On 14 Apr 2015, at 04:05, meekerdb wrote:
On 4/13/2015 4:35 PM, Bruce Kellett wrote:
LizR wrote:
On 14 April 2015 at 00:42, Bruce Kellett
<[email protected] <mailto:[email protected]>>
wrote:
The expansion of the wave function in the einselected basis of
the
measurement operator has certain coefficients. The
probabilities are
the absolute magnitudes of these squared. That is the Born
Rule. MWI
advocates try hard to derive the Born Rule from MWI, but they
have
failed to date. I think they always will fail because, as has
been
pointed out, the separate worlds of the MWI that are required
before
you can derive a probability measure already assume the Born
Rule.
The argument is at best circular, and probably even incoherent.
In an article published in the 60s (I think) Larry Niven pointed
out that the MWI lead to the following situation - if you throw a
dice you have 6 outcomes, i.e. 6 branches. But a loaded dice
should favour (say) the branch where it lands on 6. Hence the MWI
doesn't work.
My reaction to this (when I first read it, probably several
decades ago now) was that you only have 6 MACROSCOPIC outcomes -
like derivations of the second law of thermodynamics, Niven's
description of the system relies on microstates being
indistinguishable /to us/. But once you take this into account
there are more microstates ending with a 6 uppermost - and hence a
lot more than 6 branches - the MWI again makes sense using branch
counting, at least for non-quantum dice (I may not have known
terms like microstates at the time, nor was it called the MWI, but
that was basically what I thought).
I do not think that classical analogies can ever get to the heart
of quantum probabilities.
Can't the same be true of any quantum event? The essential
requirement is that any quantum event leads to results which can
be assigned a rational number, rather than an irrational one. This
gives us a finite number of branches, and counting to get the
probability. Or do quantum events lead to results with irrational
numbered probabilities?
Quantum probabilities are not required to be rational: any real
value between 0 and 1 is possible. For example, if you prepare a
Silver atom in a spin up state then pass it through another S-G
magnet oriented at an angle alpha to the original, the probability
that the atom will pass the second magnet in the up channel is
cos^2(alpha/2). This can take on any real value in the range.
One argument against branch counting is that if you have two equally
likely outcomes (which can be judged by symmetry) there are two
branches; but if a small perturbation is added then there must be
many branches to achieve probabilities (0.5-epsilon) and
(0.5+epsilon) and the smaller the perturbation the larger the number
required. Of course the number required is bounded by our ability
to resolve small differences in probability, but in principle it
goes as 1/epsilon.
I think Bruno's answer to this is that for every such experiment
there are arbitrarily many threads of the UD going throught at
experiment and this provides the order 1/epsilon ensemble. But this
somewhat begs the question of why we should consider the
probabilities of all those threads to be equal
We better should not. I am making a pause café right now. The UD does
simulate a computation going through my actual state, but with a
continuation where I hallucinate that my coffee becomes tea. Well, I
hope that the measure of such computations is less than the one in
which my coffee gently appears to taste coffee and not tea.
since we have lost the justification of symmetry.
Yes, that is why we should not consider all those threads as having
the same probability. In fact, by the rule Y = II, only those getting
highly relatively multiplied have some chance of having a normal and
stable measure.
I think this is "the measure problem".
OK.
Ah! My coffee tastes coffee!
It would not I would bet that I am dreaming in some "normal reality",
not that computationalism is false.
Bruno
Brent
I know that a branch counting approach to quantum probabilities is
disfavoured, though I can't at the moment recall the standard
argument. Clearly, the existence of real-valued probabilities, not
restricted to rational values, is a strong factor. But there is
also the fact that in the two-dimensional Hilbert space associated
with spin 1/2 projections, one only ever has two possible outcomes
for an experiment -- why should the number of branches one must
consider depend on the angle of the magnet?
Bruce
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