The Theory of (Exclusively) Local Beables

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.

32 pages, 2 figures

References in corpus (4)

• Dynamical Origin of Quantum Probabilities
• On Galilean and Lorentz invariance in pilot-wave dynamics
• On the Role of Density Matrices in Bohmian Mechanics
• What's wrong with Einstein's 1927 hidden-variable interpretation of quantum mechanics?

Cited by in corpus (16)

• J.S. Bell's Concept of Local Causality
• Applied Bohmian Mechanics
• Bell's Theorem and Locally-Mediated Reformulations of Quantum Mechanics
• The Pilot-Wave Perspective on Spin
• Computation of many-particle quantum trajectories with exchange interaction: Application to the simulation of nanoelectronic devices
• Entangled Quantum Dynamics of Many-Body Systems using Bohmian Trajectories
• Semi-classical approximations based on Bohmian mechanics
• Weak Measurement and (Bohmian) Conditional Wave Functions
• Towards a novel approach to semi-classical gravity
• A local $\psi$-epistemic retrocausal hidden-variable model of Bell correlations with wavefunctions in physical space
• A representation of the wave function on the three-dimensional space
• Implications of a deeper level explanation of the deBroglie-Bohm version of quantum mechanics
• Resonant tunneling diodes in semiconductor microcavities: modeling polaritonic features in the THz displacement current
• Laws of Nature and the Reality of the Wave Function
• Replacing the Singlet Spinor of the EPR-B Experiment in the Configuration Space with two Single-Particle Spinors in Physical Space
• Is gravitational entanglement evidence for the quantization of spacetime?