It has been proposed that the universe is in a mixed state or its quantum state is an impure density matrix, not a wave function. In this paper, I argue that this view can hardly be consistent with the latest results about the reality of the wave function.
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 Most physicists, including Hawking, believe that this model will be superseded by a more fundamental theory of quantum gravity.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.
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.
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.
The most puzzling issue in the foundations of quantum mechanics is perhaps that of the status of the wave function of a system in a quantum universe. Is the wave function objective or subjective? Does it represent the physical state of the system or merely our information about the system? If the former, does it provide a complete or partial description of the system ? We address these questions mainly from a Bohmian perspective and argue that part of the difficulty in ascertaining the status of the wave function arises from the fact that there are two different sorts of wave functions involved. The most fundamental wave function is that of the universe, which, we argue, has a law-like character. From the wave function of the universe together with its configuration one can define the wave function of a subsystem of the universe. This, although objective, has a strong informational/subjective aspect.
The wave function gives not the density of stuff, but gives rather (on squaring its modulus) the density of probability. Probability of what, exactly? Not of the electron being there, but of the electron being found there, if its position is ‘measured’. Why this aversion to ‘being’ and insistence on ‘finding’? The founding fathers were unable to form a clear picture of things on the remote atomic scale . John S. Bell (1990) Introduction The physical meaning of the wave function is an important interpretative problem of quantum mechanics. Notwithstanding nearly ninety years of development of the theory, it is still an unsolved issue. During recent years, more and more research has been done on the ontological status and meaning of the wave function (see, e.g. Monton, 2002; Lewis, 2004; Gao, 2011a, 2011b; Pusey, Barrett and Rudolph, 2012; Ney and Albert, 2013). In particular, Pusey, Barrett and Rudolph (2012) demonstrated that under certain non-trivial assumptions such as the preparation independence assumption, the wave function of a quantum system is a representation of the physical state of the system. This poses a further question, namely whether the reality of the wave function can be argued without resorting to non-trivial assumptions. Moreover, a harder problem is to determine the ontological meaning of the wave function, which is still a hot topic of debate in the realistic alternatives to quantum mechanics such as the de Broglie–Bohm theory or Bohmian mechanics (Belot, 2012). In this chapter, we will first give a clearer argument for the reality of the wave function in terms of protective measurements, which does not depend on non-trivial assumptions and can also overcome existing objections. Next, based on an analysis of the mass and charge properties of a quantum system, we will propose a new ontological interpretation of the wave function. According to this interpretation, the wave function of an N -body system represents the state of ergodic motion of N particles.