Stathis Papaioannou, <[EMAIL PROTECTED]>, writes: > Let me add a postscript to this quicky: does the multiverse include perfect > duplications, or only arbitrarily close to perfect - and does it make a > difference?
It depends on what you mean by the multiverse, and on what the laws of physics are locally. I just happened to be reading a paper linked from Max Tegmark's page which answers the question in the affirmative for the level 1 and level 2 multiverse(s). The paper is "Many worlds in one", by Garriga and Vilenkin, http://arxiv.org/abs/gr-qc/0102010. Tegmark's level 1 multiverse is our universe when it is taken to be infinite in size. There should be duplicates of each finite sized region. The level 2 multiverse is the larger ensemble predicted by inflation theory. It contains an infinite number of level 1 multiverses, each infinite in size. The Garriga/Vilenkin paper explains more clearly than anything I had previously read how we can fit an infinite number of infinite sized level 1 universes into the level 2 universe. The answer is that inflation occurs exponentially fast and lasts forever. In relativity, time and space are somewhat interchangeable. From the level 2 perspective, new space is constantly (and rapidly) being added to each level 1 universe. Because this goes on forever, the "eventual" size of each level 1 region is infinitely large. But because of the interchangeability, when we look at it from the "inside view" of each level 1 universe, it can be considered to have been born infinitely large. The other main goal of this paper is to argue that the observable finite-sized regions of the universe do have exact duplicates elsewhere in the level 1 and level 2 ensemble. The duplicates are not merely approximate, but rather they are exact. This is based on quantum theory only allowing a finite amount of information to be present in a region (the Bekenstein bound). Therefore our whole observable universe bubble has only a finite number of bits in it, and so there should be an infinite number of other bubbles with exactly the same pattern of bits, and these are exact duplicates. Another interesting result of this paper concerned "daughter universes". In some models, it may be possible to trigger the formation of new inflating regions which would "bud off" from our own space time and produce their own infinite-sized level 2 universes. The authors of this paper had proposed in an earlier one that this could be a mechanism for civilizations to survive heat death, that they could create daughter universes and somehow send information into them which could be taken up and incorporated by civilizations evolving in the daughter universes. However, in the context of the multiverse, this won't really work, because any finite number of messages are insignificant in the context of an infinitely-duplicated multiverse. Only a finite number of regions can receive the messages, compared to an infinite number of regions that either don't receive them, or receive spontaneously-generated fake messages (like our discussion earlier today of "magical" universes). Therefore the messages can have only an infinitesimal impact on the evolution of the daughter universes and cannot be considered a meaningful form of survival. Hal Finney
