Science > Physics > Quantum Gravity 114.1: The Gravitation Relationship To the Lotka-Volterra-Super-BM Scenario
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Science > Physics |
| User: |
"OsherD" |
| Date: |
06 Apr 2007 12:51:32 AM |
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Quantum Gravity 114.1: The Gravitation Relationship To the Lotka-Volterra-Super-BM Scenario |
From Osher Doctorow
So how does gravitation enter this picture, which now involves both
electromagnetism and the Schrodinger one-point potential scenario?
The clue is "one-point potential". Let's look back again at the
electrostatic and "magnetostatic" scenarios, where Coulomb's laws are
remarkably parallel to Newton's law of universal gravitation.
The electrostatic version (which works for the "magnetostatic"
scenario with magnetic dipoles replacing electric charges) compared to
the Newtonian law are respectively:
1) F = kq1q2/r^2
2) F = Gm1m2/r^2
with qi (i = 1, 2) being charges and mi (i = 1, 2) being masses. The
forces F could also in general have subscripts to label them, for
example Fem and Fg respectively with em standing for the subscript
"electrostatic", g for "gravitation". However, as long as confusion
is unlikely, let's leave them as in (1), (2).
Now let's see whether a general law could underlie both (1), (2).
Let's write instead of (1), (2), the hypothetical equation:
3) F = k1 v1v2/r^2, where v1 and v2 may or may not be m1 and m2
respectively, k1 a constant, and so on
The Probable Influence/Causation (PI) analog of y/x is 1 + y - x with
x the (Probable) Cause and y the (Probable) Effect (or representing
the same), so write:
4) F* = 1 + k1v1v2 - r^2, F* = PI analog of F in (3)
Here r^2 is supposed to be the cause x, but why r^2 and not r or 2r,
etc.? Also, k1v1v2 is supposed to be the effect, but why v1v2
(presumably v1 and v2 are of the same type) and not v^2 or something
like that?
Since r^2 is r times r, the PI analog would be r + r = 2r. Let's
make this correction in (4), changing (4) to:
5) F* = 1 + k1v1v2 - 2r
The number 2 is giving us a clue. Recall that earlier in this
thread, a phase change was found to occur between P and P', where we
have:
6) P(A-->B) = 1 + P(AB) - P(A)
7) P' (A-->B) = 1 + P(B) - P(A)
A quantity related to the second quantity P' (A-->B) was found to
occur in the interval [1, 2], while a corresponding quantity related
to the first quantity P(A-->B) was found to occur in the interval [0,
1].
If r moves from 1/2 to 1 in (5), then 2r is in this second phase,
while if it moves from 0 to 1/2 then it is in the first phase.
Applying a similar idea to kv1v2 in (5), the analog of k1v1v2 is k1(v1
+ v2). But in the usual cosmological applications, as for example
with one mass that of Earth and the other that of some relatively
small body compared to Earth, the expression (1/2)(v1 + v2) as an
average would give a better intermediate value or average for the v
quantities than v1 + v2, so k1 will be assumed to incorporate a factor
(1/2) and (5) is finally rewritten:
8) F* = 1 + k1(v1 + v2)/2 - 2r
To say that 2r represents the (Probable) Cause of (v1 + v2)/r is to
say that as r increases from first 0 to 1/2 and then from 1/2 to 1,
the transition point at r = 1/2 shifts PI from P to P' or the
quantities mentioned above corresponding to them, and this induces a
corresponding shift in (v1 + v2)/2.
Now, when B is a subset of A, then y = P(AB) is just y = P(B) up to a
set of probability 0, so the shift from P to P' (where P' involves
P(B) and P involves P(AB) ) which occurs when r passes through 1/2 in
some [0, 1] domain (precisely a probability domain!) can be regarded
as the shift from A and B as partly separate events to A suddenly
incorporating B inside A, as for example by A inflating to "overtake"
B in Inflation theory.
Since identical (Probable) Causes both formally and in detailed
"mechanisms" arguably produce identical (Probable) Effects, we can
argue that v1 and v2 can equivalently express m1 and m2 respectively
or q1 and q2 respectively and analogously with magnetic dipoles, and
that (8) represents a unified equation for all three pairs including a
phase transition and Inflation, and that literally Inflation caused
mass, charge, and magnetic poles to have their properties by a phase
change.
This puts gravitation into the scenario.
Osher Doctorow
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| User: "Noman Lapetos" |
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| Title: Re: Quantum Gravity 114.1: The Gravitation Relationship To the Lotka-Volterra-Super-BM Scenario |
06 Apr 2007 10:20:24 AM |
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"OsherD" <mdoctorow@comcast.net> wrote in message
news:1175838692.250866.15100@q75g2000hsh.googlegroups.com...
From Osher Doctorow
So how does gravitation enter this picture, which now involves both
electromagnetism and the Schrodinger one-point potential scenario?
The clue is "one-point potential". Let's look back again at the
electrostatic and "magnetostatic" scenarios, where Coulomb's laws are
remarkably parallel to Newton's law of universal gravitation.
The electrostatic version (which works for the "magnetostatic"
scenario with magnetic monopole replacing electric charges) compared to
the Newtonian law are respectively:
1) F = kq1q2/r^2
2) F = Gm1m2/r^2
then;
kq1q2/r^2 = Gm1m2/r^2
or
kq1q2 = Gm1m2
yielding;
G/k = (q1/m1)*(q2/m2)
which is the famous Malcidisk Equation of the Second Kind involving TWO
points, NOT "one-point potential"
another mistake kOsher, you used a TWO point equation.
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| User: "OsherD" |
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| Title: Re: Quantum Gravity 114.1: The Gravitation Relationship To the Lotka-Volterra-Super-BM Scenario |
06 Apr 2007 01:08:41 AM |
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From Osher Doctorow
I should emphasize that the phase change was one of distance, not
temperature as is usually thought (although temperature change could
have been another effect rather than cause). That is to say,
Inflation introduced an "intermediate" phase change boundary between 0
and infinity, despite the usual claim that there is no way of dividing
[0, infinity) or [0, infinity], such that when represented as [0, 1)
or [0, 1], 1/2 is the phase change boundary. It could be regarded
as a superluminally induced phase change boundary in distance or even
time from the Big Bang.
If this is correct, then we are today living in the superluminal or
second phase or macroscopic phase, and the microscopic or quantum or
first phase was at and very near the Big Bang. The speed of light c
may have bounded the first phase, to correspond to r = 1/2, but there
is no boundary to velocity or speed in the second phase, and we are
free to accelerate arbitrarily high depending on our power abilities.
This also answers my one objection to the papers cited recently in
this thread, namely the claim of some of the researchers that the
Clifford bundle formalism for example eliminates superluminal
scenarios. The only thing that the researchers eliminated was
Probable Influence/Causation, by not knowing it.
Osher Doctorow
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