Unreal Probabilities by Carlos C. Rodriguez Dept. of Mathematics The University at Albany...
13
Unreal Probabilities by Carlos C. Rodriguez Dept. of Mathematics The University at Albany [email protected]
-
Upload
shanna-edwards -
Category
Documents
-
view
215 -
download
1
Transcript of Unreal Probabilities by Carlos C. Rodriguez Dept. of Mathematics The University at Albany...
Real Probability
P(Whole) = 1 P(a+b) = P(a) + P(b) if ab=ú
P : A [0,1]
Real Probability
P(Whole) = 1 P(a+b) = P(a) + P(b) if ab=ú
P : A [0,1]
The Axioms
• A, Boolean algebra of propositions: a,b,c...• G, Clifford algebra: u,v,M,N...
Operations:Operations:OR : a+b AND: ab NOT: a_ 0 = FALSE 1= TRUE
Ø Defined
Hilbert Space of Ø’sHilbert Space of Ø’s
The Truth with Ø
Real TruthReal Truth
Independence
Ø makes a and b independent given c if
• symmetric• includes usual formula• generalizes to more than two propositions
Weak Law of Large Numbers
AA BB
ExampleExample
QM
x
t
xü
tü
Ú Ú»tÁ
(Û , tª)
Boolean algebra of filters: e(x,t) = “x open at time t”
“one filter on top of the other”
Independent segments
t
independent given
QM Dictionary
Amplitude Amplitude
Wave functionWave function
HamiltonianHamiltonian
i@=-1 i commutes will all the Ø’s
Schrödinger Equation
( generalized for possible non commuting Ø’s
with independent segments)
Ed, what do you think ?
