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>From Osher Doctorow mdoctorow@xxxxxxxxxxx
A. Raab of Germany, in "An approach to nonstandard quantum mechanics,"
math-ph/0612082 v1 27 Dec 2006, 29 pages, tries to use a variation of
Abraham Robinson's Nonstandard Analysis to do what A. Bohm and his
Colleagues at U. Texas Austin have done with their Rigged and
Nested/Lattices of Hilbert Spaces, but with "deeper foundations".
The basic idea of Nonstandard Analysis which was created by Abraham
Robinson (of first Hebrew U. Jerusalem, then UCLA, then Yale in his
Faculty positions, about an equal period for each of roughly 6 years)
is similar to the basic idea of Quantum Logic, namely that there exists
a "least element" which is nonzero, a sort of "atom of atoms" which is
more or less unobservable. It has been heavily criticized by A. Connes
of France (the Noncommutative Geometry Physics Connes) precisely for
being unable to exhibit an observable element even in theory. No such
charge has been raised against Quantum Logic, possibly because Quantum
Logic has usually tried to imitate Heisenberg, one of the Founding
Fathers.
If we view the unobservable "least element" of Nonstandard Analysis as
a Singularity or even a black hole in particular (even a mini-black
hole), then Raab might be on the right track, or perhaps I should say
one of the right tracks. By the way, 1 divided by the least element
turns out to be an infinite element, giving us a very nice infinite
velocity if we are inclined in that direction (Raab is not - he's too
interested in reproducing past results in a faster way).
There's a substantial literature of about 40-50 papers or so on
Nonstandard Analysis in arXiv and an approximately equal number in
Front for the Mathematics ArXiv.
I'll let readers look at the papers while I prepare to make a few
comments on the underlying ideas mentioned above.
Osher Doctorow
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