Science > Physics > Quantum Gravity Via Expansion-Contraction 23.3: The Random Variable That Generates Time
| Topic: |
Science > Physics |
| User: |
"OsherD" |
| Date: |
29 Sep 2006 01:45:39 AM |
| Object: |
Quantum Gravity Via Expansion-Contraction 23.3: The Random Variable That Generates Time |
From Osher Doctorow
We can, using the "Toy Model" of the last few Sections, come up more or
less with a random variable that generates time.
Consider the equation:
1) t = log[(p - 1)^2 + 1]
or equivalently:
2) exp(t) = (p - 1)^2 + 1
or equivalently:
3) (1 - p)^2 = exp(t) - 1
Recall that Probable Influence/Causation p is given by:
4) p = 1 + y - x, x = P(A), y = P(AB), where A Probable
Causes/Influences B
Because of the form of (3), a "natural" choice for x = P(A) is the
exponential cumulative distribution function (cdf) or its probability
density function (pdf) analog, respectively:
5) P(A) = 1 - exp(-x) (the standard exponential cdf)
6) fX(x) = exp(-x) (the standard exponential pdf)
It does make a difference whether we choose (5) or (6) to replace P(A)
in (4), the respective values of p then reducing to:
7) p = 1 + P(AB) - (1 - exp(-x)) = P(AB) + exp(-x)
8) p = 1 + P(AB) - exp(-x) = P(AB) + (1 - exp(-x))
The respective results of replacing p in (3) by (7) or (8) are:
9) (1 - P(AB) - exp(-x))^2 = exp(t) - 1
10) (1 - (P(AB) + (1 - exp(-x)))^2 = (exp(-x) + P(AB))^2 = exp(t) - 1
In (9), as the value x of the random variable X (that exerts Probable
Influence/Causation on time t or B) increases, the variable t on the
right hand side increases, with all else "constant". In equation (10),
the opposite happens.
So there is either a direct increase of X's value x as time t increases
or a direct decrease depending on whether cdf or pdf is used, and both
x and t enter exponentially into the equation with in addition x
entering quadratically. However, the sign of x in the exponential is
negative, while the sign of t in the exponential is positive.
Osher Doctorow
.
|
|
| User: "Jessie" |
|
| Title: Re: Quantum Gravity Via Expansion-Contraction 23.3: The Random Variable That Generates Time |
29 Sep 2006 06:19:26 PM |
|
|
"OsherD" <> wrote in message
news:1159512338.971056.196250@m73g2000cwd.googlegroups.com...
From Osher Doctorow
We can, using the "Toy Model" of the last few Sections, come up more or
less with a random variable that generates time.
Consider the equation:
1) t = log[(p - 1)^2 + 1]
or equivalently:
2) exp(t) = (p - 1)^2 + 1
WRONG.
How many times must I correct you?
log is base 10, ln is base e,
so your above equation is
2) 10^t = (p - 1)^2 + 1
OR DID YOU MEAN
1) t = ln[(p - 1)^2 + 1] ????
If you are going to be that sloppy with math, then delete the rest of your
post.
*FLUSH*
.
|
|
|
| User: "OsherD" |
|
| Title: Re: Quantum Gravity Via Expansion-Contraction 23.3: The Random Variable That Generates Time |
30 Sep 2006 10:44:40 AM |
|
|
From Osher Doctorow Ph.D.
Jessie AKA invalid at spamless dot com (both invalid.com and
spamless/nospam.com are the main sources of sci.physics trolls and
graffiti artists) wrote:
WRONG.
How many times must I correct you?
log is base 10, ln is base e,
Jessie doesn't know that this "convention" only applies to students
taking an elementary or intermediate calculus course, after which
professors almost always explain that "log" is used instead of "ln" for
base e logarithms since it is the most common base in logarithms. The
vast majority of research literature uses log for logarithm base e
rather than ln.
Jessie, go to study in Japan or Israel. In Japan, respect for older
people and teachers/professors/instructors is "built in" to the
socioculture, not haphazardly acquired by students whose mammas and
pappas let their children "do their own things." In Israel, Military
service precedes college (assuming that you're not in high school,
which your lack of manners suggests that you are), so that students who
enter college learn to listen and read and pause before shooting their
mouths off. Maybe this spoiled background of children is why we have
so many Terrorists in the modern world ready to shoot everybody else
first except themselves or ready to blow themselves and others up
simultaneously.
Osher
.
|
|
|
| User: "Frieta" |
|
| Title: Re: Quantum Gravity Via Expansion-Contraction 23.3: The Random Variable That Generates Time |
30 Sep 2006 02:46:58 PM |
|
|
"OsherD" <mdoctorow@comcast.net> wrote in message
news:1159631080.038573.301200@c28g2000cwb.googlegroups.com...
From Osher Doctorow Ph.D.
Jessie AKA invalid at spamless dot com (both invalid.com and
spamless/nospam.com are the main sources of sci.physics trolls and
graffiti artists) wrote:
WRONG.
How many times must I correct you?
log is base 10, ln is base e,
Jessie doesn't know that this "convention" only applies to students
taking an elementary or intermediate calculus course, after which
professors almost always explain that "log" is used instead of "ln" for
base e logarithms since it is the most common base in logarithms. The
vast majority of research literature uses log for logarithm base e
rather than ln.
WRONG AGAIN. Quite misleading people. Go read a math book, Kosher.
.
|
|
|
|
|
|
| User: "OsherD" |
|
| Title: Re: Quantum Gravity Via Expansion-Contraction 23.3: The Random Variable That Generates Time |
29 Sep 2006 02:01:24 AM |
|
|
From Osher Doctorow
The simplicity of the derivation of the results combined with the fact
that both time and probability enter exponentially suggest that we have
more than a "toy model" here and that we really have a random variable
X that generates time. Since X is random, we not only have probability
generating time, but (with two choices) a random variable that
generates time.
So far we don't have a physical name for random variable X, since X is
too new conceptually to either have a name or be identified with any
known physical variable, but we do have the ability to compare X with
the quantum scenario of the Schrodinger equation, where ww* =
probability for wave function w and its complex conjugate w*. Since
ww* = /w/^2, in a sense the Schrodinger or Born probability is also
quadratic, just as our p enters the probability-time equation
quadratically as well as exponentially.
But w was never identified with a particular random variable with
specified pdf or cdf, while our X is so identified up to the choice of
whether to use pdf or cdf. Moreover, the Born probability gave no
clue as to Inflation, while our scenario is essentially that of
Inflation as reflected by the exponential in time.
Osher Doctorow
.
|
|
|
|
|
Related Articles |
|
|
