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.
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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