[hep-th/0611043] Sinks in the Landscape and the Invasion of Boltzmann Brains

Authors:  Andrei Linde
Abstract:  This paper extends the recent investigation of the string theory landscape in hep-th/0605266, where it was found that the decay rate of dS vacua to a collapsing space with a negative vacuum energy can be quite large. The parts of space that experience a decay to a collapsing space, or to a Minkowski vacuum, never return back to dS space. The channels of irreversible vacuum decay serve as sinks for the probability flow. The existence of such sinks is a distinguishing feature of the string theory landscape. We describe relation between several different probability measures for eternal inflation taking into account the existence of the sinks. The local (comoving) description of the inflationary multiverse suffers from the so-called `Boltzman brain' problem unless the probability of the decay to the sinks is sufficiently large. We show that some versions of the global (volume-weighted) description do not have this problem even if one ignores the existence of the sinks. Finally, we describe a simplified approach to the calculations of anthropic probabilities in the landscape, which is less powerful but also less ambiguous than other methods.
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Antony Lewis
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[hep-th/0611043] Sinks in the Landscape and the Invasion of

Post by Antony Lewis » November 07 2006

This paper discusses various simple measures in eternal inflation, and whether or not they solve the Boltzmann Brain problem.

The problem is that a space with positive vacuum energy generates exponentially large volumes in the future in which fluctuations can give rise to Boltzmann Brains: thus most observers will be Boltzmann brains, in contradiction to our apparently very special memories associated with life on earth (nucleating a new bubble universe is much less likely than forming a brain). One simple solution is that the vacuum decays on the scale of a Hubble time, so the future volume remains on average finite (see e.g. hep-th/0610079). This is a short time of ~20 billion years. [Note that the anthropic reasoning here is pretty robust: there will be brains in essentially any choice of reference class you like, including an essentially identical copy of your current brain having the deluded belief that he lives on Earth]

This paper suggests instead that a 'standard' volume-weighted slicing measure of eternal inflation resolves the problem: most volume is generated in the highest energy vacuum, and most observers will therefore be formed shortly after its decay, i.e. near a thermalization surface and not a Boltzmann brain. What I don't see is how this is an acceptable solution: doesn't this weighting give the well-known 'youngness paradox' - that most observers will be in a very newly formed vacuum - in contradiction to observation that actually the universe is relatively old?

Perhaps another possibility is that there is some external clock associated with each vacuum. One logical possibility would be something like the ekpyrotic scenario (e.g. astro-ph/0605173): there is no Brain problem as long as the branes eventually re-collide and the entire expanded region is re-thermalized. Or perhaps downwards renormalization of the vacuum energy due to accumulation of super-Hubble quantum fluctuations (e.g. hep-ph/9602316) - though this seems to take too long.

Incidentally, the logical conclusion of the anthropic comments in the Discussion section is perhaps something like the proposal in math.ST/0608592 - though unfortunately it is unclear how this works in the infinite case.

Tommy Anderberg
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[hep-th/0611043] Sinks in the Landscape and the Invasion of

Post by Tommy Anderberg » November 08 2006

It only goes to show what an unsophisticated country boy I am, but I lost track of my objections to this paper when I ran out of toes to keep count of them all. So I take the easy way out and choose to contradict Antony Lewis instead: relative to what is our universe "relatively old"? The Planck time scale, sure - but for Linde's argument, wouldn't the relevant measure be more like the total lifetime of the (observable) universe?

I would argue that there is an "oldness problem" instead: in Linde's own words,
why was I born in the middle of the 20th century, if the population grows exponentially, and many more people are alive now than they were at the time when I was born?
(page 25). No reason to stop there -- why were you born so early, if this planet and solar system have billions of years left in them, and the human race (or what comes after it) is eventually going to spread all over the galaxy (and beyond)? I can hear the Prophets of Doom gallop in as I type this, but hold your horses, there is an alternative to impending disaster: if you take the Boltzmann Brain argument seriously, it's hard to see how you can dismiss Nick Bostrom's Matrix argument. Admit it, sloppy coding would explain many things (and hacker humor many more)...

(Just for the sake of argument, I am assuming that there is such a thing as the landscape, that eternal inflation is going on within it, that most volume is being generated near the highest energy vacuum, that I am not a stark raving mad Boltzmann Brain just imagining that any of this was ever written - which would be rather flattering actually, since it would imply that the devious brilliance of both Linde and Lewis is really all mine - and a whole host of other things which I don't have enough toes to keep count of).

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