Mark,
I too enjoy this exchange, and although we do not yet seem to be on the same page, we are converging.
"Again, everyone agrees there is nothing wrong with QM."
Then let me quote your earlier post:
"Many in the foundations community believe "The problem of quantum mechanics is unlikely to be solved in isolation; instead, the solution will probably emerge as we make progress on the greater effort to unify physics" (Smolin, The Trouble with Physics, p 10, 2006)."
Therefore it looks like not everyone is convinced QM is just right as it is, and moreover, there will be no (unwise) attempts to generalize it.
"Most agree, however, that QM (causally and/or constitutively non-local) is incompatible with CM".
I would say agreement is irrelevant because this can be proven mathematically. As a fine print, I am talking about a mixed QM/CM case, not about a common mathematical structure containing both CM and QM.
"I don't see anything in your approach to resolve it."
I do not need to do it because it was already done. Twice. Segal was first in finding the common axioms of QM and CM, and then Grgin and Petersen found another flavor of it. It goes something like this. A quantal algebra a dual product algebra (with product \sigma and \alpha) satisfying 3 identities:
1. Jordan identity in \alpha
2. Leibniz identity in \alpha and \sigma
3. Associator identity where LHS is in \alpha and RHS is in \sigma
For QM \alpha = commutator, and \sigma = anti-commutator
For CM \alpha = Poisson bracket and \sigma = usual multiplication
The Jordan part guarantees the Lie algebra part. The Leibniz identity introduces derivation and is a consistency condition between the 2 products. The associator is zero for CM because all observables commute, and non-zero for QM. The proportionality constant between LHS and RHS is 1/4 \hbar^2.
"The MP is resolved by those interpretations using future boundary conditions, e.g., path integral approaches and backwards causation."
Did you say backwards causation? Only when I will remember what I did tomorrow, I could agree with it.
"I can disprove this statement with a counterexample -- RBW is constitutively non-local which is in discord with CM's constitutive locality."
I was not aware of RBW until we started this exchange. I would be very interested to see how you solve the measurement problem in your approach. So here is the problem. Start with a quantum system, allow it to interact with the environment and you obtain a diagonal matrix. Each element of the matrix corresponds to a (classical) possible measurement outcome, and they are all in a superposition state. So how do you go from a superposition of the dead and alive cat to a definite state? I contend that in non-relativistic QM the solution is impossible with the exception of the multi world idea where each individual state lives in another world.
"Again, the MP can be resolved, but to say that QM is fully understood assumes you can live with the lack of integrity created by CM and QM. Many cannot, thus foundations is a thriving area."
Yes, I am at peace with the tension between QM and CM because CM is only an emergent theory and I have a physical intuition about QM. I hope my QM paper I am writing will settle many apprehensions and misunderstandings about QM. This will not be the end of the foundations research, but it will shift the focus to relativistic QM where many open problems still exist.
"Quite the contrary, it points towards the need for physics fundamental to the Standard Model. That is what is meant by "QFT as an effective theory."
QFT is also plagued by the Landau pole problem but still it is extremely successful in making predictions. I am not an expert (yet) in QFT but I do agree with your position.
Regards,
Florin
