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Quantum States of a Time-Asymmetric Universe: Wave Function, Density Matrix, and Empirical Equivalence

Chen, Eddy Keming (2019) Quantum States of a Time-Asymmetric Universe: Wave Function, Density Matrix, and Empirical Equivalence. [Preprint]

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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 (representing a pure state) but by a density matrix (representing a mixed state).

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.


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Item Type: Preprint
Creators:
CreatorsEmailORCID
Chen, Eddy Kemingeddy.chen@rutgers.edu0000-0001-5144-0952
Keywords: time's arrow, Past Hypothesis, Initial Projection Hypothesis, Statistical Postulate, typicality, unification, foundations of probability, quantum statistical mechanics, wave function realism, density matrix, quantum state of the universe
Subjects: Specific Sciences > Physics > Cosmology
General Issues > Laws of Nature
Specific Sciences > Probability/Statistics
Specific Sciences > Physics > Quantum Mechanics
Specific Sciences > Physics > Statistical Mechanics/Thermodynamics
Depositing User: Keming Chen
Date Deposited: 23 Jan 2019 16:09
Last Modified: 23 Jan 2019 16:09
Item ID: 15658
Subjects: Specific Sciences > Physics > Cosmology
General Issues > Laws of Nature
Specific Sciences > Probability/Statistics
Specific Sciences > Physics > Quantum Mechanics
Specific Sciences > Physics > Statistical Mechanics/Thermodynamics
Date: January 2019
URI: http://philsci-archive.pitt.edu/id/eprint/15658

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