Quantum Mechanics: An Empiricist View

By Bas C. Van Fraassen | Go to book overview

5 New Probability Models and Their Logic

No causal model can fit the phenomena that violate Bell's Inequalities. What sorts of models will fit? That is again an empirical question, and the exact answer cannot be a priori. Quantum theory will give us one answer, by offering models which are not causal, and do allow such violations. But the theory is not empirically empty, so these models too will have their limits.

To understand this situation, to see how this question could be answered at all, we need to broaden our concept of statistical model. This wider concept must allow for phenomena that fit into no Common Cause pattern. It must also point the way to some interesting model constructions that are worth exploring, and prepare us for the study of quantum mechanics proper. To this end I shall introduce the general notion of geometric probability models, of which the quantum-theoretical models will be a natural development, abstractly speaking. This will also introduce us to some basic elements of quantum logic (so-called) and its role in interpretation. This role is important, in my view, but there will be no suggestion of any revolution in logic generally.


1 When Are Values Indeterminate?

Much undeserved mystery has surrounded Bell's results. The proof that causality is lost, that conceivable and apparently actual phenomena rule out determinism and even the Common Cause pattern, is astonishing. But the argument is perfectly intelligible to the classical mind. The logic and the ideas about probability involved in the argument are also all of a perfectly familiar sort. Yet it has been proposed that a proper appreciation requires us to turn to non-classical logic and/or non-classical probability theory.

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