From: Nicholas Bostrom (bostrom@mail.ndirect.co.uk)
Date: Wed Aug 13 1997 - 19:09:16 MDT
John K Clark wrote:
> "Nicholas Bostrom" <bostrom@mail.ndirect.co.uk> On Thu, 31 Jul 1997 Wrote:
>
> >The Everett theory fails to make sense of the probabilities. For
> >instance, take a particle that can undergo either of two processes,
> >and say that according to quantum mechanics the first event (A) has
> >an 80% chance of occuring, and the second (B) 20%. Now, according to
> >the Everett interpretation what happens (basically) is that the
> >universe splits into two universes; and there is one copy of me in
> >each of these universes. But if this were the case, then there
> >should be a 50% chance for me (i.e. *this* copy of Nicholas Bostrom)
> >to find that A had happened and a 50% chance that B had happened;
> >which we know from experiment is not true. I don't know of any good
> >reply to this objection that would save the Everett interpretation.
>
>
> There is nothing magical about the number 2, it's just the simplest example.
> In your case the universe splits into 5, in 4 of them event A happens in one
> of them event B happens. You split just like everything else and have an 80%
> chance of seeing event A.
This is indeed a possible route: we make sense of the
probabilities by postulating multiple identical worlds. The drawbacks
of this is, first, that we need to buy a whole lot of new ontology.
This is bad but perhaps not as bad as it first seems, since what is
multiplied is not laws and explanatory principles but only the
objects (worlds) postulated by the theory. Nonetheless, if we have to
introduce an uncountable infinity of parallell worlds, that is a bit
hard to swallow.
John Clarke suggests that quantum mechanical
predictions can be exactly reproduces even without a countable
infinity, provided that we accept some indeterminism:
> For example, most of the time the world dives into exactly 2, on
>rare occasions with irrational probability it divides into exactly
>3. The probability of seeing the event is an irrational number a
>little greater than 2 but less than 3. I never said Everett was
>deterministic and got rid of probability, irrational or otherwise, I
>only said it solved the measurement problem.
As far as I can see, this would leave us with a countable infinity
of worlds, but would cost us determinism, a rather attractive feature
of the Everett interpretation. Is this bargain worthwhile?
An alternative way would perhaps be to say that the Schroedinger
equation is only right to an extremely high degree of accuracy: all
real probabilities are rational numbers; the amplitude square is only
very, very close to the real probability. Is this too inelegant to be
plausible?
Perhaps we could go further and make do with a large unbounded
*finite* number of parallel worlds?
Hal Finney wrote:
>This [the problem with an uncountable number of parallel worlds] is
>an objection to the popularized notion of "many worlds" rather than
>to Everett's original idea of eliminating state function reduction.
>IMO you can't take this "universe splitting" idea that literally.
>What I prefer is to suggest that the effect of the decoherence (and
>resulting independence) of branches of the state function is "as
>though" the universe were splitting. But there is only one state
>function; what changes is which part of it you can interact with.
But what is the difference between a universe in which branches of
the state function split off and a univerese wherein it is "as
though" there were branches that were splitting off? Are there any
observations that could distinguish between these hypotheses?
We introduced the many worlds in order to fix the probabilities.
If we scrap the worlds then we seem to be back on square one again,
with "measure" that doesn't correspond to the probabilities that stem
from the ontology.
>A good, accessible article comparing the popular many-worlds
>interpretation with Everett's original relative-state formulation is
>Am. J. Phys 58 (9), September 1990, p. 829. (Am. J. Phys. is a
>relatively non-technical journal for physics teachers and students.)
>Among the arguments against MW in the popular form is that it
>violates conservation of mass, since new universes are being created
>all the time. This is really a matter of misunderstanding Everett's
>key idea.
It is often said that deWitt is responsible for misrepresenting
Everett in his popularizations. Is this the misunderstanding you are
referring to? For my part, I don't think that the nonconservation of
energy is a very serious objection to the Everett interpretation,
even if taken to imply that literally new world are created all the
time.
------------------------------------------------
Nicholas Bostrom
bostrom@ndirect.co.uk
*Visit my transhumanist web site at*
http://www.hedweb.com/nickb
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