Quantum Bayesianism
Physics is often used to describe modern-day, macroscopic phenomena, or at least that is the way it is often taught. However, with the last century came an understanding of quantum phenomena, basically a fundamental set of rules and laws that apply across a wider set of systems. Namely, quantum can accurately describe both subatomic and macroscopic systems, but the macroscopic physics cannot describe such subatomic scenarios. Such confusion has resulted in quantum mechanics being very unsettling as it introduces the notion of “observing” and “measuring”. This is best exemplified by the question, “shouldn’t physics be talking about what is before it starts talking about what will be seen and who will see it?” (Fuchs). Such concerns have been deceptively ameliorated through the use of collapsing states, collections of discrete quantum states called multi-verses, and particles flying around due to wavefunctions. From all this jargon, we can conclude one thing: quantum mechanics is a very confusing field in need of a way to unify it’s theories comprehensively. And this is where probability comes into play. In class we had discussed Bayes’ rule as a way that, when given two events, to determine the likelihood of one of the events happening based on an effect(s). In essence, Bayes’ rule was a way to quantify the likelihood of interdependent events happening by relating current beliefs to prior beliefs. The more updates, the more accurate your prediction of the likelihood of a certain outcome became. Quantum mechanics is merely an extension of Bayes’ rule.
One thing that the founders of quantum mechanics could all agree on is the concept of information, and that there are no such things as quantum states. Such quantum states are merely expressions of information. By making such an assumption, we can eliminate the problems of having various objectified-state interpretations. In addition, we can treat probability as a way to test if a value or a set of values make sense (consistent/coherent) or don’t make sense (inconsistent/incoherent). This is where Bayesian probability comes into play as it is a “calculus of consistency”; however, it’s usually reserved for a person’s degree of belief in terms of making a decision. Unfortunately, it does not tell us how to find the correct value; it just tells us which ones are the incorrect ones.
Where Bayesian probability and quantum mechanics intersect is from where we generate the belief that something in our given set of values is inconsistent. Specifically, both approaches use no external criteria; rather, they judge adequacy from the inside, from the beliefs that are intrinsic to the system. In terms of quantum mechanics, that means there is no true quantum state as you use quantum mechanics to calculate probabilities. This is in contrast to assigning probabilities to a set of measurements, which is basically the same as assigning quantum states and is an invalid approach. By using Bayesian probabilities, we can effectively give each quantum state a “home” characterized by its probability that allows the quantum state to exist. This is just how in class we used Bayesian probabilities to not derive what actually happened, but what were the most likely possibilities implied by a certain reaction and/or belief.
Through this Bayesian way of interpreting quantum states, we can end the age-long conflict over what is a true quantum state. More often than not, people usually say that the right quantum state is the one if the observer had all the information and no uncertainty. This is rebutted with the argument that if the observer had all the information, then it’s not a true quantum state as it has the observer’s bias. By using Bayes’ Rule, we no longer think of the observer’s biases. Instead, we just think of a measurement and the data produced from that as a reaction, similar to how we use Bayes’ rule in class to figure out what action to take as a consequence of other events. Instead of finding the absolute truth, we settle for what is given to us and try to make the best of that situation by considering the probabilities of if the event did or did not happen and the pertinent phenomena. This way, we can bypass the observer entirely and wholeheartedly see the inconsistencies of the system with respect to the system, as opposed to finding an absolute.
Current research is being done as to answer why, if quantum theory really is just a super-exaggerated use of Bayes’ rule, are we still using several complex mathematical operators and functions that finally end in probability expressions. The goal of researchers at the Perimeter Institute is to try and express Bayes’ rule to express all of quantum theory while also reconcile complex Hilbert spaces and linear operators to make it a more universal and well-understood platform to operate upon. In fact, researchers took the Born rule that gives rise to quantum theory and converted it into a Quantum Law of Total Probability that consists entirely of describing quantum states and wavefunctions through probabilities, but not without its caveats. If an observer interacts with a quantum system, he’ll begin deviating form the Law of Total probability as he tries to create factual calculations. Therefore, researchers are trying to struggle with is it possible to characterize the observer’s actions through probability and Bayes’ rule, or if it is simply just not possible…. Bayes’ rule is at the center of it all
sources:
http://www.cap.ca/sites/cap.ca/files/article/1402/apr10-offprint-fuchs.pdf