Probability and Locality: Determinism Versus Indeterminism in Quantum Mechanics
Abstract
Quantum mechanics is often taken to be necessarily probabilistic. However, this view of quantum mechanics appears to be more the result of historical accident than of careful analysis. Moreover, quantum mechanics in its usual form faces serious problems. Although the mathematical core of quantum mechanicsquantum probability theory does not face conceptual difficulties, the application of quantum probability to the physical world leads to problems. In particular, quantum mechanics seems incapable of describing our everyday macroscopic experience. Therefore, several authors have proposed new interpretations including (but not limited to) modal interpretations, spontaneous localization interpretations, the consistent histories approach, and the Bohm theoryeach of which deals with quantummechanical probabilities differently. Each of these interpretations promises to describe our macroscopic experience and, arguably, each succeeds. Is there any way to compare them? Perhaps, if we turn to another troubling aspect of quantum mechanics, nonlocality. Non locality is troubling because prima facie it threatens the compatibility of quantum mechanics with special relativity. This prima facie threat is mitigated by the nosignalling theorems in quantum mechanics, but nonetheless one may find a 'conflict of spirit' between nonlocality in quantum mechanics and special relativity. Do any of these interpretations resolve this conflict of spirit?. There is a strong relation between how an interpretation deals with quantummechanical probabilities and how it deals with nonlocality. The main argument here is that only a completely deterministic interpretation can be completely local. That is, locality together with the empirical predictions of quantum mechanics (specifically, its strict correlations) entails determinism. But even with this entailment in hand, comparison of the various interpretations requires a look at each, to see how nonlocality arises, or in the case of deterministic interpretations, whether it arises. The result of this investigation is that, at the least, deterministic interpretations are no worse off with respect to special relativity than indeterministic interpretations. This conclusion runs against a common view that deterministic interpretations, specifically the Bohm theory, have more difficulty with special relativity than other interpretations.
 Publication:

Ph.D. Thesis
 Pub Date:
 January 1995
 Bibcode:
 1995PhDT........77D
 Keywords:

 BOHM THEORY;
 Philosophy; Physics: General