On Tue, 20 Apr 1999, Nick Bostrom wrote:
> Yes, you are right that on the MWI, if Adam thinks there is a
> substantial probability that the q.m. chance of a deer appearing is
> substantial, then you wouldn't get the shift that the paper refers
> to. And as you say, Adam could obtain evidence for the hypothesis
> that the q.m chance is substantial from observing his situation. Of
> course, this presupposes that we have managed to make sense of the
> MWI so that it gives probabilities in agreement with q.m. even when
> combined with the self-sampling assumption. This is not trivial. If
> q.m. says that outcome A has probability 2/3 and ¬A has probability
> 1/3, then there would have to be twice as many Adams observing A as
> ¬A. Moreover, the total number of Adams at any time should be roughly
> constant (modulo such events as Adam dying). It wouldn't do, for
> example, to just think of Adam as splitting everytime a measurement
> is made, for then almost all Adams would live very near the
> temporal end of the universe (if there is one). So it seems we would
> have to postulate an infinite (and uncountable) number of worlds. But
> then it is not easy to see how the SSA applies -- there would always
> be an infinite number of worlds where Adam is observing A and an
> equally large infinite number of worlds where he is observing ¬A.
The 'SSA' could obviously be modified so that the measure
(effective probability) is proportional to some specified measure on the
observers, not just the number of observers.
The problem with that is that it would just be an extra postulate,
ruining the simplicity of the MWI.
For a nontrivial approach that avoids that, see my web page
http://pages.nyu.edu/~jqm1584/cwia.htm
I take the effective probabilities to just be proportional to the
number of implementations of each computation. This approach still needs
work, mainly because the criteria for a computation to be implemented
are still unclear, but I have some proposals there. A criterion would be
a general mathematical tool, needed for computationalism and independent
of whether the physics is classical, quantum, or other.
Given a criterion, the approach should either be able to derive
the usual probabilities (at least in some approximation), or it should
derive wrong probabilities and prove the need for new postulates.
The fact that the number of implementations is infinite is OK: one
can use a limiting process to compare ratios just as one might say that
there are pi/4 as many points in the unit circle as in the unit square.
That requires the use of a natural or actual coordinate system (for
nonrelativitic QM one could presumably the usual wavefunction), but so
does any sensible implementation criterion as explained on my page.
- - - - - - -
Jacques Mallah (jqm1584.domain.name.hidden)
Graduate Student / Many Worlder / Devil's Advocate
"I know what no one else knows" - 'Runaway Train', Soul Asylum
My URL:
http://pages.nyu.edu/~jqm1584/
Received on Tue Apr 20 1999 - 16:57:23 PDT