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If you enjoy it D'Ariano et al's "Quantum Theory from First Principles" uses a similar diagramatic approach but is more concise and rigorous.

I would suggest having a read of a full recent model of how macroscopic commutativity arises, such the Allahverdyan et al (2011). Environmental Decoherence is actually not the dominant reason for classicality. Equilibration processes, thermalisation and the contraction of the algebra of...

Another standard reference is: Woodhouse N.M.J. "Geometric Quantization" 2nd edition, OUP

In String theory for example, if we have a background spacetime with metric ##\eta## then any other classical metric ##g## is generated from coherent states of spin-2 excitations upon this background.

I really wish more QFT texts would make this explicit.

It would be extraordinarily difficult to treat QFT for finite times. To even say there are ##N = 2## particles at finite time would be difficult for an interacting theory where multiparticle states are only defined at asymptotic times. States at finite times would not strictly have a particle...

OP another word to look for is "line bundle". It's essentially the same thing as a scalar density bundle under a different name. Many abstract treatments of QM will talk about how the wavefunction is a section of a line bundle.

Sorry I meant "experimentally absent" in that paragraph, I was clearer in the following paragraph: So quantum theory predicts we shouldn't detect interference effects for most macroscopic objects, correctly models those that do such as SQUIDS and correctly derives the material constants of...

There's no resolving this in this thread. Simple question insists/believes Nature must be deterministic. Morbert and vanhees71 are pointing out that our most successful physical theory is stochastic. This is no different from demanding a mechanical exposition of the aether for electromagnetism...

But don't coarse graining and decoherence predict the absence of interference effects for macroscopic collective coordinates? In addition quantum condensed matter correctly derives the macroscopic physical properties (e.g. friction, dielectric and many other coefficients). So the predictions of...

He's matching a general form of the full three dimensional wave-function to the form established for its restriction to the xy plane containing the lattice.

No.

No, just the general conversation.

Certainly, that's clearly what the actual formalism says and what experiments support.

Zurek has some fun papers modelling Hyperion, a moon of Saturn, with QM: Zurek, W.H.: Pointer basis of quantum apparatus: Into what mixture does the wave packet collapse? Phys. Rev. D 24, 1516–1525 (1981) Zurek, W.H.: Environment-induced superselection rules. Phys. Rev. D 26, 1862–1880 (1982)...

Well QM and QFT are stochastic theories. Morbert and vanhees71 are just saying it gives you the probability of an outcome, it doesn't tell you which specific outcome occurs. Nobody has a theory that actually tells you which outcome occurs.

Usually that's still treated in an inertial frame. Of course you don't have to, it's just easier.

The quantum state can be transformed to any frame, but there's rarely call to do it pragmatically because it would make calculations difficult.

Thanks for that. What a lovely paper. Given the above and your like of Ballentine, I think you might enjoy Talagrand's new book on QFT where he really digs deep into representations of the Poincaré group. He treats even massive Weyl Spinors.

Yeah I agree, just thought I'd clarify what I saw the question to be.

I think A. Neumaier might be asking how the outcome being definite at the detector is modelled quantum mechanically, i.e. where in the model of the atom+detector is this definiteness seen.

Without Bohr the field of discussing Bohr would have been held back decades :smile:

Yeah, unfortunately he was very private and quiet, mostly known to only people in Fermi's group and died young under mysterious circumstances.

Sorry, in case I wasn't clear, in the above I referred to Majorana not Jordan.

I only read Ballentine recently thanks to this forum. A really good text, wished I'd had it as an undergraduate. I loved the section on state tomography.

Well first of all just that. Everybody knows the name, but himself as an actual person is rarely discussed in the history of physics, which is odd because I think it's one of the more interesting stories. Outside of that he was the first to make major progress in the treatment of the...

It's also interesting how there are many people who were a major influence on the emerging theory, but don't get included in the folk story. For example Jordan, Majorana, Kramers, etc. I think it's a common tendency to concentrate history into a few "mythic" figures.

Could you expand on what you mean here?

Well in his essays Bohr never mentions collapse. The closest he gets is discussing filtering, that's about it. This is no different from the history of physics in general though. Even in Classical Mechanics the "folk history" is completely different from the actual history of what Langrange...

A POVM is fairly mundane stuff. One doesn't need to talk about cosmology, black holes, Heisenberg cuts or anything else. A POVM models measurements that have errors, thermal noise, false positives, dark counts, indirect measurements via coupling to an ancilla and so on. It's just as vanhees71...

That's incorporated into the POVM.

That's handled with POVM tomography though, not randomised observables.

Agreed, basically students are increasingly asking why can't the total closed system also be described with a CPTP evolution.

There's also a shift in the attitude to mathematics. Go back to the 30s and 40s and a non-mathematical discursive explanation of a theory was considered primary. The mathematics was simply how one implemented these ideas for quantitative use. I was surprised to find out even somebody as...

Not that it matters, but historically speaking I wouldn't necessarily agree. Back in the 19th Century there were plenty of philosophical debates about electromagnetism, even Newtonian Mechanics and Gravity. Similarly for General Relativity with things like the "hole argument". And it was...

I think the confusion comes in because in Classical Physics you can imagine a limit of preparations that fix all future measurements. It's just like how Classical Probability allows you to imagine probability as ignorance of a "totally fine grained" state where all quantities are well-defined...

Quantum Theory says that not all physical quantities take well-defined values at all times, interactions with atomic systems are inherently probabilistic and the acquisition of information fundamentally disturbs the system. The conjunction of all these facts as can be seen in results like the...

Let me give some context, because it's not really that I disagree in any way. Quantum Information is now a common enough topic at universities, either as an upper undergraduate course itself, part of a quantum computing one or aspects of it are built into basic QM courses. As students become...

It's pretty routine in Quantum Information to write down POVMs and CPTP maps, I'm not sure what you mean.

How do you know there isn't a time-translation invariant CPTP evolution?

Yeah that's true actually. You have similar measurement controlled gates in quantum computing. As you mentioned you never need to model them with randomised Hamiltonians. Such randomised Hamiltonians could always be absorbed into a CPTP map, just as randomised PVMs can just be represented as POVMs.

Such a concept wouldn't make much sense. In QM you have your algebra of observables and then per Gleason's theorem (or Busch's if you take POVMs) quantum states, i.e. statistical operators, can be derived as probability assignments to the observables. Thus they do take values...

This is what makes unitarity less fundamental in QFT in curved spacetime, since there we do not have time-translation invariance. Coming back to non-Rel QM, this is basically what I was asking. Since one can have a CPTP evolution, why wouldn't you. A. Neumaier's argument that isolated systems...

Probably more the former, but it doesn't matter too much. It's just that the usual argument of "probabilities must sum to one" isn't really sufficient.

Maybe it might help Kashmir to say there isn't really a separate Schrödinger picture* for classical mechanics. Formulae like ##v = \frac{dx}{dt}## only have an analogue in the Heisenberg picture. If you try to use them to guess at what operators should be in the Schrödinger picture you'll get...

Okay thanks. That basically lines up with what I first learned from Gottfried (1st Ed sans Yan) and the old Schwinger "Humpty-Dumpty" paper.

I understand. I'm saying that in total English has about 6% of its words, as per the monograph above, consisting of borrowings from such far away languages. This isn't that unusual. Take Japanese. 8% of its words are directly taken from such distant languages (金田一京, ed. (2001). 新選国語辞典. 小学館) and...

Yes, but often only when the relation was pretty close. Indian grammarians did recognise similarities with Persian. However nobody came close to recognising bigger families like Indo-European.

@vanhees71 , this is more out of curiosity about how you would phrase it, I'm not debating as such. We commonly say quantum theory is a probability theory where not all quantities take well-defined values at once. So if we start with a particle in an eigenstate of z-axis spin, ##S_{z}##, such...

You have to keep in mind the Poisson bracket goes to commutator aspect of quantisation and express everything in terms of the canonically conjugate quantities of position and momentum. I could similarly say momentum is ##p = m\frac{dx}{dt}##. Making a direct substitution like that would give me...