Time and quantum theory: A history and a prospectus

Pashby, Thomas

doi:10.1016/j.shpsb.2015.03.002

Cited by 9 publications

(6 citation statements)

References 40 publications

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“…When talking about the evolution of a quantum dynamical system, seen as a synchronised clock-system pair, what is usually meant by the energy observable is the Hamiltonian for the system, and what is usually meant by the time observable is the time observable for the clock. This simple observation, coupled with the following result, answers a 1930s conundrum by Schrödinger (see [21] p6). Theorem 8.2.…”

Section: Clock-system Synchronisationsupporting

confidence: 71%

Categorical Semantics for Schrödinger's Equation

Gogioso¹

2015

Preprint

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Applying ideas from monadic dynamics to the wellestablished framework of categorical quantum mechanics, we provide a novel toolbox for the simulation of finite-dimensional quantum dynamics. We use strongly complementary structures to give a graphical characterisation of quantum clocks, their action on systems and the relevant energy observables, and we proceed to formalise the connection between unitary dynamics and projection-valued spectra. We identify the Weyl canonical commutation relations in the axioms of strong complementarity, and conclude the existence of a dual pair of time/energy observables for finite-dimensional quantum clocks, with the relevant uncertainty principle given by mutual unbias of the corresponding orthonormal bases. We show that Schrödinger's equation can be abstractly formulated as characterising the Fourier transforms of certain Eilenberg-Moore morphisms from a quantum clock to a quantum dynamical system, and we use this to obtain a generalised version of the Feynman's clock construction. We tackle the issue of synchronism of clocks and systems, prove conservation of total energy and give conditions for the existence of an internal time observable for a quantum dynamical system. Finally, we identify our treatment as part of a more general theory of simulated symmetries of quantum systems (of which our clock actions are a special case) and their conservation laws (of which energy is a special case).

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Section: Clock-system Synchronisationsupporting

confidence: 71%

Categorical Semantics for Schrödinger's Equation

Gogioso¹

2015

Preprint

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“…In quantum mechanics the treatment of time is not fully resolved [88][89][90][91][92][93][94][95][96].…”

Section: Nonrelativistic Quantum Mechanics: Time As Independent From mentioning

confidence: 99%

Understanding quantum mechanics: a review and synthesis in precise language

Drummond¹

2019

Open Physics

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This review, of the understanding of quantum mechanics, is broad in scope, and aims to reflect enough of the literature to be representative of the current state of the subject. To enhance clarity, the main findings are presented in the form of a coherent synthesis of the reviewed sources. The review highlights core characteristics of quantum mechanics. One is statistical balance in the collective response of an ensemble of identically prepared systems, to differing measurement types. Another is that states are mathematical terms prescribing probability aspects of future events, relating to an ensemble of systems, in various situations. These characteristics then yield helpful insights on entanglement, measurement, and widely-discussed experiments and analyses. The review concludes by considering how these insights are supported, illustrated and developed by some specific approaches to understanding quantum mechanics. The review uses non-mathematical language precisely (terms defined) and rigorously (consistent meanings), and uses only such language. A theory more descriptive of independent reality than is quantum mechanics may yet be possible. One step in the pursuit of such a theory is to reach greater consensus on how to understand quantum mechanics. This review aims to contribute to achieving that greater consensus, and so to that pursuit.

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“…(6)Operationally, these probabilities refer to the result of an experiment in which an atom is held within a detector until the detector registers the emission of a decay product at time t d . If we 6 I first raised this difficulty inPashby [2015], which also contains a history of time in early quantum theory.…”

mentioning

confidence: 99%

“…I first raised this difficulty inPashby [2015], which also contains a history of time in early quantum theory.…”

mentioning

confidence: 99%