Alternatives to Traditional Quantum Theory
Everything that I have said up to this point about the implications of quantum theory is based on the fundamental idea of the “collapse of the wavefunction” when observations are made. This idea is not the suggestion of a radical fringe of physicists. It is the traditional way of looking at quantum theory, and is so mainstream that it is, as I have said, sometimes called the “orthodox” view. However, if one begins to take this view seriously, and ask where it leads, one comes to rather startling, and to some people shocking, conclusions.
There are two ways that physicists who dislike the traditional interpretation of quantum theory deal with the situation. Most of them respond in the way suggested by the philosopher Hume in another context: with “carelessness and inattention.”1 In other words, they just ignore the issues. This is perfectly reasonable. For the practical business of doing physics—of actually calculating what the results of experiments will be—it is not necessary to worry about the philosophical implications of the theory. However, it is not only practical absorption in their business that leads physicists to adopt this attitude. Many physicists are made uneasy and impatient by discussions of the philosophical implications of quantum theory. Partly this is because they know that these implications are strange, and they would rather not be forced to think about them or discuss them, like the doings of some embarrassing relative; and partly it is because physicists look askance at anything that smacks of metaphysics. The present-day scientific community is heavily imbued with positivist and skeptical attitudes, which lead many to dismiss all philosophical inquiry as useless playing with words.
The other reaction has been to seek a way of modifying quantum theory or of reinterpreting it so that the “observer” does not play a fundamental role. None of these reinterpretations at present commands the allegiance of more than a minority of physicists.2 I will discuss them briefly in this chapter. In my view, the alternatives to the traditional interpretation of quantum theory all either fail to come to grips with the philosophical issues, or are unsatisfactory for some other reason.
In the history of science, when a theory gives rise to seemingly insuperable problems it is often a sign that a “paradigm shift” is required, to use the term made fashionable by Thomas Kuhn. Indeed, quantum theory itself was developed partly in response to inconsistencies and paradoxes that emerged within the framework of classical physics. It is quite natural, therefore, that many physicists have regarded the paradoxical features of quantum theory as an indication that the theory is incomplete or in need of modification. This was the view of Einstein.
Another reason that many theorists have anticipated the need to modify quantum theory is that Einstein’s theory of gravity (i.e., general relativity) seemed hard to reconcile with quantum principles. Attempts to treat the force of gravity in accordance with the basic postulates of quantum theory led to mathematical absurdities. For example, when one calculates the “quantum corrections” to the predictions of Einsteinian gravity, they generally come out to be infinite. On account of these difficulties, it was often said that a synthesis of general relativity and quantum theory would only be possible in a framework in which both theories would be changed in some profound way. Recent developments have somewhat undercut this belief, however. Superstring theory appears to be a perfectly consistent quantum theory that incorporates Einsteinian gravity; and in superstring theory the basic principles of quantum theory seem to be left untouched.3 Even if superstring theory turns out to be a blind alley, it will at least have shown that Einsteinian gravity and standard quantum theory can be reconciled with each other.
Be that as it may, the search for ways to change quantum theory so as to rid it of its paradoxical features has gone on for many decades. One of the oldest ideas goes by the name “hidden variables theory.” The hidden variables idea is essentially an attempt to go back to classical concepts. We have seen that the root of the paradoxes and puzzles of quantum theory is the fact that it is inherently probabilistic in nature. Classical physics by contrast is not inherently probabilistic. In classical physics it is only because one often in practice does not have access to all the relevant information for predicting a system’s future behavior that one is forced to use probabilities. However, that is a mere practical necessity, not an absolute one. In classical physics there is no theoretical bar to acquiring all the information needed in order to dispense with probabilities altogether. The idea of hidden variables theory is that the need for probabilities in quantum theory is really ultimately of the same kind. That is, it is suggested that it only arises from the fact that we do not have practical access to all the information about the systems we study. The information we lack is contained in the “hidden variables.”
Einstein took the view that the probabilities in quantum theory merely reflect the existence of hidden variables. However, this idea has now been largely discredited. In 1965, the physicist John Bell showed that in certain situations one could distinguish the probabilities that are predicted by quantum theory from those that could arise as a result of hidden variables. The latter would have to satisfy a certain mathematical relationship, which is now called “Bell’s inequality,” whereas the former would not have to. In 1982, experiments performed by Alain Aspect and his collaborators found that in certain physical systems Bell’s inequality was definitely violated. This is regarded as decisive evidence against the hidden variables alternative to quantum theory.
Another and more subtle attempt to return to more classical concepts goes by the name of “pilot wave theory.” The basic idea here was proposed by Louis de Broglie, one of the founders of quantum theory, and has since been developed by David Bohm and many other researchers.4 In pilot wave theory there is still a wavefunction, and it still satisfies the same Schrödinger equation as in standard quantum theory. However, the wavefunction plays a fundamentally different role. It is no longer thought of as being made up of “probability amplitudes.” Rather, it is simply a conventional force field (somewhat like an electric or magnetic field, say) that influences the behavior of the physical system. The physical system itself is described by a set of coordinates, much as in classical physics. These coordinates have their own “equations of motion,” again much as in classical physics. The wavefunction field appears in these equations of motion and acts to “pilot” the motion of the system, as it were.
Pilot wave theory is thus a kind of hybrid of classical and quantum ideas. Its basic structure is classical, but some of its equations are the same as the equations of standard quantum theory. Because it is basically a classical theory, many of the paradoxical features of standard quantum theory simply do not arise.
It has been shown that pilot wave theory can reproduce the results of standard quantum theory—that is, give the same predictions for the results of experiments—when applied to a wide range of physical systems. However, most physicists do not find pilot wave theory very plausible or appealing. There are several reasons for this. One reason is technical, and may be temporary. As currently formulated, pilot wave theory treats time and space very differently from each other. It thus seems more compatible with a Newtonian conception of time than with the theory of relativity. In fact, it has not yet been shown that pilot wave theory can be applied to “relativistic” systems (i.e., systems where velocities near the speed of light are important).
A more basic objection is that pilot wave theory seems quite artificial and complicated compared to standard quantum theory. Pilot wave theory has a two-tiered structure: on top of the structure of a wavefunction evolving in accordance with a Schrödinger equation, there is added an elaborate superstructure involving classical-type coordinates evolving in accordance with a new set of equations that do not appear in standard quantum theory. This greater complexity might be worth it if pilot wave theory were more powerful or successful as a physical theory, but it is not. In fact, it seems less powerful, since it has yet to be shown that it can reproduce all of the successes of standard quantum theory.
Another aspect of pilot wave theory that makes it appear quite suspect to many physicists is the way that the two tiers of the theory are related to each other. The wavefunction or pilot wave acts upon and influences the coordinates that describe the behavior of the system, but those coordinates do not act back upon or influence the pilot wave. This is not what one is used to in physics. Usually if A influences B, then B also influences A. For example, electromagnetic fields exert forces on electric charges, and electric charges act as sources of electromagnetic fields. In fact, so pervasive is this reciprocity in physics that Einstein wrote, “[It] is contrary to the mode of thinking in science to conceive of a thing … which acts itself, but which cannot be acted upon.”5 For all these reasons, pilot wave theory is regarded by most physicists as a very interesting but probably misguided idea.
Hidden variables and pilot wave theory do not exhaust the ways that physicists have tried to modify quantum theory in order to sidestep its philosophical dilemmas. Another approach that has been tried is to change the mathematical form of the Schrödinger equation in such a way as to make it possible for it to describe the mysterious-seeming “collapse of the wavefunction.” A basic challenge for this approach is how to build the unpredictability of the collapse into the new equation.
REINTERPRETING QUANTUM THEORY: THE “MANY-WORLDS” IDEA
The foregoing ideas assume that the basic mathematical structure of quantum theory needs to be changed. If, however, that structure is here to stay—as all present indications suggest—then the only hope for a change is through a change in the way that the mathematics is interpreted.
In 1957, a new interpretation of quantum theory was proposed by Hugh Everett6 that seems to some physicists to be much simpler and more satisfying than the traditional or “orthodox” view. As we have seen, the source of much of the dissatisfaction with the traditional view is the strange phenomenon called the collapse of the wavefunction. Everett had the brilliantly simple idea that all the knotty questions raised by the collapse of the wavefunction could be avoided simply by saying that the collapse never happens. Let us see where this leads.
As explained in the previous chapter, the collapse of the wavefunction is the point at which the probabilities of quantum theory get converted into definite outcomes. It was argued that when a measurement is made on a physical system, that measurement must have a definite and unique result. If, for example, one looks to see whether a radioactive nucleus has decayed or not, the result must be either “yes” or “no.” If it is yes, then at that point the probability that it has decayed is 100 percent and the probability that it has not is 0 percent, whatever those probabilities may have been just before the measurement. Thus, a measurement involves a sudden change of the “probability amplitudes” in the wavefunction. This sudden change is the notorious “collapse.”
If we say, as Everett did, that the wavefunction of a system never collapses, then when do definite and unique outcomes happen? The answer is that they don’t. Let us consider again the example of the radioactive nucleus. Just before the observer measures to see whether the nucleus has decayed, the wavefunction may say that the probability amplitude for it to have done so has the value A, and the probability amplitude for it not to have done so has the value B. (Assume that neither A nor B is zero.) According to the Everett interpretation, just after the observer makes his measurement the probability amplitudes are still A and B (or very close to those values)—they do not jump. Even after the measurement, neither outcome has a probability of 100 percent. How is that to be understood?
In the Everett interpretation, just after the measurement there is a probability amplitude A for the nucleus to have decayed and for the observer to see that the nucleus has decayed, and a probability amplitude B for the nucleus still to be there and for the observer to see that the nucleus is still there. Both outcomes happen. Both are equally “real.” Reality has two “branches,” as it were. In one branch the observer sees that the nucleus has decayed, while in the other branch the observer sees that it has not. The probability amplitudes tell one the relative “thickness” of those branches, so to speak.
This is why the Everett interpretation of quantum theory is usually called the “many-worlds interpretation.” All the states of affairs that have non-zero probability amplitudes in the wavefunction are regarded as co-existing and as being equally real, even after a measurement. To say I performed a measurement and “know” the result of it is, strictly speaking, wrong in the Everett interpretation. What is supposed to happen, rather, is that as a result of making a measurement my consciousness splits up: one version of “me” experiences one outcome while the other versions of “me” experience the other outcomes. Each version of me—being unaware of the other versions—naturally thinks of the outcome he experiences as the one and only “real” outcome.
In the many-worlds interpretation, it is an inescapable fact that reality is infinitely subdivided, and that each human being exists in not one, or even a few, but in an infinite number of copies, with infinitely various life experiences. In some branches of reality you are reading this page, in other branches you may be lying on a beach somewhere, or sleeping in your bed, or dead.
This may seem crazy; and, in fact, it seems crazy to physicists too, even to the advocates of the many-worlds viewpoint. These advocates point out, however—and quite rightly—that this kind of co-existence of apparently contradictory possibilities is also a feature of the traditional interpretation of quantum theory, though in a less extreme form. This is illustrated by the well-known example of the “double-slit experiment.” This experiment shows that an electron, say, really can be, in a certain sense, in two places at the same time. It is one thing, however, to say that an electron, or even a macroscopic inanimate object, can have such a divided existence. But to say that a rational being can is a more radical proposal. Most physicists are just as reluctant to accept the many-worlds interpretation as they are to fully accept the implications of the traditional interpretation of quantum theory.
One argument that is sometimes made in favor of the many-worlds interpretation is that it is forced upon one by any attempt to describe the entire universe by the laws of physics. If the “system” one is studying is the whole universe, then there cannot be any observer to collapse the wavefunction, since by definition the observer has to stand outside the system and make measurements of it. But no observer can stand outside the entire universe and make measurements of it. So the wavefunction that describes the entire universe can never collapse. Consequently, the wavefunction that describes the entire universe must be interpreted in a many-worlds way.
I believe that this line of argument is based on a verbal confusion, and in particular on an equivocal use of the word outside. All that is required in the traditional interpretation of quantum theory is that the observer of a system lie (at least in part) outside the system in an informational sense, not in a geometrical sense. That is, what is necessary is that a complete specification of the values of all the variables (or “coordinates”) of the system does not give a complete description of the observer. If a human being is observing the physical universe, he indeed lies geometrically inside the universe that he is studying, in the sense that his body is contained within it. But if his intellect is not something purely physical, then even a complete specification of the values of all the variables of the physical universe would not completely describe his mind. To the extent that his mind is not entirely physical, it would indeed lie “outside” the physical universe.
The great advantage of the many-worlds idea, as seen by its advocates, is its simplicity. Everything, including everything that goes on during measurements, can be described by a wavefunction that evolves at all times simply in accordance with the Schrödinger equation. Gone is all that bizarre business of wavefunction collapse. Gone with it is the fundamental importance of the observer. The many-worlds interpretation seems to slice through all the paradoxes of quantum theory like Alexander’s sword through the Gordian knot.
While the many-worlds interpretation is simple, however, it may be too simple. With the bathwater of the collapse of the wavefunction, it may have thrown out the baby of probability. The problem has to do with how probabilities are calculated in quantum theory. I have said that the wavefunction consists of a set of numbers that are called the probability amplitudes. What I have neglected to mention until now, however, is the crucial point that these probability amplitudes are not themselves the actual probabilities of outcomes of measurements. Rather, they are related to those probabilities by a precise mathematical rule, called the “probability rule” or “measurement principle,” which is as follows. The actual probability for a particular outcome of a measurement is given by the “absolute square” of the probability amplitude for that outcome. (If the probability amplitudes were ordinary numbers, one would just take the ordinary square—the square of a number is the number multiplied by itself. But the probability amplitudes are actually what are called “complex numbers,” and the “absolute square” is a way of multiplying a complex number by itself.) For example, in standard quantum theory the probability amplitude that a nucleus has decayed might at a certain time have the value 0.60. That means that if a measurement is performed at that time its chance of showing that the nucleus has decayed is 0.60 × 0.60 = 0.36 or 36 percent.
The important point is that in standard quantum theory, just as there are two kinds of processes (the evolution of isolated physical systems, and measurements on those systems), and two kinds of change in the wavefunction (the Schrödinger evolution and the collapse), so there are two mathematical rules: the Schrödinger equation and the probability rule.
The problem with the many-worlds interpretation is that it gets rid altogether of measurement as a distinct kind of event. There is therefore no point at which the probability rule can come into play as a distinct principle. In the many-worlds interpretation one is left with only the Schrödinger evolution of wavefunctions. The trouble with that is that it is questionable whether, with only the Schrödinger equation at one’s disposal, there is any way to rigorously deduce the connection between the probability amplitudes in the wavefunction and actual real-life probabilities. Various people have claimed to have done this, but these claims are disputed.7 It has been argued by some authors that it is in fact impossible to rigorously prove the probability rule in the many-worlds interpretation of quantum theory.8 If that is indeed the case, it would be fatal to the many-worlds idea.
One point that should be emphasized is that it is in practice impossible on the basis of any experiment to decide between the many-worlds interpretation of quantum theory and the traditional interpretation (supposing, of course, that the potentially fatal problem just discussed can be resolved, and that the many-worlds interpretation makes sense at all). The other branches of reality that are supposed to exist in the many-worlds idea are unobservable. It can be shown that they “decohere” from us.
The many-worlds idea could conceivably turn out to be a viable interpretation of quantum theory. If so, it allows the materialist to escape from the apparent implications of quantum theory that I discussed in chapter 24. The statement of Wigner that materialism is not consistent with quantum theory does not apply to the many-worlds interpretation. The price to be paid for eliminating the observer and the observer’s mind from the picture in this way, however, is the postulating of an infinite number of branches of reality, with an infinite number of versions of every person, that are completely unobservable to us.
(I should make a technical point. A great deal of work has been done in recent years on the idea of “decoherence.” It has been claimed that decoherence is in itself a way of interpreting quantum theory that resolves all the philosophical issues raised by it. This is not the case, however. Decoherence is not a new interpretation of quantum theory; it is a phenomenon that happens within quantum theory however it is interpreted. While the fact of decoherence is important for making sense of quantum theory by showing that it does not contradict our everyday experience, it leaves one with the same set of alternative interpretations: either the traditional collapse of the wavefunction or the many-worlds picture.)