Science > Physics > Quantum Gravity Via Expansion-Contraction 53.0: Fundamental Equation of the Universe
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Science > Physics |
| User: |
"OsherD" |
| Date: |
23 Dec 2006 09:09:03 AM |
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Quantum Gravity Via Expansion-Contraction 53.0: Fundamental Equation of the Universe |
From Osher Doctorow
The Fundamental Equation of the Universe is arguably the Riccati
Differential Equation including its matrix and partial derivative
generalizations, which is usually written:
1) dy/dt = A(t) + B(t)y + C(t)y^2
with dy/dt generalizable to a partial derivative Dt(y). A(t), B(t),
and C(t) are (arbitrary) functions of time t and any may be identically
0 except that both B and C cannot be 0, but time itself is
generalizable to various spatial and/or abstract variables of similar
type with at least one-directional similar properties to time.
The most remarkable aspects of (1) and its generalizations include the
fact that most known continuous probabilities (probabilities of
continuous random variables) commonly used satisfy the equation with
regard to their probability density functions (pdfs) or sometimes their
cumulative distribution functions (cdfs) without any reference to
entropy/information. Until recently, I had regarded the Probable
Influence/Causation (PI) Knowledge analog of Shannon
entropy/information as the probability basis of (1), but the exceptions
are so rare that it is simpler to regard (1) as simply analogous to the
Einstein Field Equations or Schrodinger Equation in "defining"
admissible scenarios.
If (1) is the Fundamental Equation of the Universe, then Einstein was
not just wrong in asserting that "God does not play dice," but he was
fundamentally wrong in that, though Heisenberg was equally wrong in
that Causation via Probable Influence/Causation satisfies equation (1)
and so overrides "indeterminism".
Deterministic scenarios still can satisfy (1), including the
exponential function exp(kt) and exp(kx) for real constants k and so
on. The logarithmic function, commonly written log(x) with base e
understood, does not satisfy (1) without both B and C being 0.
Osher Doctorow
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| User: "louis" |
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| Title: Re: Quantum Gravity Via Expansion-Contraction 53.0: Fundamental Equation of the Universe |
23 Dec 2006 10:01:19 AM |
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"OsherD" <> wrote in message
news:1166886543.416070.40350@79g2000cws.googlegroups.com...
From Osher Doctorow
<snip>
The most remarkable aspects of (1) and its generalizations include the
fact that most known continuous probabilities (probabilities of
continuous random variables) commonly used satisfy the equation with
regard to their probability density functions (pdfs) or sometimes their
cumulative distribution functions (cdfs) without any reference to
entropy/information.
That is not even a sentence.
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| User: "OsherD" |
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| Title: Re: Quantum Gravity Via Expansion-Contraction 53.0: Fundamental Equation of the Universe |
23 Dec 2006 09:28:16 AM |
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From Osher Doctorow
It is possible (although not necessarily desirable - that depends on
the Real World) to further generalize the Riccati Differential Equation
to include both the Einstein Field Equations and the Schrodinger
Equation, although the latter has been derived by Rosu and his
colleagues directly from the Riccati Differential Equation (see my
earlier threads). For example, y might be replaced by the
differential operator D or Dx, with some type of condition like Dt
zeroing out spatial derivatives of its argument (or generalizing Dt to
an "operator" which does that). This could also explain the limitation
of the Einstein Field Equations to second order partial derivatives.
I should mention that the uniform pdf, fX(x) = 1/(b - a) on the
interval (a, b) for a and b real with b > a, does not satisfy (1)
without allowing both B and C to be 0 because Dt(k) = 0 for a constant
k and 0 is not a solution of (1) without both B and C being 0.
However, since both B and C cannot be 0, we can also exclude all three
of A, B, C being 0, so that A(t) = 0 would be excluded in the case of
Dt(k) = A(t) = 0.
Osher Doctorow
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| User: "OsherD" |
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| Title: Re: Quantum Gravity Via Expansion-Contraction 53.0: Fundamental Equation of the Universe |
23 Dec 2006 09:38:07 AM |
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From Osher Doctorow
I meant to say that we could allow all three of A, B, and C to be 0,
which would allow the uniform pdf to be included in (1). The condition
on (1) then becomes that B and C cannot both be 0 unless all three of
A, B, C are 0.
Osher Doctorow
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| User: "Karenia Brevis" |
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| Title: Re: Quantum Gravity Via Expansion-Contraction 53.0: Fundamental Equation of the Universe |
23 Dec 2006 12:58:15 PM |
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"OsherD" <> wrote in message
news:1166888287.849129.23640@42g2000cwt.googlegroups.com...
From Osher Doctorow
I meant to say that we could allow all three of A, B, and C to be 0,
which would allow the uniform pdf to be included in (1). The condition
on (1) then becomes that B and C cannot both be 0 unless all three of
A, B, C are 0.
If you set all three to Zero, then they must still be Zero, Right ?
Are you still a member of the Null Set ?
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