Our Fundamental Physical Space: An Essay on the Metaphysics of the Wave Function

TL;DR

This paper argues that in quantum theories, our fundamental physical space is more likely to be three-dimensional rather than the high-dimensional configuration space, based on topological and conceptual considerations.

Contribution

It provides a philosophical and topological analysis favoring 3D space as fundamental over the 3N-dimensional configuration space in quantum theory.

Findings

Evidence favors 3D fundamental space over 3N-dimensional space.

Topological explanations support 3D space as more fundamental.

The debate informs the understanding of theoretical equivalence in physics.

Abstract

The mathematical structure of realist quantum theories has given rise to a debate about how our ordinary 3-dimensional space is related to the 3N-dimensional configuration space on which the wave function is defined. Which of the two spaces is our (more) fundamental physical space? I review the debate between 3N-Fundamentalists and 3D-Fundamentalists and evaluate it based on three criteria. I argue that when we consider which view leads to a deeper understanding of the physical world, especially given the deeper topological explanation from the unordered configurations to the Symmetrization Postulate, we have strong reasons in favor of 3D-Fundamentalism. I conclude that our evidence favors the view that our fundamental physical space in a quantum world is 3-dimensional rather than 3N-dimensional. I outline lines of future research where the evidential balance can be restored or reversed. Finally, I draw lessons from this case study to the debate about theoretical equivalence.