Uniting the wave and the particle in quantum mechanics (1903.04087v3)

Abstract: We present a unified field theory of wave and particle in quantum mechanics. This emerges from an investigation of three weaknesses in the de Broglie-Bohm (deBB) theory: its reliance on the quantum probability formula to justify the particle law; its insouciance regarding the absence of reciprocal action of the particle on the guiding wave; and its lack of a unified model to represent its inseparable components. These problems are resolved within an analytical framework by requiring that the wave-particle composite exhibits no observable differences with a quantum system. This scheme is implemented by appealing to symmetries (global gauge and spacetime translations) and imposing equality of the corresponding conserved Noether densities (matter, momentum and energy) with their Schrodinger counterparts. In conjunction with the condition of time reversal covariance this implies the deBB law for the particle where the quantum potential mediates the wave-particle interaction (we also show how the time reversal assumption may be replaced by a statistical condition). The method clarifies the nature of the mass of the composite, and its energy-momentum conservation laws. Our principal result is the unification of the Schrodinger equation and the deBB law in an inhomogeneous equation whose solution amalgamates the wavefunction and a singular soliton model of the particle in a unified spacetime field. The wavefunction suffers no reaction from the particle since it is the homogeneous part of the unified field to whose source the particle contributes. The theory applies to many-body systems. We review the objections of de Broglie to the pilot-wave theory and suggest that our field-theoretic model provides a realization of his hitherto unfulfilled double-solution programme. A revised set of postulates for the deBB theory is given in which the unified field is taken as the basic descriptive element.