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visits member for 2 years, 11 months
seen Jul 22 at 7:51

Mar
11
asked Evidence that “space exists rather than just particles”
Mar
10
accepted How do you prove $S=-\sum p\ln p$?
Mar
9
comment Conserved quantum observables from symmetries *with density matrix*
That's my point. It seems Ballentine deduces all of the above, including the form of H and it's equation, from the Galilei group. No dynamics or Liouville is assumed. Effectively, even Schrödinger is also deduced! The only assumption is about complex Hilbert space, phase invariance and Galilei group. That's why it's interesting.
Mar
8
comment Conserved quantum observables from symmetries *with density matrix*
In the first part you transform time differentiation to H which hasn't been proven yet. I want to deduce from basics and not use ready-made Hamiltonian framework. Hmm, I don't think you get my point here, but thanks. Your answer provides part of the explanation.
Mar
8
comment Conserved quantum observables from symmetries *with density matrix*
Why does $U$ preserve the time derivative in the way shown? If that has to do with Hamiltonian formalism, then that's a postulate Ballentine doesn't need. Moreover "pluging in the concrete symmetry" is the key part and from the derivation I'm interested in. I hope to find it more in detail somewhere. It even seems that phase invariance of the way function actually plays a key role for the story of QM.
Mar
8
comment Conserved quantum observables from symmetries *with density matrix*
He basically derives the form of the observables without prior knowledge about anything but the maths of the Galilei group (existence of density matrix and trace averages are postulated). He expresses all operators in terms of position and momentum operators while phase invariance allows for one free constant.
Mar
8
comment Conserved quantum observables from symmetries *with density matrix*
I'm new to this topics, but to me it seems B. is more fundamental. He starts with saying there is a density matrix and observables as operators. Averages are the trace. Then he works with pure states knowing that states are phase invariant. For the Galilei group he deduces all commutators and operators by representation theory. In general due to gauge there is one free variable [x,px]=[y,py]=[z,pz]=A which turns out to be $\hbar$ in experiment. That's the derivation.
Mar
8
comment How can new interpretations of QM help?
Is there really no interpretation which one day would make calculations better? What is the easiest QM interpretation to teach? What are axioms good for if the imply derivations which you cannot follow in physical understanding? OK, I see where QFT is used. But I guess it will not make the double slit experiment physically more intuitive?
Mar
8
comment Conserved quantum observables from symmetries *with density matrix*
This seems to already assume QM framework? Ballentine derives representations in terms of position and momentum for the Galilei group. Can I do the same with the density matrix? Because at the beginning I don't even know that such of thing like $\hbar$ exists. It has to be derived.
Mar
8
awarded  Supporter
Mar
8
awarded  Commentator
Mar
8
comment How can new interpretations of QM help?
@Zaslavsky: Sure, but it's up to the reader to read the full question with all explanations. I could add: Does any of the interpretations potentially help advancing technology? That's all what matters really, unless you are researcher who is getting paid. It's about practicality and results and not fancy mathematical frameworks which lose imaginability of reality.
Mar
8
comment How can new interpretations of QM help?
Can you think of interpretation which potentially could make the most difference? Does QFT offer any insights into the simple double slit experiment? I mean saying the particle considers all paths and then behaves accordingly is even less intuitive than non-locality etc?! Later I'll have a look at geometric QM. But at first glance it seems like mathematical reformulation which makes is mathematically nicer but physically less understandable?!
Mar
7
asked How can new interpretations of QM help?
Mar
7
awarded  Scholar
Mar
7
accepted How are fundamental forces transmitted?
Mar
7
accepted Learn algebra and interpretation of QM
Mar
7
asked Conserved quantum observables from symmetries *with density matrix*
Mar
4
comment Why does electrical current start to flow?
I also heard that the EM field plays a key role. But your other post doesn't really answer this particular question, as merely saying "there is a voltage" provides no concrete information. I added a comment to this question above.
Mar
4
revised Why does electrical current start to flow?
added 341 characters in body