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What Einstein Did

Subtle is the Lord…’: The Science and the Life of Albert Einstein

by Abraham Pais
Oxford University Press, 552 pp., $25.00

Albert Einstein was not only respected and admired by his fellow scientists as probably the greatest physicist of this century but he also achieved extraordinary fame among people who did not have the least idea of his work. What did he accomplish? Although he is most widely known as the discoverer of the theory of relativity, he made other vital contributions which are far less well known but which, by themselves, would have placed him in the front ranks of physicists. The most important of these was his part in creating the quantum theory. He gained the Nobel prize for this, not for his work on relativity.

Abraham Pais’s book is thus particularly valuable as the first thorough study in one accessible volume of all of Einstein’s major contributions to science. A physicist who knew Einstein when they were both at the Institute for Advanced Study at Princeton, Pais presents each phase of Einstein’s work against the background of Einstein’s previous ideas and those of his predecessors. In each case he tries, as far as possible, to reconstruct Einstein’s train of thought. To do so, of course, he has to describe the technical aspects of each problem, and it will be difficult for any reader without some acquaintance with theoretical physics to follow his account. For those qualified to read it, however, his book is remarkably clear as well as authoritative.

The breadth of Einstein’s vision and his originality were shown in his work of 1905, when, as a twenty-six-year-old technical expert, third class, in the Swiss patent office in Bern, he wrote five important papers, all carefully discussed in Pais’s book. Two of these established what is now called the special theory of relativity. This starts from the long-established fact that a state of uniform motion cannot be distinguished from being at rest. It is a familiar fact that the passenger in a fast airplane experiences no sensation of being in motion, unless air turbulence or a change of direction causes the motion to be nonuniform. But it was then thought that by watching the speed of light one might be able to tell the difference. Physicists believed that light consisted of vibrations of a hypothetical, all-pervasive medium, the “ether,” and that by observing the way light travels, we could discover whether we were at rest, or moving, relative to this ether. This seems reasonable if we think of sound waves. If we were sitting on the tail of a plane, our voices shouting to a friend on top of the cockpit would seem to be traveling slowly, because they had to go against the rush of air experienced by the plane; the sound of our friend’s voice would reach us faster than normal sound. On a supersonic plane the sound of our voices would not reach the man in front at all.

We are all participating in the motion of the earth around its axis and in its orbit about the sun, and so, according to the ether theory, we should be exposed to a similar “ether wind.” It was surprising enough that such a wind did not seem to affect us in any way. But at least it was expected that the motions of the earth should influence the progress of ether waves, i.e., of light, just as the flow of air past the plane affects the progress of sound. But in a delicate experiment to test this, the American physicists Albert A. Michelson and Edward Williams Morley demonstrated that there was no effect on the speed of light. The speed of light plus any added velocity was still equal to the speed of light.

This puzzle worried many, including the physicist H.A. Lorentz and the mathematician H. Poincaré, who came close to the right answer. In his 1905 papers Einstein showed that in view of the Michelson-Morley experiments and other evidence, we had to revise our ideas of space and time. The speed of light appears the same no matter at what speed we are traveling ourselves, and this seemingly absurd statement becomes possible because time looks different to observers moving with different speeds: two observers might disagree on which of two distant events was the earlier, and which the later one.

Many important consequences of this theory have by now been verified. They include the fact that bodies become heavier with increasing speed, thus requiring more force to accelerate them further; in the end an infinitely strong force would be required to make them reach the speed of light. Therefore no object can, be accelerated to that speed, let alone beyond. This is of great practical importance for the physicists’ particle accelerators, in which particles travel at a speed less than that of light by only one part in 10 billion.

Other important consequences included the famous equation E=mcu2, which expresses the fact that matter and energy are equivalent, and which is—wrongly—considered by some to be the basis of nuclear energy. (It is true that the uranium nucleus loses some of its mass, or weight, in the process of fission, but ordinary fuel and oxygen also lose some mass in the process of combustion. The difference is one of quantity; the loss in the first case is about one part in a thousand, in the second case one in 50 billion. In either case the loss of mass is incidental to the gain in energy, not its cause.)

These ideas were immediately accepted by the community of physicists, and from then on formed the basis of much further work. But they upset many philosophers, partly because they conflicted with beliefs that had been regarded by Kant and others as evident a priori. Many were confused by the name “relativity,” which appeared to suggest philosophical relativity, the attitude that all knowledge is relative, whereas in fact the essence of the theory of relativity is to recognize the absolute physical reality which unites the different appearances that phenomena present to different observers.

Einstein’s second important idea, more revolutionary than that of relativity, concerned the light quantum. Here again Pais explains very clearly Einstein’s achievement. In 1900, Max Planck had described the light emitted by a hot body by a formula using, in an unconventional way, the principles of statistical mechanics—the description of heat in terms of the behavior of atoms. While Planck was trying to minimize the revolutionary nature of his step, Einstein saw that it required a new basic approach to the nature of light: one had to treat light as made up of separate quanta, small amounts of energy dependent on the “frequency” or “pitch” of the wave, which is about twice as large for blue as for red light. This led him to predict that in the photoelectric effect, i.e., the release of electrons from a metal surface under the influence of light, the energy of these electrons, which was known to be independent of the intensity of the light, should grow in strict proportion to its frequency. This prediction, for which Einstein was later awarded the Nobel prize, was soon confirmed by precise measurements.

But his basic concept of the light quantum took a long time to be accepted. He realized himself how basically this conflicted with the evidence that light consisted of waves. He therefore emphasized that in the description of light we must combine some wave with some particle features, an early indication of an idea that did not find its full expression until the quantum mechanics of the late 1920s.

The third important contribution of 1905 concerned Brownian motion, the irregular motion of small specks of dust, known to be caused by the irregular impact of the molecules of the surrounding gas or liquid, thus giving a vivid illustration of the fact that heat consists of the motion of molecules. Einstein’s work opened a new way of “counting atoms,” i.e., of determining how many atoms or molecules are contained in a given amount of matter. Another paper, which I shall not attempt to summarize, put forward other new ways of counting atoms, and these contributed much to the confidence of physicists in the existence of atoms.

Einstein was not satisfied with the special theory of relativity, because the restriction of his new conception of space and time to uniform motion seemed unnatural. At first sight there seems no way out of this dilemma, because nonuniform motion, whether the bumping of a car on a rough road, or the revolutions of a merry-go-round, causes sensations that make it evidently impossible to ignore that motion. But Einstein saw that the sensation caused by accelerated motion is of the same kind as that caused by another familiar phenomenon, namely gravity. He illustrated this by the picture of people in a freely falling elevator, for whom the acceleration would balance their gravity, so that they would feel weightless. The same idea is now more familiar from the experience of astronauts, who are weightless even while in the field of attraction of the earth, because the non-uniform motion of a coasting spacecraft, as a result of the attraction, compensates for their weight. This “principle of equivalence” depends on the equality of weight and mass, which had already been established with a high degree of precision.

Pais quotes Einstein as describing the application of this idea to nonuniform motion as “the happiest thought of my life,” but it took Einstein many years, many false starts, and much persistence to build on this principle a theory of gravitation. This involved interpreting gravity as a change in the structure of space, an alteration of the laws of geometry. Its predictions included a correction to the accepted orbit of the planet Mercury, and the bending of light rays passing close to the sun, observable during an eclipse. Observations during the eclipse of 1919 by expeditions organized on the initiative of the English astrophysicist Arthur Eddington confirmed this prediction, and thus led to the general acceptance of the “general” theory of relativity, while also catching the attention of the press. It was then that Einstein’s fame began with the general public.

Besides these impressive pieces of work Einstein took an interest in many minor problems of physics, and even participated in experiments and in practical inventions. But after 1919 the main direction of the development of physics by-passed his central preoccupation. Why did this occur?

Having recognized that gravitation was part of the structure of space and time, Einstein wanted to link also electricity and magnetism with the space-time structure, and he hoped that this would lead to an explanation of the existence of elementary particles, like the electron. His search for such a “unified field theory” occupied much of the rest of his life, but it ended in failure. Most of his colleagues did not believe that such a theory was possible, or even desirable. While this did not diminish their respect and affection for him, it left him isolated.

The nature of his disagreement with his colleagues did not turn simply on his search for unification. Much of the progress of our understanding of the laws of nature consists in recognizing how seemingly different phenomena are explained by common or related basic principles. The great strides made by fundamental physics during the last few years consist in a theory unifying electromagnetic phenomena with the “weak” force, which is responsible, for example, for some of the radiations from radioactive substances, and for the heat of the sun.

But the kind of unified theory Einstein was searching for was of a different nature. It was related to the fact that he was unhappy about the other great development in twentieth-century physics, which he himself had helped to initiate: the quantum theory and its finished form, quantum mechanics. This theory also requires that we adjust our intuitive prejudices, in particular that we abandon the principle of causality in its old form, and Einstein could never reconcile himself to that.

The difficulty is illustrated by the “wave-particle duality.” Einstein himself had introduced the notion of a “light quantum” which makes a flash of light behave like a stream of small particles; at the same time experiments with diffraction of light showed light to consist of waves, and these experiments continued to remain valid. The theoretical ideas of de Broglie and Schrödinger, and the experimental discovery of electron diffraction by C.J. Davisson and L.H. Germer, and by G.P. Thomson, showed that electrons and other familiar objects known to us as particles also could behave like waves.

Einstein himself first mentioned the way out of this dilemma, which is now generally accepted. He spoke of Gespensterwellen or “ghost waves” that would regulate the probability with which particles were found at any particular place, but he mentioned this as a logical possibility that he found most unattractive. Later this idea was elaborated into a full theory by Max Born, Werner Heisenberg and Niels Bohr. In this theory Planck’s “quantum of action,” which he had introduced through the energy of a light quantum of a given color, sets a limit to the accuracy with which we can observe, or even define, details of the motion of any particle. As a result, we can no longer, even in principle, predict the motion of a particle exactly, but can give only the probability of it getting to a certain place. Einstein acknowledged the success of quantum mechanics in many fields, but tried to find inconsistencies in the theory; these were always disproved by Niels Bohr. Eventually Einstein accepted that the theory was not inconsistent, but felt that it was incomplete.

At the heart of his reaction was his reluctance to accept the part that chance played in the interpretation of quantum mechanics, and in the loss of determinacy. According to the quantum theory the position of particles is a matter of statistical probability, as Einstein himself had once suggested, but could not bring himself to accept. He did not believe, in his much cited remark, that “the Lord would play dice.” He therefore hoped that the “unified field theory” for which he was searching would make it possible to maintain a deterministic description, in which the existence both of particles and of Planck’s quantum of action would be shown by field equations. In this view he became isolated from the rest of the physics community.

It is hard to understand how this great man, with the flexibility of mind and courage to introduce into physics the most revolutionary ideas, could fail to accept conclusions that all his colleagues found convincing and confirmed by ample experimental evidence. Peter Kapitza, the Russian physicist, once observed that great physicists who as they got older lost contact with the latest developments in their subject, such as de Broglie or Schrödinger, were those who did not have many pupils, while others, like Rutherford or Niels Bohr, who stayed in the front line until their deaths, were surrounded by crowds of young collaborators. It is true that Einstein did not have many pupils, but he is unique among physicists and it may be dangerous to apply general rules to him.

Pais’s book is based on Einstein’s writings, on his letters, on the published recollections of many who had conversations with him, and on Pais’s own talks with Einstein at the Institute for Advanced Study at Princeton, where Einstein used to chat with his young colleague about his work and his thoughts. Many of these conversations show Einstein’s pungent use of language, mostly in German with which he felt at home.

Typical of his way of talking is the often-quoted phrase “Raffiniert ist der Herrgott aber boshaft ist er nicht” (Subtle is the Lord, but malicious He is not), which Pais uses as his title and as a kind of leitmotif to the book. This expresses in language typical of Einstein the confidence that there must be an ultimate simplicity in the natural law, and it also shows his playful but genuine feeling of respect for a higher order. The sentiment is similar to Niels Bohr’s, in a different style: “Physics is the belief that a simple and consistent description of nature is possible.”

Einstein is often called native in matters outside physics, and with the pressure on him to make public statements on all conceivable subjects, he may occasionally have displayed ignorance of their subtleties. But Pais stresses that more often Einstein’s seemingly naive utterances were the result of his absolute and uncompromising moral principles, and an unconventional approach to human problems. In a collection of essays from the recent centenary celebration in Jerusalem of Einstein’s birth,* for example, Yehuda Elkana quotes from a letter to Chaim Weizmann: “Unless we find the way to honest cooperation and honest dealings with the Arabs, we have not learned anything on our way of two thousand years’ suffering and deserve the fate that is in store for us.” While he had come to support Zionism, he was strongly opposed to chauvinism in any form.

Pais also raises the puzzling question why Einstein occupies such a unique position in the eyes of the general public. He points to the influence of the press, to the confusion of the term “relativity” with general philosophical skepticism, to the concern of the theory with the stars, which is always a field of scientific study capable of catching the imagination of the public.

Along with his account of Einstein’s scientific work and his thoughts on other problems, Pais briefly gives some biographical details, including his unconventional education, his difficulties in finding a job until 1902, when the peaceful haven of a post in the Swiss patent office turned up, his two marriages, and his stays in several universities and teaching posts. In 1914 Einstein finally accepted an invitation to take up a full-time research appointment in Berlin; he stayed there until the rise of Nazism caused him to resign and move to Princeton, where he spent the rest of his life. But undoubtedly the strong point of the book is the story of Einstein’s work. Pais is uniquely qualified to tell it, and after an impressively thorough study of all available sources, he had done so with admirable clarity.

  1. *

    Albert Einstein, Historical and Cultural Perspectives: The Centennial Symposium in Jerusalem, edited by Gerald Holton and Yehuda Elkana (Princeton University Press, 1982), p. 237.

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