A New Look at the Position Operator in Quantum Theory

TL;DR

This paper challenges the traditional Fourier-based definition of the position operator in quantum theory, proposing a new approach that eliminates wave packet spreading and resolves related paradoxes, with implications for entanglement and quantum locality.

Contribution

It introduces a novel, consistent definition of the quantum position operator that avoids wave packet spreading and addresses foundational issues in quantum theory.

Findings

Wave packet spreading in perpendicular directions is eliminated.

Photons emitted by stars do not have cosmic-sized wave functions.

Implications for entanglement and quantum locality are discussed.

Abstract

The postulate that coordinate and momentum representations are related to each other by the Fourier transform has been accepted from the beginning of quantum theory by analogy with classical electrodynamics. As a consequence, an inevitable effect in standard theory is the wave packet spreading (WPS) of the photon coordinate wave function in directions perpendicular to the photon momentum. This leads to several paradoxes. The most striking of them is that coordinate wave functions of photons emitted by stars have cosmic sizes and strong arguments indicate that this contradicts observational data. We argue that the above postulate is based neither on strong theoretical arguments nor on experimental data and propose a new consistent definition of the position operator. Then WPS in directions perpendicular to the particle momentum is absent and the paradoxes are resolved. Different components of the new position operator do not commute with each other and, as a consequence, there is no wave function in coordinate representation. Implications of the results for entanglement, quantum locality and the problem of time in quantum theory are discussed.