Monday, November 28, 2005

Don Page & death of de Sitter

A. V. Yurov and his mirror image, V. A. Yurov have a very provocative paper attempting to reconcile the conjectured lifetime of the KKLT de Sitter vacua calculated from the low-energy effective field theory - this lifetime is not too far from the recurrence time and let's call it a "googolplex" - with the much shorter lifetime of our Universe comparable to a mere "googol" that was recently advocated by Don Page and his even more provocative paper. ;-)

Let me emphasize at the beginning that although I find the KKLT estimates somewhat uncertain, they are definitely much less speculative than anything I am gonna describe in this text.

Don Page argues that if our Universe approaches the de Sitter exponential cosmological expansion with the currently likely value of the vacuum energy, then its lifetime should be shorter than 10^{50} years or so. Why? Because if the lifetime were longer, then - I kid you not - most of our perceptions (such as the feelings of our brains expressed by a complicated projection operator onto a state of your brain) would usually occur because of random vacuum fluctuations.

Technically speaking, the projection operators onto states of our brains that we use to decide whether we have perceived something or not would have a non-zero expectation value (the probability) just because of the thermal de Sitter fluctuations, roughly speaking, and because the total probability is proportional to the spacetime four-volume, a perception would have to occur just by a chance as long as the total four-volume is large enough.

Vacuum fluctuations are unlikely to create a happy person who just sees Jesus Christ walking on the water, but if the lifetime of the Universe is long enough (longer than Don Page's upper bound), it will eventually happen. Obviously, the Universe around us does not seem to be a random fluctuation from the vacuum because it seems to be much more ordered and well-behaved. Don Page believes that the previous sentence implies that our Universe should die in less than 10^{50} years.

I think that the argument is entertaining but it is hard for me to convince myself to treat it seriously. It is an argument showing how far the anthropic and similar thinking can go. If we see an ordered Universe today, does it imply something disastrous about our world's future 10^{50} years from now? If there is such a link, does not it violate causality?

I can't use Don Page's argument because the projection operators that I use to define the states of my brain differ from his operators. My projection operators require the brain not only to look like a brain for 0.15 seconds in the volume of a few liters but they also require the past of my environment to qualitatively look like a decent evolution on a decent planet that makes sense. The probability for these things to occur as vacuum fluctuations is closer to the inverse googolplex than the inverse googol and Don Page's bound is breached. If these features are not satisfied, the vacuum fluctuation is annihilated by the projector because it is simply not my brain.

This is how I define my brain and its feelings. Everyone is allowed to define her brain projection operators in any way she wants. ;-)

On the other hand, the people who define the projectors for their brains without the careful definitions of the acceptable history won't face any contradictions either. Indeed, the people with these projectors identifying the states of their brains will mostly find themselves in a chaotic environment that does not make sense. Because they are not careful about the past of their brains prior to the measurement, they either find their brains mostly within a meaningless vacuum fluctuation, or under the influence of drugs. The perceptions are virtually identical in both cases.

The lesson is that one must be careful about LSD and about a proper definition of his or her identity if we want to avoid unphysical upper bounds on the lifetime of the Universe and if we want to avoid lives suffered in disordered perceptions that don't make any sense.

More seriously, I think that Don Page's calculation is simply flawed because the expectation value of a projector that identifies a particular brain is of order exp(-10^{26}) because 10^{26} particles must be arranged in a way that makes up a brain; the entropy of a brain is comparable to 10^{-26} and it must be exponentiated to get an estimate that the brain appears randomly. When the size of the brain is sent to the de Sitter horizon radius, the corresponding correctly calculated "upper bound" on the lifetime should approach the recurrence time.

The number mentioned in the middle of the previous paragraph would be even more drastic if I created the brain out of de Sitter thermal fluctuations. At any rate, the probability for a whole brain to emerge as a vacuum fluctuation is closer to an inverse googolplex, and correspondingly, the required spacetime volume in which the weird conclusions could be found is closer to googolplex itself, not a googol!

I tend to think that even this googolplex upper bound on the allowed lifetime of the Universe is unphysical - but this kind of science is little bit too far from the kind of science that has been tested and I would prefer to take neither of these arguments too seriously. Do we have the right to use the word "physics" for any speculation about the time scales such as 10^{50} years or even 10^{10^{50}} years?

Yurov and Yurov reach a similar conclusion (the bounds of Don Page should be raised dramatically) as my not-quite-serious argument about a not-too-serious topic above, and moreover, they think that they find evidence for the many-worlds interpretation of quantum mechanics as a by-product. ;-) Well, this is how it looks like when physics studied by pure thought gets out of control.

1 comment:

1. Dear Lumos,

How this crackpot stuff stays on arXiv.org at the expense of genuine hard work by Lunsford and others, is the interesting question. Could it simply be that the brains of the administrators have a very high entropy? ;)

best wishes,
nigel