Bohm's Alternative to Quantum Mechanics
by David Z Albert
(Part 2 of 2)
For some time, many physicists and philosophers have viewed this state of affairs as profoundly unsatisfactory. It has seemed absurd that the best existing formulation of the most fundamental laws of nature should depend on such imprecise and elusive distinctions. The challenge of either eliminating or repairing that imprecision has emerged over the past 30 years as the central task of the foundations of quantum mechanics. It has gone by a number of names: the problem of Schrodinger's cat, for example, or of Wigner's friend, or of quantum state-reduction. I will refer to it by its most common contemporary name: the measurement problem.
One particularly striking solution to the measurement problem was invented by the American-born physicist David J. Bohm. The French physicist Louis de Broglie had devised a related scheme some years earlier, but de Broglie's formulation was much less general and powerful than was Bohm's. More recently, the late physicist John Bell recast Bohm's original theory into a very simple and compelling form.
Notwithstanding all the evidence to the contrary presented above, Bohm's theory presumes that particles are the sorts of things that are invariably located in one or another particular place. In addition, Bohm's theory is a great deal clearer than is the Copenhagen interpretation about what the world is made of. In Bohm's account, wave functions are not merely mathematical objects but physical ones, physical things. Bohm treats them somewhat like classical force fields, such as gravitational and magnetic fields. What wave functions do in Bohm's theory (just as classical force fields do) is to in effect push the particles around, to guide them, as it were, along their proper courses.
The laws that govern the evolutions of those wave functions in time are stipulated to be precisely the standard linear differential quantum-mechanical equations of motion--but this time with no exceptions whatever. There are other laws in Bohm's theory as well that dictate how those wave functions push their respective particles around. All those laws are fully deterministic. Therefore, the positions of all the particles in the world at any time, and the world's complete quantum-mechanical wave function at that time, can be calculated with certainty from the positions of all the particles in the world and the world's complete quantum-mechanical wave function at any earlier time.
Any incapacity to carry out those calculations, any uncertainty in the results of those calculations, is necessarily in this theory an epistemic uncertainty. It is a matter of ignorance and not a matter of the operations of any irreducible element of chance in the fundamental laws of the world. Nevertheless, this theory entails that some such ignorance exists for us, as a matter of principle. The laws of motion of Bohm's theory literally force this kind of ignorance on us. And this ignorance turns out to be precisely enough, and of precisely the right kind, to reproduce the familiar statistical predictions of quantum mechanics. That happens by means of a kind of averaging over what one does not know, which is exactly the kind of averaging that goes on in classical statistical mechanics.
The theory describes a real, concrete and deterministic physical process--a process that can be followed out in exact mathematical detail--whereby the act of measurement unavoidably gets in the way of what is being measured. In other words, Bohm's theory entails that this ignorance--although it is merely ignorance of perfectly definite facts about the world--cannot be eliminated without a violation of physical law (without, that is, a violation of one or the other of the two laws of motion, from which everything else about Bohm's theory follows).
Bohm's theory can fully account for the outcomes of the experiments with the two-path contraption--the experiments that seemed to imply that electrons can be in states in which there fails to be any fact about where they are. In the case of an initially right-spinning electron fed into the apparatus, Bohm's theory entails that the electron will take either the up or the down route, period. Which of those two routes it takes will be fully determined by the particle's initial conditions, more specifically by its initial wave function and its initial position. Of course, certain details of those conditions will prove impossible, as a matter of law, to ascertain by measurement. But the crucial point here is that whichever route the electron happens to take, its wave function will split up and take both. It will do so in accordance with the linear differential equations of motion.
So, in the event that the electron in question takes, say, the up route, it will nonetheless be reunited at the black box with the part of its wave function that took the down route. How the down-route part of the wave function ends up pushing the electron around once the two are reunited will depend on the physical conditions encountered along the down path. To put it a bit more suggestively, once the two parts of the electron's wave function are reunited, the part that took the route that the electron itself did not take can "inform" the electron of what things were like along the way. For example, if a wall is inserted in the down route, the down component of the wave function will be missing at the exit of the black box. This absence in itself can constitute decisive information. Thus, the motion that such an electron executes, even if it took the up path through the apparatus, can depend quite dramatically on whether or not such a wall was inserted.
Moreover, Bohm's theory entails that the "empty" part of the wave function--the part that travels along the route the electron itself does not take--is completely undetectable. One of the consequences of the second equation in the box below is that only the part of any given particle's wave function that is currently occupied by the particle itself can have any effect on the motions of other particles. So the empty part of the wave function--notwithstanding the fact that it is really, physically, there--is completely incapable of leaving any observable trace of itself on detectors or anything else.
Hence, Bohm's theory accounts for all the unfathomable-looking behaviors of electrons discussed earlier every bit as well as the standard interpretation does. Moreover, and this point is important, it is free of any of the metaphysical perplexities associated with quantum-mechanical superposition.
As to the measurement problem, it can be persuasively argued that Bohm's theory can suffer from nothing of the kind. Bohm's theory holds that the linear differential equations of motion truly and completely describe the evolution of the wave function of the entire universe--measuring devices, observers and all. But it also stipulates that there are invariably definite matters of fact about the positions of particles and, consequently, about the positions of pointers on measuring devices and about the positions of ink molecules in laboratory notebooks and about the positions of ions in the brains of human observers and thus, presumably, about the outcomes of experiments.
Despite all the rather spectacular advantages of Bohm's theory, an almost universal refusal even to consider it, and an almost universal allegiance to the standard formulation of quantum mechanics, has persisted in physics, astonishingly, throughout most of the past 40 years. Many researchers have perennially dismissed Bohm's theory on the grounds that it granted a privileged mathematical role to the positions of particles. The complaint was that this assignment would ruin the symmetry between position and momentum, which had been implicit in the mathematics of quantum theory up until then--as if ruining that symmetry somehow amounted to a more serious affront to scientific reason than the radical undermining, in the Copenhagen formulation, of the very idea of an objective physical reality. Others dismissed Bohm's theory because it made no empirical predictions (no obvious ones, that is) that differed from those of the standard interpretation--as if the fact that those two formulations had much in common on that score somehow transparently favored one of them over the other. Still others cited "proofs" in the literature--the most famous of which was devised by the American mathematician John von Neumann, and all of which were wrong--that no deterministic replacement for quantum mechanics of the kind that Bohm had already accomplished was even possible.
Fortunately, those discussions are mostly in the past now. Although the Copenhagen interpretation probably remains the guiding dogma of the average working physicist, serious students of the foundations of quantum mechanics rarely defend the standard formulation anymore. A number of interesting new proposals now exist for solving the measurement problem. (There are, for example, attempts at resuscitating in a more precise language the idea of a collapse of the wave function, which I mentioned earlier.) It is against those, against other proposals yet to be invented and, of course, against the experimental facts that Bohm's theory will ultimately have to be judged. The jury on all that is still very much out.
Bohm's theory is the only serious proposal around just now that is fully deterministic. It is also the only one that denies there are any such things as superpositions, even for microscopic systems. But it is certainly not free of transgressions against what one might call common physical sense. Perhaps the most flagrant of those transgressions is nonlocality. The theory allows for the possibility that something that occurs in region A can have a physical effect in region B, instantaneously, no matter how far apart regions A and B may happen to be. The influence is also completely independent of the conditions existing in the space between A and B [see "Faster than Light?" by Raymond Y. Chiao, Paul G. Kwiat and Aephraim M. Steinberg; SCIENTIFIC AMERICAN, August 1993].
But nonlocality may be something we need to learn to live with, something that may simply turn out to be a fact of nature. The standard formulation of quantum mechanics is also nonlocal and so are most of the recently proposed solutions to the measurement problem. Indeed, according to a famous argument of Bell's, any theory that can reproduce those statistical predictions of quantum mechanics already known to be correct and that satisfies a few extremely reasonable assumptions about the physical nature of the world must necessarily be nonlocal. The only schemes that have been imagined for denying those assumptions and so avoid nonlocality are the "many worlds" and "many minds" interpretations of quantum mechanics. They suggest that in some sense all possible experimental outcomes, and not simply one or another of those outcomes, actually occur. And they are (maybe) too bizarre to be taken seriously.
Workers have raised various other concerns as well. What is the exact philosophical status of the probabilities in Bohm's theory? Does guaranteeing that every particle in the world invariably has a determinate position really amount to ensuring that every imaginable measurement has a determinate outcome and that everything that we intuitively take to be determinate is really determinate? Those questions continue to be the subject of active debate and investigation.
Finally, and most important, I must stress that all of what has been said in this article applies, at least for the moment, only to nonrelativistic physical systems. That is, it pertains just to systems whose energies are not very high, that are not moving close to the speed of light and that are not exposed to intense gravitational fields. The development of a Bohmian replacement for relativistic quantum field theory is still under way, and the ultimate success of that enterprise is by no means guaranteed. If such a replacement were somehow found to be impossible, then Bohm's theory would have to be abandoned, and that would be that.
But as it happens, most other proposals for solving the measurement problem are in a similar predicament. The exceptions, once again, are the many-worlds and many-minds interpretations, whose relativistic generalizations are quite straightforward but whose metaphysical claims are difficult to believe. Much of the future course of the foundations of quantum mechanics will hinge on how attempts at relativization come out.
In the meantime, the news is that a great deal more than has previously been acknowledged about the foundations of our picture of the physical world turns out to be radically unsettled. In particular, the possibilities that the laws of physics are fully deterministic and that what they describe are the motions of particles (or some analogue of those motions in relativistic quantum field theory) are both, finally and definitively, back on the table.
Creator of a Brave, New Quantum World
David Joseph Bohm was born in 1917 in Wilkes-Barre, Pa. After studying physics at Pennsylvania State College, he pursued graduate studies at the University of California at Berkeley. There, during World War II, he investigated the scattering of nuclear particles under the supervision of J. Robert Oppenheimer. After receiving his degree from Berkeley, Bohm became an assistant professor at Princeton University in 1946.
It was during those years that Bohm wrote his now classic defense of the Copenhagen interpretation, "Quantum Theory." At the same time, however, Bohm's doubts about the adequacy of that interpretation were becoming more acute. His own alternative emerged in published form shortly thereafter, in 1952.
By then, Princeton had forced him from its faculty. During the McCarthy era, Bohm had been called before the House Un-American Activities Committee in connection with completely unsubstantiated allegations that he and some former colleagues at the radiation laboratory at Berkeley were communist sympathizers. (During World War II, Oppenheimer began turning in to the Federal Bureau of Investigation names of friends and acquaintances who he thought might be communist agents. Bohm apparently was one of the accused.) A passionate believer in liberty, Bohm refused to testify as a matter of principle. As a result, the committee found him to be in contempt of Congress.
The incident proved disastrous to Bohm's professional career in the U.S. Princeton refused to renew his contract and told him not to set foot on the campus. Unable to find employment at any other university, Bohm left the country in 1951 to take a position at the University of Sao Paulo in Brazil. There he was asked by U.S. officials to give up his passport, effectively stripping him of his American citizenship.
After teaching in Brazil, Bohm went to the Technion in Israel and to Bristol University in England. Although he was later cleared of the contempt charges and was eventually allowed to travel back to the U.S., Bohm settled permanently at Birkbeck College, London, in 1961.
In addition to his interpretation of quantum mechanics, he contributed to mainstream physics, working on plasmas, metals and liquid helium. In 1959 he and his student Yakir Aharonov discovered what is now known as the Aharonov-Bohm effect. They showed that quantum mechanics predicts that the motions of charged particles can be influenced by the presence of magnetic fields even if those particles never enter the regions to which those fields are confined. Subsequent experiments have amply confirmed the effect [see "Quantum Interference and the Aharonov-Bohm Effect," by Yoseph Imry and Richard A. Webb; SCIENTIFIC AMERICAN, April 1989].
Later in life Bohm became interested in broader philosophical questions. He developed a picture of the universe as an interconnectedness of all things, a notion he called "implicate order." He wrote several books on physics, philosophy and the nature of consciousness. He was in the middle of a collaborative effort on another quantum mechanics book when he died of a heart attack in October 1992. Friends and colleagues remember Bohm not only as brilliant and daring but also as extraordinarily honest, gentle and generous.
DAVID Z ALBERT has done scientific and philosophical work on various aspects of the foundations of quantum mechanics, with special emphasis on the quantum measurement problem. Recently he has also been thinking about the relation between that problem and the direction of time. In 1981 he received his Ph.D. in theoretical physics from the Rockefeller University. Before taking his current position as professor of philosophy at Columbia University, he served on the faculty of the physics department at the University of South Carolina at Columbia and was a postdoctoral fellow at Tel Aviv University. His book "Quantum Mechanics and Experience" was published last year by Harvard University Press.
FURTHER READING
A SUGGESTED INTERPRETATION OF THE QUANTUM THEORY IN TERMS OF "HIDDEN" VARIABLES, I and II. David Bohm in "Quantum Theory and Measurement." Edited by J. A. Wheeler and W. H. Zurek. Princeton University Press, 1983.
ON THE IMPOSSIBLE PILOT WAVE. In "Speakable and Unspeakable in Quantum Mechanics," by John S. Bell. Cambridge University Press, 1987.
BOHM'S THEORY. In "Quantum Mechanics and Experience," by David Z Albert. Harvard University Press, 1992.
QUANTUM EQUILIBRIUM AND THE ORIGIN OF ABSOLUTE UNCERTAINTY. Detlef Durr, Sheldon Goldstein and Nino Zanghi in "Journal of Statistical Physics," Vol. 67, Nos. 5/6, pages 843-908; June 1992.
SCIENTIFIC AMERICAN May 1994 Volume 270 Number 5 Pages 58-67
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