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S11d. The minimal (statistical) interpretation
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The minimal interpretation of quantum mechanics does not model 
what really happens - it only claims probabilities.
When quantum mechanics is applied to small systems, one usually asks 
only for statistical information. Here a collapse simply means a 
change of the point of view resulting in taking conditional 
expectations, and all difficulties disappear. 
In that case, each particle simply moves in an undeclared and 
undeclarable fashion along the experimental setting, the classical 
instruments are always in a definite state, and instead of 
superpositions one has probabilities of observation of exactly one 
of the possible results in the superposition. 

Now all objectivity (sources and preparation, detectors and
measurements) is in the classical setting only, which coexists 
with the somewhat spooky quantum world, connected by quantum statistics.

The problem here is how to unify what happens classically 
and quantum mechanically. This minimal view becomes inconsistent 
once one wants to consider the classical system as a large quantum 
system - all objectivity disappears since macroscopic superpositions 
are possible.
(Generally, nonlinear modifications of the Schroedinger dynamics
are considered a possible way out, but this introduces other problems.)

The main limitation of the minimal interpretation is that it does not 
apply to systems that are so large that they are unique. 
Today no one disputes that the sun is governed by quantum mechanics.
But one cannot apply statistical reasoning to unique systems, such as 
the sun as a whole.

If quantum mechanics is a universal theory of nature, it should also 
apply to the sun as a whole. At least we know that it applies to the 
extent that it governs the energy generating processes in the sun. 
The actual numerical analysis of models of the sun use just 
treats the nuclear reactions within a classical reaction-diffusion
framework, which (in principle - I don't know whether anyone has 
actually done it) should be derivable from quantum mechanics using 
statistical mechanics arguments.

A purely statistical interpretation has also a problem with the 
notion of probability. (See the discussion on probability elsewhere
in this FAQ.) Probability (and hence the quantum state that predicts it)
is often seen as a subjective view about the experimenter's assumed 
knowledge, or the knowledge an experimenter could gain when 100%
attentive. There is the subjectivist difficulty to determine 
whose knowledge counts and why unobserved (and hence unknown) 
classical processes still make a difference;
but one could imagine an ideal classical observer of the status of
Laplace's demon, for whom these problems would be absent.