Dissertation, Rutgers University - New Brunswick (2019)

Authors
Eddy Keming Chen
University of California, San Diego
Abstract
What is the quantum state of the universe? Although there have been several interesting suggestions, the question remains open. In this paper, I consider a natural choice for the universal quantum state arising from the Past Hypothesis, a boundary condition that accounts for the time-asymmetry of the universe. The natural choice is given not by a wave function but by a density matrix. I begin by classifying quantum theories into two types: theories with a fundamental wave function and theories with a fundamental density matrix. The Past Hypothesis is compatible with infinitely many initial wave functions, none of which seems to be particularly natural. However, once we turn to density matrices, the Past Hypothesis provides a natural choice---the normalized projection onto the Past Hypothesis subspace in the Hilbert space. Nevertheless, the two types of theories can be empirically equivalent. To provide a concrete understanding of the empirical equivalence, I provide a novel subsystem analysis in the context of Bohmian theories. Given the empirical equivalence, it seems empirically underdetermined whether the universe is in a pure state or a mixed state. Finally, I discuss some theoretical payoffs of the density-matrix theories and present some open problems for future research. (Bibliographic note: the thesis was submitted for the Master of Science in mathematics at Rutgers University.)
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References found in this work BETA

Time and Chance.David Z. Albert - 2000 - Harvard University Press.
Time and Chance.S. French - 2005 - Mind 114 (453):113-116.

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Citations of this work BETA

Quantum Mechanics in a Time-Asymmetric Universe: On the Nature of the Initial Quantum State.Eddy Keming Chen - 2021 - British Journal for the Philosophy of Science 72 (4):1155–1183.
The Past Hypothesis and the Nature of Physical Laws.Eddy Keming Chen - forthcoming - In Barry Loewer, Eric Winsberg & Brad Weslake (eds.), Time's Arrows and the Probability Structure of the World. Harvard University Press.

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