Heller M, Woodin W.H. (eds.) Infinity. New research frontiers (CUP, 2011)(ISBN 1107003873)(O)(327s)_MAml_

is infinite qualitatively different from “really really big?” 189probable history is a direct “fluctuation” into the universe 5 minutes ago, complete withincoming photons, carefully arranged neurons, and so on, that fool us into thinking thatthe universe is much older than it appears. This is weird, but it gets worse. In reality,we do not know the current state of the universe – we know certain attributes A o . Thereasonable question we could ask is, “Given A o , what was the history leading up to thecurrent situation, and what will be observed in the future?” The answer will be totallycontrary to the “natural” evolution of the system because of the laws of physics.Imagine, for example, that A o is indeed “a cosmologist named Anthony on a planetaround a star in a galaxy.”Then the most probable 10 sequence of events consistent with these observations isthe following:1. The universe is in equilibrium.2. A precisely galaxy-size region replete with stars and planets fluctuates into existence, 11leaving the rest of the universe in equilibrium.3. This fluctuated region evolves back to equilibrium.How do we know this did not occur? By step 3. Because the galaxy did not evolve,but simply fluctuated, its dynamics will almost certainly lead to gross violations of“normal” physics. There would be no reason, for example, for the planets to be boundto the stars, and, in general, any data not included in A o would appear incomprehensible.By specifying more and more in A o , we could force (via this conditionalization to amore and more specific set of states) the universe to be “cohesive” for longer, butultimately we are limited by our ability to observe an A o , which is far from sufficient tospecify the macrostate of the universe. In fact, we can take this to the logical extremeand realize that all that is really necessary for (say) me to account for my experience isthe fluctuation of one disembodied brain, with the correct memories, and so forth. Ofcourse, after an instant this brain would decompress in the empty equilibrium universe.Because I repeatedly do not observe this, I can quickly rule out the whole picture, ascan the reader.This reductio ad absurdum indicates that we cannot account for the coherence ofthe world around us if we imagine that the low entropy in our past was the resultof a fluctuation from equilibrium, and this reasoning seems hard to deny. But if weapply the very same reasoning to any universe with finite entropy, we run into analmost identical problem. That is, even if such a universe starts at low entropy andspawns some “normal” observers soon thereafter, it will nonetheless attain equilibriumeventually and thereafter spawn an infinite number of “fluctuated” observers that will,statistically, infinitely outweigh the normal ones. The paradox persists.10 By most probable, I am speaking in the frequentist sense of the number of instances relative to the total numberof instances for which A o are realized. See Hartle and Srednicki (2007) for an extended argument against thisview.11 While this conventional phrase gives a feeling of discontinuity, in this scenario the region is, in fact, naturallyevolving according to its ordinary time evolution in a rather particular microstate. In fact, I strongly suspectthat the “fluctuation” process would be the time reverse of the “evolve back to equilibrium” process of thenext step. That is, the fluctuation would begin with a sort of reversal of the local arrow of time that would goon for “long enough” to reach the macroscopic configuration described by A o , but no longer.