Statistics Short-Changes Quantum Theory
- From: "OsherD" <mdoctorow@xxxxxxxxxxx>
- Date: 21 Aug 2005 20:30:38 -0700
>>From Osher Doctorow mdoctorow@xxxxxxxxxxx
COPYRIGHT NOTICE
Statistics Short-Changes Quantum Theory
Copyright By Owner Osher Doctorow Ph.D.
First Published 2005
It isn't mathematicians or mathematical probability-statistics people
who've short-changed quantum theory, but rather physicists who've been
satisfied with the Born-Bohm-Heisenberg-von Neumann
Probability-Statistics Operator Picture on Hilbert Space.
Why? Isn't quantum theory "really" concerned with "averaged"
quantities rather than Individual quantities?
You'll find most internet "explanatory" sites on quantum theory saying
"yes", and remarkably many quantum physics papers, and most of them
have no idea what loss of knowledge-information statistics involves
even in the classical domain.
Most educated people are impressed when they're told: scientist X is
going to statistically test some hypothesis. But all that a scientist
statistically tests in the overwhelming majority of cases is aggregated
or "averaged" quantities, like "the average literacy in nation A", or
"the average math scores in nation B". Even when they get away from
averages or as they're technically known "means", scientists in most of
the remaining cases test "averaged" variances or standard deviations or
averaged percentages or averaged correlations.
To actually "feel" what's involved, suppose that (as is mostly the
case) you realize that in the USA the knowledge of physics and
mathematics beyond high school is being preserved by a few million
people only, arguably less than 5% of the population. In mathematical
probability-statistics, "less than 5%" is a red flag as in
income-tax-evasion. If less than 5% is a result in statistics, it's
enough to reject hypotheses according to most statisticians - in this
case, the hypothesis that the average or mean USA person knows physics
or mathematics beyond high school level.
To get an even much better picture, suppose that an alien from outer
space lands on earth and tests the average (mean) knowledge of human
beings by taking a large random sample, and finds as he arguably will
that the average human being is content to watch TV Sitcoms and Soap
Operas, work at no job or a dull repetitive mechanical or clerical or
sales job, eat, drink, have sex, watch football, and sleep, and doesn't
read or remember most of what he/she learned past 6th grade or so.
If this alien has the authority to either quarantine or destroy a
planet with too advanced technology relative to brainpower, then the
few percent of people who study mathematics or physics in college or do
research in those fields or who apply college level math or physics in
their jobs will not reflect in the world average, and goodbye earth!
I'm not claiming that this is a "real" scenario, but as a thought
experiment it has a rather chilling message. When you give up
measuring the Individual for the Plurality or Aggregate, you might as
well join the apes if not the ants.
You cannot reconstruct the Individual from the Aggregate or Plurality!
You cannot reconstruct the Individual's brainpower from the
"expectation" or "mean" brainpower of earth's population or the USA's
population or Kenya's population. You can go partway in the reverse
direction, and if you examine each and every Individual you'll get the
whole population's aggregated or mean brainpower. So it makes sense to
do that.
In short, it makes sense for quantum theorists to worry very much about
being an "averaged" or "aggregated" field, which is what it is.
To really cause an angry reaction, I might mention how much of physics
and mathematics would be lost if we really concentrated mostly on
Averages and Aggregates. We'd lose everything with calculus/analysis
in it since these are locally pointwise defined. We'd lose all
difference equation approximations to differential equations and of
course all differential equations. We'd lose most of
probability-statistics theory which is a specialized branch of advanced
calculus/real analysis mostly. We'd lose functional analysis, real
analysis, complex analysis, nonsmooth analysis, and if a "time warp"
could take us back to the earth trying to progress in science without
such tools, try to figure out how far along we'd be by now. We'd use
all of geometry related to locality, ditto for local topology (not all
topology is global despite the claims), general relativity (the local
Euclidean property), most of the equations attributed to Sir Isaac
Newton and Leibniz and Hooke and on and on.
Osher Doctorow
.
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