Chapter Two

BOHM'S HIDDEN VARIABLES/QUANTUM POTENTIAL THEORIES, CONTINUED

The previous chapter introduced the hidden variables theories of Bohm. It also outlined their development and included responses to the von Neumann type of criticism. The current quantum potential approach of Bohm made its appearance. In this chapter I will continue that story. I will outline some of the debates between the Birkbeck interpretation and that of the usual or Copenhagen approach. Some of the philosophical ideas in Bohm's theories will surface. Finally, I will chart the success and failure of his theories in the physics community itself.

THE COPENHAGEN INTERPRETATION AND HIDDEN VARIABLES

The Birkbeck School and those holding the usual interpretation of quantum physics disagree. The measurement problem mentioned in the previous chapter provides a starting point for describing some of the chief points of difference.

The Measurement Problem

In quantum physics a mathematical object called a wave function represents a system at the quantum level. This function exists in a space whose dimensions are a multiple of three. Following a measurement of the system, the wave can only exist in three dimensions. A multiple of three has to become exactly three. This is what the collapse of the wave function means.<81> In the usual interpretation, the collapse is a given of nature. We cannot break it down, explain it, predict it, or investigate it further.<82> This process of measuring presents a problem.

A famous and vivid way of presenting the measurement problem is Schrödinger's cat puzzle. A hypothetical cat is in a sealed box. In it is also a device that would kill the cat. Whether or not the device is working depends on an event happening at the quantum level. An example of such an event is the radioactive decay of an isotope. The important question arises on opening the box. Is the cat dead or alive?

The puzzle for the usual interpretation of quantum theory comes when opening the box. Seeing what is inside the box causes the wave function of the cat-killing device to collapse. There are two ways it can collapse, producing two different events. One is that the isotope decays and the cat is dead. The other is that the isotope does not decay and the cat is alive. The collapse, according to the usual interpretation, depends on the observation. The act of seeing determines the outcome of the cat-killing device. Thus, whether the cat is dead or alive depends on someone seeing it.

Common sense disagrees. Whether the cat is dead or alive on opening the box is independent of seeing it at that point. This is the puzzle.

Something else in the usual interpretation of quantum theory compounds the weirdness. No one can know what happens to the cat while it is in the closed box. We cannot describe what happens to something between observations. Moreover, this is true in principle; this is how the world operates. It is not due to our inadequate observations.<83>

There are several solutions offered for this problem.

Some of these resort to making human consciousness the basic thing. The theory of Eugene Wigner and John Wheeler is an example. It says the observer's consciousness decides whether the cat is dead or alive. It is the human mind that determines what goes on in the world. The observed exists because someone observes it. The mind of the observer interacts with the quantum world to determine what actually exists.<84>

Hugh Everett avoids the collapse question and the dependence on consciousness by suggesting there are many universes. For each possible outcome of an observation there is a universe in which that chance becomes actual. Thus there will be some universes that contain a physicist seeing a live cat, and some a physicist seeing a dead cat. This interpretation is attractive because it takes the mathematics of quantum physics at face value (each mathematical solution is real). On the other hand, many find it uneconomic because it assumes an infinite number of universes and observers.<85>

The hidden variables/quantum potential approach of the Birkbeck School provides another possible way of solving the problem. In fact, for the Birkbeck School there is no measurement problem. The quantum potential determines the state of a system whether or not someone observes it. Thus, the device that could kill the cat would operate only if the quantum potential had a particular value. Otherwise it would not operate. There is only one possible outcome, which the value of the quantum potential determines. This opposes it to the many-universes interpretation. As opposed to the usual Copenhagen interpretation, its operation does not depend on a later observation.<86>

The Uncertainty Principle

The Birkbeck School says there really is no measurement problem. It thereby challenges the usual interpretation of quantum physics with its probability thesis. Certain beliefs of the usual approach come in for special questioning. One is the idea that quantum physics applies everywhere - it holds at all levels of the world and in all its parts. According to the Birkbeck School, the usual approach says it can provide a complete description of all it is possible to describe. They particularly disagree that the central feature of the usual theory, Heisenberg's uncertainty principle, applies everywhere. They do not believe the uncertainty holds in principle in all measurements. Quantum physics does not need this.<87>

The uncertainty principle says a measurement of a particle's momentum and position cannot provide precise and simultaneous values for them. Bohm derives this from his earlier hidden variables theory without assuming the uncertainty is basic in nature. Measuring either the momentum or the position of the particle disturbs the system. This prevents an exact measurement of the other. In particular, the motions of the hidden variables of the particle measured and of the measuring device also need considering.<88> These sub-quantum level movements do not affect the quantum level to any important extent. They do give to the position and momentum some random motion at the quantum level. These random motions satisfy the uncertainty principle.

The uncertainty principle similarly comes from the quantum potential theory. The quantum potential acting on a particle under observation depends on two things. One is the position of the particle itself. The other is the positions of all the particles within the measuring device. Since the quantum potential changes rapidly as the whole system evolves, measuring will disturb the observed particle. It will disturb it in an unpredictable and uncontrollable way. This is the uncertainty.

The way Bohm works out the uncertainty principle is much the same as originally proposed by Heisenberg. He looked at the act of observation, specifically on the passing of energy from the observing apparatus to the particle under observation. Suppose this energy is in the smallest unit possible. The quantum theory calls this a quantum and takes it to be uncontrollable and indivisible. This transfered unit of energy disturbs the particle. And it rules out completely accurate measurements because one cannot split the quantum to measure more accurately. This disturbance Heisenberg called the uncertainty principle.<89>

Bohm is saying we can in theory simultaneously know position and momentum at the quantum level; in principle they are precise. In practice we cannot do this because of physical disturbances. Thus, he accepts quantum uncertainty as a real and physical. This acceptance, however, does not assume the uncertainty applies in principle everywhere.<90>

Necessity and Contingency

The uncertainty principle helps distinguish the Birkbeck and the usual approaches. The ideas of necessity and contingency further help.

Bohm believes that, in any field of inquiry, some things are necessary and some are contingent. Some have to be as they are and others can be different from what they are. Necessity and contingency tie together. The contingencies of one field are necessities in another. In turn, the other has its own contingencies. Any description is incomplete; what happens where it applies depends on what happens beyond where it applies.

Usual quantum physics believes it applies everywhere and needs no other theory. It says there is total contingency because only mathematical probabilities can represent measurements or observations. Probabilities are not necessities. Nothing is determined. Observations cannot be necessities even in a broader context because the theory applies everywhere. This violates, according to Bohm, the ideas of necessity and contingency.<91>

The measurement problem, the uncertainty principle, and the ideas of necessity and contingency help clarify the differences between Bohm's and the usual approach. Bohm requires more determinism in his theories. The gulf is wide, reflecting considerable disagreement in philosophical beliefs.

PHILOSOPHICAL STRANDS TO BOHM'S THEORIES

Philosophical attitudes are most important when considering different approaches to physics. This is especially so when trying to understand the conflicts between Bohm's physics and the usual approach. Some of their different attitudes have already arisen, their ideas about determinism being an obvious example. There are many others. Some appear in the philosophical basis of the physics, while other as results of the physics developed.

In 1962, Stephen Toulmin isolated four philosophical strands to Bohm's argument. The first is the general claim that it is both important and correct to think about the sub-quantum world. Several physicists such as von Neumann would dispute this. Second, there is more meaning in statements about the quantum world than the indeterminism of the usual approach allows. Both this and the previous chapter have brought out this restriction which Bohm opposes.

The third of Toulmin's strands concerns the type of models Bohm uses in his explanations. It is a type rejected by the author of the uncertainty principle, Heisenberg. The particles of the quantum world Bohm compares to clouds or tidal waves. They represent, for him, "transient configurations with blurred edges, continually forming, dissolving and travelling across an underlying sub-[level]...of energy." Bohm then uses statistics to average out the behavior of large numbers of sub-quantum hidden variables. This produces the results of quantum theory.

Finally, Toulmin tells us, Bohm believes there is going to be a revolution in the geometry used by physics. Physicists are going to abandon Cartesian co-ordinate geometry. Instead, they will use the ideas of space drawn from the mathematics of topology.<92>

I shall in this section discuss certain aspects of the last two points made by Toulmin.

Causality

I have mentioned causality several times, particularly when discussing Bohm's theories as causal or based on determinism. This is to engage Toulmin's third point.

Causality insists there are causes to certain events. For Bohm, a cause is a condition or event that, when copied, will always produce the same effects. The cause is also necessary to produce those effects. That is not all. A cause needs experimental support to be sure it is in fact a cause. There are many contenders since, in Bohm's picture, all objects in the universe connect with each other. This means any event or condition could cause another. Bohm narrows the field by saying certain causes are "controlling." By this he means that copying them will "for all practical purposes" reproduce the effects. In this case he advises neglecting other causes.<93>

In its use of probabilities, quantum physics has discarded causality. Bohm suggested in 1953 that this need not continue. He gave several reasons. First, there is no positive proof that experimental fact contradicts causality. Second, quantum physics could have developed with a causal base equally well as with the usual one. An example Bohm gives is de Broglie's, as mentioned in the previous chapter. Another causal version of quantum physics is his hidden variables theory. Further, future progress in quantum theory does not require giving up more causality. Physicists need not throw causality out altogether.

Bohm believes giving up causality has brought no real advantages. The reverse is true. Now, he writes, we can only study statistical averages of certain properties at the quantum level. We will never study scientifically the real physical objects if we follow the usual interpretation. This is because it assumes there are no causal factors. It does not prove there are no causes. It just assumes objects only exist at the time of observation, that physical objects do not exist independent of ourselves.

Not only does Bohm find the giving up of causality wrong from a philosophical point of view. It also damages the progress of science. He thinks the most fruitful attitude is to assume something we cannot explain does in fact have a cause. That cause we must discover. If we assume this and there really is no cause, we will not go wrong. All that would happen is we would not succeed in finding the cause. On the other hand, Bohm thinks it much more likely there is a cause. If there is and we assume the opposite, we will overlook important and necessary new factors.

Critics chastise Bohm for wanting to bring back causality, a simple causality as found in classical physics. (Included are several who would also like to have a form of causality!) Bohm responds by rejecting the causality of classical physics when it has no bounds. The difficulties with classical physics, he thinks, have come from wrongly assuming it has unlimited validity. They have not come from the physics as such. Classical physics is approximate with limited validity.

A practical question for any field is how far a simple Newtonian type of theory works within it. Another is to search for the type of law that works there better than every other type. When he looks at the quantum world, Bohm suggests a Newtonian type of quantum theory may be partially adequate. He can accept some causality of the classical type for this level. In part this is because such a theory (namely, his hidden variables theory) is possible. He also thinks classical causality is only partially adequate. His theories are not all that are necessary. That no theory be final and universal applies also to any simple causal laws for the sub-quantum world.<94>

Wholeness

Another of Bohm's ideas that is an important part of his philosophy is wholeness. To expand on this is to address Toulmin's fourth point. This is because the Cartesian geometry of physics assumes we can divide everything into smaller and smaller parts. On the other hand, Bohm's new geometry for physics assumes we cannot keep on dividing things. At root everything connects to everything else. One of the world's basic properties is its wholeness.

In the section above Bohm speaks from his concern for wholeness. An example is his point that both the usual and the Birkbeck approaches are necessary for a full understanding of the quantum world. In part he is acknowledging the incompleteness of his theories. In part he is also criticizing the assumption that quantum physics provides the complete understanding of the world. He questions whether any theory is complete. He suggests, rather, that all theories are incomplete. They are useful only in certain places. This applies also to the whole of physics. More approaches than that of physics are necessary to understand everything. Physics is the same as any other form of human knowledge in being open ended and incomplete. It is not able even in principle to describe everything.<95>

Bohm's thinking that physics is incomplete comes in part from Bohr. Bohr emphasized the wholeness of the results of observations and of the process of experimenting. There can, at the quantum level, be no distinction drawn between something under observation and the apparatus used in or the conditions of the observation. The wave function or quantum state describing the object under observation does not exist separately from that describing the observation.<96>

Bohr presented this wholeness property of quantum theory in its early years. Bohm wants to reassert it with his approach. He applies it differently in several places than does the usual approach. The whole system imposes on its particles an interaction between them. It is, therefore, no longer correct to divide a system as does classical physics. We should stop breaking a system into separate parts whose relations do not depend on the whole. This agrees with Bohr's ideas, but with a difference. For Bohr it is meaningless to try specifying the wholeness. The Birkbeck School's interpretation, however, thinks of independent particles moving under the unifying action of the quantum potential. This is a physical means by which the wholeness may come about.<97>

The wholeness idea Bohm uses will emerge further as his physics develops. It is a key to much of his thinking.

DOUBTS ABOUT BOHM'S HIDDEN VARIABLES/QUANTUM POTENTIAL THEORIES

Bohm challenges the accepted beliefs of most physicists. It is not surprising, therefore, that they were and remain doubtful of Bohm's hidden variables and quantum potential proposals. They especially focus on the lack of clear experimental support for his theories. Besides the effect in the Bohm-Bub theory investigated by Papaliolios, Bohm's and conventional quantum physics make the same predictions. Since Bohm no longer promotes this theory, we can say the Birkbeck theories and the usual quantum physics predict the same.<98>

Reactions to Bohm's theories have been sharp and most are born of unshakable holding to the usual interpretation. In the 1950s, Leon Rosenfeld accused Bohm of going against the demands of "sound scientific method." He contrasted Bohm with those who follow the Copenhagen interpretation. Unlike Bohm, they have the "uncommitted, commonsense attitude of the true scientist."<99> Physicists referred to hidden variables as superstition, even in 1978.<100> Popper in a 1982 book refers to "David Bohm's heresy." He cannot side with Bohm's program, and he quotes Max Born: "To dream of a way back, back to the classical style of Newton-Maxwell...seems to me hopeless, off the way, bad taste." He continues: "it is nothing but dreams which these gentlemen [Schrödinger, Bohm, Einstein, et al.] indulge in....And we could add, `it is not even a lovely dream.'"<101> In 1987, David Finkelstein still considered Bohm's cause hopeless. His reasons were conceptual.<102>

In comparison with many responses, the following summary by Hanson is mild.<103>

There is only one kind of theory in the field now. It is the work of many....It is a theory...algebraically [expressed], experimentally detailed and...powerful in explanation. What precisely is the present alternative [namely, the hidden variables theory of Bohm] to this physical theory? It is a [collection] of excitingly vague, bold-but-largely-formless, promising-but-as-yet-[undeveloped], speculations.

He continues by stating that speculation is not working physics. There are no good reasons for thinking hidden variables physics will account for all that orthodox quantum theory can describe.<104>

Hanson wrote in 1962. The same type of attitude existed 26 years later. John Polkinghorne says there are two reasons most physicists reject Bohm's "ingenious ideas" and opt for convention. Special relativity so far eludes Bohm, he says, but naturally fits with the usual approach. Thus Bohm's theory fails to be fruitful. Second, he thinks most physicists feel Bohm's theory is contrived. "Not only is it hard to believe that even so clever a man as he would have thought of his equations without having those of quantum theory first before him, but also, and above all, the way the statistical character is inserted into the theory has an arbitrary air about it." On the other hand, one could say the Copenhagen approach to quantum theory is anti-intuitive. Thus, Polkinghorne has philosophical reasons for preferring the conventional approach.<105>

Bernard d'Espagnat recently said hidden variables theories are fruitless.<106> Jauch also recently commented that nothing useful has come from them.<107> Lee Smolin finds them "not very satisfying." None so far are physically convincing.<108> Other physicists like C.F. von Weizsäcker prefer to reserve their judgment. They hesitatingly include Bohm's interpretation though it may not follow from quantum theory.<109> The success of quantum theory makes the introduction of a radically new theory unlikely.

Experimental support is the key. William Honig recently writes of his confusion over programs like Bohm's. He quotes a comment Einstein made to Born just after Bohm's first hidden variables paper appeared. He said, as Honig paraphrases it, "Bohm's ideas are somehow too cheap." Einstein was wrong, Honig continues, in that Bohm was bravely facing complete support for quantum theory. "I remember that the subject of anti-QM was then anathema because of the prevailing climate of opinion and it was impossible to even complete a sentence on this subject without it being banished from the conversation."

Honig also agrees with Einstein. He has come across hundreds of attempts to change or replace accepted theories. Most of them would provide the same experimental results predicted by the reigning theory. He feels strongly that a new theory must predict results the current theory does not suggest. Experiments must also confirm them. Otherwise, the ideas do not deserve attention by physicists. Einstein probably meant this by his comments to Born, Honig concludes. He had accepted what Bohm was saying but wanted the ideas taken further.<110>

Support for hidden variables/quantum potential theories is largely philosophical.<111> Bohm makes his case for the theories chiefly by pointing out philosophical problems with the usual interpretation and the advantages of his own. He especially criticizes the uncertainty principle when taken as absolute for all physical theories.<112> Today philosophical support may have more weight than it used to. d'Espagnat concludes his review of Bohm's Wholeness and the Implicate Order by commenting on "philosophy in physics." We need philosophy within physics to seek the meaning of what is ordinarily done in it. Bohm's works in this "are rare and excellent examples."<113>

The Birkbeck physicists are trying to close over inadequacies in their theory. This also helps answer the critics. An example is for those situations where relativity theory applies. Until the early 1980s, no one had adapted Bohm's theory to them. This changed. A 1984 paper by Bohm and Hiley extends the quantum potential approach to a form of relativity theory. The authors show it leads to results that fit with all those known from relativity.<114> A few months after this paper appeared, Longtin and Mattuck published further support for the theory. They claim to have a simple first step toward a general version of the Bohm-Bub hidden variables theory that also satisfies relativity theory.<115> In a 1987 publication the Birkbeck scholars extended their approach to quantum field theories and to another situation in which relativity theory applies.<116> Thus, the hidden variables/quantum potential approach is conquering old uncertainties about it.

The Birkbeck theory also explains in a causal way strange ideas that arise from quantum theory. An example is the delayed-choice experiment of Wheeler. Here the choice of which property to measure can affect events for a considerable time before choosing. The Birkbeck explanation parallels its answer to the measurement problem, as related above. It is a way of avoiding an approach such as Wheeler's and Wigner's.<117>

Such defenses of the Birkbeck approach have their merits. The important question is still whether there is experimental proof for it.

Bohm and Bub's hidden variables theory raised Tutsch's hopes for such proof. He thought "the hidden variables need not remain hidden." There may be laboratory tests for the validity of the Bohm-Bub theory.<118> Support for it may come by making measurements over shorter time spans than those used so far. There is interest in pursuing this, but no action. Until the theory receives experimental support, it is out of the running.

The search for experimental support continues. In a 1989 paper, Bohm and Hiley propose distinguishing in laboratory tests the stochastic interpretation of quantum theory from the usual interpretation. The stochastic version is a close relative of their quantum potential theory. Their proposal involves explaining a correlation between certain simultaneous events that have no normal connections. The stochastic approach suggests a casual connection between them which is not instantaneous, but nearly so. So it does not travel at an infinite speed, but at a finite speed very much greater than that of light. Normal quantum physics says the events happen at exactly the same moment. If technology were available to test this difference - and it is not at present - here is a way to judge between the two interpretations.<119> The next chapter discusses this subject in more detail.

The Bohm theories may have theoretical and philosophical support. Perhaps it is a good time to build his new theories for the sub-quantum world.

Maybe, but the physics community has the final say on whether they are to be part of physics. Since Bohm's claims are highly technical, wrote Toulmin in 1962, "theoretical physicists must...fight out the issues among themselves." To be in the running, Bohm must present his theories in detail. They must also explain the known facts better than does the existing quantum theory. Bohm must show the merits of his ideas in the only way his fellow physicists cannot refute. "Unless [Bohm] succeeds in doing this, orthodox quantum physicists...will continue to regard his criticisms of quantum physics as backward-looking - as a revival of Einstein's counter-revolution." They will not see them as the theory of the future. When Bohm does this, continues Toulmin, we can decide if his ideas are "based only on hunches and guesswork or [if] they...serve as the starting point for a genuine...breakthrough."<120>

Toulmin overlooks another reason for the physics community being more open to the Birkbeck theories. Bohm's challenge to physics may interest younger physicists more than older ones. The change in attitude may require the older generation, with its staunch holding to the Copenhagen interpretation, to move over.<121>

In the next few chapters I will follow what Bohm sees in or underlying his hidden variables/quantum potential ideas.<122> His family of theories expresses his philosophical or metaphysical ideas, one of whose themes is the unending depth of nature. This idea is also part of his recent implicate order theory - a further topic for the chapters below. Such continuing thrusts into controversial physics may appear as a guiding light for many philosophical, religious or spiritual people. Like the hidden variables theories, however, the world of physics does not thoroughly support them.