On measuring the Quantum Universe

TL;DR

This paper explores a quantum cosmology model with torsion, analyzing the universe's wave function through Hamiltonian formalism, weak measurement, and Bohmian interpretation, challenging traditional collapse postulates.

Contribution

It extends the WDW approach to include torsion, introduces weak measurement to avoid wave function collapse, and discusses boundary conditions and interpretations.

Findings

Wave function as superposition of Hamiltonian eigenfunctions

Cosmic time conjugate to eigenvalues of the Hamiltonian

Discussion of boundary conditions and interpretations

Abstract

We present a theoretical analysis of the WDW approach to quantum cosmology extended to gravity theories with torsion. The dynamics of the FLRW universe is formulated as a classical Hamiltonian problem of point particle mechanics. Unlike in the WDW formalism, the Hamiltonian is not zero, though, and the 3rd quantization does not enforce the cosmic time to vanish. The wave function of the Universe appears as a superposition of eigenfunctions of the quantum Hamiltonian with the cosmic time being the conjugate to its eigenvalues, spatial curvatures. The notion of weak measurement is then introduced to avoid the collapse of the total universal wave function upon measurements of the parameter set describing matter and spacetime. The collapse postulate of the standard Copenhagen quantum theory is discussed and the de Broglie-Bohm interpretation of the effective wave function introduced. The question of the boundary conditions for both, the wave function and the Bohmian guidance equation, is addressed. The corresponding numerical calculations will be published in a separate paper.