Year: 2023
Type: article
Abstract: A ubiquitous feature of quantum mechanical theories is the existence of states of superposition. This is expected to be no different for a quantum gravity theory. Guided by this consideration and others we consider a framework in which classical reference frames may be in superposition relative to one another. Mirroring standard quantum mechanics we introduce a complex-valued wavefunctional, which takes as input the transformations between the coordinates, Ψ[x(x′)], with the interpretation that an interaction between the reference frames may select a particular transformation with probability distribution given by the Born rule — P[x(x′)] = probability distribution functional ≡ |Ψ[x(x′)]|2. The cases of two and three reference frames in superposition are considered explicitly. It is shown that the set of transformations is closed. A rule for transforming wavefunctions from one system to another system in superposition is proposed and consistency with the Schrodinger equation is demonstrated.
Source: Journal of Mathematical Physics
DOI: 10.1063/5.0144924
Authors: Elliott Tammaro, H. Angle, E. Mbadu
Institutions: Chestnut Hill College, University of Delaware, Drexel University
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4389998785