I What is really that density matrix in QM?

[Auto-Didact]

Well, "shutup and calculate", is a better advice than getting lost in questions that cannot in any way objectively be settled.

Correction: has not been settled yet; it only needs to get settled once. You can only claim unsettleability of these arguments through mathematical proof of non-existence, which I as a constructivist almost see as an impossibility; obviously, there aren't any such proofs in the literature either.

The "interpretational issues of QT" are just a matter of personal belief but not natural science. The only thing decidable by objective science is the minimal interpretation, which just tells you to take the probabilistic nature of QT (generalized Born's rule) as a fundamental property of nature. Every assumption in addition (like Bohmian trajectories in non-relativistic QM, parallel universes a la MWI, etc.) is just not part of science, though maybe sometimes of some intellectual interest or amusement (as some esoterics is really funny, as long as it doesn't hurt anybody).

Mathematics is a form of science and mathematical physics is definitely science, despite what anyone claims; the minimal interpretation on the other hand is operationalism which replaces mathematics with heuristics. To use the words of Redhead: Operationalism is not sidestepping the need for philosophical analysis, but is itself just bad philosophy!

 

[PeterDonis]

This heuristic attitude among physicists actually seems to be imparted during the training of students (shut up and calculate), which contemporary physicists of course learned from their own teachers, because it was adequate for that period in history of physics when there were experiments to analyze; unluckily, this attitude has become educational dogma which doesn't change even when change is needed.

"shutup and calculate", is a better advice than getting lost in questions that cannot in any way objectively be settled.

It strikes me that this dispute cannot be objectively settled unless and until somebody either comes up with a proven theory of everything that is demonstrated to be mathematically consistent, or proves that one cannot exist. Neither of which seems likely to happen any time soon.

Given that, this subthread on foundations should end at this point.

 

[Auto-Didact]

As a closing remark, I paraphrase Kierkegaard: The history of physics can only be understood backwards; but it must be lived forwards.

 

[vanhees71]

Correction: has not been settled yet; it only needs to get settled once. You can only claim unsettleability of these arguments through mathematical proof of non-existence, which I as a constructivist almost see as an impossibility; obviously, there aren't any such proofs in the literature either.

Mathematics is a form of science and mathematical physics is definitely science, despite what anyone claims; the minimal interpretation on the other hand is operationalism which replaces mathematics with heuristics. To use the words of Redhead: Operationalism is not sidestepping the need for philosophical analysis, but is itself just bad philosophy!

Of course, mathematics is a structural science (not a natural science). What I talk about is fruitless philosophical debates about apparent problems, which are not objectively there, and cannot be settled other than finding new empirical evidence. There's not the slightest hint to where standard Q(F)T breaks down, which in some sense is a nuissance, because we lack guide from observations how to complete QFT to also describe gravity in a consistent way with all other interactions. For sure, philosophical debates won't solve this problem. We need empirical input and an ingenious physicists's and mathematician's idea, how to formulate it. Maybe it settles also some of the philosophical questions, but most likely the philosophers won't like the then hopefully revealed facts even less than the known ones and then claim to have new "problems".

 

[vanhees71]

It strikes me that this dispute cannot be objectively settled unless and until somebody either comes up with a proven theory of everything that is demonstrated to be mathematically consistent, or proves that one cannot exist. Neither of which seems likely to happen any time soon.

Given that, this subthread on foundations should end at this point.

The foundations have been settled in 1926, when Born gave his probabilistic interpretation of the quantum formalism. Quantum states are descibed by a statistical operator $\hat{\rho}$ and has the usual probabilisticmeaning, predicting the probabilities for the outcome of measurements on ensembles prepared in that state. With this you can close the thread ;-))).

 

[Lord Jestocost]

"Is it not good to know what follows from what, even if it is not really necessary FAPP? Suppose for example that quantum mechanics were found to resist precise formulation. Suppose that when formulation beyond FAPP is attempted, we find an unmovable finger obstinately pointing outside the subject, to the mind of the observer, to the Hindu scriptures, to God, or even only Gravitation? Would not that be very, very interesting?"

John Bell

 

[vanhees71]

But QT doesn't resist precise formulation. It's among the most precisely formulated theories ever. What Bell discredits as "FAPP" is just the physics content of QT, no more no less.

I'm never sure, whether Bell would have liked to see the predictions of QT concerning the violation of his inequality, based on local deterministic HV theories, would turn out to be wrong, i.e., whether he had wished to prove QT wrong and a return to the deterministic classical world view possible.

That's of course wishful thinking. Nature doesn't care about our philosophical prejudices, and thus Bell's work, which brought the philosophical speculations about possible problems with standard QT to the realm of objectively testable facts and thus indeed is among the most profound ideas concerning these foundations ever. Nowadays I think it's fair to say that the objective facts are revealed in a plethora of Bell tests in favor of standard QT, and local HV theories are simply counterfactual.

 

[PeterDonis]

The foundations have been settled in 1926

QT doesn't resist precise formulation. It's among the most precisely formulated theories ever

If you don't mind the term "measurement" not having a well-defined meaning. You can make these statements as your opinion, but I don't think you can assert them as simple facts.

With this you can close the thread ;-))).

And with that, it is closed.