Is Stern-Gerlach experiment a proper idealization of measurnment?

[Jarek 31]

I have met statements that Stern-Gerlach experiment can be seen as idealization of quantum measurement: we start with random direction of spin (continuous), end with parallel or anti-parallel alignment (discrete).

Is it a proper analogy/idealization of measurement? How to characterize the differences?
Are there some interesting different analogies?

In Stern-Gerlach we have magnetic dipole traveling in external magnetic field, what means torque (tau = mu x B) hence precession - additional energy e.g. kinetic ... unless parallel or anti-parallel alignement (tau=0), so can it be seen as radiation of excessive energy like for atom deexcitation?

ps. Recent "Tracking the Dynamics of an Ideal Quantum Measurement" https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.124.080401

 

[PeroK]

What precisely is your question?

 

[Jarek 31]

As in the title: is Stern-Gerlach proper analogy/idealization of quantum measurement? (and why)

 

[PeroK]

As in the title: is Stern-Gerlach proper analogy/idealization of quantum measurement? (and why)

Okay, but that question sounds like it requires an essay to answer! My short answer would be yes, of course. Why wouldn't it be?

Can you give more context to your question? What do you precisely want to find out?

 

[Jarek 31]

My short answer would be yes, of course.

Great! I would also agree.

However, many people need e.g. conscious observer for measurements, while in Stern-Gerlach we have nearly classical situation: tiny magnet in external magnetic field aligns to minimize energy.

So can we use Stern-Gerlach intuition for other measurements, or does it miss something quantum like need of conscious observer?

 

[PeroK]

Great! I would also agree.

However, many people need e.g. conscious observer for measurements, while in Stern-Gerlach we have nearly classical situation: tiny magnet in external magnetic field aligns to minimize energy.

So can we use Stern-Gerlach intuition for other measurements, or does it miss something quantum like need of conscious observer?

Modern QM (since the 1930's) has no concept of a conscious observer.

One important point is that the SG magnet itself does not constitute a direct measurement of spin. The only measurement is the particle impacting the screen. We never actually measure directly the spin. This tends to be true generally of QM phenomena: the measurements are not directly of the phenomenon itself, which is inferred from some indirect measurement. For example, you cannot study a hydrogen atom and watch the electron jump from one energy level to another. Instead, you infer the energy transitions from the emitted spectrum of light.

In SG we infer the spin of the outermost electron (you can't zoom in and look at it spinning!) from the position of impact on the screen.

 

[vanhees71]

I'm not sure, whether I understand your question right, but in some sense the Stern-Gerlach experiment (SGE) is almonst an ideal von Neumann filter measurement. Why almost?

In most textbooks, it's claimed that a SGE is really an ideal von Neumann filter measurement. That's based on the idea to have $\vec{B}=B(\vec{x}) \vec{e}_z$ such that you get a 100% entanglement between the spin-component in $z$ direction an the position of the particles.

This is, however only true approximately, because there's no magnetic field of this kind, because it must be inhomogeneous and to fulfill $\vec{\nabla} \cdot \vec{B}=0$. So you always have some probability that in the partial beam, which would be completely spin up, to have spin down. With the right choice of the field (large homogeneous component in $z$ direction with small inhomogeneous components in the other directions, in regions relevant for the particles moving through the field) you can make this probability very small, because due to the rapid precession of the spin around the $z$ direction in such a setup the deflection of the "false" spin-component particles can be neglected with very good accuracy.

 

[Jarek 31]

Modern QM (since the 1930's) has no concept of a conscious observer.

I am coorganizing QM foundations seminar ( http://th.if.uj.edu.pl/~dudaj/QMFNoT ) and especially Bell theorem people still love to use conscientiousness, free will-based argumentation (e.g. https://en.wikipedia.org/wiki/Counterfactual_definiteness ).
SG is great for offering purely physical intuitions about measurement.

A related question is if measurement is instant?
While it seems a common QM view, there are now experiments measuring attosecond-scale delays in photoemission (https://science.sciencemag.org/content/328/5986/1658) or this week: of zeptosecond-scale delays of EM wave propagation through orbitals ( https://science.sciencemag.org/content/370/6514/339 ).
But if it is not instant, what exactly happens during this time?

 

[PeroK]

I am coorganizing QM foundations seminar ( http://th.if.uj.edu.pl/~dudaj/QMFNoT ) and especially Bell theorem people still love to use conscientiousness, free will-based argumentation (e.g. https://en.wikipedia.org/wiki/Counterfactual_definiteness ).
SG is great for offering purely physical intuitions about measurement.

Perhaps that should have been in your original post!

 

[vanhees71]

I am coorganizing QM foundations seminar ( http://th.if.uj.edu.pl/~dudaj/QMFNoT ) and especially Bell theorem people still love to use conscientiousness, free will-based argumentation (e.g. https://en.wikipedia.org/wiki/Counterfactual_definiteness ).
SG is great for offering purely physical intuitions about measurement.

A related question is if measurement is instant?
While it seems a common QM view, there are now experiments measuring attosecond-scale delays in photoemission (https://science.sciencemag.org/content/328/5986/1658) or this week: of zeptosecond-scale delays of EM wave propagation through orbitals ( https://science.sciencemag.org/content/370/6514/339 ).
But if it is not instant, what exactly happens during this time?

Nothing jumps according to modern quantum theory. The recent zeptosecond-scale measurement that the ultimate speed limit of the Universe, the speed of light in vacuo, holds also in the "quantum world"!

 

[Jarek 31]

Yes, I completely agree - physics should be continuous, limited by speed of light.
However, there is discussion if e.g. Feynman ensemble should use physical paths: of finite speed? (personally I see these nonphysical as mathematical trick like in derivation of Brownian motion).

And this is asking for some dynamics hidden below QM, like of measurement.
Or for "excited atom -> deexicted atom + photon", in which photon can be seen as (Noether's) EM wave carrying difference of energy, momentum and angular momentum ... but of what exactly field configuration? It has period in femtoseconds - what happens in atom during production of this EM wave?

 

[vanhees71]

I guess by "Feynman ensemble" you mean the path integral, which is a functional integral over phase-space trajectories (for the 1st-quantization formalism) or field configurations (for the 2nd quantization formalism). I'm not sure, how rigorous you can make the path integral. I don't know, whether there is a mathematically fully strict definition.

I think all there is, is the unitary time evolution of the formalism. As in classical mechanics we cannot solve this exactly for macroscopic systems and use thus statistical methods to derive effective dynamics for the relevant macroscopic observables. The quoted processes with single atoms and photons are examples, where you can solve to a high level of accuracy the dynamical equations. It's all smooth, and nothing jumps. It depends on the time resolution of your measurement whether you can resolve the time evolution or whether it's "for all practical purposes" like an "instantaneous jump".

 

[Jarek 31]

Regarding Feynman ensemble, it concerns all:
- path ensembles, usually as in derivation of Brownian motion: nowhere differentiable, not bounded by the light speed. I have worked on kind of intermediate MERW ( https://en.wikipedia.org/wiki/Maximal_entropy_random_walk ): uniform/Boltzmann-path ensemble based diffusion: it would be great to go to nicer trajectories (like Brownian -> Langevin), but it becomes much more complex.
- ensembles of Feynman diagrams (2nd quantization) - can we ask for EM field configuration behind a given Feynman diagram? Using particles as perfect points ( https://physics.stackexchange.com/questions/397022/experimental-boundaries-for-size-of-electron ?), charges would mean infinite energy of electric field alone - bringing question of regularization of EM fields to finite energy.
- then taking it further, like dynamical triangulation approach: spacetime ensembles for GR quantization ... or imagining history of the Universe as ensemble of possibilites (~Many Worlds) - should such ensembles contain only physical scenarios?

Regarding possibility of unitary evolution, I agree there should be one - requiring better descriptions.
For example the produced photon e.g. in atom deexcitation goes into environment - which is neglected in Schrödinger equation (somehow averaging over it) - hence this description needs to "close eyes" during deexcitation
Imagining Wavefunction of the Universe, there is no longer exterior, hence it should have unitary evolution - the question is how to get information like EM field configuration of optical photon?