The Guided Wave Theory of Louis de Broglie and David Bohm - Brief Article

Martin Gardner

There is little doubt that the mathematical formalism of quantum mechanics (QM) is accurate. No theory of physics has been more spectacularly successful in making predictions about the outcome of measurements. Some are accurate to many decimal places. Where experts disagree is not about the mathematics of QM but about how to interpret its equations. Even more than relativity theory, QM bristles with wild paradoxes that radically violate common sense and for which at present there are no agreed-upon resolutions.

The most notorious of these paradoxes is the EPR, named after the initials of Einstein and two associates, Boris Podolsky and Nathan Rosen. In 1935 they published an explosive paper in which they argued that their paradox proved that QM is incomplete, destined to be replaced or radically modified by a deeper theory.

The EPR paradox has several forms, but the easiest to understand was proposed by the late American physicist David Jacob Bohm (1917-1991). It involves a mysterious property of particles called spin. Spin is roughly similar to the motion of a top because it has angular momentum that always takes one of two forms variously called left or right, plus or minus, up or down. Imagine a quantum reaction that creates two identical particles A and B which go off in opposite directions. In standard QM each particle has its left and right spins "superposed." When particle A is measured for spin, its "wave function" (a formula specifying the probabilities that certain values will be found when a particle is measured for a given property) is said to "collapse" (vanish). The particle at once acquires either a left or right spin with equal probability.

Now for the magic. To conserve angular momentum, after A is measured and so acquires a definite spin, B must acquire the opposite spin. Assume that A, measured in Chicago, has a left spin. (Remember, it does not have a definite spin until measured.) On a planet in a distant galaxy a physicist measures B when it gets there. It is certain to have a right spin. How does B "know" the outcome of the measurement of A? Does A send some kind of telepathic signal to B, either simultaneously or at a speed equal to or exceeding the speed of light? Einstein ridiculed this as "spooky action at a distance." He believed that his proposed experiment, then only a thought experiment, proved that QM was not complete. There must be local "hidden variables" giving definite spins to both particles before one is measured.

The standard Copenhagen interpretation of QM, based on the opinions of Niels Bohr, is that regardless of how far apart A and B get, they remain a single quantum system with a single wave function. When A is measured, the entire system's wave function vanishes and the two particles simultaneously acquire opposite spins. The particles are said to be "correlated," or in more recent terminology, "entangled."

Does this resolve the paradox? It does not. The mystery remains of how A and B can stay entangled when they are light-years apart unless there is some kind of connection between them that allows information to go from A to B.

All physicists agree that there is no possibility of sending coded messages by using the EPR phenomenon. The situation is like two persons, one in New York, the other in Paris, who simultaneously flip a penny. For reasons unknown, if one penny falls heads, the other must fall tails, and vice versa. If one could control the outcome of a flip in Chicago, then of course the Chicagoan could send a message in a binary code of ones and zeros. But there is no way to control the outcome of a measured spin. Like the heads and tails of a flipped coin, it becomes left or right with equal probability. The sequence of lefts and rights, at each end, is always a random, meaningless sequence. If it were otherwise, cipher messages presumably could be sent with a speed exceeding that of light, thereby violating a basic law of relativity.

The EPR paradox remained unconfirmed until recent years when the late Irish physicist John Stewart Bell thought of a brilliant way to test the paradox over short laboratory distances. The paradox has since been completely validated many times. The two entangled particles behave precisely as QM predicts.

Several conflicting efforts have been made to explain the EPR paradox. Here I confine my remarks to how it is resolved by what is called the pilot wave or guided wave theory (GWT). Obviously I'm no expert on QM, only a science journalist, so I haven't the foggiest notion of whether GWT will someday be confirmed. However, this theory, long ignored by physicists, is now gaining increasing support. [1] It deserves to be better known.

It was the French Prince Louis de Broglie (pronounced de Broy), one of the architects of QM, who first proposed GWT. He abandoned it after heavy ridicule by Copenhagenists, but took it up again after it was improved by Bohm. Now known as the Broglie! Bohm GWT, it has become the interpretation of QM favored by a raft of experts that include Bell, Jeffrey Bub, the French physicist Jean-Pierre Vigier, and many others. So far its predictions are exactly the same as those of the Copenhagen school, although there may be subtle ways it can be tested by difficult experiments not yet performed.

In standard QM every particle can be observed either as a particle or as a wave. The wave is nor physical, like water or sound waves, but a wave of probability in an abstract space. When a photon goes through one slit in a barrier, to register on a detection screen, it is a particle. When two slits are open, the photon behaves like a wave and it is impossible to tell which slit it goes through without destroying the wave. If many photons are sent through a barrier with two openings, each registers on the screen as a particle, but they display an interference pattern that could only be produced by a wave going through both slits. The photon is a mysterious thing. It is neither wave nor particle, but something that can act like one or the other depending on the measuring apparatus.

In Bohm's revolutionary theory, as refined by his associate Basil Hiley, particles are as real as golf balls. At all times they have precise, unfuzzy properties such as position and momentum, and precise paths through spacetime. The particles are never waves. Associated with each particle is an invisible, undetectable wave in a field which Bohm called the "quantum potential." Its pilot waves are real waves, not probability waves. They guide the particle's motion in a manner somewhat like the way a rivers wave guides the movement of a floating leaf, or, in a better analogy, the way radar information guides a ship. This quantum field, like the fields of gravity and electromagnetism, permeates all of spacetime, but unlike those fields its intensity doesn't diminish with distance. Also unlike other fields, it exerts no force on particles. Essentially it is a wave of undecaying information.

It is the ad hoc nature of this undetectable pilot wave that reminds so many of Bohm's antagonists of the old stagnant ether of the nineteenth-century, a substance that could not be detected as a carrier of electromagnetic waves, and which Einstein discarded as useless. As J.C. Polkinghorne, in his marvelous little book The Quantum World (1984) said: "In the opinion of many Bohm had jumped out of the indeterminate frying pan into a crackling non-local fire."

When just one slit is open, the pilot wave guides each photon through the opening and there are no interference bands. When both slits are open, each particle goes through just one slit, but its pilot wave, quite separate from the particle, goes through both to guide a stream of photons along paths that produce the wave interference pattern on the screen. It is not a case of an entity being either a wave or a particle, but a case of there always being present both a wave and a particle. Comic versifier Armand T. Ringer put it this way:

As a photon flew close to slit 2, She said to her pilot wave, "you Must slide through both slits, Or Bohm's fans will have fits, And he forced to abandon their view."

Here is how GWT explains the EPR paradox. When A is measured, its guiding wave, in the unobservable quantum potential field, twists A into either a left or right spin. At the same instant, no matter how far away B is, it twists B the opposite way. This invisible field, extending throughout the cosmos, has the nonlocal power to act simultaneously on both particles. No information travels from A to B. Instead, it travels simultaneously from the quantum field to the two particles, giving them opposite spins. This, of course, is action at a distance, and was probably the main reason Einstein did not care much for Bohm's theory.

How does the pilot wave manage to guide the paths of particles? This is one of the darkest mysteries of GWT. It is able to push particles around without at the same time exerting any force on them. If it did, photons would have their energies altered. But this doesn't happen. The photons arrive on the screen without any change of energy. Somehow each photon must pick up information from its pilot wave without having its energy modified. This may be spooky, but no more spookier, say Bohm's supporters, than the probability waves in orthodox QM which decide on how a wave function will create certain properties when it collapses.

Could the two particles of the EPR paradox be just projections in our space of a single particle moving in a higher dimension? Bohm once speculated on this possibility. Imagine a tank, he wrote, in which a fish is swimming. Two television cameras film the tank from two different directions. We see only the two films projected on two screens. We think we are watching two fish, and are amazed by the curious way their movements are correlated. The tank is in the unseen higher dimension. In Bohm's later terminology, it is in the "implicate order" which lies beyond the "explicate order" of the world open to our experience. What we think are two fish are really projections in our world of a single entity.

Bohm suffered all his life by the contempt with which followers of Bohr viewed his GWT. Bohr called it "foolish." J. Robert Oppenheimer called it "juvenile deviarionism," and advised physicists to ignore the theory. Even Einstein, who for a time admired de Broglie's work, decided that Bohm's GWT was "too cheap" a way to resolve QM paradoxes.

Bohr's antagonism toward Bohm was extreme. The German-born physicist Ernest J. Sternglass, who favors Bohm's pilot wave, tells in his book Before the Big Bang (1997) about a meeting with Bohr during which they discussed Bohm's theory. "It was embarrassing," Sternglass writes, "for me to see Bohr so emotionally upset about Bohm's work. [ldots] The vehemence of this otherwise mild-mannered and kindly man really surprised me [ldots] it seemed to me that Bohr had almost the fanatical approach of a fundamentalist preacher, intensely concerned to save my soul from perdition."

Mathematician David Wick, in his great book The Infamous Boundary (1995)--the title refers to the gulf between the micro world of QM and the macro world of relativity theory, cosmology, measuring apparatus, and you and me--bashes Richard Feynman for a similar opposition to Bohm. Feynman is often quoted, from his famous "red books" of lectures, to the effect that nobody understands how the double slit experiment works. "The question is," Feynman asks, "how does it really work? What machinery is actually producing this thing? Nobody knows any machinery. Nobody can give you a deeper explanation of this phenomena than I have given; that is, a description of it."

"Very well," comments Wick, "what is wrong with the pilot wave?" Wick attributes Feynman's "overheated rhetoric" to his refusal, like that of von Neumann, Heisenberg, and other quantum experts, to take Bohm seriously.

The great Hungarian mathematician John von Neumann wrote a famous book about QM in which he thought he proved that QM could never be modified by introducing hidden variables. By this he meant local hidden variables--variables attached to particles. He failed to realize that QM could be modified by introducing non-local variables such as Bohm's quantum potential. It is a scandal that so few of today's physicists and their students realize that Bohm succeeded in doing exactly what von Neumann thought was impossible. We can describe his achievement by altering some words in a well-known poem by Eddie Guest:

Von Neumann said that it couldn't be done, But Bohm with a chuckle replied, That maybe it couldn't, but he would be one Who wouldn't say so til he tried. "A quantum potential? The field is essential!" If David Bohm doubted he hid it. He started to sing as he tackled the thing That couldn't be done, and he did it!

Bohm's quantum potential binds the entire universe together into what he liked to call a seamless "unbroken wholeness." Every particle in the universe is connected by the quantum potential to every other particle. He likened the cosmos to a hologram in which each point on the film carries information about the entire picture. Bohm's GWT, far more sophisticated than de Broglie's crude version, is a "holistic" vision in which all parts of the universe are joined to every other part. "Interconnectedness" was one of Bohm's favorite words. He saw the universe as resembling the unity of a living organism, a kind of pantheism not unlike Spinoza's--a pantheism Einstein himself favored.

Although Bohm's GWT is identical with standard QM in its predictions, its way of talking about quantum phenomena is entirely different. The randomness of the Copenhagen interpretation which so disturbed Einstein ("God does not play dice") is replaced by a strict determinism. There are no quantum jumps. No superpositions. No collapsing of wave functions. Indeed, there is not even a "measurement problem." The probabilities of QM, which seem to spring from pure chance in Bohm's theory, result from our ignorance of a true, highly complicated, stare of affairs. The universe is real, "our there," independent of you and me. Human consciousness is not essential, as von Neumann and Eugene Wigner, and others supposed, to collapse wave functions.

Like Einstein, Bertrand Russell, Karl Popper, and almost all philosophers and scientists, Bohm was a thoroughgoing realist in believing that the universe and all its laws are independent of human minds. The Moon is "our there," regardless of whether it is observed by any creature. Bohm would have been horrified by the social constructivism of today's postmodernists who see all science and even mathematics as cultural creations similar to art, music, and fashions in clothes.

John Bell, who died in 1990 at age 62, became an enthusiastic defender of Bohm. Bell was convinced that Einstein was intellectually superior to Bohr, a deeper thinker who saw clearly the need for QM to rest on a subquantum level (Bohm's potential field) that would restore both realism and determinism. Here is how Bell puts it in his paper Six Possible Worlds of Quantum Mechanics," reprinted in his entertaining book Speakable and Unspeakable in Quantum Mechanics (1987)

Is it not clear from the smallness of the scintillation on the screen that we have to do with a particle? And is it not clear, from the diffraction and interference patterns, that the motion of the particle is directed by a wave? De Broglie showed in detail how the motion of a particle, passing through just one of two holes in screen, could be influenced by waves propagating through both holes. And so influenced that the particle does not go where the waves cancel our, but is attracted to where they cooperate. This idea seems to me so natural and simple, to resolve the wave-particle dilemma in such a clear and ordinary way, that it is a great mystery to me that it was so generally ignored.

My next column will be a sketch of Bohm's life, with special focus on his friendship with the Indian philosopher and mystic Jiddo Krishnamurti.

Martin Gardner's two-volume Annotated Alice has recently been reprinted in a onevolume edition.

Note

(1.) See, for example, David Z. Albert's vigorous defense of Bohm's theory in "Bohm's Alternative to Quantum Mechanics," in Scientific American (May 1994). Albert is a professor of philosophy at Columbia University, with a Ph.D. in physics. More on Bohm's theory can be found in his book Quantum Mechanics and Experience (Harvard University Press, 1992.)

References

Bohm, David. 1954. Quantum Theory.

______ 1980. Wholeness and the Implicate Order. Peat, David F. 1997. Infinite Potential: The Life and Times of David Bohm.

Peat, David F., and B.J. Hiley eds. 1987. Quantum Implications: Essays in Honour of David Bohm.

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