On Saturday, August 17, 2002, at 11:37 PM, Hal Finney wrote: > Now you might say, so what, the whole idea that we formed in this way > was so absurd that no one would ever take it seriously anyway. But the > authors of this paper seem to be saying that if you assume that there is > a positive cosmological constant (as the cosmological evidence seems to > show), eventually we will get into this de Sitter state, and based on > some assumptions (which I didn't follow) we really should see Poincare > recurrences. Then by the anthropic principle we should be > overwhelmingly > likely to be living in one.
OK, let us assume for the sake of argument that we should be overwhelmingly likely to be living in one of these "time-reversed cycles" (which I distinguish from "bounces" back to a Big Bang state, the more common view of cycles). By the same Bayesian reasoning, it is overwhelmingly likely that any observer would find himself in a TRC in which other parts of the universe eventually visible to him (with telescopes) are "incompletely reversed." Let me give a scenario to make the point clearer. It is 1860. Telescopes exist, but are still crude. The Milky Way is only known to be a nebula, a swirl of stars. The existence of galaxies other than our own is unknown. Professor Ludwig calls together several of us friends (perhaps on the Vienna version of the Everything List) and outlines his theory. "We are very probably in a recurrence phase of the Universe, where a worn-out, gaseous phase of the Universe has randomly arranged us into this low-entropy, highly-ordered state we find ourselves in today. It took a very long time for this to happen, perhaps 1,000,000,000,000,000 million years, but here we are." (Reactions of his audience not presented here...maybe in the novel some distant version of me will write.) "All that we see around us, our Sun, the planets, even the gas balls we call stars, were formed thusly out of a random rearrangement of gas molecules. My young mathematician friend in Paris, Msr. Poincare, says this sort of recurrence is inevitable in any sufficiently rich phase space." "Now, if this is correct, it is overwhelmingly likely that of all of the time-reversed cycles, or TRCs, the TRC we find ourselves in will have only reversed time (or created low entropy structures) in our particular region of the Universe. In a hugely greater amount of time, even more regions of the Universe we will be soon be able to observe would be subject to this reversal, but the times involved are even more hideously enormous than the very long times needed to create our own TRC pocket in which we find ourselves." "So, overwhelmingly, observers who draw the conclusions I have reached will find themselves in a Universe where only a region sufficient to have "built" them and their supporting civilization will have the low entropy order of a TRC." "Thus, gentlemen, by a principle I call "falsifiability," I predict that when the new telescopes being built now in Paris and London become operational, we will see nothing around our region of the Universe except gas and disorder." And, of course, within his remaining lifetime Professor Ludwig was astonished to learn that distant galaxies looking very much like nearby galaxies existed, that if a Poincare recurrence had in fact happened, it must have happened encompassing truly vast swathes of the Universe...in fact, the entire visible Universe, reaching out ten billion light years in all directions. The unlikelihood that an observer (affected causally only by events within a few light years of his home planet) would find himself in one of the comparatively-rare TRCs which affected such a big chunk of the Universe convinced Professor Ludwig that his theory was wrong, that the new ideas just being proposed of an initial singularity, weird as that might be, better explained the visible Universe. --Tim May (who also thinks the difficulty of time-reversing things like ripples in a pond, radiation in general, and all sorts of other things makes the Poincare recurrence a useful topological dynamics idea, but one of utterly no cosmological significance)
