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Is there density matrix realism

Shan Gao

Published Mar 15, 2019• 0 citations
OpenAlex

Abstract

In a recent paper ["Quantum Mechanics in a Time-Asymmetric Universe: On the Nature of the Initial Quantum State", The British Journal for the Philosophy of Science, 2018], Chen uses density matrix realism to solve the puzzles of the arrow of time and the meaning of the quantum state. In this paper, I argue that density matrix realism is problematic, and in particular, it is inconsistent with the latest results about the reality of the wave function.

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Quantum Mechanics in a Time-Asymmetric Universe: On the Nature of the Initial Quantum State

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In a quantum universe with a strong arrow of time, we postulate a low-entropy boundary condition (the past hypothesis, PH) to account for the temporal asymmetry. In this article, I show that the PH also contains enough information to simplify the quantum ontology and define a natural initial condition. First, I introduce ‘density-matrix realism’, the thesis that the quantum state of the universe is objective and impure. This stands in sharp contrast to wave-function realism, the thesis that the quantum state of the universe is objective and pure. Second, I suggest that the PH is sufficient to determine a natural density matrix, which is simple and unique. This is achieved by what I call the ‘initial projection hypothesis’: the initial density matrix of the universe is the (normalized) projection onto the PH-subspace (in the Hilbert space). Third, because the initial quantum state is unique and simple, we have a strong case for the nomological thesis: the initial quantum state of the universe is on a par with laws of nature. This new package of ideas has several interesting implications, including on the harmony between statistical mechanics and quantum mechanics, theoretical unity of the universe and the subsystems, and the alleged conflict between Humean supervenience and quantum entanglement.

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In a recent paper ["Quantum Mechanics in a Time-Asymmetric Universe: On the Nature of the Initial Quantum State", The British Journal for the Philosophy of Science, 2018], Chen uses density matrix realism to solve the puzzles of the arrow of time and the meaning of the quantum state. In this paper, I argue that density matrix realism is problematic, and in particular, it is inconsistent with the latest results about the reality of the wave function.
In a quantum universe with a strong arrow of time, we postulate a low-entropy boundary condition (the past hypothesis, PH) to account for the temporal asymmetry. In this article, I show that the PH also contains enough information to simplify the quantum ontology and define a natural initial condition. First, I introduce ‘density-matrix realism’, the thesis that the quantum state of the universe is objective and impure. This stands in sharp contrast to wave-function realism, the thesis that the quantum state of the universe is objective and pure. Second, I suggest that the PH is sufficient to determine a natural density matrix, which is simple and unique. This is achieved by what I call the ‘initial projection hypothesis’: the initial density matrix of the universe is the (normalized) projection onto the PH-subspace (in the Hilbert space). Third, because the initial quantum state is unique and simple, we have a strong case for the nomological thesis: the initial quantum state of the universe is on a par with laws of nature. This new package of ideas has several interesting implications, including on the harmony between statistical mechanics and quantum mechanics, theoretical unity of the universe and the subsystems, and the alleged conflict between Humean supervenience and quantum entanglement.
In a quantum universe with a strong arrow of time, we postulate a low-entropy boundary condition (the Past Hypothesis) to account for the temporal asymmetry. In this paper, I show that the Past Hypothesis also contains enough information to significantly simplify the quantum ontology and clearly define a unique initial condition in such a world. First, I introduce Density Matrix Realism, the thesis that the quantum universe is described by a fundamental density matrix (a mixed state) that corresponds to some physical degrees of freedom in the world. This stands in contrast with Wave Function Realism, the thesis that the quantum universe is described by a wave function (a pure state) that represents something physical. Second, I suggest that the Past Hypothesis is sufficient to determine a unique and simple density matrix. This is achieved by what I call the Initial Projection Hypothesis: the initial density matrix of the universe is the projection onto the special low-dimensional Hilbert space. Third, because the initial quantum state is unique and simple, we have a strong case for the Nomological Thesis: the initial quantum state of the universe is completely specified by a law of nature. This new package of ideas has several interesting implications, including on the dynamic unity of the universe and the subsystems, the theoretical unity of statistical mechanics and quantum mechanics, and the alleged conflict between Humean supervenience and quantum entanglement.
Abstract Realism about quantum theory naturally leads to realism about the quantum state of the universe. It leaves open whether it is a pure state represented by a wave function, or an impure one represented by a density matrix. I characterise and elaborate on Density Matrix Realism, the thesis that the universal quantum state is objective but can be impure. To clarify the thesis, I compare it with Wave Function Realism, explain the conditions under which they are empirically equivalent, consider two generalisations of Density Matrix Realism, and answer some frequently asked questions. I end by highlighting an implication for scientific realism.
This article examines the case for preferring density matrix realism over wave function realism, as an approach to the fundamental ontology of our world. To date, there are two arguments that have been used to motivate density matrix realism. One is that we get a simpler and more appealing metaphysics if we move from wave function realism to density matrix realism. The second is that density matrices are more general than wave functions. In both cases, a key purported advantage is that density matrix realists can allow that the universe could be in a mixed state. To be convincing, however, these arguments can’t simply assume that our universe could be in a mixed state, since standard definitions of mixedness seem to preclude such a possibility. Thus, to make density matrix realism plausible, one would need to appeal to some scientifically backed argument that standard definitions of mixedness need revision, that what seemed to be perplexing before represents a genuine way that our world could fundamentally be. Here, Hawking’s model of black hole evaporation seems poised to come to the rescue, and so, we develop a novel argument to this effect. Although we find this way of arguing for density matrix realism to be intriguing and worthy of investigation, we show that there is substantial reason to be cautious. Most physicists, including Hawking, believe that this model will be superseded by a more fundamental theory of quantum gravity. Despite a lack of agreement on the details of such a theory, the guiding principles that do enjoy some consensus point away from an interpretation of black hole evaporation in which the universe as a whole evolves into an (objectively) mixed state. We conclude that there do not seem to be compelling motivations coming from fundamental physics to favour a metaphysics in which the universe is fundamentally a density matrix rather than a wave function.