From Osher Doctorow
If you go to a university engineering-mathematics or physics research
library and look at the statistical or probabilistic or statistical
physics or probabilistic physics sections (you probably will have to
wander through the stacks to do this, that is to say the shelves and
aisles relating the shelves and various floors), then you'll probably
find E. Nelson's Stochastic School of Quantum Mechanics from the 1960s
or an updated version of Nelson's theories and applications.
To put it another way, although a large number of physicists and even
mathematicians believe that Quantum theory is "statistical" but not
fundamentally probabilistic (which, by the way, is a contradiction
since statistics uses probability as it main mathematical tool), the
probabilistic school (often called stochastic school) is alive and
well and even thriving, while people who keep talking about the
"statistical" school are usually outsiders to the non-deterministic
field who may be experts in black holes but neither expert in
statistics nor in probability.
But where do you find these people and their papers in arXiv or Front
for the Mathematics ArXiv? Well, one way is to look through the
Probability section of Front, although if you read every paper there,
you may never get to the end of that section. A better way is to
look at D. Bar's paper of 2007, referenced earlier in this Section,
and look at the references in that paper.
A curious thing then happens. Italian and Japanese researchers
become key aside from Bar (an Israeli) and Kuchar (of U. Utah USA,
although previously from Czechoslovakia). These include G.
Constantini, G. (Giuseppe) Florio, S. Pascazio, Antonio Trullo,
Rosario Fazio, Vittorio Giovannetti, K. Yuasam S, Tasajum G, Kimura,
H. Nakazato, I. Ohba.
Let's stop at I. Ohba, who actually alone unravels the mystery. By
the way, you have to look at the coauthors of P. Facchi in Bar's
references under keywords "P. Facchi" in order to find Ohba, and then
look at the keyword author "Ohba" or "I. Ohba". Although Ohba only
has 9 papers in arXiv, while Giovannetti has 53 and Pascazio has 51
for example, Ohba of Waseda U. Tokyo goes back to Nelson in Ohba's
1996 paper:
"Effects of inelastic scattering on tunneling time in generalized
Nelson's Quantum Mechanics," Kentoro Imafuku, Ichiro Ohba, and Yoshiya
Yamanaka, all of Waseda U. Tokyo except that Yamanaka is from Waseda
U. Senior High School Tokyo, Japan. This is quant-ph/9611007 v1 6
Nov 1996.
Ohba and his colleagues generalized Nelson's stochastic theory in that
paper! Nelson had adhered rather rigorously to the Copenhagen
Interpretation. One almost had to do that in order to get in print in
those days, or else adhere to one of the other fundamental
interpretations of the Mainstream. Ohba and his colleagues appear to
have had a recent course in graduate probability (I kid you not!),
which enabled them to add to Nelson's theory the idea of combining two
interpretations, or two probabilistic methods, the new one being
somewhat analogous to tossing a coin and making the outcome relate to
quantum jumps (e.g., a quantum jump is roughly speaking a coin toss or
whatever "payoff" one gets from it).
Now that you know this, you might be more interested in reading Bar's
paper cited in this thread, and other papers of his, in more detail.
If not, you can always come back next year if the Planet has not been
destroyed (a bet which I no longer make).
Osher Doctorow
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