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Sunday, July 15, 2007



Can continuous eigensystems such as those associated with the position space wavefunction be treated rigrourously in an infinite dimensional Hilbert space? It is AM Monday morning and Wolfram and his crew are still hard at work and I am curious to see how long they go so I am going to comment on this talk while I wait.
I thought this guy was ridiculous. He will probably not let this comment be posted - but if he doesn't, wouldn't that indicate he was afraid of intellectual opposition, vital for intellectual development? He presented ridiculous propositions as if they were firmly grounded in some sort of science. Since I thought he was so ridiculous in his speculations I am not going to maintain a high level of rigor in this blog but merely outline why what he said was in my opinion nonsense and be rather blunt. If this comment doesn't go through the moderator I will do it with rigour.
The whole problem (and this is not specific just to him, but to most physicists) is that you can't properly treat continuous eigensystems in a Hilbert space. You need to use a more general notion of a Banach space. Thus all this mumbo-jumbo about foam and discreteness and the number of bits in the universe and the rest is just a result of trying to treat a continuous eigensystem in a Hilbert Space and running into problems. Even the infinite dimensional Hilbert space won't work because it is the wrong order of infinity to cope with the continuous eigensystems of position space wavefunctions rigourously. Each point in space is a basis for the position space wavefunctions. This is too many bases to fit in a Hilbert space, so people discretize things somehow with various lines of mumbo-jumbo instead of doing it properly in a more general Banach space.
All this bit about Planck tiling the boundary of the universe and that determining the inside of the universe seems to me to be just a confusing way to state a boundary value problem and the information you need to solve it.
He threw so many buzz words like "dark matter" and claimed that composed most of the universe. There is scant empirical evidence for this. The observation that there seems to be extra gravity could perhaps be accounted for by many other explanations than the buzz word dark matter. What about a changing norm over long distances so that gravity locally obeyed an inverse square law but not globally? Then we don't have to confuse everbody with buzz words. Anyways, I suppose every once in a while people need to check if the emperor is wearing clothes or not. Is it me or him who is undressed? - look into it and see what you think. In this case, I think this talk was a series of essentially flawed reasonings presented as some kind of profound commentary.
I am not saying there is no discreteness in qauntum mechanics. Surely there is. But the wavefunction can only have non-finite compact support at most at one instant in time and then it grows tails again. This is the nature of the Schrodinger equation. Anyways, I am getting tired waiting so my mind is slipping. I don't think that, particularly for an audience of non-specialists, that this kind of buzz word loaded talk should be presented as if there was no question about whether or not what he was saying was true. I think it is questionable whether or not he was actually even uttering sensible locutions. This is one opposing opinion I have crafted as I try to stay awake to see how long Wolfram will keep going with his crew out of curiosity. I may be wrong but at least I acknowledge that most of what both he said and I have said here is debatable and should not be let go unchecked in a presentation to an audience that is in large part not able to evaluate his claims because they are cloaked in a presumed technical background that most attendees were lacking, so they probably took his word for it. I think what he said was utter nonsense. It is 1:52 AM and I have tired of my wait so I will end now. I rarely wax vitriolic but to everything there is a season.

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