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How Bayesian Probability Might Help Provide a Realist Interpretation of the Quantum Formalism

John Hemp

Published Aug 1, 2019• 0 citations
OpenAlex

Abstract

We offer a realist interpretation of non-relativistic quantum mechanics in which dynamical properties are properly possessed by the system in question, and are supposed to have definite values at any time. Like the QBists, we employ Bayesian probability, but we adopt something closer to the Bayesian statistics of E. T. Jaynes than to the subjective Bayesian statistics of B. de Fenetti employed by the QBists. Accordingly, we view calculated Bayesian probabilities as rational degrees of expectation of dynamical property values rather than as personal degrees of expectation of future (measurement) experiences. Probabilities are, for us, based on knowledge of the value of some dynamical property of the system, not on knowledge of previous experiences unassociated with system dynamical properties. As some Bayesians might, we take a probability equal to 1 not generally to indicate certainty but only (full) expectation; and we disallow probabilities of conjunctions of propositions claiming incompatible properties. Then, by reinterpreting and adding a little to the quantum formalism, we argue that we can maintain the advantages of the QBist interpretation. So, for us (as for the QBists), there is no unexplained collapse of the wave function, no need for ‘spooky action at a distance’, and no problem raised by the double slit experiment, the Kochen-Specker paradox or Bell type theorems. By holding on to a realist perspective, modelling (of ideal measurements, of system preparation processes etc.) is possible, and we can claim certain dynamical laws of quantum mechanics without leading to contradiction.

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We offer a realist interpretation of non-relativistic quantum mechanics in which dynamical properties are properly possessed by the system in question, and are supposed to have definite values at any time. Like the QBists, we employ Bayesian probability, but we adopt something closer to the Bayesian statistics of E. T. Jaynes than to the subjective Bayesian statistics of B. de Fenetti employed by the QBists. Accordingly, we view calculated Bayesian probabilities as rational degrees of expectation of dynamical property values rather than as personal degrees of expectation of future (measurement) experiences. Probabilities are, for us, based on knowledge of the value of some dynamical property of the system, not on knowledge of previous experiences unassociated with system dynamical properties. As some Bayesians might, we take a probability equal to 1 not generally to indicate certainty but only (full) expectation; and we disallow probabilities of conjunctions of propositions claiming incompatible properties. Then, by reinterpreting and adding a little to the quantum formalism, we argue that we can maintain the advantages of the QBist interpretation. So, for us (as for the QBists), there is no unexplained collapse of the wave function, no need for ‘spooky action at a distance’, and no problem raised by the double slit experiment, the Kochen-Specker paradox or Bell type theorems. By holding on to a realist perspective, modelling (of ideal measurements, of system preparation processes etc.) is possible, and we can claim certain dynamical laws of quantum mechanics without leading to contradiction.
Quantum Bayesianism, or QBism, is a recent development of the epistemic view of quantum states, according to which the state vector represents knowledge about a quantum system, rather than the true state of the system. QBism explicitly adopts the subjective view of probability, wherein probability assignments express an agent’s personal degrees of belief about an event. QBists claim that most if not all conceptual problems of quantum mechanics vanish if we simply take a proper epistemic and probabilistic perspective. Although this judgement is largely subjective and logically consistent, I explain why I do not share it.
QBism is currently one of the most widely discussed 'subjective' interpretations of quantum mechanics. Its key move is to say that quantum probabilities are personalist Bayesian probabilities and that the quantum state represents subjective degrees of belief. Even probability-one predictions are considered subjective assignments expressing the agent's highest possible degree of certainty about what they will experience next. For most philosophers and physicists this means that QBism is simply too subjective. Even those who agree with QBism that the wave function should not be reified and that we should look for alternatives to standard Psi-ontic interpretations often argue that QBism must be abandoned because it detaches science from objectivity. The problem is that from the QBist perspective it is hard to see how objectivity could enter science. In this paper, I introduce and motivate an interpretation of quantum mechanics that takes QBism as a starting point, is consistent with all its virtues, but allows objectivity to enter from the get-go. This is the view that quantum probabilities should be understood as objective degrees of epistemic justification.
Abstract In the 1950s and 1960s it was causing interest among physicists that in the formalism of quantum mechanics (complex-valued) ‘probability amplitudes’ obeyed laws similar to the laws obeyed by probabilities in the ordinary probability calculus. But this did not then lead decisively to the claim that probabilities should be represented by complex numbers. It became fashionable instead to regard probability amplitudes as an abstract concept from which actual probabilities could be derived by taking the squared moduli of the amplitudes. In this monograph, however, we make another attempt to show how probability amplitudes might after all be identified with actual probabilities. To do this, probability itself is interpreted in a rational Bayesian manner (i.e. as an extension of logic) and a new (complex-valued) probability theory is formulated that incorporates the uncertainty principle (i.e. that takes account of the fact that acquisition of knowledge of a quantum mechanical process generally interferes with it). Taking this probability theory as the new logic of science, and assuming certain physical laws and properties of matter, an interpretation of non-relativistic quantum mechanics is built up. It is consistent with the usual quantum mechanical formalism but allows a clear distinction to be made between the physical world and our knowledge of it.
QBism is a recently developed version of Quantum Bayesianism. QBists think that the primitive concept of experience is the central subject of science. QBism refuses the idea that the quantum state of a system is an objective description of this system. It is a tool for assigning a subjective probability to the agent's future experience. So quantum mechanics does not directly say something about the "external world". A measurement (in the usual sense) is just a special case of what QBism calls experience and this is any action done by any agent on her external world. The result of the measurement is the experience that the agent gets from her action on her personal world. For Qbists, this way of seeing the measurement helps rejecting any non-local influences. We will examine if these claims are robust and will show that a certain number of issues needs to be clarified in order to get a coherent picture. Depending on the way these necessary clarifications are made, the global image given by Qbism can vary from pure instrumentalism to interpretations making the observer play a radical role.
Quantum mechanics is the most useful and powerful theory physicists have ever devised. Yet today, nearly 90 years after its formulation, disagreement about the meaning of the theory is stronger than ever. New interpretations appear every year. None ever disappear. Probability theory is considerably older than quantum mechanics and has also been plagued from the beginning by questions about its meaning. And quantum mechanics is inherently and famously probabilistic. For the past decade, Carl Caves, Chris Fuchs, and Rüdiger Schack have been arguing that the confusion at the foundations of quantum mechanics arises out of a confusion, prevalent among physicists, about the nature of probability [1]. They maintain that if probability is properly understood, the notorious quantum paradoxes either vanish or assume less vexing forms. Most physicists have a frequentist view of probability: Probabilities describe objective properties of ensembles of “identically prepared” systems. Caves, Fuchs, and Schack take a personalist Bayesian view: An agent assigns a probability p to a single event as a measure of her belief that the event will take place [2]. Such an agent is willing to pay less than $ p for a coupon that will pay her $1 if the event happens, and she is willing to underwrite and sell such a coupon for more than $ p . Surprisingly, the standard rules for probability follow from the requirement that an agent should never face certain loss in a single event. (For example, if p exceeded 1, she would pay more than $1 for a coupon that returned at most $1; if p were negative, she would pay somebody to take a coupon from her that might cost her another $1.) Avoiding certain loss is the only constraint on an agent's probability assignments. The probability of an event is not inherent in that event. Different agents, with different beliefs, will in general assign different probabilities to the same event. The personalist Bayesian view of probability is widely held [3], though not by many physicists. It has profound implications for the meaning of quantum mechanics, which Fuchs and Schack call quantum Bayesianism—QBism for short. Since quantum states determine probabilities, if probabilities are indeed assigned by an agent to express her degree of belief, then the quantum state of a physical system is not inherent in that system but assigned by an agent to encapsulate her beliefs about it. State assignments, like probabilities, are relative to an agent.
By comparing Schrödinger's cat with its classical counterpart, I show that a quantum superposition should be understood as an expectation over possible eigenstates weighted by wave-like probabilities. Upon the occurrence of a certain event, the quantum system is randomly realized into one of the possible eigenstates due to its intrinsic stochasticity. While the randomness of a single realization cannot be controlled or predicted, the overall distribution can be regulated via experimental setup and converges as the number of events increases. A measurement is indeed an activity employing a certain event to convert a quantum effect into a macroscopic outcome. Consequently, the puzzling concepts of wavefunction collapse, many worlds, and decoherence become unnecessary for understanding quantum superposition. This expectation-realization interpretation, which integrates probability theory with wave mechanics, can also be extended to quantum pathways. Moreover, it reframes tests of Bell's inequalities as validating the wave-like probability nature of quantum mechanics, with no need to invoke the mysterious notions of quantum non-locality and "spooky action at a distance".