In reply to posts by Hal Finney and Bruno Marchal--
I found the paper you referred to, and it certainly has some very interesting ideas, for example the idea that the arrow of time is actually an anthropic artefact. I admit that I have much reading to do if I am to understand the paper properly, but I am not sure what I was proposing - that all possible worlds will at some stage exist - is the same thing as the Poincare recurrences discussed in this paper. It possible that only a subset of possible events (everything that has occurred so far, and then some) will cycle endlessly, and if so, as Nietzche commented, that'll suck (or words to that effect). I probably gave the wrong example when I proposed as my unlikely event the formation of an exact copy of our solar system and its inhabitants in far future interstellar space; much more interesting would be a rather different copy, where you would be resurrected with intact personality and memories of your past life, with enhanced intelligence and physical abilities, and a whole new civilization with scientific wonders, intelligent aliens, and things so strange that no-one today has even imagined them, all to explore. Of course, you will also experience burning in hellfire as the flipside to this happy state, but who was it that said it was better to burn than to disappear?
I agree that my four assumptions are dubious, but I chose them, for the sake of argument, as being (a) most inimical towards Many Worlds theories, (b) closest to what most people would think of as common sense, and (c) least controversial/ most conservative in the scientific community. I do think they are internally consistent, even if they are completely wrong. I do not understand your comment that by saying the universe is unique, finite, expanding and cooling forever, it is contradictory to allow that my example of an unlikely event will occur as time approaches infinity. The increase in entropy and cooling which go with the model I suggested are average trends over time. It is possible within this long term decline to have pockets of order/ decreasing entropy, both in classical statistical mechanics and quantum mechanics. It is a mathematical fact, independent of the actual physics, that given enough time (and eternity is certainly enough time), any event that is possible, however close to zero its probability per unit time, will occur with probability arbitrarily close to 1. What rather surprised me, however, is the fact that the last statement is only true in general if the probability per unit time stays constant or increases with increasing time; if it decreases, limiting towards zero as time approaches infinity, then it is possible that this event, which still always has non-zero probability per unit time, may never actually occur. For example, if Pr(P)=1/(t^2), as t goes from 2 to infinity, the cumulative probability that P will occur at some point is 1/2.
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