Quantum generations, p.15
Quantum Generations, page 15
FROM SPECIAL TO GENERAL RELATIVITY
My first thought on the general theory of relativity was conceived two years later, in 1907. The idea occurred suddenly. . . . I came to realize that all the natural laws except the law of gravity could be discussed within the framework of the special theory of relativity. I wanted to find out the reason for this, but I could not attain this goal easily. . . . The breakthrough came suddenly one day. I was sitting on a chair in my patent office in Bern. Suddenly a thought struck me: If a man falls freely, he would not feel his weight. I was taken aback. This simple thought experi ment made a deep impression on me. This led me to the theory of gravity. (Einstein 1982, 47)
This was how Einstein, in a 1922 address, described the start of the route that led him to one of the most fundamental theories ever in the history of science. In spite of interesting technical contributions by David Hilbert, Gunnar Nordström, and a few others, general relativity was very much Einstein’s work. According to the principle of equivalence, no mechanical experiment can distinguish between a constant (unaccelerated), homogeneous gravitational field and a uniformly accelerated reference frame in which there is no gravitational force. In 1907 Einstein formulated this principle in a generalized way, to be valid for all kinds of experiments, whether mechanical or not. From this point of view, there is no essential difference between inertia and gravitation. Einstein did not immediately follow up on this idea, but in 1911 he developed a first version of a new research program, namely, to find a new theory of gravitation that led both to the equivalence principle and an extended theory of relativity. This first generalization of the relativity principle resulted in two remarkable predictions: First, that the propagation of light was acted on by gravity, and, second, as Einstein had already realized in his 1907 paper, that the rate of a clock is slowed down near a large gravitating mass. As to the first prediction, Einstein found that for a ray grazing the sun, the deflection would be a little less than one arc-second, 0.83". The clock of the second prediction might be a luminating atom, as measured by a monochromatic spectral line, and here Einstein calculated how the received wavelength increased became redshifted with the gravitational field. The result, a direct consequence of the equivalence principle, was Δλ/λ = ΔΦ/c2, where ΔΦ is the difference between the gravitational potentials at emission and reception of the light.
Einstein realized that his 1911 theory was only a step toward the theory he was looking for. During the next four years, he immersed himself fully in the still more complex search for the new relativistic theory of gravitation. The key to the problem turned out to lie in mathematics. “In all my life I have labored not nearly as hard,” he wrote to Sommerfeld in 1912; “I have become imbued with great respect for mathematics, the subtler part of which I had in my simple-mindedness regarded as pure luxury until now” (Pais 1982, 216). Helped by his friend, the mathematician Marcel Grossmann, he recognized that the proper mathematical tool for the theory was the absolute differential calculus (or tensor analysis) originating with the nineteenth-century works of Gauss and Riemann. In collaboration with Grossmann, Einstein developed a tensor theory of gravitation in which space-time was no longer seen as an inert background of physical events, but was itself subject to changes due to the presence of gravitating bodies. He now definitely abandoned the line element of special relativity and replaced it with a more complex tensor expression that in general consisted of ten quadratic terms: ds2 = Σgmndxmdxn. Similarly, he no longer based his theory on the Lorentz transformations, which he wanted to replace with a more general invariance group. In 1913, Einstein discussed the requirement of general covariance that is, that the field equations must have the same form in every frame of reference. He considered physical laws satisfying this requirement to be preferable, as this would minimize the arbitrariness and maximize the simplicity of the world picture. However, having formulated the principle of general covariance, he abandoned it and instead proposed a set of field equations that did not have this property. Einstein’s main reason for this retrograde step was that his generally covariant equations failed to reduce to the Newtonian limit for weak static gravitational fields. He developed an argument, later known as the “hole argument,” which convinced him that a theory based on generally covariant equations could not be the correct answer. The reason was that such a theory, Einstein mistakenly thought, would violate determinism and causality. It took him two years of hard thinking before he was forced to realize that general covariance was indeed the key to all his problems. This phase culminated during the summer and fall of 1915, and in November 1915 he presented to the Berlin Academy of Sciences the final form of his generally covariant field equations for gravitation. It was, he wrote to Sommerfeld, “the most valuable discovery I have made in my life.”
Einstein’s paper of November 18, 1915 did not only include a new set of gravitational field equations that were generally covariant and logically satisfactory. He also used his new theory to conclude that his earlier prediction of gravitational deflection of light was wrong by a factor of 2. According to the improved theory, a light ray passing the sun should be deflected an angle of 1.7". Apart from the theory’s appealing logical structure, it was another prediction that really made Einstein feel that his theory was correct, and this time it was a prediction of a known effect, namely, the anomalous precession of Mercury’s perihelion. It had been known since 1859 that Mercury does not move around the sun exactly as it should according to Newtonian mechanics. Its perihelion precesses slowly around the sun, as explained by celestial mechanics, but with a slightly different speed of rotation. The anomaly was only 43" per century (about 8 percent of the observed precession), yet was enough to constitute a problem for Newton’s theory of gravitation. Einstein was not the first who sought to explain the Mercury anomaly, but he was the first to give a quantitative explanation based on a fundamental theory not tailored to solve the problem. His calculated value of the precession agreed almost perfectly with the observed value. Einstein had long known that the Mercury perihelion problem would be a litmus test of any new theory of gravitation. As early as Christmas day 1907, he wrote to his friend Conrad Habicht: “I hope to clear up the so-far unexplained secular changes of the perihelion length of Mercury . . . [but] so far it does not seem to work.”
In early 1916, while Europe was bleeding in World War I, Einstein had his general theory of relativity ready. Few physicists were able to understand (or even have access to) the theory because of its complexity and unfamiliar mathematical formulation. But the theory resulted in three predictions, which could be tested in order to judge whether the theory was really correct physically and not just the dream of an imaginative mathematician. The prediction of Mercury’s perihelion advance was a great success, but far from enough to convince skeptics about the truth of Einstein’s theory. After all, Einstein had known about the anomaly all along, so perhaps he had somehow built the result into his theory. And couldn’t the correct result be obtained without the doubtful theory of relativity? This was what a few German antirelativists claimed, referring to a theory that Paul Gerber had published in 1902 and in which he obtained the same expression for the perihelion advance of a planet as Einstein did in 1915. Ernst Gehrcke, a leading German antirelativist, had the paper republished in 1917 in order to use it against the theory of relativity and Einstein’s priority. The result was a minor controversy, but few physicists, even among the antirelativists, were fooled. Gerber’s theory was simply wrong and his correct perihelion expression purely coincidental.
The gravitational redshift prediction, the same in 1915 as in 1911, was extremely difficult to test, primarily because the measured spectral lines came from the sun’s hot atmosphere, where a gravitational redshift could not be easily distinguished from other effects such as the Doppler effect. Between 1915 and 1919, several researchers tried to verify the “Einstein effect,” but in all cases they failed to find an effect of the size predicted by Einstein. On the other hand, in 1920 two physicists from Bonn University, Albert Bachem and Leonhard Grebe, reported results in essential agreement with the prediction. Unsurprisingly, Einstein quickly endorsed the Bachem-Grebe results. Although the German claim was criticized by other experimentalists and the whole question not clarified until much later, from about 1920 many physicists came to believe that Einstein’s prediction agreed reasonably well with observations, or, at least, that there was no clear disagreement. For example, the American astronomer Charles E. St. John at the Mount Wilson Solar Observatory believed, from 1917 to 1922, that his careful observations were at variance with Einstein’s theory, but in 1923 he “converted” to relativity and decided that he had confirmed Einstein’s prediction. There are reasons to assume that St. John’s change in attitude, as well as that of many other researchers, were to a large extent the result of the third test, the 1919 eclipse measurements that so spectacularly confirmed the light-bending prediction.
Shortly after Einstein’s first (and incorrect) prediction of 1911, a few astronomers sought to test the prediction by measuring the position of stars near the rim of the sun during an eclipse. Eclipse expeditions in 1912 in Brazil and in 1914 in southern Russia failed to produce any results, in the first case because of persistent rain and in the second case because of the outbreak of the war. In 1918 American astronomers at the Lick Observatory succeeded in taking photographs of an eclipse passing the United States. The report, which included data conflicting with the 1915 prediction, was not published, however. It was instead the British expedition headed by Frank Dyson and Arthur Eddington and planned by 1917 that produced the confirming results. The total solar eclipse of 1919 was studied at two locations, at Principe Island off the West African coast (by Dyson) and at Sobral in Brazil (by Eddington). Photographs were taken by both expeditions; when they were analyzed, they showed a deflection of light in excellent (but not perfect) agreement with Einstein’s theory. Dyson, who reported the results at a joint meeting of the Royal Society and the Royal Astronomical Society on November 6, 1919, concluded, “A very definite result has been obtained that light is deflected in accordance with Einstein’s law of gravitation” (Earman and Glymour 1980a, 77). This was, in fact, a too-optimistic conclusion that could be obtained only by a treatment of the available data that came close to manipulation, including the rejection of data that did not agree with Einstein’s prediction. Eddington, the British authority in and prophet of relativity, was fully convinced of the truth of the general theory of relativity and his preconceived view colored the conclusion. At any rate, the theory was accepted by the majority of physicists and astronomers, if not by all. As Gehrcke had invoked Gerber’s old theory as an alternative to Einstein’s Mercury perihelion calculations, so did conservatives like Wiechert and Larmor suggest elaborate electromagnetic explanations of light bending in the early 1920s. But compared with the enormous interest in Einstein’s theory, these and other nonrelativistic attempts attracted little attention. The 1919 eclipse expedition became a turning point in the history of relativity, if more from a social than from a scientific point of view.
According to the recollections of Ilse Rosenthal-Schneider, who was a student of philosophy and physics at Berlin University in 1919, when Einstein received the news about the Dyson-Eddington confirmation, he was “quite unperturbed.” He said to her, “I knew that the theory is correct. Did you doubt it?” To Rosenthal-Schneider’s question of what he would have said if the observations had disagreed with the theory, Einstein replied, “I would have had to pity our dear God. The theory is correct all the same” (Rosenthal-Schneider 1980, 74).
The picture of Einstein as an all-knowing and somewhat arrogant rationalist who did not care about experiments is undoubtedly widespread and part of the Einstein myth. But it is basically wrong, at least as far as the younger Einstein is concerned. On the contrary, Einstein was deeply interested in experimental tests of his theories and often tried to arrange for such tests. For example, when Einstein predicted that light would be deflected in gravitational fields in 1911, it was he who tried to interest the astronomers in testing the prediction. Einstein emphasized the closed and logical structure of his general theory of relativity, which to him implied not that it must therefore be correct, but that it could not be modified in order to accommodate some experimental refutation. In a 1919 letter to Eddington, he wrote, “I am convinced that the redshift of spectral lines is an absolutely inevitable consequence of relativity theory. If it were proven that this effect does not exist in nature, the whole theory would have to be abandoned” (Hentschel 1992, 600). He expressed himself similarly with regard to the predicted deflection of light rays. Far from being “unperturbed,” he expressed great joy when he heard about the results. Rosenthal-Schneider’s story is not reliable. That Einstein later came to adopt a Platonic, rationalist attitude with regard to experiments versus mathematical theories is another matter.
RECEPTION
Einstein’s theory of relativity shared with Darwin’s evolutionary biology, Röntgen’s invisible rays, and Freud’s psychoanalysis the fact that it was met with an enormous interest outside as well as within the scientific community. It became one of the symbols of the modernism of the interwar period and, as such its importance extended far beyond physics. Einstein’s theory was labeled “revolutionary,” a term commonly associated with the passage from Newtonian to Einsteinian physics. The theory of relativity was indeed a kind of conceptual revolution and in the early 1920s the revolution metaphor, freely associating to political revolutions, became a trademark of Einstein’s theory. It was a trademark that Einstein did not want to sanction. Einstein did not consider himself a revolutionary; in papers and addresses, he repeatedly stressed the evolutionary nature of the development of science. The theory of relativity, he often said, was the natural outcome of the foundations of physics laid by Newton and Maxwell. Thus, in a 1921 paper, Einstein noted, “There is someting attractive in presenting the evolution of a sequence of ideas in as brief a form as possible, and yet with a completeness sufficient to preserve throughout the continuity of development. We shall endeavour to do this for the theory of relativity and to show that the whole ascent is composed of small, almost self-evident steps of thought” (Hentschel 1990, 107).
The general public including many scientists and most philosophers discovered relativity only after the end of World War I, in part as a result of the much-publicized eclipse expedition announcing the confirmation of Einstein’s theory. A large part of the literature on relativity in the 1920s was written by nonscientists who, more often than not, thoroughly misunderstood the theory and discussed its implications in areas where it could not be legitimately applied. Some authors “applied” relativity to art theory, some to psychological theories, and still others drew wide-ranging philosophical and ethical consequences from Einstein’s theory. Not uncommonly, ethical relativism was claimed to follow from the theory of relativity, which for this reason was declared unwanted in some quarters. Didn’t Einstein claim that everything is relative and that no point of view is better than any other point of view?
The eminent Spanish philosopher José Ortega y Gasset was one of those who misused Einstein’s theory to argue his own pet philosophy, which he called “perspectivism.” Here is a sample: “The theory of Einstein is a marvelous proof of the harmonious multiplicity of all possible points of view. If the idea is extended to morals and aesthetics, we shall come to experience history and life in a new way. . . . Instead of regarding non-European cultures as barbarous, we shall now begin to respect them, as methods of confronting the cosmos which are equivalent to our own. There is a Chinese perspective which is fully as justified as the Western” (Williams 1968, 152). Incidentally, Ortega y Gasset’s perspectivism would later be accepted as politically correct by many Westeners and used in criticizing the scientific worldview. Whatever the merits of perspectivism or relativism, these ideas have nothing to do with the theory of relativity.
Figure 7.1 shows the annual distribution of German books on relativity between 1908 and 1944, with a sharp peak in 1921 when the public debate culminated. The figure refers to both textbooks in physics and to popular, philosophical, and antirelativist books and booklets, of which the latter category made up about three-quarters of the total number of titles published during the peak years 1920 22. Of course, physicists had “discovered” relativity many years before 1921, in the shape of the special theory, although, as mentioned, until about 1913 many physicists did not clearly distinguish between Einsteinian relativity and the equations of the electron theories. The fine structure of early relativity publications is displayed in figure 7.2, curiously starting in 1900. Note the German dominance, the lack of French literature until about 1912, and the decrease in the total number of publications between 1910 and 1915 (see also table 7.1). The latter feature probably reflects that, by 1911, the special theory of relativity was widely accepted among physicists and was no longer considered to be at the cutting edge of physics. It was only after the extended theory appeared in 1915 that momentum was regained.
