Quantum theory may be more like Einstein's relativity than we think

In June this year, 300 people, including physicists, four Nobel Laureates, and journalists, converged on an island in the North Sea called Heligoland. It was here 100 years ago that Werner Heisenberg, seeking to escape to the treeless island to relieve a severe bout of hay fever, formulated the first equations of quantum mechanics.

Heligoland. Wikipedia. Dionysos1970

Even 100 years on, world-renowned experts in quantum theory cannot agree on what it means, whether there is a sharp boundary between the quantum and classical worlds, or even if we ourselves have a quantum nature.

The question comes down to: what happens when we observe something?

Some physicists, such as Anton Zeilinger, one of the 2022 Nobel Prize winners, for example, argue that the quantum world Heisenberg described does not even exist and that it is all in our heads. Observations are a purely mental phenomenon, and the wider universe does not give a fig whether we do or not.

This class of interpretations, the most popular of which is Quantum Bayesianism or QBism, interprets the outcomes of quantum measurements as representing subjective information, much as probability represents the subjective experience of abstract reality.

In this article, I want to talk about a new interpretation of QBism through the lens of a relativity-style philosophy. The standard metaphysical understanding of QBism is anti-realist, meaning that QBists tend to believe that as we interact with the quantum world, our observations participate in creating reality. But this isn’t the only way to interpret QBism. I will show that not only could you come up with a form of Einstein’s theory of spacetime that is similar to QBism but ultimately wrong, but that a realist like Einstein can embrace QBism without giving up on reality as an objective metaphysical concept. This ontological QBism is, as far as I know, not something that has been talked much about in the literature.

QBism draws inspiration from the work of Frank Ramsey, a gifted young Cambridge mathematician and philosopher of the early 20th century who died tragically young at age 26. (His equally gifted brother Michael, meanwhile, went on to become Archbishop of Canterbury.) Ramsey is best known among mathematicians for Ramsey theory, which is about the appearance of certain patterns in structures of sufficient size. Ramsey, however, was a polymath who challenged the reigning economist of the time, John Maynard Keynes, on the very nature of probability.

Frank Ramsey. 1921

Keynes argued in his seminal work A Treatise on Probability that probability and logic were objective knowledge, i.e., disembodied, God’s-eye reality. Ramsey said just the opposite. He proposed that probability was subjective.

If I say there is a 50% chance a coin lands heads or tails, that 50% is all in my head, according to Ramsey. The coin lands as it lands, and my interpretation of its probable behavior is more about my beliefs about what I will observe in the future than about any reality built into the coin.

Extending Ramsey’s concept to quantum theory, QBism points out that probability does not exist in classical physics except as a subjective belief about future experience. Therefore, why would the probability of quantum outcomes be any more objective?

In other words, if my chance of measuring a particle in one location versus another, such as when it passes through one of two holes, is a probability such as 50%, then that is only my subjective understanding of that particle’s location. The reality of the particle is beyond my ability to experience, in the same way that the reality of the coin in the future is until it happens. Once the future becomes the present, i.e., once the coin lands, its probability is 100% whatever happened, heads or tails. Once I detect the particle, its probability is 100% whatever I measure.

QBism argues that these are effectively the same situation. The future state of the coin does not exist until it is the present or the past. The particle likewise has no state until it is measured, other than my own beliefs about it. The wavefunction, which supposedly represents the probability of the particle, is, in fact, a human abstraction, a mathematical representation of a future measurement. I could, just as well, write a probability function for my coin, but that doesn’t mean that the probability function is the coin or that the coin carries the probability function as a real thing.

Take Schrödinger’s cat thought experiment. In this experiment, we have a cat in a box in a state of superposition. The Copenhagen interpretation claims that the cat is both dead and alive because its wavefunction contains both the dead cat state and the living cat state in superposition. When we open the box to observe the cat, the wavefunction collapses into one or the other.

QBism says that the cat being both dead and alive in superposition is all in our minds since there is no objective wavefunction. The state of the cat before we open the box is, rather, indeterminate in much the same way that the state of the coin before it lands is indeterminate.

The main difference between the classical coin and the quantum wavefunction is that the rules are different. The wavefunction is a wave that has both phase and magnitude, while probability only has magnitude. Also, two objects in quantum physics can share a single wavefunction, regardless of how far apart they are, while classically, probabilities are confined to single locations.

These, however, are merely different rules for how probability works in the quantum world. When I make a measurement, I update my own belief system with the new measurement information. The wavefunction, far from being a real property of particles, is merely my internal accounting system for my beliefs about measurements I might make. Every person has their own, and they need not agree. Rather, they take into account both what measurements I make and what I expect to hear from anyone else who makes measurements.

Take quantum entanglement, where two particles, A and B, prepared in a certain way, appear to “share” a quantum wavefunction. When one observer, Alice, measures a particle A’s spin, it appears to “collapse” the wavefunction for both particle A and particle B, thus influencing what Bob will measure for particle B and then communicate to Alice. QBism argues that there is no shared wavefunction, but rather this wavefunction represents Alice’s belief system about both what she will measure about particle A and what Bob will tell her about his measurement of particle B. When she makes her measurement, nothing collapses; rather, she updates her beliefs, and, when Bob tells her his measurements, she further updates them.

QBism claims that shared objective reality is a myth. When quantum experiments appear to send information faster than light, for example, that is a consequence of assuming that quantum probabilities (or any probabilities) describe an objective world and that to keep that objective world synchronized, some information must travel from one particle to another so that the second particle “knows” what state it should have when it is measured. In reality, quantum probabilities are merely private expectations of the individual.

Thus, QBism holds that claims like spooky action at a distance are fictions and that what is wrong is that we are applying classical probability rules to quantum systems.

As its biggest proponent, Christopher Fuchs says, such

violations tell us something deep about the structure of the world: the world resists being represented as a machine of causes and effects that we can see from the outside. Quantum theory is a tool for agents inside that world to navigate their experiences.

By rejecting objective reality as a playing field for probability, Fuchs argues,

Quantum theory does not tell us what the world is; it tells us how any agent should gamble on what the world will do in response to her actions.

This helps us to tease apart what is going on in quantum theory versus what is going on out in the world. Quantum theory is about my own belief system and how it should operate in a quantum world. The quantum world itself, meanwhile, follows rules of its own that, when they provide feedback to my belief system, correspond to quantum theory.

Thus, for example, the gambler who understands roulette will know that the ball lands on black 18/38 times. While there is a relationship between that probability and the design of the roulette wheel and the motion of the ball, the gambler’s belief system itself is not encoded into objective reality. The ball and wheel are simply obeying the laws of physics.

In the same way, the design of a quantum experiment sets up a certain belief system in the mind of the experimenter, but the particles and detectors in such an experiment are merely obeying laws of physics. Quantum theory can only tell us how the experimenter should gamble on certain outcomes.

Mind you, QBists do believe there is an underlying physical reality, but they reject the Einsteinian notion that underlying reality can be described independently of the observer. There is no God’s eye view of quantum reality as far as we mere mortals are concerned.

QBists also often take a page out of physicist John Wheeler’s book in believing that reality is participatory, meaning that when we interact with the world, making measurements and observations, reality comes into being. Thus, discovery is a process of continual creation.

As I mentioned in the introduction, this metaphysical framework isn’t necessary to QBism since all that is required is some kind of underlying reality that constrains all agents’ probabilities to obey quantum rules.

There are hints in QBism itself that could lead to a more objective understanding of reality. One of these is that QBism is only the total of all agents’ belief systems. These agents can be real or made up. Thus, each agent represents, in a sense, a space of probabilities with a point of view.