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Considering a superposition of classical reference frames
Quantum Physics · Submitted 21 Dec 2023
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim 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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The abstract, sentence by sentence
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.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | A ubiquitous feature of quantum mechanical theories is the existence of states of superposition. | background 1.00 | 0.04 | 0.02 | asserted 1.00 |
| s1 | This is expected to be no different for a quantum gravity theory. | background 1.00 | 0.06 | 0.04 | hedged possibility 0.63 |
| s2 | Guided by this consideration and others we consider a framework in which classical reference frames may be in superposition relative to one another. | contribution 0.97 | 0.87 | 0.13 | asserted 0.49 |
| s3 | 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 - $P[x(x')] = \text{probability distribution functional} \equiv \vert \Psi[x(x')] \vert^2$. | method 0.86 | 0.88 | 0.12 | asserted 0.93 |
| s4 | The cases of two and three reference frames in superposition are considered explicitly. | contribution 0.87 | 0.92 | 0.07 | asserted 0.94 |
| s5 | It is shown that the set of transformations is closed. | result 0.99 | 0.90 | 0.14 | asserted 1.00 |
| s6 | A rule for transforming wavefunctions from one system to another system in superposition is proposed and consistency with the Schrodinger equation is demonstrated. | contribution 0.55 | 0.92 | 0.32 | asserted 0.94 |
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Original 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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Interpreting the meaning of such states, which is an end goal, is an open question, which likely cannot be resolved without recourse to a particular quantum gravity theory [ref] .
Einstein's Equivalence principle for superpositions of gravitational fields and quantum reference frames · Introduction · 0.93
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