On 11-07-2016 13:49, Bruce Kellett wrote:
On 11/07/2016 9:31 pm, Bruno Marchal wrote:
HOLIDAY EXERCISE:
A guy undergoes the Washington Moscow duplication, starting again
from Helsinki.
Then in Moscow, but not in Washington, he (the one in Moscow of
course) undergoes a similar Sidney-Beijing duplication.
I write P(H->M) the probability in H to get M.
In Helsinki, he tries to evaluate his chance to get Sidney.
With one reasoning, he (the H-guy) thinks that P(H-M) = 1/2, and
that P(M-S) = 1/2, and so conclude (multiplication of independent
probability) that P(H-S) = 1/2 * 1/2 = 1/4.
But with another reasoning, he thinks that the duplications give
globally a triplication, leading eventually to a copy in W, a copy
in S and a copy in B, and so, directly conclude P(H-S) = 1/3.
So, is it 1/4 or 1/3 ?
Neither. The probability that the guy starting from Helsinki gets to
Sydney is unity. This is the problem with probabilities in the MWI --
how do you interpret probabilities when all possible outcomes occur
with probability one?
Bruce
In duplication experiments the prior probability to exist at all in any
of the possible states increases after the duplication, while in unitary
QM this is conserved (except if one or more of the possible outcomes is
death). The correct way to analyze Bruno style duplication arguments is
to start with assigning some measure m to the observer before any
duplication is carried out, in this case the observer at H.
Then H gives rises to two copies in states W and M (we can call them
copies, but they are actually different observers as they have different
memories stored in their brains, so they are different algorithms). The
measures will be m for each of these observers. Then W is not going to
be copied, while M gives rise to S and B, so we end up with 3 observers
each with measure m. The probability is thus 1/3.
In an analogue MWI setting, the outcome is different, at each
duplication the measure for a particular outcome is halved. W thus has a
measure of m/2, while S and B each have a measure of m/4, the
probability is thus 1/4.
Saibal
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