Schrödinger's original interpretation of the Schrödinger equation had many attractive features lost in later interpretations of the quantum theory. But that interpretation runs into a number of formidable well-known and not so well-known objections. I argue, following the methodological precepts of Paul Feyerabend, that we need not regard any of these objections as fatal, provided we are prepared to opt for a number of bold and rather radical mathematical and theoretical conjectures. These would amount jointly to the conjecture that a fully time-symmetric consistently classically interpreted non-second-quantized analogue of existing quantum field theory would (pace Jaynes, Tomonaga, Bell, and others) ultimately prove predictively equivalent to orthodox second-quantized theory.

Introduction

Schrödinger initially proposed his equation as a classical theory of matter waves directly analogous to Maxwell's theory of electromagnetic waves. |ψ|2 represented a classical charge density functioning in the ordinary classical way as a source of electromagnetic fields, and acted on by these fields via the potential term in the matter–wave equation. This is a theory of coupled classical fields with no probabilities entering into its interpretation, and from a modern point of view it can be thought of in terms of the coupled Dirac and Maxwell fields, without second-quantization and interpreted in a purely classical manner.