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

The mathematical structure of realist quantum theories has given rise to an interesting ongoing 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? In this essay, I review the debate between the 3N-Fundamentalists (wave function realists) and the 3D-Fundamentalists (primitive ontologists). Instead of framing the debate as putting different weights on different kinds of evidence, I shall evaluate them on how they are overall supported on the basis of: (1) the dynamical structure of the quantum theory, (2) our perceptual evidence of the 3D-space, and (3) mathematical symmetries in the wave function. I show that the common arguments based on (1) and (2) are either unsound or incomplete. Completing the arguments, it seems to me, render the overall considerations based on (1) and (2) roughly in favor of 3D-Fundamentalism. A more decisive argument, however, is found when we consider which view leads to a deeper understanding of the physical world. In fact, given the deeper topological explanation from the unordered configurations to the Symmetrization Postulate, we have strong reasons counting in favor of 3D-Fundamentalism. I therefore conclude that our current overall evidence strongly favors the view that our fundamental physical space in a quantum world is 3-dimensional rather than 3N-dimensional. I also outline future lines of research where the evidential balance can be restored or reversed. To push the analysis further, I draw some lessons from this case study to the debate on theoretical equivalence.