To those who still cling to a single-universe world-view, I issue this challenge: explain how Shor’s algorithm works. I do not merely mean predict that it will work, which is merely a matter of solving a few uncontroversial equations. I mean provide an explanation. When Shor’s algorithm has factorized a number, using 10500 or so times the computational resources that can be seen to be present, where was the number factorized? There are only about 1080 atoms in the entire visible universe, an utterly minuscule number compared with 10500. So if the visible universe were the extent of physical
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My only grievance with an argument based on finite atoms in the universe as the limit of computation is Deutsch’s own argument that knowledge transforms our environment to things greater than the collection of atoms. That’s said, since computation is a finite task, bound in physical reality, then there is indeed a limit on what computations can be done, or as he said there are computations that are physically intractable. I suppose the knowledge required here to get around those limits is in fact interference and the explanation is to use the physical limits of the multi-verse to increase what can be computed.
