Considering a superposition of classical reference frames

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, $\Psi [x(x^{\prime })]$, with the interpretation that an interaction between the reference frames may select a particular transformation with probability distribution given by the Born rule - $P[x(x^{\prime })]=\text{probability distribution functional}\equiv |\Psi [x(x^{\prime })]{|}^2$. 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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