  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 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 Past Hypothesis 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 Past Hypothesis
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.
