Science > Physics > Quantum Gravity 149.6: More Re The Fundamental Equation of Expansion-Acceleration
| Topic: |
Science > Physics |
| User: |
"OsherD" |
| Date: |
03 Jun 2007 10:11:43 AM |
| Object: |
Quantum Gravity 149.6: More Re The Fundamental Equation of Expansion-Acceleration |
From Osher Doctorow
We can further operate on the equation(s) using the fact that:
1) (A-->B) U (A --> B ' ) = (A ' U B) U (A ' U B ' ) = Universe
Taking the probability of both sides of 1 and recalling that
P(Universe) = 1, we get:
2) P{(A-->B) U (A-->B ' )} = 1
But the left hand side has form P(C U D) = P(C) + P(D) - P(CD) for C =
(A-->B), D = (A-->B ' ), so (2) becomes:
3) P(A-->B) + P(A-->B ' ) - P({(A-->B)(A-->B ' )}) = 1
Since we have:
4) (A-->B)(A-->B ' ) = (A ' U B)(A ' U B ' ) = A ' A ' U A ' B ' U BA
' U BB '
and BB ' = "0" (the null set) while A ' A ' = A ' and the other sets
reduce to A ' because C U D = C when D is a subset of C in set theory,
(4) becomes:
5) (A-->B)(A-->B ' ) = A '
and inserting from (5) into (3) results in:
6) P(A-->B) + P(A-->B ' ) - P(A ' ) = 1
and using P(A ' ) = 1 - P(A) which always holds, we get:
7) P(A-->B) + P(A-->B ' ) - 1 + P(A) = 1
and therefore:
8) P(A --> B ' ) = 2 - [P(A) + P(A-->B)]
Notice, by the way, that P(A) + P(A-->B) is at least as large as 1
because P(A-->B) = P(A ' U B) > = P(A ' ) and P(A) + P(A ' ) = P(A) +
1 - P(A) = 1. So the expression on the right hand side of equation
(8) is between 0 and 1 as required for a probability. Using 2 - P(A)
= 1 + 1 - P(A) = 1 + P(A ' ), we could rewrite (8) if desired as:
9) P(A --> B ' ) = 1 + P(A ' ) - P(A-->B)
This is "almost" 1 = P(A-->B) except for the term P(A ' ).
Osher Doctorow
.
|
|
|
Related Articles |
Quantum Gravity Via Expansion-Contraction 77.2: More Re Fundamental Equation of Quantum Gravity
Quantum Gravity Via Expansion-Contraction 77.3: More Re Fundamental Equation of Quantum Gravity
Quantum Gravity Via Expansion-Contraction 77.1: More Re Fundamental Equation of Quantum Gravity
Quantum Gravity Via Expansion-Contraction 53.0: Fundamental Equation of the Universe
Quantum Gravity Via Expansion-Contraction 2.9: EMA Via Riccati Differential Equation
Quantum Gravity Via Expansion-Contraction 41.1: Scalar Einstein Equation in Probable Causation of Tensors, Matrices, Determinants
Quantum Gravity 154.5: Using Independence-Dependence To Obtain Radial Expansion Equation
Quantum Gravity Via Expansion-Contraction 13.1: B, C Negative in Riccati Differential Equation
| Quantum Gravity Via Expansion-Contraction 7.0: How the Universe Split Into Microscopic and Macroscopic Parts via the Sine-Gordon Equation
Quantum Gravity 149.5: The Fundamental Equation of Expansion-Acceleration
Quantum Gravity Via Expansion-Contraction 77.6: Incredible Conformity in Adding Stochastic Terms to Einstein's Equation For Fundamental Equations of Quantum Gravity
Quantum Gravity Via Expansion-Contraction 23.2: The time-probability equation t = log[(p-1)^2 + 1] in Inflation
Quantum Gravity Via Expansion-Contraction 2.8: Lambert's W, FIbonacci Numbers, Feigenbaum constant, Golden Ratio, Logistic Map and Riccati Differential equation, Fine Structure Constant
Quantum Gravity Via Expansion-Contraction 77.0: Fundamental Equation of Quantum Gravity
Quantum Gravity Via Expansion-Contraction 4.0: Genus, Eigenvalues, and Other Piecewise Constants Satisfy Riccati Differential equation
|
|
|
