From: Richard McGough (richard@biblewheel.com)
Date: Wed Jul 02 2003 - 14:10:22 EDT
What has happened to sciam?
The article under discussion was featured on the cover of the May 2003 Scientific American, where it was flatly asserted, with no question or qualification, that parallel universes really exist. This is ludicrous in the extreme. At best Tegmark has some evidence for his hypothesis. He certainly has nothing like scientific proof. This makes the cover of sciam look rather like the National Enquirer.
How Tegmark ever got his article past peer review is beyond me. When I first looked at his basic claim, I knew it was false. It took only minutes to prove it false. I refer to these calculations from his article:
http://www.sciam.com/article.cfm?articleID=000F1EDD-B48A-1E90-8EA5809EC5880000&pageNumber=2&catID=2
>About 10 to the 10^92 meters away, there should be a sphere of radius 100 light-years identical to the one centered here, so all perceptions that we have during the next century will be identical to those of our counterparts over there. About 10 to the 10^118 meters away should be an entire Hubble volume identical to ours.
>These are extremely conservative estimates, derived simply by counting all possible quantum states that a Hubble volume can have if it is no hotter than 10^8 kelvins. One way to do the calculation is to ask how many protons could be packed into a Hubble volume at that temperature. The answer is 10^118 protons. Each of those particles may or may not, in fact, be present, which makes for 2 to the 10118 possible arrangements of protons.
It appears Tegmark only counted the eigenstates. He ignored the fact that each superposition of these eigenstates corresponds to a different physical configuation of the system.
Consider a single electron. Consider just its spin. Its state is a linear superposition of the two eigenstates:
|s> = a|u> + b|d> with aa* + bb* = 1
There is a continuous infinity of possible states for the spin of this one electron. Now couple this state with that representing its position and momentum, and its interaction with all other particles and you will have an uncountable infinity of inifities required to represent all possible configurations of matter in just the room I'm sitting in, let alone a Hubble Volume.
The number 2^10^118 as a measure of all possible physical configurations in a HUbble volume is patently absurd.
Tegmark could try to resuscitate his theory by doing an ergotic style analysis, but I can guarantee it would be extremely difficult (if it even is possible), as should be obvious by estimating the order of infinity involved in representing real physical states. But even then it would have the problem of only establishing that systems would repeat "within epsilon" - so that any aspect of the system that depends on exact values would not necessarily be duplicated anywhere.
-- Richard Amiel McGough Discover the sevenfold symmetric perfection of the Holy Bible at www.BibleWheel.com --
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