Another link to Sean Carroll's blog: Squelching Boltzmann Brains (And Maybe Eternal Inflation). The discussion of Boltzmann brains has come up many times on LW, starting from this Eliezer's post. Now Sean and his collaborators argue that in an empty expanding universe:
Quantum fluctuations are not dynamical processes inherent to a system, but instead reflect the statistical nature of measurement outcomes. Making a de nite measurement requires an out-of-equilibrium, low-entropy detection apparatus that interacts with an environment to induce decoherence. Quantum variables are not equivalent to classical stochastic variables. They may behave similarly when measured repeatedly over time, in which case it is sensible to identify the nonzero variance of a quantum-mechanical observable with the physical fluctuations of a classical variable. In a truly stationary state, however, there are no fluctuations that decohere. We conclude that systems in such a state|including, in particular, the Hartle-Hawking vacuum never fluctuate into lower-entropy states, including false vacua or con gurations with Boltzmann brains.
Although our universe, today or during inflation, is of course not in the vacuum, the cosmic no-hair theorem implies that any patch in an expanding universe with a positive cosmological constant will asymptote to the vacuum. Within QFT in curved spacetime, the Boltzmann brain problem is thus eliminated: a patch in eternal de Sitter can form only a finite (and small) number of brains on its way to the vacuum.
In other words, in an empty universe no macroscopic areas of low entropy can form. And a non-vacuum expanding universe like ours becomes vacuum after a time too short to form more than a few Boltzmann brains.
String theorist Luboš Motl strongly disagrees with the analysis writing "Sean Carroll has no clue about physics and is helping to bury the good name of 2 graduate students".
Scott Aaronson on Motl's reliability, or lack thereof, with details of a specific case.
20Shmi
Calling Luboš Motl a string theorist is reaching. He hasn't done any research in forever. His contrarian opinions have more chance of being wrong than right and so can be safely ignored. His blog is mostly of entertainment value if you enjoy reading putdowns. I would wait until real QFT/GR/Cosmology experts chime in.
Another link to Sean Carroll's blog: Squelching Boltzmann Brains (And Maybe Eternal Inflation). The discussion of Boltzmann brains has come up many times on LW, starting from this Eliezer's post. Now Sean and his collaborators argue that in an empty expanding universe:
Quantum fluctuations are not dynamical processes inherent to a system, but instead reflect the statistical nature of measurement outcomes. Making a de nite measurement requires an out-of-equilibrium, low-entropy detection apparatus that interacts with an environment to induce decoherence. Quantum variables are not equivalent to classical stochastic variables. They may behave similarly when measured repeatedly over time, in which case it is sensible to identify the nonzero variance of a quantum-mechanical observable with the physical fluctuations of a classical variable. In a truly stationary state, however, there are no fluctuations that decohere. We conclude that systems in such a state|including, in particular, the Hartle-Hawking vacuum never fluctuate into lower-entropy states, including false vacua or con gurations with Boltzmann brains.
Although our universe, today or during inflation, is of course not in the vacuum, the cosmic no-hair theorem implies that any patch in an expanding universe with a positive cosmological constant will asymptote to the vacuum. Within QFT in curved spacetime, the Boltzmann brain problem is thus eliminated: a patch in eternal de Sitter can form only a finite (and small) number of brains on its way to the vacuum.
In other words, in an empty universe no macroscopic areas of low entropy can form. And a non-vacuum expanding universe like ours becomes vacuum after a time too short to form more than a few Boltzmann brains.