The Theory of (Exclusively) Local Beables

TL;DR

This paper introduces a local beables theory derived from pilot-wave theory that eliminates the wave function on configuration space, replacing it with local fields in physical space, offering a new perspective on quantum causation.

Contribution

It constructs a local beables theory based on pilot-wave ideas that does not include the configuration space wave function, providing a novel, empirically viable quantum framework.

Findings

Reproduces standard quantum predictions for spinless non-relativistic particles with analytic wave functions.

Replaces the configuration space wave function with local fields in physical space.

Offers a new perspective on causation in pilot-wave theories.

Abstract

It is shown how, starting with the de Broglie - Bohm pilot-wave theory, one can construct a new theory of the sort envisioned by several of QM's founders: a Theory of Exclusively Local Beables (TELB). In particular, the usual quantum mechanical wave function (a function on a high-dimensional configuration space) is not among the beables posited by the new theory. Instead, each particle has an associated ``pilot-wave'' field (living in physical space). A number of additional fields (also fields on physical space) maintain what is described, in ordinary quantum theory, as ``entanglement.'' The theory allows some interesting new perspective on the kind of causation involved in pilot-wave theories in general. And it provides also a concrete example of an empirically viable quantum theory in whose formulation the wave function (on configuration space) does not appear -- i.e., it is a theory according to which nothing corresponding to the configuration space wave function need actually exist. That is the theory's \emph{raison d'etre} and perhaps its only virtue. Its vices include the fact that it only reproduces the empirical predictions of the ordinary pilot-wave theory (equivalent, of course, to the predictions of ordinary quantum theory) for spinless non-relativistic particles, and only then for wave functions that are everywhere analytic. The goal is thus not to recommend the TELB proposed here as a replacement for ordinary pilot-wave theory (or ordinary quantum theory), but is rather to illustrate (with a crude first stab) that it might be possible to construct a plausible, empirically viable TELB, and to recommend this as an interesting and perhaps-fruitful program for future research.