1108.3080 (Max Tegmark)

How unitary cosmology generalizes thermodynamics and solves the inflationary entropy problem    [PDF]

Max Tegmark

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.

View original: http://arxiv.org/abs/1108.3080