Of course you have to use approximations and any measurement has a finite error, but you shouldn't refer to wrong qualitative descriptions to begin with, at least if you know better!
This is not true at all. Already Stern and Gerlach in 1924 got the value of the electron magnetic moment being about 1 Bohr magneton within a few percent not with a 100% error as you claim. It's well known that nowadays it's among the most precise measured values ever. For the comparison to...
Indeed for a measurement you need precisely the opposite: A good measurement entangles the measured observable with the pointer state of the apparatus!
The qualitative reason to understand this is simple: Phonons are "quasiparticles". The physics of them, i.e., the "thing" observable in the lab (in this case in everyday life) is that they are vibrations (i.e., sound waves) of a piece of macroscopic matter, not some point-like object that you'd...
In the SGE the "pointer" is the particle's position, right? If you accept this, it's the most simple example for a measurement describable completely by quantum dynamics (sic!), i.e., the motion of a neutral particle with a magnetic moment through an inhomogeneous magnetic field!
No, wave functions do not make sense in QFT since QFT describes not a situation, where you have a fixed number of particles but you can create and destroy them in interactions, and that's why it's the natural description for collisions at relativistic energies (despite all the much more formal...
Observables are something else than functions of the state. It's the most important first thing you have to learn about QT to make sense of it at all. Again, your "thermal interpretation" is not a satisfactory substitute for the standard minimal interpretation. For me it's even clearly violating...
In this connection: Does anybody have a reference to a Stern-Gerlach measurement, where not the magnetic moment of a spin-1/2 angular momentum has been measured but some higher angular-momentum state, like an atomic SGE with atoms of larger total ##\vec{j}##?
Sure, there's not a mathematical justification for (41) in this paper, but it provides precisely what I'm still lacking in explaining the meaning of POVMs. Now it would be great if somebody could write a paper merging this paper by a practitioning experimenter, providing the physical meaning of...
Indeed, isn't this the most general surprising, for many physicists of the first "quantum generation" even disturbing, discovery of QT to begin with: No matter how accurately you may be able to prepare a system in (and the most "accurate" states possible are just the pure states, i.e...
If I understand it right, what @DarMM refers to is the fact that, in contradistinction of classical (statistical) physics, in QT the sample space "all possible observables on the system" does not make sense, i.e., there are no states (pure or mixed) for which all observables take predetermined...
The irony is that this view was already provided by Planck, but Einstein's view of 1905 prevailed though Einstein himself said that he was still puzzled by what "radiation really is" till his death. It's also ironic that Einstein got his Nobel prize for the only theory of his that didn't stand...
Well, we are discussing how to describe the sources and detectors with a POVM. Then I expect that you describe the POVM for your example you give. A TPC is quite common, and I think I roughly understand how it works (though as a theorist usually I have to trust the experimentalists to understand...
The problem is that even in otherwise good textbooks this wrong picture of a "photon" as some localized lump of matter (like a miniature "billard ball") persists. It's just laziness of textbook writers to introduce QM in an "as simple as possible but not simpler" way. In the case of...
There's not much to add to @strangerep 's answer.
I want just say that in my opinion, what's called "collapse" is simply the epistemic update of the description due to gained knowledge from a measurement. It's like knowing on Saturday evening which numbers came out from the drawing of the...
Of course, we can philosophize endless about the "ontology of photons/elementary particles". There's enough paper wasted on this fruitless subject ;-)). For me the particles of the standard model simply "exist" in the very specific sense you describe it: There are predictions of the theory (QED)...
My lay-man's view of probability theory is that it provides a mathematical axiomatic system, like e.g., Kolmogorov's. That system of axioms, however just gives a framework and does not define the concrete probabilities. That's of course a feature, since it should have this flexibility.
The art...
Of course, a proton is not a little classical bullet. It has for sure a fuzzy "boundary". What we are discussing here is the charge radius, as operationally defined by measuring the socalled form factor. The latter quantity is defined by scattering processes, and electron scattering this is...
Well, it was an example, which I thought is close to what's done when position of a particle is measured with a photoplate or CCD cam. If you need more complicated error analysis than the usual Gaussian assumptions, because the errors of distinct outcomes are correlated, then you have to do it...
Sure, that's why the SI units still have finite uncertainties in their practical realization. Again, we discuss physics here, not mathematical abstractions. Any measurement is only complete with a thorough estimate for the "statistical" and "systematical" errors!
You cannot define observables...
I mean the complete asymptic wave function, including the incoming asymptotic free wave. As I said, a very thorough discussion of scattering theory (using the traditional wave-mechanics approach, which of course is particularly intuitive for scattering theory to begin with) is the famous...
I'd not say QT is a generalization of probability theory but it's an extension to provide a scheme to predict concrete probability measures for the outcome of measurements on physical systems. As I understand it from the many discussions in this forum, the most general mathematical scheme to do...
A WRONG description is never useful. Physics is an exact science, and we should do our best to describe it correctly. Again: You cannot define the position of a photon (to some extent maybe you can define "transverse position" somehow). All you can define are probability distributions for a...
It is important to carefully take into account the "##\mathrm{i} \epsilon## prescription to understand, why this is the "vacuum-to-vacuum transition amplitude under influence of the external source ##J##". See my QFT manuscript,
https://itp.uni-frankfurt.de/~hees/publ/lect.pdf
In Sect. 1.10...
Are you talking about hadrons in pp, pA or AA collisions? Then have a look for "rapidity distributions". There is for sure tons of material online. It would be better, you'd tell us some details about what you are after!
I've not followed the argument in the paper yet, but in classical electromagnetic theory energy is always strictly conserved. You only have to carefully take into account the total energy-momentum-stress tensor.