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Philosophy of Science

Quantum Mechanics and 3N-Dimensional Space

Bradley Monton

Published Dec 1, 2006• 90 citations
Publisher

Abstract

I maintain that quantum mechanics is fundamentally about a system of N particles evolving in three-dimensional space, not the wave function evolving in 3N-dimensional space.
DOI
10.1086/518633

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In quantum mechanics, the wave function of a N-body system is a mathematical function defined in a 3N-dimensional configuration space. We argue that wave function realism implies particle ontology when assuming: (1) the wave function of a N-body system describes N physical entities; (2) each triple of the 3N coordinates of a point in configuration space that relates to one physical entity represents a point in ordinary three-dimensional space. Moreover, the motion of particles is random and discontinuous.
The question concerning the dimensionality of our fundamental physical space is arguably one of the most profound cases of underdetermination in non-relativistic quantum mechanics. Those who take the wave function to represent fundamental reality think that the world fundamentally has 3N dimensions, where N is the total number of particles. Against this, various versions of quantum mechanics postulate certain entities in 3-dimensional space as fundamental. An important argument for the latter view suggests that this is not strictly a case of underdetermination of theory by evidence, because a view that does not include some entities in 3-dimensional space fails to explain how there can be empirical evidence for quantum mechanics in the first place. A critical assessment of this argument will clarify how the debate on dimensionality depends on the evaluation of non-empirical virtues which is well-known from other debates on underdetermination.