Cosmic-time quantum mechanics and the passage-of-time problem

TL;DR

This paper introduces a novel framework merging quantum mechanics with cosmology, emphasizing a genuine passage of time and hyperbolic spatial sections, offering new insights into cosmic evolution and conformal invariance.

Contribution

It presents a new dynamical paradigm that integrates quantum dynamics with cosmological models, highlighting the passage of time and hyperbolic spatial structures.

Findings

Hyperbolic spatial sections as asymptotic supports of wave functions

A new formulation of conformal invariance for non-zero fields

Framework accommodates matter fields in cosmological quantum models

Abstract

A new dynamical paradigm merging quantum dynamics with cosmology is discussed. Time evolution involves a genuine passage of time, which distinguishes the formalism from those where dynamics in space is equivalent to statics in space-time. Hyperbolic spatial sections occur as asymptotic large-cosmic-time supports of quantum wave functions. For simplicity, the wave functions are defined on $n$-dimensional Minkowski spaces. We begin with empty universe, but then outline the formalism that involves matter fields. As a by-product, we arrive at a new formulation of conformal invariance of $m\neq 0$ fields.