by Lee Smolin
Einstein elaborated in a paper in honor of Born, posing an objection. Bohm’s theory predicts the motion of the particle, and one consequence is that in a stationary state of an atom, the electron is predicted to be simply standing still. As Einstein explained, “The vanishing of the velocity contradicts the well-founded requirement, that in the case of a macro-system the motion should agree approximately with the motion following from classical mechanics.”4 But it doesn’t because, according to classical mechanics, the electron should be orbiting the nucleus, and not just standing still.
It should have been immediately apparent that Einstein’s objection is wrong, because atoms are not “macro-systems.” But nonetheless, Einstein’s objection points to how different the particles of pilot wave theory are from those of Newtonian physics. As I stressed earlier, de Broglie had understood from the beginning that his particles would move in ways that violate basic principles of Newtonian physics, such as the principle of inertia and the conservation of momenta. This was necessary if light quanta could bend their trajectories to diffract around obstacles. De Broglie’s and Bohm’s guidance equations resulted in trajectories that diffracted and refracted, but there was a price to pay, which was apparent violations of basic principles. Particles that just stood still in an atom, and did not need to orbit to keep from falling into the nucleus, also contradicted these principles. For Einstein, it seemed, the price was too high.
Einstein’s dislike of pilot wave theory didn’t prevent him from writing sympathetically when he heard through a mutual friend about Bohm’s “feeling of distress for being closed out and closed in at the same time. What impressed me most was the instability of your belly, a matter where I have myself extended experience.”5
Indeed, the other responses Bohm received or heard about were not likely to have helped his digestion.
Heisenberg replied that from his operational point of view, the particle trajectories in Bohm’s theory constituted an extraneous “ideological superstructure.” There were two possible fates for any proposed alternative to quantum mechanics. Either the new theory gave predictions that disagreed with those of quantum mechanics, in which case it is most likely wrong, or it predicts the same phenomena, in which case it has nothing new to offer physics. He wrote that “Bohm’s interpretation cannot be refuted by experiment. . . . From the fundamentally ‘positivistic’ (it would perhaps be better to say ‘purely physical’) standpoint, we are thus concerned not with counter-proposals to the Copenhagen interpretation, but with its exact repetition in a different language.”6
Pauli issued a similar criticism, but after further study, conceded: “I do not see any longer the possibility of any logical contradiction as long as your results agree with those of the usual wave mechanics and as long as no means is given to measure the values of your hidden parameters.”7
In fact, there are circumstances in which the predictions of pilot wave theory disagree with those of quantum mechanics, but it took some time for that to become clear. We will return to this point shortly.
Not everyone was so kind. Back in Princeton, Robert Oppenheimer declined to read Bohm’s papers, calling them a waste of time. But this did not prevent him from pronouncing that Bohm’s work was “juvenile deviationism.”8 Doesn’t that sound exactly like language one Marxist would use to condemn another? Oppenheimer’s last word on the subject was “If we cannot disprove Bohm, then we must agree to ignore him.”9
The mathematician John Nash, now famous for his theorem on equilibrium in economics, wrote to Oppenheimer to complain about the dogmatic attitudes he found among the Princeton physicists, who treated anyone who “expresses any sort of questioning attitude or a belief in ‘hidden parameters’ . . . as a stupid or at best quite ignorant person.” Nonetheless, he was with the other losers, because he confessed, “I want to find a different and more satisfying under-picture of a non-observable reality.”10
The complete rejection of his breakthrough work by Oppenheimer, who had been both a mentor and a father figure to Bohm, must have hurt deeply. Bohm was doubly exiled from Princeton, then the center of American physics, for his rebellion against the Copenhagen philosophy and his simultaneous refusal to capitulate to the McCarthyist witch hunt. One must admire the courage that took, while remembering the cost. Bohm was isolated at what must have felt to him like the end of the Earth.
Bohm’s friends and his biographer intimate that Oppenheimer had motives to distance himself from a suspected “red,” as he was himself in danger, about to be caught up in the same witch hunt. But even putting that aside, it would be naive to believe that in the absence of his political catastrophe and exile, a Bohm who had stayed in Princeton would have succeeded any better in gaining interest in his subversion of the Copenhagen ideology.
In any case, the response from Copenhagen appeared equally dismissive. There is a report, by the philosopher Paul Feyerabend, who visited Copenhagen then, that Bohr was at least momentarily “stunned” by Bohm’s papers. But if he was stunned it was not enough to ever mention in his own writings, let alone pick up a pen and respond to Bohm directly. Instead, Bohm received a letter from a protégé of Bohr named Léon Rosenfeld.
Here is a sample of Copenhagen-speak, taken from that letter:
I certainly shall not enter into any controversy with you or anybody else on the subject of complementarity, for the simple reason that there is not the slightest controversial point about it. . . . [T]here is no truth in your suspicion that we may be talking ourselves into complementarity by a kind of magical incantation. I am inclined to retort that it is just among your Parisian admirers that I notice some disquieting signs of primitive mentality.
The difficulty of access to complementarity which you mention is the result of the essentially metaphysical attitude which is inculcated to most people from their very childhood by the dominating influence of religion or idealistic philosophy on education. The remedy for this situation is surely not to avoid the issue but to shed off this metaphysics and learn to look at things dialectically.11
Reading this alone in his São Paulo apartment, David Bohm must have felt a long way from Kansas, or, in his case, Pennsylvania.
Despite his disappointments, Bohm was productive during his time in Brazil. He continued to make contributions to plasma physics while he focused on his new quantum theory, and he began a collaboration with Jean-Pierre Vigier, a student and colleague of de Broglie. But he was not happy in Brazil and in 1955 moved to the Technion in Israel, then a few years later to England. After a stay in Bristol he ended his odyssey at Birkbeck College, University of London, where he was to stay for the rest of his life.
In London, Bohm moderated his communist sympathies; like many who had given the Soviet Union the benefit of the doubt, he was shocked as the thawing of Soviet power under Nikita Khrushchev led to the confirmation that the Stalinist gulag had indeed been every bit as murderous as had been reported. Bohm’s desire for a road to the perfectibility of human beings then turned to mysticism, and after a short immersion in the teachings of the mystic Gurdjieff, he fell under the influence of the Indian guru Krishnamurti.
Bohm meanwhile continued his relentless search for a deeper viewpoint on nature that would take him beyond the quantum theory. This led him to develop a highly original line of thought, frankly speculative and philosophical, both related to and transcending his physics. He wrote several books, through which he reached a new audience of artists, philosophers, and seekers, while his dialogues with Krishnamurti became very popular in the wider world.
* * *
—
ALTHOUGH HIS LATER WORK is of no relevance for judging the importance of his work on pilot wave theory, I do feel it would be irresponsible and cowardly to not attempt a summing up of the life’s work of this complex and contradictory sage. I feel a genuine sympathy for David Bohm in his search for transcendence, first through the Marxist vision of a new human psychology arising f
rom the dream of a just and equal society, and then, when that fantasy was exposed as a cruel illusion, through his work with mystics.* From Oppenheimer to Krishnamurti, some weakness in Bohm made him susceptible to that kind of dominating, supremely confident figure.
But as much as one can criticize Bohm for what in retrospect looks like the naive and ignorant suspension of his better judgment, his years of hard, determined effort in search of the science beyond the quantum rescues his life’s work and restores to it integrity, seriousness, and promise. He was on a quest for a new transcendent form of science, informed simultaneously by the deepest strands of what is best called religious thought and the knottiest puzzles of theoretical physics. It is a domain few good physicists have explored; perhaps only David Finkelstein can be mentioned here. It is easy to say that Bohm failed, and that his greatest achievements by far were his early contributions to quantum physics. At the same time, he explored a road that few of us have had the courage or the vision to even take one step toward, in spite of the obvious fact that the greatest dangers we face as a species can be tied to the utter incoherence of human culture, a break that has its roots in the incommensurability of scientific and spiritual understandings of the world.
* * *
—
IN THE WAKE OF what we’ve learned from Bohm, let’s sum up. The pilot wave theory explains everything that ordinary quantum mechanics does, without the awkwardness of Rule 2. The wave function evolves always according to Rule 1, so it never jumps or collapses. What is new is that there is a particle that moves according to its own law, guided by the wave function. Together the two laws give an entirely realist description of quantum phenomena.
In addition, pilot wave theory explains what quantum theory does not. It gives a complete description of what goes on in every individual process. It explains how and why electrons move. It explains where the uncertainties and probabilities come from, which is our ignorance about the starting positions of the particles. And it solves the measurement problem because there is no need to distinguish experiments from other processes.
In the second paper Bohm wrote in 1952 on the new theory, he studied the measurement process in detail and showed that, in the case of an atom interacting with a detector set up to measure some property of it, the detector ends up correlated with the atom, in terms of where the particles are as well as in terms of the wave functions. Thus, measurements work correctly on both sides of the double ontology.
From a realist point of view, pilot wave theory is vastly superior to the Copenhagen interpretation. By its very existence it gives the lie to Bohr and Heisenberg’s argument that it is impossible to have a realist description of quantum physics. One might have thought that the community of physicists would have jumped to embrace pilot wave theory, either when de Broglie first proposed it to the Solvay conference in 1927 or in 1952 when Bohm proposed it again. This is clearly what Bohm expected, and his disappointment, as he waited in São Paulo, may be ours as well.
Some historians have suggested that the embrace of anti-realism by the European physics community in the 1920s was part of a larger cultural movement which embraced irrationality as a response to the slaughter in the trenches that their generation had recently experienced. But this does not explain the similar rejection of pilot wave theory by the physics community of the 1950s, which had recently come to be dominated by the triumphant, optimistic, and pragmatic American spirit.
Some might explain it by the power of research schools led by charismatic leaders, particularly Niels Bohr, who inspired and mentored many of the quantum revolutionaries who came from across Europe and America to work with him. De Broglie, by contrast, had just a few students throughout his long life, and they were, to my knowledge, all French. His small group of acolytes was isolated even within the community of French physicists.
Bohm inspired the development of a community of theorists in Brazil, for which he is unappreciated beyond that country. After Brazil, in Israel and London, he had a few good students, one of whom, Yakir Aharonov, became a leading theorist with his own ideas and program, quite different from Bohm’s. A handful of Bohm’s students became specialists in quantum foundations, but they pursued diverse ideas and did not form into a coherent Bohmian school of thought. It didn’t help that, by the time Bohm had relocated to London and was back in a place where he could assert influence, much of his attention was captured by mysticism.
Nonetheless, interest in pilot wave theory grew slowly but steadily over the years, as it was taken up and developed by a small number of good scientists around the world. By the 1990s, what was sometimes called “Bohmian mechanics” constituted a small but distinct and visible subculture of the community of scientists, mathematicians, and philosophers who devoted themselves to the puzzles of quantum foundations.
* * *
—
DUE TO THE WORK of these “Bohmians,” some subtle questions about pilot wave theory have been raised and answered. One of the trickiest questions has to do with how probabilities arise in pilot wave theory. The theory is deterministic. Given a wave function at one time, we can use Rule 1 to determine the wave function at any future time. The equation that describes how the wave function guides the particle is also deterministic, and if we specify where the particle is at an initial time, it will tell us exactly how the particle moves from then on. Each particle has a definite trajectory.
So where do probabilities come from? Probabilities enter for the same reason they can enter Newtonian physics: because of our ignorance about the exact positions of the particles. As we cannot know where the particle starts out, we are uncertain about where it will be in the future. Probabilities in pilot wave theory express our ignorance of where the particles were initially.
To make sense of probabilities in pilot wave theory, we have to picture a collection of systems with the same wave function, but with different starting positions of the particles. The particles are distributed initially according to a probability distribution function, which tells us how common the different initial positions are in the collection.
We are free to choose the initial positions of the particles, to make the probability distribution function be anything we like. We evolve the system forward in time, using Rule 1 to evolve the wave function and the guidance law to move the particles around. When we do this, the probability distribution function changes in time as well, reflecting the particles moving around.
In quantum mechanics, as I described earlier, the probabilities of finding the particles in different places are given by Born’s rule to be the square of the wave function. That is simply posited in quantum mechanics as part of Rule 2. In pilot wave theory the particles have their own reality, and we are free to choose the initial probability distribution function. One choice we can make is that it is given, just as in quantum mechanics, by Born’s rule. To do this, we distribute the particles so that the larger the square of the wave function is, the more particles in the collection are placed there.
When we make this choice, it is maintained in time. The particles move around and the wave function changes in time, but it remains true that the square of the wave function gives the probability of finding a particle.
But in de Broglie’s formulation, there is more. Suppose one starts the collection off with a different probability distribution for the particles, one not given by the square of the wave function. Then the system will evolve in a way that brings the actual probability distribution into agreement with that given by the square of the wave function. This was shown in an important result of Antony Valentini’s.12 It has been confirmed by numerical simulations since.13
This is analogous to how thermodynamics works. When a system of many particles is in equilibrium with its surroundings, the entropy is maximal. This is because entropy is a measure of disorder, which typically increases over time. If one starts the system off in a different configuration, one more ordered than equilibri
um, it is most probable that the disorder will increase until the system is in equilibrium.
The case of de Broglie’s pilot wave theory is very similar. We can say that a quantum system is out of quantum equilibrium if the probability distribution for where a particle might be found is different from that given by the square of its wave function. When they agree, the system is in quantum equilibrium. Valentini’s theorem tells us that a quantum system out of quantum equilibrium is most likely to evolve until it reaches the state of quantum equilibrium.
Once a system is in equilibrium, the predictions of pilot wave theory agree with those of conventional quantum mechanics. Thus, one has to somehow drive a system out of quantum equilibrium to set up a situation in which an experiment could distinguish pilot wave theory from quantum mechanics.
Physics out of quantum equilibrium contains several surprises. One is that it becomes possible to send information faster than light. This is a consequence of another result of Valentini’s, which tells us that while the system is out of quantum equilibrium, information and energy can be sent instantaneously, contradicting special relativity.14 Needless to say, if this were to be confirmed experimentally it would be of the first importance for our understanding of nature and possibly even for technologies that science fiction writers dream of. This is one way an experiment could very dramatically distinguish pilot wave theory from conventional quantum mechanics. There have been a few attempts to drive quantum systems out of quantum equilibrium and test these predictions, but, so far, they haven’t succeeded in either discovering quantum non-equilibrium or ruling out pilot wave theory.
One place to look for out-of-quantum-equilibrium physics is in the very early universe. Valentini and collaborators have hypothesized that the universe began in the big bang out of equilibrium, and equilibrated as it expanded. This might have left traces in the cosmic microwave background, or CMB, which are being searched for, but there is no clear evidence yet.15
