Science > Physics > A Rare Event Knowledge (Semantic Information) From E = wLF
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Science > Physics |
| User: |
"OsherD" |
| Date: |
14 Jan 2005 01:38:08 AM |
| Object: |
A Rare Event Knowledge (Semantic Information) From E = wLF |
From Osher Doctorow
COPYRIGHT NOTICE
A Rare Event Knowledge (Semantic Information) From E = wLF
Copyright By Owner Osher Doctorow Ph.D.
First Published 2005.
On sci.stat.math, I've discussed the equation:
1) E = wLF
where E is complex energy E = E1 + iE2 where E1 is the usual real
measured energy, for example in quantum mechanics, E2 is the
David Bohm quantum potential, w is the Schrodinger wave function
w = x + iy, L is either a characterisic or variable length or
distance, F is resultant one-dimensional force from two forces
acting in opposite directions on the boundary (points) of an
object. From ww* = P (a la Max Born) we get:
2) EE* = /E/^2 = PL^2/F/^2
and therefore:
3) /E/ = P^(1/2)L/F/
If for simplicity we zero out E2, we can put:
4) E = P^(1/2)LF
and let's for simplicity use E = (1/2)mv^2 (so very low potential
energy in the classic sense) and F = ma where v = dx/dt and a =
Dtt(x) (the second derivative of x with respect to time). The
remarkable thing is that if we set L = 1 (constant length one),
and use the fact that ww* = P to get x^2 + y^2 = P with y zeroed
out as above, then x^2 = P and either approximating this by
x = P or changing axis labels, we'll use x = P to solve (4), the
solution being (as the reader can check):
5) t = 1 - (1 + p)/exp(p)
up to an arbitrary constant.
This certainly motivates study of the L = 1 case, but what about
general L? Hopefully, I'll have time to discuss that next time.
Osher Doctorow
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| User: "Old Man" |
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| Title: Re: A Rare Event Knowledge (Semantic Information) From E = wLF |
14 Jan 2005 11:28:41 PM |
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"OsherD" <> wrote in message
news:1105688288.334958.61490@c13g2000cwb.googlegroups.com...
From Osher Doctorow
COPYRIGHT NOTICE
A Rare Event Knowledge (Semantic Information) From E = wLF
Copyright By Owner Osher Doctorow Ph.D.
First Published 2005.
On sci.stat.math, I've discussed the equation:
1) E = wLF
where E is complex energy E = E1 + iE2 where E1 is the usual real
measured energy, for example in quantum mechanics, E2 is the
David Bohm quantum potential, w is the Schrodinger wave function
w = x + iy, L is either a characterisic or variable length or
distance, F is resultant one-dimensional force from two forces
acting in opposite directions on the boundary (points) of an
object. From ww* = P (a la Max Born) we get:
2) EE* = /E/^2 = PL^2/F/^2
and therefore:
3) /E/ = P^(1/2)L/F/
If for simplicity we zero out E2, we can put:
4) E = P^(1/2)LF
and let's for simplicity use E = (1/2)mv^2 (so very low potential
energy in the classic sense) and F = ma where v = dx/dt and a =
Dtt(x) (the second derivative of x with respect to time). The
remarkable thing is that if we set L = 1 (constant length one),
and use the fact that ww* = P to get x^2 + y^2 = P with y zeroed
out as above, then x^2 = P and either approximating this by
x = P or changing axis labels, we'll use x = P to solve (4), the
solution being (as the reader can check):
5) t = 1 - (1 + p)/exp(p)
up to an arbitrary constant.
This certainly motivates study of the L = 1 case, but what about
general L? Hopefully, I'll have time to discuss that next time.
Osher Doctorow
Where's the physics ? OsherD isn't the originator of
a complex Hamiltonian in QM. Here's an everyday
physical application:
In order to account for the effects of absorption in
elastic scattering theory, a phenomenological imaginary
potential, i*W(r) is added to the elastic scattering
potential, V(r), such that
H = T + U(r), U(r) = V(r) + i * Wr)
where V(r) and W(r) are real. For a simple analytical
solution (optical model), look in any book on Nuclear
Physics. Old Man recommends:
"Introductory Nuclear Physics" K.S. Krane
ISBN 0-471-80533-X
[Old Man]
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| User: "OsherD" |
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| Title: Re: A Rare Event Knowledge (Semantic Information) From E = wLF |
18 Jan 2005 06:07:54 PM |
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Very useful! Look on the bright side of it: I'm a mathematician
telling physicists to loosen up their axioms. Remember that the
Einstein Field Equation and Schrodinger/Schroedinger Equation and
Heisenberg's stuff haven't been supplemented by equally simple and
fundamental equations since the early 1900s (well, the first 3 decades)
despite the superstring and loop quantum gravity people. If
mathematics were that slow in proposing fundamental changes, where
would you physicists get your mathematical ideas?
Osher Doctorow
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| User: "OsherD" |
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| Title: Re: A Rare Event Knowledge (Semantic Information) From E = wLF |
18 Jan 2005 08:34:16 PM |
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From Osher Doctorow
Of course, we mathematicians get some of our physical ideas from you
physicists, but at the present time I suspect that the physicists and
engineers are disproportionately heavily funded and so on. However,
I'll try to be of good cheer about it all and get back on topic.
Where is the physics, Old Man asks. Let me see, Energy E = wLF where F
is force. We now have generations of physicists and mathematicians
staring energy and force in the face and saying that it is nonsense to
propose an equation of form:
1) E = f(F)
or E = f(F, some other variable(s))
which goes as deep as quantum theory and/or general relativity.
On the other hand, engineers to the rescue! We are told that engineers
would like to someday be able to "terraform" the solar system and
beyond, and maybe even move asteroids around, and various ideas of M.
Kaku and his interviewees, etc. We don't say it, but force seems to be
a bit of a problem there. No reason to speculate about
E = f(F, etc.) or F = g(E, etc.) where functions f, g, etc.? No
"motivation" except interdisciplinary? Maybe even astrophysics and
cosmology?
Then, of course, there are exobiologists and so on who tell us that
Type 1, 2, 3 or equivalent numberings of hypothetical civilizations
should be able to move around planets, stellar systems, galaxies, etc.
Bigger and bigger forces. But we're not allowed to propose E = f(F,
etc.), right?
Then there is condensed matter and continuum physics, and Glocker and
the others who have argued very well that force is a key concept in
physics, but it goes against the discrete universe fad, eh? And the
energy fad, which doesn't give us much in the way of force.
I could go on and on, and there is actually more, but I remind readers
that fluid mechanics was largely built by dimensional analysis, and
that astrophysics and cosmology make heavy use of dimensional analysis
in models, as does materials science/engineering, etc.
I did make a mistake in assuming that physicists necessarily know
dimensional analysis. In dimensional analysis, it is very, very
important to guess correctly what variables are involved in a problem
on an intuitive basis and experiential basis, and we could call that
theoretical physics intuition or mathematical physics intuition. My
allegation is that energy and force and distance/characteristic length
are key in various of the above problems, and I added one "unexpected"
quantity, the Schrodinger wave function! Now do a dimensional
analysis and tell me whether you do or do not get E = wLF with or
without a dimension of probability. Four variables (energy, force,
distance, wave function), and three dimensions (M, L, T) yield 1
dimensionless product k, and can you get anything except E^(-1)LFw = k
from those variables?
Osher Doctorow
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| User: "OsherD" |
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| Title: Re: A Rare Event Knowledge (Semantic Information) From E = wLF |
14 Jan 2005 02:09:10 AM |
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From Osher Doctorow
The small p's in (5) should be P's.
I should mention that the right-hand-side of (5) has an advantage over
Shannon and Shannon-types of logarithmic information-entropy in not
blowing up at P = 0 or near P = 0 and also in increasing as P
increases, which for "semantic information" unlike syntactic or message
information is useful since I take P to be Probable Influence (PI) or
Probable Causation P(A-->B) = P(A' U B) = 1 + P(AB) - P(A) which is a
probability on a set/event analog of the logical conditional for
propositions a, b, namely the proposition (a-->b) = ~(a ^ ~b) = ~a V b,
and the set (A-->B) = (AB' )' = A' U B is an analog of the former. We
would want Semantic information or Knowledge to increase as Probable
Causation or Probable Influence increases! See my postings at
sci.stat.math and math-history-list of Math Forum, especially under PI,
Probable Influence, P(A-->B), Riccati Equation, etc.
Osher Doctorow
Osher Doctorow
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| User: "Uncle Al" |
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| Title: Re: A Rare Event Knowledge (Semantic Information) From E = wLF |
14 Jan 2005 10:53:41 AM |
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OsherD wrote:
From Osher Doctorow
COPYRIGHT NOTICE
A Rare Event Knowledge (Semantic Information) From E = wLF
Copyright By Owner Osher Doctorow Ph.D.
First Published 2005.
[snip]
First ridiculed, 14 Jan 2005,
"ACK! THBBFT!"
--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
http://www.mazepath.com/uncleal/qz.pdf
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| User: "OsherD" |
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| Title: Re: A Rare Event Knowledge (Semantic Information) From E = wLF |
18 Jan 2005 06:01:44 PM |
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From Osher Doctorow
Well said, Uncle Al (except I'll have to get my wife to to translate
ACK! THBBFT!, as I don't speak pig Latin which I assume that is). The
copyright wasn't my idea but an attorney's whom I know, who pointed out
the curious fact that internet postings don't belong to the poster but
to the public unless they have the copyright notice. Since, according
to the site you referenced, if I interpret it correctly, the public
already thinks it/they know too much, I feel somewhat justified in
copyrighting my own stuff. Don't hesitate to criticize, though, and
even stomp on it if it makes somebody feel better.
Osher
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