Quantum mechanics as a space-time theory

TL;DR

This paper proposes a novel space-time interpretation of quantum mechanics using a variable real number continuum called qrumbers, which offers a different geometric perspective on atomic and subatomic systems compared to classical space-time.

Contribution

It introduces a quantum space-time framework based on qrumbers, constructed from Hilbert space entities, providing a new geometric understanding of quantum phenomena.

Findings

Quantum systems can be localized in the quantum continuum despite non-locality in classical space-time.

The quantum continuum differs geometrically from classical space-time.

Comparison with Bohmian mechanics highlights differences in space-time descriptions.

Abstract

We show how quantum mechanics can be understood as a space-time theory provided that its spatial continuum is modelled by a variable real number (qrumber) continuum. Such a continuum can be constructed using only standard Hilbert space entities. The geometry of atoms and subatomic objects differs from that of classical objects. The systems that are non-local when measured in the classical space-time continuum may be localized in the quantum continuum. We compare this new description of space-time with the Bohmian picture of quantum mechanics.