Brent: ". . . It seems to me that an information theoretic analysis should be able to place a lower bound on how small a probability can be and not be zero."
Norman: Doesn't a lower limit on probability repudiate the notion of Tegmark, Vilenkin, et al, that there are necessarily duplicate worlds to ours, if only we go out far enough?
Brent: I don't see why these questions are related. There are only *necessarily* duplicate worlds if there is an infinity of worlds of a higher order than the information content of a world.
Norman: I don't understand what "higher order than the information content of a world" means.
Norman: If you repudiate duplicate worlds, do you also repudiate infinite space?
Brent: Space could be infinite without there being duplicate worlds. "Repudiate" is too strong a word. I doubt they are relevant.
Norman: I asked that because my understanding is that "In infinite time and space, whatever can happen must happen, not only once but an infinite number of times." Do you disagree?
Norman: E.g., Alex Vilenkin ("Beyond the Big Bang," Natural History, July/August 2006, pp 42 - 47) says, "A new cosmic worldview holds that countless replicas of Earth, inhabited by our clones, are scattered throughout the cosmos." Vilenkin's view is that this conclusion arises from Alan Guth's theory of inflation and "false vacuum" put forth in 1980. The unstable false vacuum (which eternally inflates exponentially) has regions where random quantum fluctuations cause decay to a true vacuum.
Brent: You can't "go to" those different universes. Their supposed existence is entirely dependent certain theories being correct. But those theories are contingent on suppositions about a quantum theory of spacetime - which is not in hand. So, while I'm willing to entertain them as hypotheses, I neither accept nor deny their existence.
Norman: The difference in energy of the false vacuum and the true vacuum results in a "big bang." In the infinity of the false vacuum there are, therefore, an infinity of "big bangs." The big bangs don't consume the false vacuum because it inflates faster than the big bangs expand. Vilenkin figures the distance to our clone at about 10 raised to the 10^90 power, in meters. (This roughly agrees with Tegmark's number.) (An unanswered question is where and why did this initial infinity of high-energy false vacuum originate?)
Brent: If one can originate, then any number can. But I don't see that such an infinity has any implications.
Norman: To me, an initial infinity of high-energy false vacuum, without an origin, is not logical. I ask the question because I'm hoping for an hypothesis that is logical.
Norman: Now 10 raised to the 10^90 power is a big number. Therefore the ratio of duplicate Earths to all worlds is exceedingly small - but not zero! Do you think it should be zero?
Brent: I think it might be of measure zero. Or there might not be any duplicate universes.
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Received on Fri Aug 18 2006 - 11:10:53 PDT