A quantum stochastic equivalence leads to a retrocausal model for measurement consistent with macroscopic realism

• URL: http://arxiv.org/abs/2205.06070v2
• Date: Sat, 6 Aug 2022 09:12:24 GMT
• Title: A quantum stochastic equivalence leads to a retrocausal model for measurement consistent with macroscopic realism
• Authors: Margaret D Reid and Peter D Drummond
• Abstract summary: We show how retrocausality arises naturally from within quantum mechanics, and explain quantum measurement consistently with macroscopic realism. A Deutsch-like 'causal consistency' and Born's rule emerge naturally. For macroscopic superpositions, the macroscopic outcome of the measurement is considered determined prior to the onset of the measurement.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In this paper, we show how retrocausality arises naturally from within quantum mechanics, and explains quantum measurement consistently with macroscopic realism. We analyze a measurement $\hat{x}$ on a system prepared in a superposition of eigenstates $|x_{j}\rangle$ where the measurement is modeled by amplification. By deriving a path-integral theorem, we prove an equivalence between a quantum probability distribution $Q(x,p,t)$ and simultaneous back-in-time and forward-in-time stochastic equations for amplitudes $x(t)$ and $p(t)$, respectively. The backward and forward trajectories are linked at the initial-time boundary. A Deutsch-like 'causal consistency' and Born's rule emerge naturally. A feature is the vacuum noise associated with the eigenstate. Unlike the eigenvalue, this noise is not amplified and is not measurable, the precise fluctuations originating from past and future boundary conditions. We find consistency with macroscopic realism: For macroscopic superpositions, the macroscopic outcome of the measurement $\hat{x}$ is considered determined prior to the onset of the measurement. This leads to hybrid macro-causal and micro-retrocausal relations, and other models of realism. Our results support that the 'collapse' of the wave function occurs with amplification: The distribution $Q_{j}(x,p,0)$ for the initial 'state' postselected on the outcome $x_{j}$ is not a quantum state but approaches the eigenstate $|x_{j}\rangle$ for a macroscopic superposition. The full irreversible collapse is simulated by coupling to a meter. We discuss Einstein-Podolsky-Rosen and Bell correlations.

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