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From: "Brent Meeker" <meekerdb.domain.name.hidden>
Brent, you say, ". . . 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."
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? If you repudiate duplicate worlds, do you also repudiate infinite space?
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. 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?)
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?
Norman Samish
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Received on Thu Aug 17 2006 - 22:38:18 PDT