QBism is a development of Quantum Bayesianism. This stands for applying ‘Bayesian probability‘ to the probabilities in quantum mechanics. It means that the probabilities of events in the world, even the outcomes of subatomic experiments, are defined solely by what the individual has directly experienced and observed in the world up until now. Yes, it seems to make no sense whatsoever, but it works. As the authors state, this:

removes the paradoxes, conundra, and pseudo-problems that have plagued quantum foundations for the past nine decades (Fuchs et al., 2013, 1)

But this is so deeply alien to our current way of thinking it seems inconceivable. The massive challenge to take on is that everything unobserved is indeterminate, unreal. Moreover, each world is personal to the individual. It is nothing like the world as we know it.

This, however, is not the whole story. There is a real world, and this is the basis of all physical reality. And it all works and exists just as we think it does. What is shown here is that both types of world are real, and this makes complete sense of the whole thing. In this context QBism can be seen as evidence for the relative type of world. The ‘superworld’ is the ontology.

Bayesian Probability

Bayesian probability is a longstanding technical method of calculating probabilities in everyday situations. The science of probabilities goes back centuries, using basic methods of counting how often something specific happens. Each side of a tossed coin comes up half the time, so the probability is one half. This is called frequentist probability. Bayesian probability, based on Bayes’ theorem, is a well-established technique used when there is no frequentist data. Essentially, this is based on relevant data of events in the past, and an analysis of how this data affects the probabilities of possible events in the future. In other words, probability is calculated from the logical expectations based on previous events. The successful recovery of a ship lost at sea is a famous example. The revolutionary nature of QBism is saying that Bayesian probabilities are what govern interactions down at the quantum level.

The wave function is the fundamental definition of physical reality, as described in Quantum Theory. QBism takes the radical stance that the wave function is not an objective definition of reality, but a purely subjective phenomenon. In other words, as Fuchs the main author argues, the wave function does not describe the world, it describes the observer. In his interview with Quanta Magazine he goes so far as to say “Quantum mechanics is a law of thought.” (Gefter, 2015). Which of course is diametrically opposite to the current worldview of modern physics. As he says, he is aiming to cause some good natured mischief.

It sounds crazy, but the physics clearly works. If we assume that physical reality is determinate solely where observed, the paradoxes (specifically measurement and locality) go away. But how do we explain what it really means? The authors claim that this means there is no objective reality of any kind. What is more, this carries the bizarre implication that different people actually live in different versions of the world. As the authors state:

This means that reality differs from one agent to another. (2013, 3)

The resolution presented here is that all this weirdness is the correct description of just one type of world, the subjective physical reality of each conscious individual. But there is nonetheless an ordinary objective physical reality as well, the quasi-classical world of the current worldview.

Two Types of Real World

QBism is not an intrinsically new concept. As quoted in Quantum Theory, Vaidman defines this type of relative world as a well known alternative to the standard concept of the quasi-classical world. The new concept presented here is the explanation of the relative type of world, what it is actually made of, the ontology. The world of the conscious individual is a superposition of quasi-classical worlds, a ‘superworld’. And this makes sense of the whole thing.

  • Firstly this provides the physical explanation of the QBism type of world, by definition indeterminate except where experienced.
  • Secondly, this explains is why the world is probabilistic. For any given future event, the probability is the percentage of worlds in the class in which this event happens. In the case of Schrödinger’s cat this is half and half.
    This is essentially the counting worlds approach of Deutsch (1999) and Żurek (2005).
  • Thirdly this explains why quantum mechanics is Bayesian. The probabilities are determined by the observations because this is the only information in the system in this physical frame of reference.

The Born Rule

How do we know this is right? Fuchs has discovered that the ‘Born rule’ can be rewritten almost entirely in terms of this Bayesian probability.

The Born rule is the law in quantum mechanics that gives the probability of a specific outcome to an observation of a quantum system. This is the exercise of the collapse dynamics in quantum mechanics.

So Fuchs has demonstrated that the Bayesian rules of everyday probability, based solely on the observations made, apply directly to the fundamental components of physical reality in the collapse dynamics. So it would seem we have evidence that this dynamics is in fact a phenomenon operating in the relative world, rather than in the objective physical world as we think of it.

This can be seen as proof of the relative world in action. In principle the quantum state defining reality is immutable. It is a permanent component of existence. It cannot change. Collapse is the change of the quantum state. It can only be a phenomenon meta to the quantum state, somehow contextual to. But …

Again the superworld makes sense of all this. Collapse is simply the result of the redefinition of the class of worlds in the superworld, a second-logical-type phenomenon. On observation, the world hologram is changed, and thus exists in a different class of worlds forming the superworld. Naturally, therefore, the collapse dynamics operates solely in the superworld, and there is nothing of this nature in the ordinary objective world.

Collapse Happens Only In Consciousness

This is of tremendous importance because it tells us the change apparently induced in a physical system under observation is nothing of the sort. It means this can only be a phenomenon operating purely in the subjective frame of reference, the inside view of the personal superworld. As stated by mathematician Euan Squires, in a quantum experiment with two outcomes:

The complete description of the “physics” in orthodox quantum theory … contains both terms, i.e. both “results”. The unique result of which I am aware does not exist in physics – but only in consciousness. The Born rule does not have anything to say about physics – it says something about consciousness. (1996, 3)

This of course resolves the measurement problem. Collapse happens only in consciousness. Equally of course, consciousness cannot be allowed in the physics, unless we can come up with a reason for this differentiation. The resolution is the second-logical-type nature of the world of the inside view, the superworld. The physical reality experienced by consciousness is the superposition of all the worlds in which this world hologram exists, a ‘class-of-worlds-as-a-world’. And this world operates exactly as described by QBism.

The Born rule has never been derived from any principles of physics. It is simply a formula that fits all the observations we make. Fuchs is showing this is a Bayesian rule. This remarkable result is described in a very accessible manner by Hans von Baeyer in his article Quantum Weirdness? It’s All in Your Mind (2013). As he states in the overview, QBism sweeps away the bizarre paradoxes, but the cost is that “… quantum information exists only in your imagination”. This is naturally the case in the superworld. The world hologram, the imagination, defines the determinacy of the superworld. But at the same time the objective physical reality is still the fundamental type of world. This is physical reality at the first level of logical type, as each element of the class-of-worlds-as-a-world.

It’s All Right

Fuchs holds that quantum mechanics is a law of thought, but here it is proposed that it is more correctly considered as a law of observations in the mind – which is the second-logical-type ontological domain. In other words, the presumed epistemology, the science of how we know, is also the effective ontology, the physics of what is. As Don Page remarks, the correct many-worlds interpretation is a “many-perceptions” framework (2011, 1). On this basis QBism is a fully correct interpretation of quantum mechanics.