Einstein's Unfinished Revolution

by Lee Smolin

  Bohr grew up in an academic family, the son of a professor of physiology, the brother of a mathematician. He was that fortunate sort who got to live his whole life in the city of his birth, in more or less the same setting as his parents. But in his case, a simple and conservative life was an incubator of radical thought.

  In this comfortable, intellectual milieu, he and his wife brought up six sons, several of whom also became professors. One even followed his father to a Nobel Prize in physics. Another son, the oldest, drowned while sailing with his father. Still another son represented Denmark at the Olympics, as did an uncle.

  Denmark is a small country that values science, and Bohr’s leadership of the quantum revolution was facilitated by the creation of a new institute to support his activities, sponsored by the Danish government and the Carlsberg beer company. This gave Bohr the perfect setting in which to extend his influence, by surrounding himself with the best young theorists from around the world. They were stimulated by a steady stream of visitors who came to collaborate with Bohr or to argue with him about quantum theory. The institute provided him with a comfortable house, where Bohr and his family hosted many of the visitors.

  Niels Bohr’s sons had to share him with many of these young quantum revolutionaries, who looked up to him as a mentor. His wife looked after them and played matchmaker, introducing several of them to the women who would become their wives. (There were few women who were scientists in Bohr’s circle.)

  Bohr clearly fascinated those who worked with him. He saw science as a dialogue with nature and his method of working was also based on dialogue—although of a kind that often lapsed into monologue. He used collaborators as scribes, who had the job of taking down Bohr’s thoughts, uttered in whispered riddles, corrected and corrected again, as Bohr paced in circles around the room.

  Bohr began to work on quantum physics shortly after receiving his PhD. He went right to the heart of the problem by proposing a simple but radical quantum model of the atom. He built on Einstein’s nascent quantum theory, particularly the idea that energy is carried by photons. To address the problem of the stability of the electron orbits, Bohr simply postulated that Maxwell’s theory is wrong on the atomic scale. He hypothesized, instead, that there are a small number of orbits of the electron, which are stable. To distinguish these good orbits, he made use of Planck’s constant, which is the conversion factor between frequency and energy. This conversion factor has units of a quantity called angular momentum. This works just like momentum, but for circular motion. A spinning body has an inertia to continue rotating. This is because spinning or orbiting bodies carry angular momentum, which, like energy and regular momentum, cannot be created or destroyed. It is this conservation of angular momentum that keeps a bicycle wheel spinning; it is also what causes a figure skater to spin more rapidly when she pulls her arms in.

  Let’s think about a hydrogen atom, which has only a single electron. Bohr postulated that the good orbits are those in which the electron has certain special values of angular momentum. These special values are integer multiples of the unit of angular momentum, given by Planck’s constant. Bohr called these stationary states. There is an orbit with zero angular momentum which also has the lowest possible value of energy for an electron in orbit around the nucleus. This state is stable; it is the ground state. At higher energies above the ground state are a discrete series of energies which are the excited states.

  Atoms can absorb light, gaining energy, and they can also radiate energy away by giving off light. Bohr next postulated that these processes happen when the electron jumps between the stationary states. To describe these jumps, Bohr made use of Einstein’s photon hypothesis. When an electron jumps down from an excited state to the ground state, it gives off a photon. That photon has an energy equal to the difference in energies of the two states, so that the total energy is unchanged. It has a specific frequency, given by Planck and Einstein’s relation between frequency and energy.

  If you reverse this process you can cause an electron to jump from the ground state up to an excited state, by giving it a photon with an energy equal to the difference of the two states.

  A given atom can then give up or absorb light only at the special frequencies that correspond to these energy differences between states of its electrons. These special frequencies are called the spectrum of the atom.

  By the time Bohr worked this all out, in 1912, chemists had measured the spectrum of hydrogen. Using the ideas I’ve just described, Bohr was able to calculate the spectrum, and his simple theory reproduced what the experimentalists had seen.

  This was a huge step, but it was only a first step toward an understanding of the quantum. There remained many open questions and problems. What is an electron such that it can travel freely outside the atom, but can exist only in one of the stationary states when in an atom? And, most urgently, can the theory be applied to atoms besides hydrogen?

  The next decade was taken up by numerous clever attempts to apply Bohr’s theory to different atoms and other systems. We can generously say the results were mixed, even as we admire the ingenuity of the attempts. This was the situation by the time a young French aristocrat named Louis de Broglie started graduate school in Paris around 1920.

  Louis Victor Pierre Raymond, duc de Broglie, was born of a noble family in the last years of the nineteenth century and studied history before switching to physics. He served in the army during the First World War in the wireless telegraphy section; he was stationed at the Eiffel Tower.

  The small world of theoretical physics was then, as it is now, intensely social. During the crucial period when quantum mechanics was being developed, the proponents were continually in touch by letter and postcard, and they made frequent train trips to visit and consult. The aristocrat de Broglie was an outsider to this world by dint of his personality and position, and because Paris was at the time a backwater in theoretical physics. Louis de Broglie spoke regularly about his work with only one person, his brother, Maurice de Broglie, an experimental physicist who worked on X-rays.

  Isolation is usually an obstacle for scientists, but sometimes it can lead to someone stumbling on an insight that everyone in the crowd has missed. De Broglie was still a doctoral student when he shook physics to the core by putting forth an audacious hypothesis: that the wave-particle duality is not just a feature of light—it is universal. In particular, electrons, like light, are waves as well as particles.

  As he remarked, “When in 1920 I resumed my studies . . . what attracted me . . . to theoretical physics was . . . the mystery in which the structure of matter and of radiation was becoming more and more enveloped as the strange concept of the quantum, introduced by Planck in 1900 in his researches into black-body radiation, daily penetrated further into the whole of physics.”1

  The power of a fresh mind taking a fresh look at a problem is one of the wonders of the world. The young de Broglie had the obvious idea, which had somehow eluded even Einstein and Bohr. They sought to avoid the embarrassment of the wave-particle duality. De Broglie doubled down on it. If light was both a wave and a particle, why couldn’t the same be true of electrons? Why not hypothesize that the wave-particle duality applies universally to all matter and radiation?

  As de Broglie later recounted it, “As in my conversations with my brother we always arrived at the conclusion that in the case of X-rays one had both waves and corpuscles, thus suddenly . . . I got the idea that one had to extend this duality to material particles, especially to electrons.”2

  What motivated de Broglie to come up with an idea which many more experienced physicists had missed? De Broglie was engaged in an ambitious project to reinvent physics from the ground up to incorporate the wave-particle duality. He started with light, where there was already good evidence for a duality of waves and particles, and asked a simple question few had asked before: How do the light quanta move?

  Recall that Newton h
ad favored a particle theory of light because he believed that particles travel in straight lines. The same assumption had led Thomas Young to abandon the particle picture and embrace the idea that light is a wave when he understood that light could bend when diffracted by an obstacle or refracted by passing between two media. It makes sense that if light doesn’t travel in straight lines, it is not made of particles. What then of photons? Didn’t they have to travel in straight lines? De Broglie’s idea was that they don’t because they are guided by the waves, which do diffract and refract.

  This is stunningly revolutionary. The idea that particles travel in straight lines is a consequence of the most basic principle in all of physics, which is Newton’s first law of motion. Also called the principle of inertia, it states that a particle with no forces on it moves at a constant speed in a straight line. One consequence is that momentum is conserved. It is also closely related to the principle of relativity, for another consequence is that velocity is a purely relative quantity.

  De Broglie understood that light quanta were going to have to bend around obstacles, violating all these fundamental principles. The goal of his thesis was to formulate a revolutionary new theory of motion, which would apply to the particles contemplated by the wave-particle duality. In this context, it was a small and necessary step to extend the wave-particle duality from light to all forms of matter and energy.

  In 1924 he wrote this up as his PhD thesis. The thesis was short and uncompromising. The legend is told that had he not been from the aristocracy, it is possible de Broglie would simply have been failed. Not knowing what else to do, his committee sent the thesis to Einstein to evaluate. Einstein saw de Broglie’s point and recommended approval. At the same time, he sent de Broglie’s thesis to a few people he knew would be very interested in it.

  One of these was his friend Max Born, then a young professor in Germany. An experimentalist colleague of his, Walter Elsasser, heard of it and suggested that de Broglie’s prediction that electrons could be diffracted might be tested by scattering a beam of electrons off a crystal. Max Born passed the suggestion to experimentalists in England. None succeeded, but meanwhile two American experimentalists working at Bell Labs, Clinton Davisson and Lester Germer, were, for other reasons, studying how electrons scatter off the surfaces of metals. They accidentally discovered the diffraction of electrons when, in 1925, they tried a new procedure which had the unintended consequence of developing a layer of atoms organized in the regular arrays of a crystal on the surface of their sample. When they measured where the electrons went that scattered off the metal with the crystal surface, they saw interference patterns. Davisson was unaware of the significance of this until he attended a conference in Oxford in the summer of 1926, and happened to listen to a talk by Max Born, who showed a figure from one of Davisson’s own papers as evidence for de Broglie’s revolutionary hypothesis of matter waves. When Davisson returned, he and Germer went back to the lab and were able to definitively confirm that electrons diffract, just as de Broglie had predicted.

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  ERWIN SCHRÖDINGER WAS A brilliant mathematical physicist, originally from Vienna, who had become a professor at the University of Zurich. Schrödinger was closing in on forty and did not belong to the young generation of de Broglie and the other physicists who were revolutionizing their field. On November 23, 1925, he attended a colloquium by Peter Debye, who gave an enthusiastic presentation of de Broglie’s matter wave hypothesis. Debye ended by saying there was one thing missing from de Broglie’s beautiful picture: an equation to describe how the electron waves travel in space. Leaving his wife behind in Zurich, Schrödinger took de Broglie’s papers with him to a Christmas holiday in the mountains with his girlfriend. (His wife was spending the Christmas holidays with her lover, the great mathematician Hermann Weyl, who was also Schrödinger’s best friend.) The first day, he excused himself from skiing, stayed in their chalet room, and read de Broglie’s papers. He challenged himself to invent the equation that would govern de Broglie’s electron wave. He succeeded the next day, and by the time he returned from the mountains, he had captured the equation that bears his name, the fundamental equation of quantum theory.

  Not only that, but, shortly after returning, with the help of Weyl, Schrödinger solved his equation for the case of a single electron in orbit around a nucleus, and reproduced Bohr’s theory of stationary states and his prediction of the spectrum of hydrogen. The key idea is that the electron waves have to fit around an orbit, as we see in figure 7. The thoughts of the girlfriend—and, indeed, her name—are lost to history. But legend tells us that when Schrödinger went to Stockholm to receive his Nobel Prize he showed up with his wife and their girlfriend.

  FIGURE 7. Electron waves in the atom. The wave on the left fits around the nucleus in three steps, so the wavelength is the diameter of the atom divided by three. The right figure has half the wavelength and so fits around in six steps.

  Thus quantum mechanics was born. The question everyone then faced was how to think of the electron wave that de Broglie had invented and Schrödinger had tamed. Schrödinger at first thought that the electron simply is a wave. This didn’t hold up because it was easy to show that the wave tended to spread out in space as it traveled, whereas one could always find a localized particle. Max Born then proposed his rule that the wave is related to the probability of finding the particle.

  For Einstein, the wave-particle duality, while a profound challenge, had been limited to speculation about the constitution of light. Confined to that domain, it did limited damage, perhaps because particle and wave theories of light each had long histories and recognized virtues. But the idea of matter waves came as a complete shock. De Broglie and Schrödinger transformed physics by bringing the wave-particle duality into the core of physics, where it sat enshrined as the central mystery of the revolutionary new quantum physics.

  The question was no longer “How can light be both a particle and a wave?” but rather, “How can everything be both a particle and a wave?”

  Einstein, who had been the first to formulate the wave-particle duality, was stumped. Despite, by his own admission, spending far more time on quantum physics than he ever did on relativity, he was unable to make a convincing move. His peerless intuition failed him, and it is worth wondering why. Perhaps his realism, his demand for complete conceptual clarity, held him back.

  Schrödinger also was, for a time, at a loss. As were most others.

  Of the great pioneers, only Bohr knew what to do. It was his moment and he seized it, announcing the birth not just of a new physics but of a new philosophy. The moment for radical anti-realism had come, and Bohr was ready for it.

  Bohr called the new philosophy complementarity. Here is how he talked about it: Neither particles nor waves are attributes of nature. They are no more than ideas in our minds, which we impose on the natural world. They are useful as intuitive pictures that we construct from observing large-scale objects such as marbles and water waves. Electrons are neither. Electrons are microscopic entities that we cannot observe directly, and so we have no intuition about them. To study electrons we must construct big experimental devices to interact with them. What we observe is never the electron itself; it is only the responses of our big experimental devices to the tiny, invisible electrons.

  To describe how the experimental devices respond to electrons, we may find it useful to employ intuitive pictures such as the wave picture or the particle picture. But we cannot take these pictures too seriously because different experiments require different pictures. The different pictures would contradict each other if we forgot the context and applied them to the electrons themselves. But there is no actual contradiction so long as we remember two things. The pictures are useful only as a description of an electron in a specific context, which is in a particular experimental device. And there is no experimental device that forces us to apply both contradictory pi
ctures simultaneously.

  Bohr’s position is anti-realist in the extreme, in that he denies it is even possible to talk about or describe an electron as it is in itself, outside the context of an experiment we construct. Science according to this picture is not about electrons; it is about how we talk about our interactions with them.

  For Niels Bohr, complementarity was more than a principle; it was a proposal for a whole philosophy of science. And what a radical proposal it was. Bohr championed the philosophy of complementarity throughout his life, as did other founders of quantum mechanics, including, to some extent, Heisenberg.

  For Bohr, science is not about nature. It does not and cannot give us an objective picture of what nature is like. That would be impossible, because we never interact with nature directly. We gain knowledge about the natural world only through intermediaries, which are experimental devices we invent and construct.

  Thus, we must give up the idea that science gives us an objective description of nature, or has anything at all to say about what nature is like, absent our existence and our interventions. Science is rather an extension of a common language we use to describe to each other the results of our interventions into nature.

  In essays and books, Niels Bohr argued that his philosophy of complementarity had wide applicability. It has been claimed he got the idea of complementarity from the Kabbalah, the Jewish mystical writings, which speak of the complementarity between God’s love and God’s justice. Bohr talked about the complementarity between life and physics, between energy and causation, and, indeed, between knowledge and wisdom. For Bohr the lesson of quantum mechanics was a revolution that extended beyond physics, beyond science.