From Osher Doctorow
Quantum Probability is not just the extreme non-existent "classical
probability" alleged by the Finnish and U. Penn. researchers mentioned
in Section 4.0, and also not just the extremely different probability
related to "amplitudes" and conditional probability that one finds in
the Mainstream literature by Parsarathy and others (who sometimes call
themselves the "Stochastic" or "Quantum Probability" schools,
depending on who they are), but actually most fundamentally at least
in the Mainstream comes from Max Born who showed that in the
Schrodinger Equation the quantity:
1) ww* = /w/^2 = P(finding a particle/wave in a volume of space V)
There is nobody in Quantum Theory who has ever been able to
successfully challenge Born's "absolute value of the wave function w"
of (1) above, and the claim by the anti-probability crowd that Quantum
Theory is non-probabilistic is absurd in view of (1).
So what does this anti-probability crowd (in Finland and parts of
Greece and the USA) actually mean? Well, they are using a hodgepodge
of half-truths. It is generally considered by the Mainstream, rather
illogically in my opinion, that the Schrodinger equation is a
"determinstic equation" despite (1), and since the anti-probability
crowd is rather poor at discriminating facts about probability, they
think that this means that quantum theory is not probabilistic at
all.
The Mainstream regards Schrodinger equation as "deterministic" due to
a technicality which has almost nothing to do with intuition but
rather history. Mainstream probability-statistics has usually found
that probabilities and probability density functions (pdfs) are
usually associated with either equations of random variables with an
error term e or else with rather special equations like the former
specifying pdfs. But those are historical coincidences, because as
I've shown in numerous threads on sci.physics, the entire field of
Probable Influence/Causation (PI) involves equations that don't
necessarily require special error terms e or even random variables or
their analogs, and in fact random variable equations can be derived
from non-error-term PI equations.
The claim that the Schrodinger Equation is "deterministic" just means
that there is no random variable e called an "error term" or "random
coefficients" specified in the equation. Neither are there such
quantities in PI equations necessarily. But the joke is on the
critics because Born's probability ww* (w* is the complex conjugate of
wave function w) arises nevertheless in the Schrodinger equation and
can't be avoided, showing that explicit separate "error terms" or even
explicit "error coefficients" are not required for equations involving
probability.
In fact, the pdf of any random variable obeys an equation with neither
error terms nor random coefficients, as almost any specialist in
mathematical probability or probability-statistics knows.
Osher Doctorow
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