Hi Michael,
"1) Textbook NRQM which includes only: the claim that QM applies to everything, Schrodinger dynamics, the Eigenstate-eigenvalue link and the Born rule leads to the measurement problem (MP)."
I agree.
"2) If you want to solve the MP head-on you must modify NRQM in some way such as Bohm or GRW. Otherwise, you can go Everett or some kind of statistical interpretation-SI. If you think Rovelli's relational interpretation is an exception to this please explain how, how EXACTLY does this interpretation solve the MP then."
I disagree.
Bohm is looking backwards towards the CM ideals and is not a viable solution. GRW is technically not quite standard NRQM, but this may be a way to go forward if no other solutions to MP are found. If we strictly agree with (1), GRW should not be considered. Everett is not falsifiable and is not science. Rovelli does not solve the MP, it only points out that the wavefunction is a relational object and is a nice way to introduce Bayesian reasoning.
My take on this is that a solution to MP is best found in relativistic QM by looking for ways to generalize Gleason's theorem. Gleason is based on von Neumann algebras which define a statistical measure, but this does not quite work in non-commutative geometry framework. I do know how Born rule generalizes to relativistic QM and there must be another way (different than Gleason) to derive Born rule in NRQM that is better suited to the relativistic QM setting.
Relativistic QM is still QM and any solution to MP in relativistic QM should be applicable to NRQM as well.
Yesterday I had searched the literature and found out that Zurek may have found a solution to the MP in the context of NRQM using "environment--assisted invariance = envariance" (http://arxiv.org/abs/quant-ph/0405161) This looks promising and it does resonate with my way of thinking, but I need some time to asses if this is indeed a valid solution.
"Moving to RQFT by itself doesn't solve the MP."
I agree with a caveat: the solution of MP may be simpler there.
"Environmental interaction (decoherence) makes QM systems behave classical FAPP but does NOT solve the MP."
I agree, but now Zurek has this new idea of envariance and he uses this to derive decoherence from it.
5) Nothing in QM (including the free will theorem" of Conway and Kochen) gives any reason to believe in free will (FW). Note: Conway and Kochen don't think their theorem establishes FW and there are now SEVERAL papers showing that the theorem doesn't entail FW. Belief in free will is maybe motivation for not liking BW but isn't an argument against it. Note that FW is equally screwed by mere dynamical determinism and indeterminism!
I partially agree/disagree. Yes, FW theorem presupposes experimenter's free will in arranging the orientation of his measurement device, so technically this does not prove FW completely, but is surely it is very likely.
"Note that FW is equally screwed by mere dynamical determinism and indeterminism!"
Of course I am aware of those arguments and this is why classical mechanics is at odds with FW. QM is qualitatively different because of 2 things: 1. the experimenter is free to choose what he wants to measure, and 2. the measurement outcome does not exist before the experiment (no hidden variables). So this is neither fully deterministic, nor fully chaotic. Still this is not a proof of FW, I am only restating the gist of Conway's argument.
"6) Merely using the path integral approach doesn't solve the MP either. Likewise for the Heisenberg approach."
I agree.
PART II
"You claim: Connes' and Conway's result refute a BW interpretation, and further that this is accepted wisdom on the part of the physics community. Please explain in DETAIL why this is true. "
In BW there are no genuine choices and from everyday life we do know free will is a reality. Still, this is only handwaving. What Conway's result prove is that nature posses FW if the experimentalist has it. Not a complete proof for FW, but for the remaining original assumption of Conway's result we can then turn to experiments and see if there are any "conspiracies" ever present stopping us to do whatever experiments we choose. Because there are none, I think this completely settles the FW question and now the burden of proof is upon you to show that BW interpretation is compatible with FW. I do not see how this can ever be achieved, but anything is possible until proven impossible.
"Are you talking about this citation: A. Connes and C. Rovelli, Von Neumann algebra automorphisms and time-thermodynamics relation in general covariant quantum theories, arXiv:gr-qc/9406019 (1994)? I have looked at this and I don't see how it refutes a BW at all--is your whole argument based on this paper from 94; Stuck you should see for yourself and respond directly. Florin you say: Connes proved that the "time parameter" is independent of state in the context of measurement theory, spectral theorem, and von Neumann's algebras and this is big and I believe it kills the BW interpretation. Even if this is true (Stuck check this out) please explain EXACTLY how this rules out BW."
Yes, that is the paper. See also the references inside. There are two basic interpretations of time. One is the standard NRQM interpretation: time as a parameter. Why there should be this parameter, we do not quite know, but it is, and this is fully compatible with a BW interpretation. I would say that this is a gross oversimplification of the notion of time.
From Connes and others, here comes the richer notion of time. As an emergent phenomenon, time is compatible only with hyperbolic evolution equations and Cauchy initial value problems. No elliptical PDEs , no index theorems, no global self-consistency conditions.
Before Connes, there was no solid mathematical justification for time as an emergent phenomena. There were clues, but not a proof. Now again, the same scenario from FW applies. If you want BW to be accepted, then you have to prove that BW is compatible with time as an emergent phenomenon. Yet again, I do not think this is possible, but that does not mean anything because I am not working in this approach. In my (possible wrong) view, emergent = now = initial value problem.
"I suspect that the strongest argument you could have here is that perhaps certain algebraic approaches, if true, lead to certain conclusions, if there are theorems based in algebraic approaches PROVING that BW is ruled out or that a SI of the wave function is impossible that would be news to most of the people that I know. "
To the best of my knowledge, there are no such theorems in the algebraic approaches.
"You say: A BW interpretation is time independent [by the way, is that necessarily true?]"
That is my understanding of it, see my answer above. What you need to do is to prove me wrong. I do not think this is possible though, but it is only an opinion at this point.
"You say: A BW interpretation is time independent [by the way, is that necessarily true?] and this runs aground of the Tomitza-Takesaki theorem which provides a God-given time parameter. Please explain this or tell me where to look. Are you saying this theorem proves that there has to be a preferred frame of reference? "
Please excuse the sloppy formulation, but here is the gist. There are no preferred frames of reference, but "now" is qualitatively different from "future" because "now" is emergent from "past" and "future" did not "emerge" yet.
"2)That all statistical interpretations-SI (including ours) are committed to deriving superselection rules from a Bayesian interpretation which is impossible. So again, please explain in DETAIL why all SI are committed to a Bayesian account of the wave function and why our account in particular can't explain or isn't consistent with superselection rules. I'm not sure I'm getting you here, for example, how does this relate to our claim that:
This is similar with the quantum eraser. In other words, the interpretation of the wavefunction depends on the experimenter's point of view, and this is why Roveli is right. This only makes sense in the Bayesian formalism. "
For a Bayesian interpretation in QM see: http://arxiv.org/abs/0706.2274
"3) Please explain this claim in detail and why this tells against RBW:
Space, time, locality, superselection rules are concepts outside non-relativistic QM. Space, time, and locality are concepts inside relativistic QM. By a leap of faith, I conjecture superselection rules should also come from inside relativistic QM. "
Those are only facts, not claims against RBW.
"4) Please explain this claim also:
The relative frequency approach is intuitive, but not mathematically feasible. You simply cannot derive any proof from it because your series has to go to infinity. The right "philosophy" is Kolmogorov's axioms. "
There are several approaches to probability: Laplacean principle of indifference, frequentist approach, Kolmogorov's approach as a model. I was only stating that to infer consequences one uses either a model (Kolmogorov), or reasons by knowledge gain (Bayesian - Laplace's approach) but one cannot say anything definite in the frequentist approach because there is always the possibility of counterexamples as the infinite series goes to infinity.
Cheers,
Florin