On Sat, Jun 11, 2005 at 07:43:30PM -0700, "Hal Finney" wrote: > Jesse Mazer writes: > > But I explained in my last post how the ASSA could also apply to an > > arbitrary "next" observer-moment as opposed to an arbitrary "current" > > one--if you impose the condition I mentioned about the relation between > > conditional probability and absolute probability, which is basically > > equivalent to the condition that each tank is taking in water from other > > tanks at the same rate it's pumping water to other tanks, then the > > probabilities will be unchanged. > > One thing I didn't understand about this example: how do you calculate > the probabilities which relate one observer-moment to a potential > successor observer-moment? And do they have to satisfy the rule that > > p(x) = sum over all possible predecessor OM's y of (p(y) * p(x|y)) > > where p(x|y) is the transition probability from predecessor OM y to > successor OM x? In other words, is probability conserved much as fluid > flow would be in tanks which had constant fluid levels? >
In this notation, the ASSA gives a measure p(x)=\sum_y p(y) p(x|y),
and the RSSA gives p(x|y) for the same OM.
Also the ASSA gives a non-zero measure p(z), where z weas a
predecessor of y. However, the RSSA gives p(z|y) = 0.
The event on the left hand side should be read "next observer moment".
The two sampling assumptions do not add up!
> I'd be interested in any ideas for how one might calculate a priori the
> p(x|y) probabilities.
Use the Born rule. Using bra-ket notation, p(x|y), where x is at time
t, and y is at time 0,
p(x|y) = <x|exp(-i\hbar Ht) |y>/\sqrt{<x|x>}\sqrt{<y|y>}
For the gory details, read section 4 of "Why Occam's Razor".
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