Considering a superposition of classical reference frames

• URL: http://arxiv.org/abs/2312.13540v1
• Date: Thu, 21 Dec 2023 02:46:45 GMT
• Title: Considering a superposition of classical reference frames
• Authors: Elliott Tammaro, Hunter Angle, Edmund Mbadu
• Abstract summary: We consider a framework in which classical reference frames may be in superposition relative to one another. A rule for transforming wavefunctions from one system to another system in superposition is proposed and consistency with the Schrodinger equation is demonstrated.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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, $\Psi[x(x')]$, with the interpretation that an interaction between the reference frames may select a particular transformation with probability distribution given by the Born rule - $P[x(x')] = \text{probability distribution functional} \equiv \vert \Psi[x(x')] \vert^2$. 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.

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