Quantum Gravity Via Expansion-Contraction 77.6: Incredible Conformity in Adding Stochastic Terms to Einstein's Equation For Fundamental Equations of Quantum Gravity

**OsherD** · #1 January 22nd 07 posted to sci.physics

From Osher Doctorow

I pointed out in the last few posts that we are now making contact
with a substantial research literature on adding stochastic term(s) to
the Schrodinger or similar equations, but there are actually two
choices that need to be made.

1) Add a random variable called "error", often written e or e_i or ei,
with or without modifications (such as additional factors) to various
other terms of Schrodinger.

2) Add a probability, for example Probable Influence/Causation (PI)
P(A--B), instead of a random variable in (1).

Readers may be surprised to learn that there is NO literature on (2).

The reason for the absence of research literature on (2) is arguably an
incredible history of Ingenious Imitation in the relationships between
Mathematical Probability-Statistics and Physics. For a previous
example of this as "serious", readers would have to look at Euclidean
Geometry, whose practitioners imitated each other for thousands of
years.

While originally in history mathematicians arguably came first with
Euclidean geometry and then physicists imitated them, in recent
centuries physicists tended to come first with at least
experimental/observational discoveries, after which mathematicians
imitated them and then concentrated on the purely mathematical aspects
of equations mostly but to a small but varying extent on feedback to
physics. Thermodynamics and mechanics came from the physicists, and
then mathematical statisticians imitated them, and mathematical
statisticians in turn were imitated by 3 parties: other mathematical
statisticians, mathematical probability theorists interested in the
pure probability aspects of the equations of the former, and
physicists/engineers trying to incorporate everybody else's results
into somewhat large-scale theories.

One of the little known consequences of all this was a parallel
development in mathematical statistics called Regression Analysis,
especially Linear or Multilinear Regression, in which an "error" term e
as a random variable was added to one side of a deterministic equation
and by a rather interesting "trick" another term was transformed to
something in conditional probability called a conditional expectation
or conditional mean. Statisticians then went back to this and mostly
dealt with the sample form of the equation(s) and how it fit into their
usual obsession with the difference between population and sample
quantities. Probability theorists then took the statisticians'
viewpoint as a "given" and spent their time examining the probabilistic
aspects of the "given" equations without changing their basic forms
except in a rather curious way of relating them to differential
equations in what became the subfield of Stochastic Differential
Equations in Probability and lately in Statistics.

Why nobody thought of simply adding a probability or probability
density function (pdf) or cumulative distribution function (cdf) or
Probable Influence/Causation instead of a random variable called
"error" (e), was simply due to the fact that the imitation was not
explicitly discussed early on, and later people just imitated the early
people in not doing it.

But why should probability rather than a random variable be added to
the Schrodinger or similar scenarios? Because probabilities are
SIMPLE, while random variables are extremely complicated. For
example, a random variable describing a person's height as randomly
sampled is not an ordinary function or measure, unlike a probability
which is a measure (except for conditional probability which is a
relative measure) and which can be expressed as function. A random
variable has a value, say 60" (sixty inches) for height, but it doesn't
asssign this value x in the range of the random variable to an element
w in the domain of the random variable. It is in a sense "multivalued"
in that it doesn't take on the value 60" or x deterministically but
with a certain probability, or more precisely for continuous random
variables the probability is called a cumulative distribution function
F(x):

3) F(x) = P(random variable X = x) = P{w: X(w) = x}

where w are elements of the probability space or domain.

The result of all this is that it is super-ponderous to attempt to
progress in stochastic differential equations, for example, whereas if
you add a probability P to a deterministic equation (say, to the left
hand side), you don't introduce any complications since you don't keep
track separately of both values of P and probabilities of being =
those values, unlike for random variables. Your new equation is
treated as just having a new function P, which may be a function of
time as in P(t) or P_t or Pt, or even additional arguments. The other
"deterministic" variables when normalized are now regarded as either
probabilities or functions of probabilities which become deterministic
only when the probabilities are fixed or constant for some reason.

Stochastic differential equations are far more difficult to solve in
general than "deterministic" differential equations. You have to
literally learn machinery called Ito and/or Stratonovich integrals and
their differential or derivative aspects if any, and a typical paper in
stochastic differential equations satisfies itself with just solving a
particular stochastic differential equation or a rather small class of
stochastic differential equations, somewhat analogous to the way that
the complications of algebraic geometry and algebraic topology have
removed theoretical physics largely from the realm of easy and elegant
and quick solutions and theories into the realm of ponderous, slow
progress requiring almost endless "machinery" or sub-theorems and
sub-subtheorems and definitions and so on.

Osher Doctorow

**OsherD** · #2 January 22nd 07 posted to sci.physics

From Osher Doctorow

Of course, everything that I've said about the Schrodinger equation
applies also to the Einstein Field equation in terms of adding
stochastic terms (in the last post).

Readers may be slightly skeptical at this point, since I am presumably
the first person who has told you this, and others aren't talking.

Why me? Well, I'm 68 years old, and a Nonconformist, which means that
I'm not connected with a Bureaucracy, whether Big Corporation or Big
Government including Big Education. If a member of the Princeton
University faculty were to criticize fellow physicists or
mathematicians for being mostly or even entirely Ingenious Imitators,
he/she arguably would have to work every day alongside those people and
receive their angry glances if nothing else. Some people even are
threatened by angry professors in academia including being screamed at
in the hallway outside class. The only place I have to worry about is
the internet, and I can choose not to read graffiti artists or trolls
or screaming professors, for example based on the titles of their
replies.

Being older also has a curious effect depending on whether you've been
a Conformist or Nonconformist. If you've been a Conformist, you
probably attained Tenure in academia and are receiving retirement
pension from it, and if you still want to publish as you did before,
you would be wary about insulting everybody including the "impartial"
peer reviewers who happen to be professors in your field. If you don't
want to publish, you probably haven't noticed anything wrong anyway.

If you're a Nonconformist and have been for a long time, then you
probably didn't achieve Tenure in academia or arguably anywhere else,
since people outside academia tend to be as Conformist as inside (from
baseball or football to politics to sex to clothes to etc.). And if
you're over 65, you probably won't get hired for any job that pays more
than a security guard. So you might as well tell the truth, since
you're not going anywhere but down so to speak (well, down in life at
least). And in addition, you just might know the truth since you're
more alert to Ingenious Imitation if you're a Nonconformist.

Does this read something like the Salem Witch Trial scenario of the
1600s? Are old people really either receiving lucrative pensions or
"sentenced to death" indirectly or directly for Nonconformity? Yes in
my opinion, unless they're heirs or heiresses or have incredibly dumb
luck. I typically get 100% rejections, no matter what academic or
research or corporate or government job that I apply for. And I apply
very "correctly" except that I don't lie about wanting to imitate the
"boss" or "teamwork".

Osher Doctorow

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