Probability and the Mystery of Quantum Mechanics

Michele Caponigro

We discuss and review the philosophy and interpretations of quantum mechanics.Technically, QM is a set of mathematically formulated prescriptions that serve for calculations of probabilities of different measurement outcomes. The most serious problem has been the inability to demarcate with mathematical precision just where microscopic processes leave off and where macroscopic processes begin. The fact that observers report definite outcomes of experiments has, therefore, been a mystery. Explanations of this mystery have supplemented QM with a wide variety of additional assumptions.

Arthur I. Fine

Bryce de Witt

John Halpin

The nature of quantum mechanical probability has often seemed mysterious. To shed some light on this topic, the present paper analyzes the logical form of probability assignment in quantum mechanics. To begin the paper, I set out and criticize several attempts to analyze the form. I go on to propose a new form which utilizes a novel, probabilistic conditional and argue that this proposal is, overall, the best rendering of the quantum mechanical probability assignments. Finally, quantum mechanics aside, the discussion here has consequences for counterfactual logic, conditional probability, and epistemic probability.

David Papineau

An increasingly popular interpretation of quantum mechanics holds that in any genuinely chancy situation, all possible outcomes occur.1 For example, if the spin of a typical electron is measured in a given direction, then both 'up' and 'down' results will be registered. (True, 'up' and 'down' won't occur within the same 'branch of reality', for that would be inconsistent. Rather, the idea is that reality comes to contain two elements, with 'up' registered relative to one, and 'down' registered relative to the other.) This kind of 'many worlds' or 'many minds' interpretation of quantum mechanics has advantages and disadvantages. The main advantage is that it avoids any 'collapse of the wave function' and so avoids the measurement problem, mysterious non-local interactions, and the like. The most obvious disadvantage is that its burgeoning world of duplicate histories seems repugnant to common sense. Some commentators think that there is another disadvantage. They argue that this interpretation undermines itself by destroying any notion of objective probability. Quantum mechanics is, if anything, a theory which specifies the objective probabilities of certain results. But in what sense is there an objective probability for 'up' and 'down' in a spin measurement, if both results always happen? (Albert [1]; Albert and Loewer [3], [4]; Healey [5]; Squires [9]; Stein [8].) This looks like a good objection. But I shall show in this note that it is not. The proposed interpretation does leave objective probability as a rather mysterious notion. But it is no more mysterious on the proposed interpretation than on the conventional view of the world. This is not the place to go into details about the 'many minds'2 interpretation of quantum mechanics, but one point may help readers. If both the 'up' and 'down' results occur, why do we experience only one?

Diederik Aerts