Deterministic Interpretations of the Quantum Theory

Joseph Shaffer

Anthony Sudbery

Examines a suggestion by Bell (1984) that a deterministic model might be furnished by the continuum limit of an objective stochastic model which he has proposed for quantum field theory on a lattice. The virtues of models of Bell's type for general quantum systems are discussed, and it is shown that for a system of a fixed number of particles such a model does yield the deterministic de Broglie-Bohm model in an appropriate limit. It is argued, however, that a deterministic limit is unlikely to emerge from a quantum field theory capable of describing particle production and decay. An interpretation of quantum field theory is proposed which has the advantages of Bell's interpretation but is closer to conventional quantum mechanics.

Lev Vaidman A

Gerard ’t Hooft

A sharper formulation is presented for an interpretation of quantum mechanics advocated by the author. We claim that only those quantum theories should be considered for which an ontological basis can be constructed. In terms of this basis, the entire theory can be considered as being deterministic. An example is illustrated: massless, noninteracting fermions are ontological. Subsequently, as an essential element of the deterministic interpretation, we put forward conservation laws concerning the ontological nature of a variable, and the uncertainties concerning the realization of states. Quantum mechanics can then be treated as a device that combines statistics with mechanical, deterministic laws, such that uncertainties are passed on from initial states to final states.

Ralph Schiller

David Hodgson

Abstract This article begins with an account of how quantum physics represents physical systems and how it differs from classical physics, focusing on three features of quantum theory that have been thought to be relevant to free will: indeterminism, nonlocality, and observer-participation. It examines various interpretations of quantum theory, including deterministic interpretations, such as the “many-worlds” interpretation and hidden variable interpretations. It considers other topics, puzzles about Schrodinger's cat and a recent challenge to deterministic interpretations of quantum theory, called “the free will theorem” by mathematicians John Conway and Simon Kochen. It discusses the views of three thinkers who have argued in different ways for the relevance of quantum theory to both consciousness and free will: mathematician Roger Penrose, physicist Henry Stapp, and neuroscientist and Nobel laureate John Eccles.