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From: rick_s on 23 May 2010 05:56
In article
<c3085ce5-9d36-4e4b-9a65-d1ded4914460(a)31g2000prc.googlegroups.com>,
osherdoctorow87(a)gmail.com says...
>
>
>From Osher Doctorow
>
>Rigged Hilbert Space (RHS) rather than Hilbert Space turned out to be
>the correct space for Quantum Mechanics, although physicists now
>usually refer to RHS as "Hilbert Space" for simplicity. See:
>
>1) Rafael de la Madrid, "The role of the Rigged Hilbert Space in
>Quantum Mechanics," 31 pages, arXiv: quant-ph/0502053 v1 9 Feb 2005
>
>and Arno R. Bohm (U. Texas Austin) Phys. Rev. D71 2005 085018 among
>others.
>
>It turned out that expectations, uncertainties, commutation relations
>were not defined on the whole Hilbert Space for unbounded observables
>with continuous spectrum, including continuous and resonance
>spectra. The theory of Distributions was used to solve or repair
>this difficulty, the word "Rigged" referring to "equipped (with
>additional things)", and it has many relationships to Probability
>theory.
>
>The Dilemma in P(A-->B) - P(B|A) taking on values between 0 and 1 is a
>somewhat analogous dilemma, because of the following:
>
>2) If u and v are variables in [0, 1] and u - v takes values from 0 to
>1 either inclusively (including 0 and 1) or non-inclusively (except
>for 0 and/or 1), then the "variation" in a generalized sense between u
>and v is as large as the range of u and of v (inclusively or non-
>inclusively).
>
>It is thus necessary to have two theories: one for P(A-->B) (Probable
>Causation/Influence) and one for P(B|A) (Conditional Probability), and
>to compare the predictions from each, rather than leave the question
>of whether one is using one or the other "undecided" or even
>"negative" (only using one of the two).
>
>Since physics and mathematics already use P(B|A), therefore P(A-->B)
>needs to supplement the former in both fields and applications.
>
>There are 22 papers in arXiv on "Rigged Hilbert Space," from 1995
>through 2006. The ending of arXiv contributions in 2006 was because
>the incorporation of Rigged Hilbert Space into Quantum Mechanics was
>regarded as completely solved. Wikipedia's article "Rigged Hilbert
>Space" includes the de la Madrid reference, but surprisingly omits to
>mention its main uses!
>
>Osher Doctorow

Now correct me if I am wrong but as I see it, Hilbert space is the same
as n dimensional space and also hyperspace. Any space which is outside of
the real physical 3 dimensions we exist in.

There are only 3 real dimensions all other spaces such as n dimensional
space have no real physical existence wrt physical objects like people or
that which we can detect using physical means.

Outside of a closed universe, beyond the edge of the big bang universe,
is nothing. Not even a skin or shell, but the pure vacuum, the void, and
it has no space. It exists in our mind as a concept, and hence a
dimension, and we speculate that this is hyperspace, and you can have
worm holes in space, that consists of a perfect vacuum, and hence the
distance betrween two um space terminals if such a thing existed for
wormholes like4 a stargate, the distance would be zero between doors yet
in real space the distance is squillian light years.

So Hilbert Space relates to extra dimensions which we should realize are
in truth convenient imaginary constructs. And then Rigged Hilbert Space
has to include the real part so that together you can have the real and
imaginary described.






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