There are psi-epistemic models that do not take an anti-realist position, in that they accord a reality to the quantum world, but nonetheless argue that the wavefunction is not a part of this real world; rather, it is about our knowledge of that world. Einstein is thought to have been a proponent of this view of quantum mechanics.
The alternatives to the Copenhagen interpretation examined so far—the de Broglie-Bohm theory, collapse theories, and the many worlds interpretation—are all realist about the wavefunction. They argue for an objective world out there that exists independent of observers. In other words, there is an ontology of the quantum world, and the wavefunction is part of this ontology, making these alternatives psi-ontic.
But in all these cases, the quantum state (given by the wavefunction), whether it’s epistemic or ontic, is associated with the quantum system—something that all observers can objectively agree upon. QBism takes a radically different stance. “We’d say: in nature there aren’t any things called quantum states,” Fuchs said. “They just aren’t out there.”
QBism is definitely psi-epistemic, but the wavefunction is associated with each individual observer studying a quantum system, not with the quantum system. So if I’m making a quantum measurement, the wavefunction I use for the quantum system encodes my expectations for the consequences of the action I’m about to take on it. These expectations are dictated by my beliefs about the system.
So take a photon going through a beam splitter. If you, the agent, had no idea of what a beam splitter does, then you might associate a wavefunction to the photon as it goes past the beam splitter that encodes your uncertainty. The wavefunction is a linear combination of two components (the transmitted and the reflected paths). Let’s say you assign a probability of 1/3 for finding the photon in detector D1 and of 2/3 for finding it in detector D2. This is the same as assigning amplitudes of 1/√ 3 and √ 2 /√ 3 to the reflected and transmitted parts of the wavefunction, so that squaring the amplitudes gives you the respective probabilities.
But experience—say of doing the experiment over and over again or understanding the physics of the beam splitter or reading textbooks or talking with your colleagues—would tell you that these probabilities are wrong. You’d update the wavefunction until it accurately represents your belief that the photon will go to D1 half the time and D2 half the time. This idea can be extended to the full Mach-Zehnder interferometer and, by extension, to the double slit, though the argumentation gets more involved. Regardless of the complexity of the system, the key idea here is that the probabilities you assign to the outcomes of experiments are contingent upon your personal set of beliefs about what might happen.
“All of this is personal Bayesian probability,” said Fuchs. “The Bayesian notion is that you write down a probability assignment as a measure of what you can’t predict. You might write down a probability assignment just because you don’t have all the facts. [It’s] not an objective feature of things, it’s rather a statement about the person making the [prediction].”
Some physicists have argued that QBism is simply Copenhagen in sheep’s clothing. But Fuchs vehemently disagrees. He points out that in the Copenhagen interpretation, the wavefunction is associated with the quantum system being studied, and removing the observer doesn’t remove the wavefunction: it still exists, independent of the observer, as an objective, epistemic statement about the system. Not so in QBism. Remove the observer and there is no quantum state, no wavefunction to talk of. Moreover, Copenhagen is anti-realist. QBism is not, according to Fuchs. It does not deny that there is a real world out there. All it does is state, unequivocally, that the quantum states in the formalism are not about the real world but about our beliefs about the real world. They are subjective, not objective.
What does all this achieve, however? For one, the whole issue of the collapse of the wavefunction becomes, well, a nonissue. There is nothing physical that is collapsing. All that happens is that you update your beliefs about the world: the wavefunction, which quantifies your expectations, changes. Nothing physical happened ( note that the same argument can be made for any psi-epistemic theory—that the collapse has nothing to do with the physical system, but rather, it’s about the change in our knowledge of the system).
“For QBism, you don’t need a physical story anymore,” said Fuchs about the need to explain collapse. “Instead you say this: I took an action that led to a consequence, and because of the consequence I believe new things. The things I believe are captured by this mathematical symbol, ψ. Because I believe new things, instantaneously, upon the new experience, this mathematical object changes instantaneously.”
As far as interpretations or alternative theories of the quantum world go, QBism is one of the newest kids on the block, and it goes against the grain for most physicists, who shrink from the idea of personalizing science. For a while, except for Fuchs and Shack, there were few takers. But QBism got a boost when David Mermin, a highly regarded solid state physicist at Cornell University in Ithaca, New York, came on board.
“What really appealed to me about QBism was that it gave a context in which Copenhagen made more sense, and gave an explanation of why Copenhagen was so hard to grasp,” Mermin told me when I met him at his office in Ithaca on a blustery, bitingly cold winter’s day. “Because what everybody was doing was what scientists had been taught to do almost forever, which was to construct an understanding of the external world that made no reference whatsoever to the people who are trying to understand it. And a lot of the clumsy, awkward things about Copenhagen involved trying to objectify things that aren’t objective, that are subjective and personal.”
QBism lays itself open to charges of solipsism, which is the argument that the only thing that is real is what I experience. According to Mermin, there is a fallacy in such arguments. We have language to communicate with each other about our private experiences—including the language of science and mathematics—and this makes our subjective experience a shared reality.
Nonetheless, there is nothing like an objective third-person view of reality in QBism. This has implications for questions about whether the universe is local or nonlocal or whether there is a quantum-classical divide—the other axes along which we can sort out the various interpretations. Take nonlocality. Copenhagen argues that the quantum world is nonlocal but provides no explanations for why it might be so. It just is. The de Broglie-Bohm theory resorts to nonlocal hidden variables to explain nonlocality. Collapse theories are nonlocal, in that they take the wavefunction seriously—and the collapse of the wavefunction (whether it happens stochastically as in GRW or because of gravity as in the Diósi-Penrose theories) is a nonlocal event. And according to some proponents of the many worlds interpretation, the universe is local. QBism says so too. And both of them resort to similar arguments to argue why.
Recall Alain Aspect’s experiment about Alice and Bob doing measurements on entangled photons and finding correlations that imply instantaneous action at a distance between, say, Alice’s measurements and Bob’s photons, or vice versa. So if Alice and Bob make measurements, and their measurements have definite outcomes, then when analyzed from a third-person perspective, these measurement outcomes are correlated in ways that cannot be explained without the assumption of nonlocality. But the third-person perspective doesn’t make sense in the many worlds interpretation. In his book The Emergent Multiverse , David Wallace argues that when it comes to many worlds, “ from the third-person perspective from which Bell’s theorem is normally discussed, no experiment has any unique definite outcome at all.”
Wallace explains: “ From the perspective of a given experimenter, of course, her experiment does have a unique, definite outcome, even in the Everett interpretation. But Bell’s theorem requires more: it requires that from her perspective, her distant colleague’s experiment also has a definite outcome. This is not the case in Everettian quantum mechanics—not, at any rate, until that distant experiment enters her past light cone.” Meaning that
the instant at which one can talk about measurements by Alice and Bob in the same breath is when one gets access to the other’s world—which cannot happen faster than the speed of light.
On the whiteboard in his office in Boston, Fuchs drew cartoons for Alice and Bob to explain why QBism takes a somewhat similar stance. “This is a bit like many worlds, which I’ll be honest about,” he said. In both QBism and many worlds, from Alice’s perspective, there’s no click on Bob’s detector and vice versa. Bell’s analysis, however, insists that there be a click on both sides, as seen from a third-person perspective. This isn’t possible in QBism. It’s only after Alice walks over to Bob—which cannot happen faster than the speed of light—and Bob’s results become part of her experience that she can update her beliefs about what has happened. But until then, there is no notion of correlations between the results obtained by Alice and Bob. “ Quantum mechanics, in the QBist interpretation, cannot assign correlations, spooky or otherwise, to space-like separated events, since they cannot be experienced by any single agent. Quantum mechanics is thus explicitly local in the QBist interpretation. And that’s all there is to it.”
There’s a similar dismissal of the idea of the quantum-classical divide in QBism. In the Copenhagen interpretation, there is a divide that exists by diktat. There are some things that are quantum and others that are classical, but without any solid explanation for why that might be so. Explanations using decoherence get us partway to understanding why quantum states might end up as classical, but they don’t complete the job. In the de Broglie-Bohm theory, there is no divide. There is always a fact of the matter as to where the particles that make up any object are, however big or small the object. Collapse theories argue for an emergent divide that is brought about by the stochastic process of collapse itself. The many worlds interpretation does not distinguish between the classical and the quantum—the wavefunction is all there is, evolving, forever. QBism, on the other hand, asks us to rethink the very notions of what we mean by the quantum and the classical, given that these terms are usually talked about from an impersonal, objective third-person perspective. “ Science is about the interface between the experience of any particular person and the subset of the world that is external to that particular user . . . It is central to the QBist understanding of science,” wrote David Mermin in his essay “Why QBism Is Not the Copenhagen Interpretation and What John Bell Might Have Thought of It.” So, in QBism, what one thinks of (and “one” here means a particular person) as classical or quantum has simply to do with one’s beliefs about the world outside.
If all this makes our heads reel, we should rest assured that we are not the only ones suffering. Physicists who are deeply immersed in these questions are not immune to being flummoxed. There are experts on Bohmian mechanics who profess to being clueless about QBism, QBists who think collapse theories are misguided, collapse theorists who claim the many worlds theory is extravagant nonsense, and advocates of many worlds who dismiss Bohmian mechanics as unnecessarily contrived. And, of course, all those who work on alternative interpretations of quantum mechanics think Copenhagen should be consigned to the dustbin of history. And the Copenhagen folks, well, they are yet to be decisively knocked down from their somewhat lofty perch.
Some young minds—à la Heisenberg when he was twenty-four—might cut through this clutter. There’s insight in a comment that Anton Zeilinger made to Fuchs, after Fuchs had given a talk on QBism that wasn’t terribly well received in Fuchs’s own estimation. Fuchs thought that the veteran Alain Aspect, who was in the audience, had written him off “ as a nutcase.” Even Mermin, a well-wisher, walked up to Fuchs and said, “ We need to talk. That was the worst talk you’ve ever given.” Zeilinger said, “ Great talk!” to which Mermin responded, “ No, it wasn’t!” Fuchs recalled (in his writings) that Zeilinger looked past Mermin and addressed him directly: “ You know what I would do when I was young, being dismissed by the old professors on the front rows of the seminar? I would not look to them as I spoke, but rather to the back rows where the young students were sitting. They were the ones ready to hear something new.”
—
It might well take someone new, young, and unbiased to make incontrovertible sense of the quantum world. I met physicists who are deeply convinced that they are on the correct path, as they must be to summon the energy needed to devote an entire lifetime to the pursuit of the nature of reality. I met physicists who remain dissatisfied with the status quo, uncommitted to any one path, as they should be to discern any cracks in the foundations of quantum mechanics. Surely, all interpretations and formalisms can’t be simultaneously correct. Maybe one of them is, maybe none are. Or, tantalizingly, maybe they are all touching the truth in their own way and giving us glimpses of a deeper reality. If so, the cracks will let the light through, and we’ll be better able to tell whether it goes through two doors at once. Or not.
Epilogue
WAYS OF LOOKING AT THE SAME THING?
D uring the late 1970s and early ’80s, Werner Erhard, the founder of est, organized a series of physics conferences, using the wealth from his self-help empire to indulge his fascination for physics. “ The est foundation’s physics conferences attracted star after star of the physics firmament,” wrote David Kaiser in his book How the Hippies Saved Physics: Science, Counterculture, and the Quantum Revival . One of these stars was Leonard Susskind, a theoretical physicist at Stanford University. One evening, Susskind was having dinner with Richard Feynman and Sidney Coleman at Erhard’s home in San Francisco. Erhard had also invited two young philosophers to the dinner. “They were spouting all sorts of philosophical verbiage, academic style philosophical verbiage . . . which it was clear that Feynman had no patience with and he took them apart. It was cruel. I don’t know how to describe what he did to them. With simple words, he took a pin and punctured their balloon in a way that you might call ugly, but the saving grace is that they were totally enchanted by him,” Susskind told me.
But despite his distaste for bloviating philosophers, Feynman “was possibly the most philosophical of all the physicists I ever knew,” said Susskind.
This side of Feynman was clearly evident during his lectures at Cornell. In one talk, he asked his audience to consider two theories, A and B, which have different takes on the nature of reality but which are mathematically equivalent, make the same empirical predictions, and are impossible to tell apart experimentally (he could have been talking about the Copenhagen interpretation and Bohmian mechanics, but he wasn’t—he was making a general point). Feynman argued that it’s important to understand that the philosophies behind A and B can lead us in different directions even if they are indistinguishable at some stage of the scientific process.
“ In order to get new theories, these two things are very far from equivalent. Because one gives a man different ideas than the other,” said Feynman.
For example, it might be possible to make a tiny tweak to A that isn’t possible with B. In which case, A can lead to a very different theory after the change. “ In other words, although they are identical before they are changed, there are certain ways of changing one which look natural, which don’t look natural in the other. Therefore, psychologically we must keep all the theories in our head,” said Feynman. “And every theoretical physicist that’s any good knows six or seven different theoretical representations for exactly the same physics and knows that they are all equivalent and that nobody is ever going to be able to decide which one is right at that level . . . but he keeps them in his head, hoping that they’ll give him different ideas.”
In Brisbane, Australia, Howard Wiseman tries to do exactly that: keep the different interpretations of quantum mechanics in mind, and see what emerges. One obvious intuition is that these theories and interpretations are each shining a light on a different aspect of the same reality. “A lot of progress in philosophy of science has been made by showing that things which were thought of as being separate are actually just different ways of look
ing at the same thing,” Wiseman told me.
This approach, when applied to quantum mechanics, is providing some surprising insights. Take collapse theories and a hidden variable theory like Bohmian mechanics—two very different views of the nature of reality. In Bohmian mechanics, if you consider a two-particle system, the wavefunction is a function of two variables, the position of particle A and the position of particle B; these particles also have actual positions, the hidden variables in the theory. Now, hypothetically, if you knew the exact position of particle A (which in practice you cannot, but let’s go with the argument) you can plug that into the equations and the wavefunction reduces—or effectively collapses—to a function of one variable, the position of particle B.
This inspired Wiseman to think of collapse theories—in which the wavefunction stochastically collapses at some rate at different points in spacetime—as theories in which the wavefunction is entangled with some other large system with hidden variables that we are unaware of. Changes to the values of these hidden variables, unbeknownst to us, can influence the wavefunction of the system we are studying—and it can seem like the wavefunction is subject to stochastic collapses. In this way of thinking about collapse theories, they become hidden variable theories, except that the variables are, well, truly hidden—and we are privy only to their effects.
Wiseman has also found ways of connecting Bohmian mechanics to the idea of many worlds. Take a single particle going through a double slit in Bohmian mechanics. If you knew its exact initial position and velocity, you could predict its exact trajectory through the apparatus. But in order to tally with the probabilistic predictions of quantum mechanics, Bohmian mechanics adds a dash of uncertainty to our knowledge about the initial state of the particle. Its starting position is given by a probability field, meaning the particle could be in one of many locations, with a different probability for each starting position. It’s like imagining a virtual ensemble of particles whose starting positions are dictated by this probability field, given by the modulus-squared of the wavefunction. The real particle is in one of those positions, we just don’t know which. Now, as this virtual ensemble evolves through the double slit, Bohmian mechanics gives us a virtual ensemble of trajectories, but, of course, only one of them is real—and for one run of the experiment, we’ll see the consequence of one such trajectory. We’ll find the particle landing somewhere on a screen, an outcome to which we could have assigned only a certain probability. And if you do this experiment over and over again, with the same virtual ensemble of particles, you’ll get a slew of trajectories, which taken together form an interference pattern.
Through Two Doors at Once: The Elegant Experiment That Captures the Enigma of Our Quantum Reality Page 21