Measurement and Quantum Dynamics in the Minimal Modal Interpretation of Quantum Theory
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Measurement and Quantum Dynamics in the Minimal Modal Interpretation of Quantum Theory Jacob A. Barandes1 · David Kagan2 Received: 7 November 2019 / Accepted: 26 August 2020 / Published online: 7 September 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract Any realist interpretation of quantum theory must grapple with the measurement problem and the status of state-vector collapse. In a no-collapse approach, measurement is typically modeled as a dynamical process involving decoherence. We describe how the minimal modal interpretation closes a gap in this dynamical description, leading to a complete and consistent resolution to the measurement problem and an effective form of state collapse. Our interpretation also provides insight into the indivisible nature of measurement—the fact that you can’t stop a measurement part-way through and uncover the underlying ‘ontic’ dynamics of the system in question. Having discussed the hidden dynamics of a system’s ontic state during measurement, we turn to more general forms of open-system dynamics and explore the extent to which the details of the underlying ontic behavior of a system can be described. We construct a space of ontic trajectories and describe obstructions to defining a probability measure on this space. Keywords Quantum theory · Quantum mechanics · Many-body quantum systems · Foundations ofphysics · Quantum foundations · Decoherence · Interpretations of quantum theory · Quantum dynamics · Quantum measurement problem
1 Introduction Consider the axioms governing the dynamics of quantum systems as set out by Dirac and von Neumann [1, 2]:
* David Kagan [email protected] Jacob A. Barandes [email protected] 1
Jefferson Physical Laboratory, Harvard University, Cambridge, MA 02138, USA
2
Department of Physics, University of Massachusetts Dartmouth, North Dartmouth, MA 02747, USA
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Foundations of Physics (2020) 50:1189–1218
1. Unitary Evolution When a quantum system is closed, its state vector evolves according to the Schrödinger equation. 2. Collapse When a measurement is performed, the state vector collapses into one of the measurement’s mutually exclusive outcomes. The reference to measurements within these axioms is deeply problematic. One could posit that measurement is somehow fundamental, but then how does one rigorously determine in a practical, physical scenario under what precise circumstances one should declare that a measurement has taken place? Is there a sharp way to define which kinds of systems are capable of carrying out measurements and which are not? And if measurements are not fundamental, but are instead processes carried out on quantum states by measurement devices that register their results in terms of quantum states of their own, how does one avoid charges of circular reasoning that stem from the assertion that quantum states are nothing more than collections of probabilities for measurement outcomes? Any interpretation of quantum theory that claims to refrain from m
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