Science > Physics > Born's Quantum Probability Cancels Out in [P(X-->Y)]^2
| Topic: |
Science > Physics |
| User: |
"OsherD" |
| Date: |
20 Jan 2006 01:38:43 AM |
| Object: |
Born's Quantum Probability Cancels Out in [P(X-->Y)]^2 |
From Osher Doctorow
COPYRIGHT NOTICE
Born's Quantum Probability Cancels Out in [P(X-->Y)]^2
Copyright By Owner Osher Doctorow Ph.D.
First Published 2006
From my ongoing thread on P(X-->Y)^2, Born's quantum probability ww*
cancels out in [P(X-->Y)]^2 by:
1) ww* = 2xy = 2FX(x)F(x, y)
In detail, let P(X-->Y) = 1 + y - x with x = P(A), y = P(AB), A = {w:
X(w) < = x1}, B = {w: Y(w) < = y1}. Then:
2) [P(X-->Y)]^2 = (1 + y - x)^2 = x^2 + y^2 + 1 + 2y - 2x - 2xy
Setting ww* = x^2 + y^2 = 2xy, we are left with:
3) [P(X-->Y)]^2 = 1 + 2y - 2x = P(C --> D)
where P(C) = 2P(A) = 2x and P(D) = 2P(AB) = 2y were constructed as
described in the above-mentioned ongoing thread on P(X-->Y)^2.
Equation (3) is especially interesting in reducing the square of a
probability [P(X-->Y)]^2 to a probability, which is as surprising in a
way as reducing ww* to a probability in Born's probabilistic
interpretation of QM.
Notice from the line above (3) that if ww* = x^2 + y^2 = 2xy, then:
4) x^2 + y^2 - 2xy = 0
and therefore:
5) (x - y)^2 = 0
so x = y. But x = y optimizes P(A-->B) for any A, B as well as
P(X-->Y)! This is because 1 + y - x = 1 (maximum value) iff y = x.
The only disadvantage of all this is to the complex variable form of QM
since if x = y in ww*, then w fails to describe an enormous part of the
unit square with lower left vertex at (0, 0) in the first quadrant and
only describes its diagonal. This may be why QM gives discrete energy
levels usually and so on. Arguably we should start looking for the
missing energy.
Osher Doctorow
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| User: "OsherD" |
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| Title: Re: Born's Quantum Probability Cancels Out in [P(X-->Y)]^2 |
20 Jan 2006 01:56:26 AM |
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From Osher Doctorow
To summarize the situation as it looks now, QM failed to discover
Probable Influence (PI) because Born's quantum probability ww* in his
probabilistic interpretation of QM cancels out from [P(X-->Y)]^2, where
w is the Schrodinger wave function. Although ww* cancels out of PI, it
optimizes PI at 1 (maximum), though at the same time this excludes most
of the actual domain of variation of real events!
We already knew that QM involves "averages" rather than individual
trajectories for example, but the reason for this now becomes clear,
namely QM drops Knowledge/Semantic Information when it excludes most of
the domain of variation of real events even though it optimizes PI.
At the same time, the accuracy of much of QM and QFT (quantum field
theory) is explained by their optimization of PI, with the provision
however that QM and QFT only scratch the surface of what's "out there"
by restricting themselves to the diagonal of the unit square.
By optimizing PI, QM and QFT become super-causal rather than acausal
theories, since they optimize Probable Causation! The only difficulty
is that most of the Universe isn't super-causal.
Another curiosity of an optimized PI is that probabilistically it is
somewhat "boring". That is, PI = 1 + y - x for y = x (optimized) is
just 1. So although ww* optimizes PI, both ww* and this optimal PI
arguably become less interesting for researchers than PI < 1. As for
the averaging (expectations, expected values, population means) in QM
and QFT, they arguably need to be replaced by individual particle or
string or brane theories using PI < 1 usually.
Osher Doctorow
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