zefram_c said:
if we could show that the interaction between a quantum object and a macroscopic measuring apparatus causes the wave function of the quantum object to change to a sharply localized gaussian (in whatever parameter space one is 'measuring'), the problem would be solved and we would have an entirely self-consistent, pure quantum description of the measurement process. Unfortunately it is not possible to write down the wave function of the measuring apparatus, since it consists of O(10^23) particles.
Yes, we can: look: |psi>
There are 2 fundamental problems with the view that "well, a complicated measurement apparatus probably effectuates a collapse, but we can't show it".
The first problem is that, no matter how complicated, the time evolution (which you correctly identify as being deterministic) is given by a unitary operator, which can never give rise to a collapse (it being an invertible, linear operator). But this problem could be fixed by saying that we don't have an absolutely exactly unitary time evolution operator (nevertheless, this is a very basic postulate of QM, so we are changing QM fundamentally here).
The second problem is with locality. EPR situations show that, if collapse is an ontologically happening process, it is non-local and (hence) not Lorentz invariant.
There are 3 ways out:
1) the positivist one: there is no "reality", QM just gives us rules that give us relations between observed probabilities. There is a variant: Copenhagen, which denies reality to objects that are ruled by QM, but gives reality to "classical" objects, without specifying where there is a boundary.
2) MWI - style: (my preferred view) we keep all of QM and SR, and we claim that the full wave function has ontological status, while the Born rule tells us how subjective experiences are derived from it: collapse is not an objective phenomenon, but a perceived, subjective experience.
3) the "new physics" realist one: what we observe corresponds to an ontological reality, and we then throw overboard as well QM and the superposition principle, as locality (and hence SR).
cheers,
Patrick