On 4/15/2015 12:58 AM, LizR wrote:
On 14 April 2015 at 14:05, meekerdb <meeke...@verizon.net <mailto:meeke...@verizon.net>>
wrote:
On 4/13/2015 4:35 PM, Bruce Kellett wrote:
LizR wrote:
On 14 April 2015 at 00:42, Bruce Kellett <bhkell...@optusnet.com.au
<mailto:bhkell...@optusnet.com.au> <mailto:bhkell...@optusnet.com.au
<mailto:bhkell...@optusnet.com.au>>> 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 since we have
lost the
justification of symmetry. I think this is "the measure problem".
I believe it's an open question as to whether these systems (angle of rotation of a
magnet for example) are continuous or quantised. If quantised then there are merely a
(perhaps) very large number of branches but no measure problem.
I'm quite willing to say that there can only be finite precision in any physical
measurement, so the measurements are effectively quantized even if the theory is built on
real numbers. But I don't think that solves the measurement problem. It doesn't justify
considering all the possible values equi-probable; that requires some symmetry principle.
Brent
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