate inversely proportional to these same masses. If one body moves relative to the other, the change in its attracting force propagates at infinite speed.

In Einstein's Special Theory of Relativity, space and time are merged into a single medium (spacetime), a four-dimensional "field." Time is no longer universal, but depends on the location and speed of the clock that measures it. No object can move faster than the speed of light, a firm speed limit in nature. These constraints lead to the famous equality of mass and energy, E=mc2.

In the General Theory, which includes the results of the Special Theory as a special case, spacetime becomes curved in the presence of a massive body. The curvature is proportional to the mass of the body. In this sense Newton's force of gravity in a flat space is replaced by the curvature of spacetime.

By mid-century, the General Theory had taken on the aura of revealed truth. Even the most prominent physicists were dazzled by its simplicity and scope. Many young theorists were engaged in working out its consequences, but few questioned its ultimate validity. Among those few was Dicke, a soft-spoken associate professor who was teaching in the same town as the mythical Einstein.

The two men differed markedly in their methods. Einstein relied on his incredible physical intuition and on his aesthetic sense to fashion representations of reality. He firmly believed that any theory that describes nature accurately should be simple and elegant. His "experiments" were purely mental but led him unerringly to correct physical principles.

Dicke, despite his flair for theory, is the ultimate empiricist, a man who measures. He has a strong skeptical streak, as befits a man born in Missouri. He already had a distinguished reputation as he began to reexamine relativity. In 1948, George Gamow and colleagues proposed what is now known as the "Big Bang" hypothesis for the origin of the heavy elements. A consequence of a hot, expanding universe was the existence of a remnant fireball, the Cosmic Background Radiation with a present-day temperature of about 3 kelvin above absolute zero. Dicke and his students, P.J.E. Peebles and D.T. Wilkinson, built a microwave antenna in 1964 to detect the fireball. But, before they finished, Arno Penzias and Robert Wilson detected some puzzling radio noise in their tests of microwave antennas at Bell Telephone Labs. Dicke and his students identified the noise as the cosmic radiation. Penzias and Wilson were later awarded a Nobel Prize for their discovery. Since Nobel prizes are given only for discoveries, not interpretations, Dicke received only the admiration of his colleagues.

Dicke began thinking about General Relativity in the mid-1950s and was struck by its weak experimental support. Three quantitative predictions of the Theory had been confirmed by observations, but none with the degree of precision Dicke thought convincing. Dicke was also troubled by the philosophical basis of the Theory. Why, he asked, should gravity be the only force in nature that is not transmitted by a particle, as, for example, electromagnetic forces are by photons? Why are physicists so impressed with the mathematical elegance of the Theory? Does nature necessarily prefer only beautiful theories, as Einstein came to believe?

The Precession of Mercury

Dicke decided to reexamine the most convincing proof of the Theory, its exact prediction of the anomalous precession of Mercury's orbit. The orbit precesses by 5,600 arcseconds per century. Newtonian theory can account for all but 43 arcseconds. Einstein's theory predicts this excess 43 arcseconds precisely. Could another explanation be found, Dicke wondered. For example, if the Sun were not exactly spherical, but had a slight equatorial bulge due to a rapidly rotating core, its tidal forces on Mercury could account for the observed effect.

The bulge required to account for Mercury's motion is only 0.1 arcseconds, while the Earth's atmosphere normally blurs the edges of the Sun's image by as much as two or three arcseconds. Dicke and his students built a special telescope with a rotating focal-place shutter, to extract the tiny effect from the noise. They took extraordinary precautions to rule out the extraneous effects. In 1967, after much hard work, they reported a significant equatorial bulge, more than enough to account for Mercury's motion.

This result excited a controversy that rocked back and forth over the next 20 years. First, several astronomers argued that Dicke had underestimated the effect of solar faculae, bright areas that cluster near the edges of the Sun and thus could bias his results. Dicke reanalyzed his data, using his critics' criteria, and reconfirmed his result. Then, some theorists suggested that a pole-equator temperature difference of only 30 kelvin could account for the apparent oblateness. Dicke demonstrated that such a temperature difference would result in serious problems of energy and momentum balance in the solar interior.

The facular criticisms would not go away, but with each sally of his opponents, Dicke was able to refute them with more sophisticated analyses. Moreover he found a wholly unexpected result: the oblateness measurements implied that the core of the Sun rotates with a period of 12.4 days, about half of the surface rotation period.

What was needed to settle the arguments were new independent data. A fresh crop of Princeton graduate students was marshaled to build another version of the oblateness telescope and a new series of limb brightness measurements was carried out between 1983 and 1985.

Meanwhile, Henry Hill, a former colleague of Dicke and a superb experimentalist in his own right, decided to repeat Dicke's important experiment. In the early 1970s he built his own telescope, similar to the one he had helped Dicke to build, and with his students showed that the Sun was indeed flattened, but no more than expected from its surface rotation, and far less than required to account for Mercury's anomalous motion.

Hill's contradictory results drove Dicke to continue his own series of measurements. In different years his derived oblateness seemed to vary: from 45 milliarcseconds in 1966, to 18.3 in 1983, to a mere 5.6 in 1984. Moreover, the 12.4-day core rotation did not appear in the new data. Dicke was puzzled by these erratic results, and suggested they might be varying in phase with the eleven year solar cycle. The discrepancy between the two independent sets of measures has never been explained satisfactorily, but most astronomers now accept Hill's results.

Gradually, Dicke and his students gave up trying to measure the solar oblateness and concentrated instead on small, latitude-dependent temperature differences over the solar surface. They found interesting results with important consequences for the solar interior (a real pole-equator difference of 0.1 degree kelvin), but not the one originally sought. General Relativity had survived Dicke's test unscathed.

An Alternative Theory

In searching for a new theory of gravitation, Dicke was influenced by the conjectures of Ernst Mach, a 19th-century physicist and positivist philosopher. Mach had published a devastating critique of Newton's notions of absolutely empty space which had strongly influenced Einstein. Mach also speculated that the resistance a body exhibits toward a change in its motion (its inertial mass) arises from some kind of long-range force from very large and distant masses, which we can now associate with distant galaxies. Einstein rejected this idea as unnecessarily complicated, and insisted on the predominance of local forces. Dicke thought that Mach's idea was plausible, however, and should be rejected only by experiments.

Influenced by Mach's ideas, and rejecting Einstein's extrapolation of the Principle of Equivalence [see sidebar on page 26], Dicke and his student Carl Brans published an alternative theory of gravitation in 1961. In the Brans-Dicke theory, masses throughout the universe generate an extra field, in addition to Einstein's curvature of spacetime, which can influence the strength of gravity from point to point. This means that Newton's gravitational "constant," G, need not be constant either in space or time.

General Relativity makes two other predictions about gravity. One concerns the amount of gravitational reddening of starlight. Because of the equivalence of mass and energy (E=mc2), a photon of light with energy, E, has an effective mass, m. As the photon leaves the surface of a star it is pulled back slightly by gravitational attraction and loses a bit of its energy -- it "reddens." Secondly, when a photon from a distant star grazes the surface of the Sun, it will be slightly deflected because of the gravitational pull of the Sun. Such deflections had been observed during total eclipses.

The Brans-Dicke theory contains an adjustable dimensionless parameter, omega. When omega is set at its most probable value, 5, the theorys predictions for the gravitational redshift and the deflection of starlight are smaller by only 9 percent and 6 percent, respectively, than the predictions of Einstein's Theory. Thus a clear choice of theories could only be made by a radical improvement in the precision of these experiments.

James Brault, a student of Dicke, measured the reddening of sodium spectrum lines in the gravitational field of the Sun, and, in 1962, found agreement with the General Theory to within 5 percent. Later measurements by R.V. Pound and his associates improved this agreement to 1 percent. Decaying nuclei that are embedded in a crystal, emit photons with a very narrow range of energies. Pounds used this so-called Mossbauer effect to measure the changes in a photon's energy as it flies up a test tower in the Earths gravitational field. The General Theory, which rests on the Principle of Equivalence, was thus confirmed to higher precision and the Brans-Dicke alternative was shown to require an uncomfortably large value of omega.

Lunar Laser Ranging

Dicke recognized that only a careful physical experiment could decide the issue of General Relativity. In 1965, he and some colleagues pointed out the feasibility of "optical radar," using corner reflectors on the Moon. Corner reflectors employ three mirrors mounted at right angles to each other, like the corner of a cube. They reflect any incident beam of light in exactly the direction from which it came.

The idea was that the Apollo astronauts could place several of these reflectors on the Moon, that these reflectors would return a small but detectable part of powerful laser pulses aimed at the Moon, and that the accurate timing of the return beam would give the distance of the Moon to within a few meters. Such measurements, carried out over a sufficiently long time, would pin down the orbit of the Moon to incredible accuracy. Any departure from the calculated orbit could reveal relativistic effects. In addition, lunar laser ranging could reveal the detailed size and shape of the Earth and provide precise checks on several astronomical methods of measuring time.

The ranging proposal was funded in 1965, and, after the astronauts placed reflectors on the Moon, observations began at Lick Observatory and later at MacDonald and Haleakala observatories. The distance to the Moon could be determined daily within 40 centimeters out of 400,000 kilometers. As observations accumulated, this limit gradually shrank.

Shortly before the first Apollo landing, Ken Nordtvedt, a young theorist at the University of Montana, predicted that if the Brans-Dicke theory was correct, the Earth-Moon distance should vary by nine meters with a period of 29.53 days. This effect would arise if the Moon's gravitational and inertial masses were different. Thus, lunar ranging could test Einstein's assertion that the inertial and gravitational masses of a body are identical. By 1976, a sufficient body of lunar ranging data was in hand to test. Two groups analyzed the data independently and came to the same conclusion: the Principle was valid, Einstein was correct in his conjecture, and the extra field that the Brans-Dicke theory incorporated could account for a few percent at most of the gravitational force between the Earth and Moon.

At this point, a scientist less motivated than Dicke might have given up his searching critique of General Relativity. But as we have seen, Dicke continued with his solar oblateness experiments into the mid-1980s, tenaciously investigating the puzzling effects he uncovered.

A number of critical experiments have validated General Relativity in recent years. The gravitational reddening of light was demonstrated to agree within 1 percent of theory. The deflection of microwaves from quasars by the Sun was also shown to agree with theory to 1 percent. Gravitational delays of radar signals to the planets provided new evidence in favor of the General Theory. And the spindown, or gradual slowing, in the rotation of a binary pulsar demonstrates the existence of gravitational waves in complete accord with the theory, a result which won the 1994 Nobel Prize for Joseph Taylor and R. Hulse.

If Dicke ever feels disappointed in not finding flaws in General Relativity, he can look back with satisfaction on a career that sparked intense interest in experimental relativity, that created a theoretical framework in which all relativistic theories might be compared, and that trained a corp of brilliant experimentalists. These are not minor achievements in a lifetime of independent thought and sustained effort.

Sidebar: A Critical Test

The Principle of Equivalence asserts that an objects inertial and gravitational masses are the same, and is a fundamental assumption underlying Einstein's General Theory of Relativity. An objects inertial mass is a measure of its resistance to a change in its velocity: a train requires a strong pull to get started because it has a large inertial mass. An objects gravitational mass is a measure of the pull it feels due to the presence of another body: a train weighs a lot (near the Earth) because it has a large gravitational mass.

In principle, these two kinds of mass could be different, but Newton's experiments with pendulums showed they are equal to about one part in a thousand. A test by Roland von Eötvös in 1895 found that the inertial and gravitational masses of a bodyany kind of bodyare the same within five parts in a billion. Einstein took this result to mean that they are exactly identical (or "equivalent"), with the important corollary that no physical experiment of any kind can distinguish inertial forces (such as centrifugal forces) from gravitational forces. Robert Dicke thought Einstein had over-interpreted Eötvös' results.

In 1964, Dicke and his colleagues at Princeton repeated Eötvös' experiment, confirming that the two masses are the same with an accuracy of one part in 100 billion. Lunar laser ranging experiments have confirmed the Principle to even greater accuracy, suggesting Einstein was correct in his conjecture.

FIGURE CAPTIONS

Robert H. Dicke (Courtesy Princeton University)

Consider a bowling ball lying on a stretched rubber sheet. The sheet represents spacetime near the ball and is curved because of the balls mass. A marble rolling toward the ball, is deflected because of the curvature of the sheet. To anybody watching this event, the ball seems to attract the marble with a gravitational force. In this way we can visualize how the curvature of four-dimensional spacetime replaces the force of gravity.

 
 
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