At the end of last time, we started to talk about the algorithm that was developed over the course of the 1920s for predicting the outcomes of experiments, the kinds of experiments we have been discussing here: two-path experiments, double-slit experiments, and so on. The algorithm turns out to be astonishingly general. The kinds of results it gives for the sorts of physical situations that classical mechanics is good at describing match up very well with the predictions of classical mechanics.
And it is making fantastically accurate predictions, not just in these specific experimental circumstances, but in all of the circumstances that we have any idea how to set up, about the observed behaviors of subatomic particles. We said last time that there are two attitudes one can take toward this algorithm.
One attitude people took toward this algorithm was Bohr's. His view was that the apparent logical contradictions you run into carry a lesson: the very aspiration to tell yourself a story about what the electrons are doing in the double-slit experiment, or in the two-path experiment, or in any situation like that, is simply mistaken. This is not what physics can offer us. According to those who share this view, the human imagination was developed for hunting and gathering, not for understanding the comings and goings of subatomic particles, and is just not able to get its head around situations like this.
The world, in a phrase that was often used, is not merely stranger than we know, but stranger than we can know. What you get from this is a very militantly instrumentalist attitude toward what science can do for you. What science can do is make predictions about how an experiment set up in a certain way is going to come out, and that is it.
There may be a temptation to tell yourself stories about what is going on between the beginning of the experiment and the end of the experiment. That temptation will not pan out. That way leads to madness.
There was already, toward the beginning of quantum mechanics, a divergence in how its founders understood the theory, though it is not clear how aware they were of the extent to which they disagreed. Thinkers like von Neumann were clearly approaching the problem very differently. The contradiction dissolves, on this view, if one lets go of the conviction that there must always be an intelligible question of the form: which slit did the particle go through, or which path did the particle take through the two-path apparatus?
The lesson of quantum mechanics may not be that we cannot tell ourselves coherent stories about the physical world, but rather that the stories we are forced to tell will be very strange and very unfamiliar, though not logically unintelligible. What one might say is that when an electron is passing through the two-path apparatus, it is in a perfectly definite physical situation, one that physicists came to call a superposition. It is a feature of that situation that asking which path the electron is on amounts to what philosophers have long called a category mistake.
Asking which path the electron is on, in this view, is like asking about the marital status of the number five, or about the weight in grams of Catholicism, or about the political affiliations of a table. The number five is simply not the kind of thing that has a marital status. Similarly, when the electron is passing through the two-path apparatus, it somehow becomes not the kind of thing about which it makes sense to ask what path it is on.
This is a way of preserving anti-instrumentalist intuitions about what science can do for us. It is an attempt to tell a story, a strange story to be sure, about what is actually going on in the world.
Part of this algorithm is a mathematical object called the wave function. Someone like Bohr would regard the wave function as merely a piece of mathematical apparatus, playing a certain role in the algorithm for predicting the outcomes of future experiments given the outcomes of past experiments. Someone like Von Neumann, on the other hand, wanted to think of the wave function as an actual description of what the particle is doing even in between those two experiments.
On Von Neumann's view, the wave function tells you when the particle goes into a superposition of being on one path or another, and when there is a fact of the matter about which path the particle is on. Von Neumann argues that the algorithm must apparently include some explicit stipulation about this. To see why, let us return to the two-path experiment we examined last time.
Here is the hardness box, the hard path, the soft path, the mirrors, and the black box. We noted that if you stop the experiment in the middle by placing a detector at some point along one of the paths, a detector that clicks if a particle passes near it, the results change dramatically. When the detector is turned off, every white particle fed into the apparatus comes out white on the other side.
If you turn the detector on, so that you are in a position to ascertain which path the particle took, what happens is that half the time the detector clicks and half the time it does not. Whenever it clicks, any other detector placed farther along the same path will also click. That is, from the moment of the first click, the electron begins to behave as though there is a determinate fact of the matter about which path it is on, and all of its subsequent behavior, including its color statistics at the output, is compatible with the claim that it is traveling along the hard path.
On the other hand, if you do not place detectors in the apparatus, or if you leave them turned off, you get 100% white particles at the output. This is behavior that is flatly incompatible with the idea that there is any fact of the matter about which path the electron takes through the apparatus.
The algorithm tells us that when we feed a white electron into a hardness box, it will emerge from that box in a superposition of being on the hard route and being on the soft route. This is one of the circumstances in which such superpositions arise. The passage of a white electron through a hardness box leaves the electron in one of those conditions for which it simply does not even make sense to ask which path it is on, one of those conditions for which asking what path it is on is like asking about the marital status of the number five.
But it is also part of our experience that if you place a detector to see where the electron is, the operation of that detector apparently forces the electron to choose a path. It forces the electron back into a situation in which there is a fact of the matter about which path it is on, a situation in which asking which path it is on is no longer like asking about the marital status of the number five.
In order to account for both of these behaviors, Von Neumann concluded that the algorithm for predicting the behaviors of all physical systems, now presenting itself as an absolutely general, fundamental physical theory of the world, would need to contain two distinct laws.
Von Neumann identified two laws governing quantum systems. The first, given by the famous Schrödinger equation, a differential equation describing how the wave function evolves, applies when measurements are not being carried out. The second law describes how the states of systems behave when measurements are being carried out. The essence of that second law is this: when you carry out a measurement, you force the measured system to choose some value of the observable you are measuring. It snaps suddenly into a state for which questions about that value make sense, and for which the particular value it has is precisely the one you measured it to have.
Von Neumann did more than simply state these two laws. A natural intuition, and it is a reasonable one, is that what happens to the physical state of the world during a measurement ought to be just a special case of the general laws that govern the physical state of the world at all times. A measurement, after all, is just a name we give to a particular kind of collision between two physical objects. Two particles can collide with one another, two tables can collide with one another, and a measuring device can have a collision with some other system, a certain property of which it is designed to measure. Presumably all of these interactions ought to fall under the same set of fundamental laws.
The very important thing Von Neumann was able to show is that this is not the case in quantum mechanics. The phenomenon people came to call collapse, this business of forcing a system to pick a definite value, will not emerge if you try to derive it from Law One alone, applied to the special case of a collision between an electron and a measuring device. If you apply Law One to the measurement process itself, it yields a definite, deterministic prediction: the measuring device will go into a superposition of having clicked and not having clicked, and the brain of an observer who looks at the device will go into a superposition of having heard a click and not having heard a click.
At the end of that process, there would be no fact of the matter even about what the sentient observer took the outcome of the measurement to be. Yet we know, by a method more certain than virtually any other source of knowledge available to us, namely, direct introspection on our own phenomenal states, that this is not what happens. Experiments do not end that way. Law One therefore cannot be completely general; it cannot account for what happens when we perform these measurements.
What you find in Von Neumann's book is a very bizarre formulation. He says that there are apparently two fundamental laws: the law that governs the behavior of physical systems when they are not being measured (that is Schrödinger's equation, law number one) and the law that governs what happens to physical systems when they are being measured. That second law is the collapse postulate, the demand that the state of the system snap into one or the other of the values of whatever property is being measured, either into a state where it is on the hard path or into a state where it is on the soft path, after which things proceed as before in accord with Schrödinger's equation until the next measurement occurs.
So the way things are left in Von Neumann's famous book is that the fundamental laws of physics look like this: law number one applies when measurements are not going on, and law number two applies when measurements are going on. That, of course, is insane. If for no other reason, the word measurement is a vague English word that does not have anything like the requisite precision to be playing this kind of foundational role in a theory that is supposed to be the fundamental and universal physical theory of the world.
Audience: And the reason you said that Von Neumann was an improvement over the previous attitude is because at least he tried to introduce two explicit laws?
Well, yes, at least that.
First of all, I'm not even sure I would call it an improvement, although from my point of view it certainly is. But there is the following contrast. Von Neumann is clearly not satisfied with being an instrumentalist in the way that Bohr is. Von Neumann is in the business of trying to tell a story about what happens between one moment and the next. It is a strange story, but it is not a logically unintelligible one.
Bohr, by contrast, seems to have elaborated further on the very impossibility of telling such a story. This is just one among many puzzling things about Bohr's attitude. His response to this kind of logical tension was to develop a position he referred to as complementarity.
Bohr argued that the impossibility of telling any unified story about a quantum particle comes down to this: if you place a detector here, you must treat the particle, from the very beginning, as having a position that you are detecting. If you do not place a detector here, you must treat the particle, from the very beginning, as having a definite color. Those two properties are complementary, and you cannot entertain them both at the same time.
One might have responded to Bohr by saying, "Fine, then let us learn a new language, the language of superposition." But Bohr seems to have regarded it as a very deep principle that we simply do not have that option, that we cannot leave the classical language behind.
Von Neumann is trying to do something precisely contrary to that. His position is that we need a new language to describe what the electron is doing, and that there is no reason in principle why we cannot learn it, why we cannot, so to speak, go native. Bohr seems to have thought that was simply a misguided ambition, though I wish I had something more illuminating to say about why he thought so. Subsequent developments have certainly not borne out the claim that this is a language we are incapable of learning and using descriptively.
Von Neumann differs from Bohr on precisely this point. His view is that we can have a logically coherent, if very strange, story about what the electron is doing. Von Neumann is unmistakably in the business of trying to tell a realistic story about the electron, but the realistic story he initially has to tell is, frankly, a crazy one.
In popular circles, people often look at the interference pattern in the double-slit experiment and say, "This shows wave-particle duality — sometimes electrons behave like waves and sometimes like particles." A natural question is whether, in this framework, that distinction falls along the lines of the two laws of evolution: wave-like under the deterministic law, particle-like under measurement. That is not quite the right way to draw the line.
It is more like this. If you only perform a measurement at the beginning and at the end, if you do not place a detector at either slit, you are setting up a situation in which you must represent the system as a wave, one that can in some sense take both routes, though not in any familiar classical sense. If, on the other hand, you place a detector beside one of the slits, then in order to get the right results you must model the electron as a particle. The wave-particle distinction is really about which experimental arrangement you have set up.
Consider the double-slit experiment concretely. You have an electron gun, a screen with two slits, and a fluorescent detection screen beyond it. Interference patterns of this kind are familiar from water waves, sound waves, and light waves: waves pass through two openings and produce a characteristic pattern of alternating bands on the far side.
When both slits are open and there is no detector telling you which slit the electron passed through, you get exactly that interference pattern. To make sense of it, you must think of the electrons as a wave, whatever, precisely, that is supposed to mean. When you switch on a detector at one of the slits, the interference pattern disappears and is replaced by a simple two-band landing pattern. To make sense of that, you must think of the electrons as particles.
If you then ask, "But what is the electron, considered in itself?" that, according to this view, is the wrong question, an incoherent question. The lesson is supposed to be that you must think in a new, complementary way: the electron is neither wave nor particle in isolation; it is one or the other depending on the experimental context. Bohr, who had a very thorough late-nineteenth-century European philosophical education, framed all of this in terms of Hegelian thesis and antithesis.
That is, I think, an elaborate way of saying: you want a single underlying story, and there is no such thing. I am conscious of not making the kind of sense of Bohr that a teacher feels obliged to make, but I genuinely do not know what the man was talking about. We are on the train with von Neumann now.
Von Neumann is trying to tell a realistic story, but he has a terrible story. On the other hand, von Neumann has shown that there is no option of simply throwing out the collapse postulate, because you cannot derive it from Law One. And you cannot throw out Law One either, because Law One is absolutely crucial to making the right predictions about how experiments come out. So you are apparently stuck with these two laws, and what you need to do is find a way of locating the boundary between that set of physical situations in which Law One applies and that set of physical situations in which Law Two applies.
Von Neumann's suggestion was that the location of that boundary is indicated by the word measurement. That is not a good way to locate the boundary. Astoundingly, for about forty or fifty years afterward, people wasted their time coming up with equally ridiculous ideas about where the boundary lay. Instead of using words like measurement, people used words like macroscopic: once you get into macroscopic superpositions, Law Two kicks in. But what does macroscopic mean?
Others proposed thermodynamic irreversibility: once you reach the level of thermodynamically irreversible processes, Law Two kicks in. What does that mean? Or: once recordings of the outcome of an experiment have become indelible, Law Two kicks in. Does it matter what kind of ink you use? This history of speculation was clearly getting nowhere, and it was, frankly, undignified. Let me discuss in a little more detail what is perhaps the most interesting and most extreme episode in this particular history of speculation about where to draw the boundary.
Eugene Wigner, a distinguished physicist and Nobel Prize winner who made enormous contributions to the development of quantum mechanics, was deeply interested in this problem. He thought that a principled place to draw the line might be at the level of consciousness, that consciousness might have something important to do with the collapse. The proposal runs roughly as follows: Law One applies under all circumstances unless and until the evolution proceeding in accord with it produces a situation where an embodied sentient being enters into a superposition of two states corresponding to two different conscious mental states, the mental state of hearing the click on the detector and the mental state of not hearing the click on the detector.
The thought was that it is precisely this kind of superposition that nature abhors. Law One is there to forbid superpositions of consciously distinct states. Nature evolves in accord with Law One until, as von Neumann had proved many years earlier, that evolution lands us in a situation where we are dealing with a superposition of a state in which I heard the device click and a state in which I did not hear the device click. In such a state, asking whether I heard the device click is like asking about the marital status of the number five: there is simply no fact of the matter about whether I even think I heard it click or not.
Audience: That would mean that if you place the particle detector in the two-path apparatus before you look, the interference pattern is not wiped out.
Correct. Before I look, there is no fact of the matter about whether the detector clicked or not. It is only when I look and become conscious of whether it clicked that Law Two kicks in and the collapse occurs.
Wigner wrote an essay which became very famous and widely read in the 1960s and '70s, and which subsequently gave rise to a vast New Age industry where it still flourishes today. The essay was called On the Mind-Body Problem, and its central thought was the following. On this view, conscious entities behave physically differently than entities that are not conscious. It is only in the evolution of conscious entities that the second law, the collapse law, ever applies. Physical, inanimate, unconscious entities never evolve by themselves in accord with law two; they always obey law one.
Wigner thought this was the most remarkable thing in the world, and here is why. There had long been an anxiety to the effect that the mechanical conception of the world we inherit from Newtonian mechanics and Maxwellian electrodynamics leaves no space for anything like a mind. The worry centered on questions about free will versus determinism, and on a broader, persistent unease that there was a tension between the picture of the world presented by post-Renaissance physics and the way we are accustomed to thinking of ourselves as agents and as sentient beings.
Wigner's response was to point out the profound irony in this situation. If he was right, it is not merely the case that physics is not hostile to the existence of mental entities utterly distinct from mere collections of billiard balls. Physics actually needs that. Consciousness is precisely what produces collapses, and collapses are what we need in order to explain the experimental results.
Wigner believed that quantum mechanics had turned the traditional mind-body problem on its head. It is not merely that our conception of ourselves as physical objects and our conception of ourselves as something more are not in tension with one another. They need each other. The only thing in the world capable of producing these collapses is mentality.
Indeed, Wigner went further and proposed that quantum mechanics actually supplies a precise answer to the question of what distinguishes mental objects from material ones. What we mean by a purely material object is a system that always obeys law one. What we mean by an embodied consciousness is a system that sometimes obeys law two. That is the difference between minds and bodies, and that is why a physical account of the world and a dualistic, mentalistic account do not merely coexist; they require one another.
Audience: The fun thing about listening to your lectures more than once is I'm just as lost the second time as the first time. It sounds to me as though there may at times be no facts of the matter about the world.
No, no. When I say there is no fact of the matter about the position of the electron, that is nothing like saying there are no facts of the matter about the world. When I say there is no fact of the matter about the marital status of the number five, that doesn't threaten the existence of facts generally. There are perfectly good facts about the sum of five and three, and so forth. It just happens that marital status is not among the things the number five has a fact about. Similarly here: there are certain circumstances in which, according to someone like Von Neumann, there is a perfectly definite fact of the matter about the situation of the world when an electron is passing through a device. You want to know what that fact is? It is given by the wave function, which tells us the electron is in a superposition of being on this path and being on that path. That is a perfectly definite fact. It is just that there are things we always imagined there would always be facts about, such as the positions of particles, and sometimes there simply are not.
Audience: Is Wigner's position a dualist position?
Absolutely, and not only is it a dualist position, it is the most extreme kind of dualist position imaginable. It is not an epiphenomenalist position, it is not a parallelist position; it is what is called an interactive dualist position. It is the very dualist position that Descartes held, and one that not many thinkers since Descartes have been willing to espouse. The claim is not merely that minds and bodies are metaphysically distinct kinds of things, and not merely that the physical state of the world can affect mental states, which everyone agrees with, but that mental states can in turn affect physical states.
Audience: Wherever one is coming from when approaching physics, one of the motivations would seem to be precisely to set dualism aside. How does one go from physics to Wigner's view?
I don't know what to tell you. Look, we have serious trouble here, and desperate times call for desperate measures. This is, in a way, a desperate measure. But Wigner also saw a flip side: he thought this move actually resolved an old problem. On his view, the distinction between there being consciousness and there not being consciousness is sharper than any of the other candidate distinctions, between measurement and non-measurement, macroscopic and microscopic, indelible and non-indelible, and so on. Of course, the moment you think carefully about it, there is no compelling reason to say that.
I myself, as a graduate student, in one of the more depressing moments of my life, heard Wigner expound this theory and express the opinion that dogs could probably cause collapses, but mice probably could not. And you find yourself thinking, as you were just implying, that this is not the right way to do physics. It seems really, really bad, and here is this man who apparently has views about mice. I genuinely do not know what to make of it.
What Wigner was saying, in his own terms, was this: we are in trouble, we have these two laws, and we must find some demarcation, some principled boundary between those situations in which the first law applies and those in which the second law applies. Von Neumann had mathematically proved that one is not a consequence of the other, that they make genuinely contradictory claims about how the wave function evolves. So we are stuck, and Wigner is trying to solve the problem. His proposal is an example of how a solution could imaginably work. I think he is wrong. But he is not an idiot, and it is not as though one cannot understand the reasoning that led him there, reasoning that a distinguished physicist working squarely within a scientific tradition could have followed to reach precisely these conclusions.
One has to pause and reflect on something I touched on at the end of our last session. These researchers were simply trying to figure out how rocks work, how inanimate material objects behave. And yet, in a way that is not entirely surprising once you trace the steps, they found themselves drawn into speculations about dualism, about the mind-body problem, and so on. It is remarkable how deeply physics became entangled in questions it never set out to answer.
The scientific project, as it was traditionally understood, was brought into a profound crisis in two distinct ways. The first came with Bohr, who essentially declared that the entire enterprise of constructing a coherent story about what is happening between one observation and another is hopeless. Many physicists refused to accept that conclusion and pressed ahead, figures like Von Neumann, determined to tell a realistic story about quantum mechanics, however strange that story might be.
In pressing ahead, they were forced to entertain a series of increasingly uncomfortable speculations about precisely where the collapse of the wave function, law number two, actually kicks in. And before long, they found themselves neck-deep in the mind-body problem. That is the tough, deep challenge presented to us by the behavior of subatomic particles, by the very stability of matter itself.
There is something genuinely astonishing in all of this, something that speaks to how much is truly at stake. Nobody was looking for trouble. These scientists were measuring rocks, feeding them through machines, and trying to see what happens. And they got dragged into very weird places indeed.