Three-space as a quantum hyper-layer in 1+3 dimensions

TL;DR

This paper introduces a formalism where the universe is modeled as a quantum hyper-layer with a finite timelike width, and explores its implications through a harmonic oscillator example, revealing a potential mass variation over time.

Contribution

It proposes a novel universe model as a quantum hyper-layer and treats curvature as a quantum observable, extending classical cosmology concepts.

Findings

Reconstruction of standard quantum results at large $ au$

Effective mass of oscillator decreases with $ au$

Masses of distant quantum systems may be greater than local measurements

Abstract

We discuss a formalism where a universe is identified with the support of a wave function propagating through space-time. As opposed to classical cosmology, the resulting universe is not a spacelike section of some space-time, but a hyper-layer of a finite timelike width, a set which is not a three-dimensional submanifold of space-time. We test the formalism on the example of a universe that contains a single harmonic oscillator (a generalization of the curvature-dependent Cari\~nena-Ra\~nada-Santander (CRS) model). As opposed to the original CRS formulation, here the curvature is not a parameter but a quantum observable, a function of the world-position operator. It is shown that asymptotically, for large values of the invariant evolution parameter $\tau$, one reconstructs the standard quantum results, with one modifiication: The effective (renormalized) mass of the oscillator decreases with $\tau$. The effect does not seem to be a peculiarity of harmonic oscillators, so one may speculate that masses of distant elementary quantum systems are greater from their values known from our quantum mechanical measurements.