We analyze cosmology assuming unitary quantum mechanics, using a tripartite
partition into system, observer and environment degrees of freedom. This
generalizes the second law of thermodynamics to "The system's entropy can't
decrease unless it interacts with the observer, and it can't increase unless it
interacts with the environment." The former follows from the quantum Bayes
Theorem we derive. We show that because of the long-range entanglement created
by cosmological inflation, the cosmic entropy decreases exponentially rather
than linearly with the number of bits of information observed, so that a given
observer can reduce entropy by much more than the amount of information her
brain can store. Indeed, we argue that as long as inflation has occurred in a
non-negligible fraction of the volume, almost all sentient observers will find
themselves in a post-inflationary low-entropy Hubble volume, and we humans have
no reason to be surprised that we do so as well, which solves the so-called
inflationary entropy problem. An arguably worse problem for unitary cosmology
involves gamma-ray-burst constraints on the "Big Snap", a fourth cosmic
doomsday scenario alongside the "Big Crunch", "Big Chill" and "Big Rip", where
an increasingly granular nature of expanding space modifies our life-supporting
laws of physics.
Our tripartite framework also clarifies when it is valid to make the popular
quantum gravity approximation that the Einstein tensor equals the quantum
expectation value of the stress-energy tensor, and how problems with recent
attempts to explain dark energy as gravitational backreaction from
super-horizon scale fluctuations can be understood as a failure of this
approximation.Comment: Updated to match accepted PRD version, including Quantum Bayes
Theorem derivation and rigorous proof that decoherence increases von Neumann
entropy. 20 pages, 5 fig
