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Time and the Foundations of Quantum Mechanics

Pashby, Thomas (2014) Time and the Foundations of Quantum Mechanics. University of Pittsburgh.

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Abstract

Quantum mechanics has provided philosophers of science with many counterintuitive insights and interpretive puzzles, but little has been written about the role that time plays in the theory. One reason for this is the celebrated argument of Wolfgang Pauli against the inclusion of time as an observable of the theory, which has been seen as a demonstration that time may only enter the theory as a classical parameter. Against this orthodoxy I argue that there are good reasons to expect certain kinds of 'time observables' to find a representation within quantum theory, including clock operators (which provide the means to measure the passage of time) and event time operators, which provide predictions for the time at which a particular event occurs, such as the appearance of a dot on a luminescent screen. I contend that these time operators deserve full status as observables of the theory, and on reflection provide a uniquely compelling reason to expand the set of observables allowed by the standard formalism of quantum mechanics. In addition, I provide a novel association of event time operators with conditional probabilities, and propose a temporally extended form of quantum theory to better accommodate the time of an event as an observable quantity. This leads to a proposal to interpret quantum theory within an event ontology, inspired by Bertrand Russell's Analysis of Matter. On this basis I mount a defense of Russell's relational theory of time against a recent attack.


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Pashby, Thomastom.pashby@gmail.com
Additional Information: Submitted to the Graduate Faculty of the Dietrich School of Arts and Sciences in partial fulfillment of the requirements for the degree of Doctor of Philosophy. (This version corrects some typos.)
Keywords: time, quantum, quantum mechanics, quantum theory, events, clocks, observables, quantum clocks, Pauli's Theorem, Spectral Theorem, Naimark Dilation, Neumark Dilation, POVMs, Positive Operator Valued Measures, relational time, Russell, Analysis of Matter, event ontology, event times, event time observables, conditional probabilities, time operators, time observables
Subjects: Specific Sciences > Physics > Classical Physics
General Issues > History of Philosophy of Science
General Issues > History of Science Case Studies
General Issues > Laws of Nature
General Issues > Models and Idealization
Specific Sciences > Physics
Specific Sciences > Physics > Quantum Mechanics
General Issues > Realism/Anti-realism
Specific Sciences > Physics > Symmetries/Invariances
Depositing User: Dr. Thomas Pashby
Date Deposited: 05 Jun 2014 13:08
Last Modified: 05 Jun 2014 13:08
Item ID: 10723
Journal or Publication Title: Department of History and Philosophy of Science
Publisher: University of Pittsburgh
Subjects: Specific Sciences > Physics > Classical Physics
General Issues > History of Philosophy of Science
General Issues > History of Science Case Studies
General Issues > Laws of Nature
General Issues > Models and Idealization
Specific Sciences > Physics
Specific Sciences > Physics > Quantum Mechanics
General Issues > Realism/Anti-realism
Specific Sciences > Physics > Symmetries/Invariances
Date: 2014
URI: http://philsci-archive.pitt.edu/id/eprint/10723

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