Science > Physics > Quantum Gravity 154.1: First and Second Order Probable Causation of Gravitation by Expansion
| Topic: |
Science > Physics |
| User: |
"OsherD" |
| Date: |
11 Jun 2007 05:45:59 PM |
| Object: |
Quantum Gravity 154.1: First and Second Order Probable Causation of Gravitation by Expansion |
From Osher Doctorow
The expression for first order Probable Causation of Gravitation by
Expansion hasn't been defined. We do define for an arbitrary event A
and for B = gravitation (contraction) and B ' containing expansion:
1) P(A-->B) (gravitation caused by A)
2) P(A-->B ' ) (expansion and "all else" caused by A)
which yielded the earlier equation:
3) P(A-->B ' ) = 1 - P(A-->B) + 1 - P(A)
Now calculate:
4) P{P(A--> B ' ) --> P(A-->B) }
which is the second order Probable Causation of Gravitation. Readers
can fairly easily prove:
5) P{P(A--> B ' ) --> P(A-->B)} = 2P(A-->B) - (1 - P(A))
Readers familiar with conditional probability will recall that:
6) P(B|A) = P(B) is equivalent to A, B independent
The analog with PI is:
7) P(A-->B) = P(B) is equivalent to A, B PI-independent (of one type)
The reason for the qualification "of one type" is that there are
several types of PI-independence. It can be proven that (7) does not
hold if A is a rare event or in fact if P(A) < 1/2.
Readers can try to interpret (5) in physical terms. Hint: start with
1 - P(A) close to 0 or with P(B) close to 0.
Osher Doctorow
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