On the physical origin of the quantum operator formalism

TL;DR

This paper explains the physical origin of quantum operators by linking them to the resonant response of particles to vacuum field modes, providing a physical basis for the operator formalism in quantum mechanics.

Contribution

It offers a novel physical interpretation of quantum operators as arising from the particle's resonant response to vacuum field modes, connecting stochastic electrodynamics with operator formalism.

Findings

Quantum commutators originate from the particle-vacuum field interaction.

Response coefficients of position and momentum relate directly to matrix elements.

The operator formalism encodes the Hamiltonian properties of the vacuum field.

Abstract

We offer a clear physical explanation for the emergence of the quantum operator formalism, by revisiting the role of the vacuum field in quantum mechanics. The vacuum or random zero-point radiation field has been shown previously, using the tools of stochastic electrodynamics, to be central in allowing a particle subject to a conservative binding force to reach a stationary state of motion. Here we focus on the stationary states, and consider the role of the vacuum as a driving force. We observe that the particle responds resonantly to certain field modes. A proper Hamiltonian analysis of this response allows us to unequivocally trace the origin of the basic quantum commutator, by establishing a one-to-one correspondence between the response coefficients of x and p and the respective matrix elements. The (random) driving field variables disappear thus from the description, but their Hamiltonian properties become embodied in the operator formalism. The Heisenberg equations establish the dynamical relationship between the response functions.