Bohm's Alternative to Quantum Mechanics
This theory, ignored for most of the past four decades, challenges the probabilistic, subjectivist picture of reality implicit in the standard formulation of quantum mechanics
by David Z Albert
(Part 1 of 2)
The study of the behavior of subatomic particles in this century is supposed to have established at least three exceedingly curious facts about the physical world. First, pure chance governs the innermost workings of nature. Second, although material objects always occupy space, situations exist in which they occupy no particular region of space. Third and perhaps most surprising, the fundamental laws that govern the behaviors of "ordinary" physical objects somehow radically fail to apply to objects that happen to be functioning as "measuring instruments" or "observers." That at any rate is what the founders of quantum mechanics decided; that is what has since become the more or less official dogma of theoretical physics; and that is what it says, to this day, in all the standard textbooks on that subject.
But it is now emerging that those conclusions were settled on somewhat too quickly. As a matter of fact, a radically different, fully worked-out theory exists that accounts for all known behaviors of subatomic particles. In this theory, chance plays no role at all, and every material object invariably does occupy some particular region of space. Moreover, this theory takes the form of a single set of basic physical laws that apply in exactly the same way to every physical object that exists.
That theory is principally the work of the late David J. Bohm of Birkbeck College, London. Although his formulation has existed in the scientific literature for more than 40 years, it has until quite recently been mostly ignored. Throughout that period, the thinking about such matters has been dominated by the standard dogma, usually referred to as the Copenhagen interpretation of quantum mechanics because it can more or less be traced back to the Danish physicist Niels Bohr and his circle.
I will begin this article with an outline of the main arguments for the standard dogma. I will then indicate briefly how Bohm's theory manages to get around some of those arguments. Finally, I will say a little about how and where Bohm's theory fits into contemporary speculation about the foundations of quantum mechanics.
Perhaps the simplest way of formulating the arguments for the standard dogma is in the context of certain experiments with electrons. The experiments all involve measurements of two components of what are usually called the spins of electrons. For simplicity's sake, I will refer to them as the horizontal spin and the vertical spin.
It happens to be an empirical fact (as far as we know) that the horizontal spins of electrons can assume only one of two possible values. The same applies for vertical spins. I will call the values of the horizontal spin right and left and those of the vertical spin up and down.
Physicists can measure the horizontal and vertical spins of electrons easily and accurately with currently available technologies. Spin-measuring devices typically work by altering the direction of motion of the electron fed into the device based on the value of its measured spin component. In this way, the value of that spin component can be determined later by a simple measurement of the electron's position. I will refer to these measuring devices as horizontal and vertical boxes.
Another empirical fact about electrons is that as a rule there are no correlations between their horizontal spin values and their vertical spin values. For example, of any large collection of right-spinning electrons fed into the entry aperture of a vertical box, precisely half (statistically speaking) will emerge through the "up" aperture and half through the "down" aperture. The same applies for left-spinning electrons fed into the entry aperture of a vertical box and for up- and down-spinning electrons fed into horizontal boxes.
Another experimental truth about electrons, and an extremely important one for our purposes, is that a measurement of the horizontal spin of an electron can disrupt the value of its vertical spin, and vice versa, in what appears to be a completely uncontrollable way. If, for example, one carries out measurements of the vertical spins of any large collection of electrons in-between two measurements of their horizontal spins, what always happens is that the vertical spin measurement changes the horizontal spin values of half of the electrons that pass through it, leaving those of the other half unchanged.
No one has ever been able to design a measurement of vertical spin that avoids such disruptions. Moreover, no one has ever been able to identify any physical properties of the individual electrons in such collections that determine which of them get their horizontal spins changed in the course of having their vertical spins measured and which do not.
What the official doctrine has to say about these matters is that in principle there can be no such thing as a vertical spin measurement that has anything other than precisely that effect on horizontal spin values. Furthermore, the standard doctrine dictates that it is a matter of absolutely pure chance which electrons get their horizontal spins changed by measurements of their vertical spins and which do not; the laws governing those changes simply fail to be deterministic. And these conclusions certainly seem innocent and reasonable given the experimental data.
If measuring one type of spin indeed always uncontrollably disrupts the value of the other, then there can be no way of ascertaining the values of both the horizontal and vertical spins of any particular electron at any particular moment. This phenomenon is an example of the uncertainty principle: certain pairs of measurable physical properties, such as position and momentum or, in our case, horizontal and vertical spin, are said to be incompatible with each other. Measurements of one will always uncontrollably disrupt the other. Many other known examples of incompatible pairs of physical properties exist as well.
So much for indeterminism. But there are still more puzzling features of subatomic particles. Displaying them will require a more complicated experiment. Imagine a box that measures the vertical spins of electrons. Up-spinning electrons emerge from the box along a route labeled up; down-spinning electrons exit along a route labeled down. We can then arrange a pair of "reflecting walls" to make the two paths cross at some other point. These surfaces can be designed so as not to alter the spin properties of electrons in any way. At the point where the two paths intersect, we place a "black box" that merges the paths back into one, again without altering spin values.
Suppose we feed a large collection of right-spinning electrons, one at a time, into the vertical box. The electrons travel along the paths to the black box. Then as they emerge from the exit of the black box, we measure their horizontal spins. What sorts of results should we expect? Our previous experience informs us that statistically half of such electrons will turn out to be up-spinning and will take the up route through the apparatus. The other half will turn out to be down-spinning and take the down route. Consider the first half. Nothing along the paths between the vertical box and the exit point can have any effect on the vertical spin values of the electrons. Therefore, they will all emerge from the apparatus as up-spinning electrons. In accord with our earlier data, 50 percent of them will turn out to be right-spinning and 50 percent left-spinning. The down-spinning half will have precisely the same horizontal spin statistics. Putting all these expectations together, it follows that for any large set of right-spinning electrons fed into this apparatus, half should be found at the end to be right-spinning and half to be left-spinning.
These conclusions seem absolutely cut-and-dried. But a funny thing happens when you actually try this experiment. Exactly 100 percent of the right-spinning electrons initially fed into this apparatus (one at a time, mind you) come out right-spinning at the end.
It is no exaggeration to describe this result as one of the strangest in modern physics. Perhaps modifying the experiment somewhat will clarify matters. Suppose that we rig up a small, movable, electron-stopping wall that can be slid at will in and out of, say, the up route. When the wall is out, we have precisely our earlier apparatus. But when the wall is in, all electrons moving along the up route are stopped, and only those moving along the down route get through to the black box.
What should we expect to happen when we slide the wall in? To begin with, the overall output of electrons at the exit of the black box ought to drop by 50 percent, because one path is blocked. What about the horizontal spin statistics of the remaining 50 percent? When the wall was out, 100 percent of the right-spinning electrons initially fed in ended up as right-spinning electrons. That is, all those electrons ended up as right-spinning whether they took the up or the down route. Thus, because the presence or absence of the wall on the up route cannot affect electrons on the down route, the remaining 50 percent should all be right-spinning.
As you may have guessed, what actually happens in the experiment runs contrary to our expectations. The output is down by 50 percent, as predicted. But the remaining 50 percent are not all right-spinning. Half are right-spinning, and half are left-spinning. And the same thing happens if we insert a wall in the down path instead. (Readers familiar with quantum mechanics may recognize that this experiment is a logically streamlined version of the famous double-slit experiment.)
How can one understand the discrepancy between the results of these experiments and our expectations about them? Consider an electron that passes through the apparatus when the wall is out. Consider the possibilities as to which route it could have taken. Could it have taken the down route? Apparently not, because electrons taking that route (as the experiment with the wall in reveals) are known to have horizontal spin statistics of 50-50, whereas an electron passing through our apparatus without the wall is known with certainty to be right-spinning at the apparatus exit. Can it have taken the up path, then? No, for the same reasons.
Could it somehow have taken both routes? No: suppose that when a certain electron is passing through this apparatus, we stop the experiment and look to see where it is. It turns out that half the time we find it on the up path and locate nothing at all on the down path, and half the time we find it on the down path and see nothing at all on the up path. Could it have taken neither route? Certainly not. If we wall up both routes, nothing gets through at all.
Something breathtakingly deep, it would seem, has got to give. And indeed, something does--at least according to what has become one of the central tenets of theoretical physics over the past half-century (it is the second of the three official dogmas to which I alluded in the opening paragraph, the one about the indefiniteness of position). That doctrine stipulates that these experiments leave us no alternative but to deny that the very question of which route such an electron takes through such a contraption makes any sense. Asking what route such an electron takes is supposed to be like asking about, say, the political convictions of a tuna sandwich or about the marital status of the number 5. The idea is that asking such questions amounts to a misapplication of language, to what philosophers call a category mistake.
Hence, what physics textbooks typically declare about such electrons is emphatically not that the particles take either the up route or the down route or both routes or neither route through the apparatus. Rather there is simply not any fact about which route they take--not merely no known fact, but no fact at all. They are in what the textbooks term a superposition of taking the up route and the down route through the apparatus.
Notwithstanding the profound violence these ideas do to our intuitive picture of the world, to the very notion of what it is to be material, to be a particle, a compact set of rules has been cooked up that has proved extraordinarily successful at predicting all the observed behaviors of electrons under these circumstances. Moreover, these rules--known of course as quantum mechanics--have proved extraordinarily successful at predicting all the observed behaviors of all physical systems under all circumstances. Indeed, quantum mechanics has functioned for more than 70 years as the framework within which virtually the entirety of theoretical physics is carried out.
The mathematical object with which quantum mechanics represents the states of physical systems is referred to as the wave function. In the simple case of a single-particle system of the kind I have been discussing, the quantum-mechanical wave function takes the form of a straightforward function of position. The wave function of a particle located in some region A, for example, will have the value zero everywhere in space except in A and will have a nonzero value in A. Similarly, the wave function of a particle located in some region B will have the value zero everywhere in space except in B and will have a nonzero value in B. And the wave function of a particle in a superposition of being in region A and in region B--the wave function, for example, of an initially right-spinning electron that has just passed through a vertical box--will have nonzero values in both of those regions and a zero value everywhere else.
And it is a cardinal rule of quantum mechanics (a rule that Bohm's theory will explicitly break) that representing physical objects by a wave function represents them completely. It states that absolutely everything there is to be said about any given physical system at any given instant can be read from its wave function.
What the laws of physics are about--indeed, all that the laws of physics could be about, all that there is for the laws of physics to be about, according to quantum mechanics--is how the wave functions of physical systems evolve in time. The textbook version of quantum mechanics refers to two categories of such laws. And what is particularly peculiar about this formulation is that one of those categories applies when the physical systems in question are not being directly observed, and the other applies when they are.
The laws in the first category are usually written down in the form of linear differential "equations of motion." They are designed to entail, for example, that an initially right-spinning electron fed into a vertical box will emerge from that box in a superposition of traveling along the up route and traveling along the down route. Moreover, all available experimental evidence suggests that those laws govern the evolutions of the wave functions of every single isolated microscopic physical system under all circumstances. So, because microscopic systems are the constituents of everything that exists, there would on the face of it seem to be good reason to suppose that those linear differential equations are the true equations of motion of the entire physical universe.
Yet that conclusion cannot possibly be quite right if wave functions are indeed complete descriptions of physical systems, as quantum mechanics maintains. To begin with, the laws expressed by those equations are completely deterministic, whereas an element of pure chance seems to play a role in the outcomes, for example, of experiments with the spin boxes.
Consider the outcome of a measurement of the position of an electron that is initially in a superposition of being in region A and being in region B. Straightforward calculations reveal that the linear differential equations of motion offer a definite prediction about the end of such a measuring process. Those equations, however, do not predict that the measuring device would either indicate that the electron was found in A or that the electron was found in B (which is what happens when you actually make measurements like that). Rather those equations say the measuring device would with certainty end up in a superposition of indicating that the electron was found in A and indicating that the electron was found in B. To put it slightly differently, those equations predict that the measuring device would end up in a physical state in which there is simply no fact about what it is indicating. It hardly needs mentioning that such superpositions (whatever they are, precisely) do not correctly describe how things end up when you actually make such a measurement.
As a result, according to the official reasoning, the first category of laws needs to be supplemented with a second, which will be explicitly probabilistic. It demands, for example, that if the position of an electron that is initially in a superposition of being in region A and region B were to be measured, there would be a 50 percent chance of finding that electron in region A and a 50 percent chance of finding it in region B. In other words, if the position of the electron were measured, there would be a 50 percent chance that the electron's wave function will be altered in the course of the measurement to one whose value is zero everywhere other than in region A and a 50 percent chance that its wave function will be altered to one whose value is zero everywhere except in region B. (This alteration is sometimes called a "collapse" of the wave function.)
How does one distinguish those conditions in which the first category of laws applies from those in which the second category does? All the founders of quantum mechanics had to say was that it has something to do with the distinction between a "measurement" and an "ordinary physical process," or between what observes and what is observed, or between subject and object. [Continued in
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