Time's Arrow in a Quantum Universe I: On the Simplicity and Uniqueness of the Initial Quantum State

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