Quantum measurement of a Strontium ion

[Demystifier]

Yeah, and you can judge textbooks pretty well by taking the math to text ratio...

Yes. I prefer books in which this ratio is not very far from 50:50.

Anyway, since you talk casually, would you advise your readers to not take too seriously your non-mathematical statements on quantum interpretations?

 

[vanhees71]

Well, I don't think that one should take too seriously any non-mathematical statement on quantum interpretations too seriously. What can be observed is defined what the experimentalists can measure in the lab and a physical theory or model can be judged how well it describes the observations with a sound and solid basis of model assumptions. For QT this clearly is simply the minimal statistical interpretation or even the "shutup and calculate interpretation".

The only real fundamental problem from a physics point of view left is to find a mathematical description of the gravitational interaction that is fully compatible with quantum theory. I've no clue what such a successful extension of QT this might be or whether it brings a true new revolution in the natural sciences. Note that there were only two revolutions in the history of physics yet: (a) the discovery of the modern scientific method in the Renaissance leading to classical physics (theorywise: Newtonian mechanics, relativity and Maxwell's electrodynamics, and classical statistical physics) and (b) the discovery of modern quantum theory (non-relativistic QM and relativistic QFT).

 

[Demystifier]

Well, I don't think that one should take too seriously any non-mathematical statement on quantum interpretations too seriously.

Thank you for making this explicit! I will have it in mind in all the future discussions of quantum foundations with you.

 

[Lord Jestocost]

Well, I don't think that one should take too seriously any non-mathematical statement on quantum interpretations too seriously.

In the book “What Little I Remember” Otto Robert Frisch remarks on Bohr: "He never trusted a purely formal or mathematical argument. 'No, no' he would say 'You are not thinking; you are just being logical'."

 

[Demystifier]

In the book “What Little I Remember” Otto Robert Frisch remarks on Bohr: "He never trusted a purely formal or mathematical argument. 'No, no' he would say 'You are not thinking; you are just being logical'."

"We use mathematics in physics so that we won’t have to think."
Bryce DeWitt

 

[vanhees71]

In the book “What Little I Remember” Otto Robert Frisch remarks on Bohr: "He never trusted a purely formal or mathematical argument. 'No, no' he would say 'You are not thinking; you are just being logical'."

That's why have never learned much from reading Bohr or Heisenberg. I prefer Born, Dirac, and Pauli.

 

[Killtech]

Sorry for the late reply; i was on vacation.

Yes. I strongly suggest that you spend some time learning about how a Stern-Gerlach apparatus actually works and how it is modeled mathematically in QM. I briefly described it in words in post #48; notice how what I said in that post looks nothing at all like what you said.

But i cannot find much advanced stuff on Stern-Gerlach. The basic modelling of the experiment in QM you were referring to is in itself pretty simple and i do understand it. And I also understand how the resulting superposition of spin up/down states maps to the experimental outcome using the classic QM interpretation/measurement mechanics. Within that framework all you said is of course correct.

But when it comes to talking about the collapse of the wave function this simplistic handling is at the range of validity. To begin within that framework the measurement is not well defined from a mathematical perspective – or at least I couldn’t find any strict axiom set from which one could derive that the measurement (or rather collapse or equivalent) does or does not happen directly at the SG device (please correct me if I’m wrong). And that's a no go for me. Annoyingly experimentally either way makes no difference for SG outcome (assuming the default setup. It can be rearranged to make a difference however). And that’s my bigger problem: I cannot find sufficient experiments to look at to resolve these ambiguities (guess there is a reason why there are no QM axioms resolving this). And taking an entirely different particle within an entirely different interaction (the photon in MZ interferometer you mentioned) as an analogy makes way too many unverified assumptions for me to stomach. I am not much the believer type so unless anyone can point me to proper experimental foundation for every of these implicit assumptions made it remains a speculation for me that cannot be accepted without some scrutiny, sorry.

So hopefully you can understand why i have my reservations of using the classical QM modelling to things where the modelling is not well defined - especially when it seems that we can fix this if we apply advanced theories like QED. But as it is, these problems leave me often sleepless at night which is why I am looking for anything more solid than that.

Anyhow as for the classic example I made, it is purely interesting for giving an idea for what kind of other physics might be involved/interesting here. And indeed in order to get a classical object to reproduce the only two discreet impact points one requires a kind of classical 'collapse' mechanic to achieve the moving from a continuous to a discretized distribution. sure, classical physics offers many ways to dampen an oscillation but interestingly enough classical electro-dynamics has a natural process for that - albeit in normal circumstance loss of energy due to such type of radiation is barely noticeable. In any case if classic parameters are in the proper range this can yield the desired result. So I do not understand that, if this kind of physics can play a big role classically (and also reproduce QM results) why would we assume it’s suddenly irrelevant in QM without even checking?

Yeah, the problem is that this kind of interaction requires to do full QED with a fairly complex bound state – fair, that’s a nasty thing to handle calculation wise. So I thought doing a shortcut via the mean lifetime of excited Zeeman energy levels would be an obvious way to skip most of the difficult stuff to at least get a good sense what is happening there. And so far no one has explained to me where the error in this approach lies.

 

[PeterDonis]

I couldn’t find any strict axiom set from which one could derive that the measurement (or rather collapse or equivalent) does or does not happen directly at the SG device

There isn't one. Where you say that a "measurement" has occurred in QM is not derived from any axiom. The rule is that a measurement has occurred when an irreversible change has occurred; but "irreversible change" has no axiomatic definition. In practice "irreversible" means "we don't know of any feasible way to reverse it". We can reverse the change that occurs when an electron (or silver atom or strontium ion or whatever) passes through the SG magnet--just bring the two beams back through another SG magnet in the reverse direction to recombine them--so we can't say a measurement has occurred when the electron passes through the magnet. (And we know how to write down the unitary evolution for that process, so we can model the reversibility of it mathematically.) But nobody knows how to reverse the process of the electron hitting the detector screen, nor does anyone expect that we will figure out how to reverse it in the foreseeable future. So that's where we say the measurement has occurred.

It can be rearranged to make a difference however

How?

in order to get a classical object to reproduce the only two discreet impact points one requires a kind of classical 'collapse' mechanic to achieve the moving from a continuous to a discretized distribution

I have no idea what you're talking about here. Classical objects have single trajectories. So any classical object automatically has one starting point and one ending point. There is no need to "move from a continuous to a discretized distribution".

if this kind of physics can play a big role classically (and also reproduce QM results)

Again, I have no idea what you are talking about here.

 

[Killtech]

There isn't one. Where you say that a "measurement" has occurred in QM is not derived from any axiom. The rule is that a measurement has occurred when an irreversible change has occurred; but "irreversible change" has no axiomatic definition. In practice "irreversible" means "we don't know of any feasible way to reverse it". We can reverse the change that occurs when an electron (or silver atom or strontium ion or whatever) passes through the SG magnet--just bring the two beams back through another SG magnet in the reverse direction to recombine them--so we can't say a measurement has occurred when the electron passes through the magnet. (And we know how to write down the unitary evolution for that process, so we can model the reversibility of it mathematically.) But nobody knows how to reverse the process of the electron hitting the detector screen, nor does anyone expect that we will figure out how to reverse it in the foreseeable future. So that's where we say the measurement has occurred.

That's reasonable. Now going back to my original question, you can just translate it into "is the beam splitting in this instances verifiably reversible"? I would wanted to see an experiment showing just that. In this particular case where the initial beam changes its energy level through the interaction with the magnetic field and the two resulting beams even have a mismatching energy. This is quite different then in most other interferometer experiments and the underlying reason for my initial question. A rough idea was that energy exchanges usually come along with some information exchange so it isn't maybe entirely award to ask if a portion of information might have gotten lost irreversibly through that.

How?

Doing interferometry as i mentioned in one of my earlier posts. Now if you can recombine the two beams back together and the superposition is still maintained (as you would expect from the simple QM model) then you can do something alike an interference by sending the recombined beam onto another SG device and than compare it to the combined results when one of the beams is filtered. The observations should clearly differ between the beam being a superposition and an ensemble of spin up/down states.

I have no idea what you're talking about here. Classical objects have single trajectories. So any classical object automatically has one starting point and one ending point. There is no need to "move from a continuous to a discretized distribution".

I was talking about the distribution of the outgoing objects or in case of quantum particles this would be the spatial distribution of events on the final detector screen. Well, for me it wasn't that clear that detecting an outgoing distribution of only spin up/down states cannot be achieved classically. Because I immediately a had a few ideas how that could happen. So I looked into such a classical setup where outgoing objects should achieve a distribution of trajectories focusing only around two angles (up/down) leaving the SG device with nearly none in between. Such a setup sounded initially more obvious in my mind that it turned out to be thus i wrote it down to check it even really works here: https://www.physicsforums.com/forums/classical-physics.61/. In any case it is of course impossible to get a superposition or anything alike classically such that the I know this comparison to QM will always be limited.

 

[PeterDonis]

you can just translate it into "is the beam splitting in this instances verifiably reversible"? I would wanted to see an experiment showing just that.

As I think I said before, I don't know if anyone has done this experiment for electrons (or silver atoms as were used in the original SG experiment), but it has certainly been done for photons; the simplest example is a Mach-Zehnder interferometer. I don't think anyone doubts that if it could be done for electrons, the beams would recombine the same way the photon beams do in an MZI.

If you prefer not to believe the result for electrons until it's actually done, I can't stop you, but the prediction of the math of QM is unequivocal that the result will be what I said above.

the initial beam changes its energy level through the interaction with the magnetic field

Assuming this energy level change does occur (I haven't done the math), passing through a second SG device, oriented the same way, in the opposite sense will exactly reverse this interaction, so it won't prevent the beams from recombining.

In any case, you could in principle run the SG experiment with free electrons and eliminate this complication.

A rough idea was that energy exchanges usually come along with some information exchange so it isn't maybe entirely award to ask if a portion of information might have gotten lost irreversibly through that.

The SG magnet interaction with the electron (or silver atom) is unitary, therefore reversible. At least, that's what the math of QM says. (If you want to be precise, the math of QM says you can model this interaction as unitary and reversible, whereas it says we don't know how to model the electron or silver atom hitting the detector as unitary and reversible.)

Also, your more general idea that "energy exchanges usually come along with some information exchange" is very vague, and if you try to make it precise I think you will find a lot of exceptions. The SG magnet interaction itself might well be one: what information gets exchanged? So I would not rely on this vague intuitive idea in physical reasoning.

you can do something alike an interference by sending the recombined beam onto another SG device and than compare it to the combined results when one of the beams is filtered.

Ah, I see--similar experiments to what is done with photons, but using SG devices instead of beam splitters. Yes, since both cases are modeled using the QM math of qubits, the predictions of QM would be similar.

Note, however, that none of this would solve the problem you appear to have with "when does collapse occur", because from the standpoint of collapse interpretations like Copenhagen, experiments where you have multiple beams that are brought back together to interfere and thus demonstrate the existence of superpositions during the intermediate processes do not involve any collapses during those intermediate processes. The only collapses are at the very end, where detectors are triggered to record final results, and those events are irreversible on any QM interpretation, so they don't help you any.

for me it wasn't that clear that detecting an outgoing distribution of only spin up/down states cannot be achieved classically

The classical prediction for the SG experiment is well known, and is at sharp variance with the actual result that was obtained. Stern and Gerlach knew that when they first did the experiment, and so did all the other physicists; that's why the experiment was such a crucial one in the development of QM.

The classical prediction is that the detector should show a bright region in the center, with intensity decreasing outward in both directions. The actual result was that the detector showed bright regions at the two edges, with intensity sharply decreased in the middle. There is no way to get that result from classical physics.

i wrote it down to check it even really works here: https://www.physicsforums.com/forums/classical-physics.61/.

This is a link to the Classical Physics forum. Can you give a link to the actual thread?

 

[vanhees71]

The closest that comes to an answer of the question of reversibility in SG experiments is the following paper by Schwinger et al

https://link.springer.com/article/10.1007/BF01909939
https://link.springer.com/article/10.1007/BF01384847

Of course, in theory it's reversible as the electromagnetic interaction is T-invariant but in practice it's so hard to achieve that one can pretty safely say it's not doable.

 

[Killtech]

As I think I said before, I don't know if anyone has done this experiment for electrons (or silver atoms as were used in the original SG experiment), but it has certainly been done for photons; the simplest example is a Mach-Zehnder interferometer. I don't think anyone doubts that if it could be done for electrons, the beams would recombine the same way the photon beams do in an MZI.

If you prefer not to believe the result for electrons until it's actually done, I can't stop you, but the prediction of the math of QM is unequivocal that the result will be what I said above.

For photons the interferometer setup entirely different. wavelengths/energies of incoming and both outgoing beams at the splitters are identical. On the other hand if you force and electron into a curved trajectory it will radiate photons (e.g. synchrotron radiation) and thereby lose a small amount of energy and information which is in practice irreversibly lost (have fun catching every photon to recombine it with its master later). Similar effects apply for other cases where energy levels of states change. Visible with full QED where all fields can exchange energy amongst each other but ignored in simple QM. However these processes are in theory still unitary but it's almost like entropy/an egg falling down to the floor - you won't get it back together in practice "almost surely".

Assuming this energy level change does occur (I haven't done the math), passing through a second SG device, oriented the same way, in the opposite sense will exactly reverse this interaction, so it won't prevent the beams from recombining.

Shouldn't it? Due to Zeeman spin up and down states should differ in energy levels, no?

So i am looking for the experimental cases where this is done for any charged or neutral particles with a magnetic moment and where the beam is split via a magnetic field (i.e. Zeeman applies).

Note, however, that none of this would solve the problem you appear to have with "when does collapse occur", because from the standpoint of collapse interpretations like Copenhagen, experiments where you have multiple beams that are brought back together to interfere and thus demonstrate the existence of superpositions during the intermediate processes do not involve any collapses during those intermediate processes. The only collapses are at the very end, where detectors are triggered to record final results, and those events are irreversible on any QM interpretation, so they don't help you any.

Okay the idea is two fold: interferometry allows to distinguish between a superposition of states and the corresponding ensemble of same states - which is otherwise quite hard to do. A collapse on the other hand can be understood as breaking a superposition into an ensemble of the corresponding eigenstates of an observable operator. So if i want to know if a particular collapse type has occurred (defined by its observable/eigenstates) i just have to do interferometry with those states and see the results.

This is a link to the Classical Physics forum. Can you give a link to the actual thread?

oh, my big fail here, sorry. here you go. can't correct the link in the original post anymore.

 

[vanhees71]

Have a look at the two papers mentioned in #18, which discusses the issue to "reverse" the Stern-Gerlach beam splitting. You need to be very accurate in your magnetic field, so that it's theoretically possible to reverse the time evolution but in practice impossible.

It's in the same sense impossible as what you describe in terms of electrodynamics. Even in classical electrodynamics for every "retarded solution" (i.e., waves fulfilling the Sommerfeld radiation condition) in principle also the "time reversed advanced solution" is a valid solution and theoretically existent in nature, but it's very hard to realize since you'd have to construct a global initial condition for the field precisely such as to radiate backwards and precisely being absorbed by the source.

 

[Killtech]

The closest that comes to an answer of the question of reversibility in SG experiments is the following paper by Schwinger et al

https://link.springer.com/article/10.1007/BF01909939
https://link.springer.com/article/10.1007/BF01384847

Of course, in theory it's reversible as the electromagnetic interaction is T-invariant but in practice it's so hard to achieve that one can pretty safely say it's not doable.

thanks for the links. i am not done checking them out yet. but hehe yeah, Humpty Dumpty and my egg comparison is basically the same idea. However they seem to focus on macroscopic challenges of the $B$ field setup while i am more concerned about the unavoidable field interactions withing QED.

[EDIT: damn i don't have an institutional subscription or anything to access them]

In any case this kind of indicates that no experiment was able to achieve this yet for this instance.

Have a look at the two papers mentioned in #18, which discusses the issue to "reverse" the Stern-Gerlach beam splitting. You need to be very accurate in your magnetic field, so that it's theoretically possible to reverse the time evolution but in practice impossible.

It's in the same sense impossible as what you describe in terms of electrodynamics. Even in classical electrodynamics for every "retarded solution" (i.e., waves fulfilling the Sommerfeld radiation condition) in principle also the "time reversed advanced solution" is a valid solution and theoretically existent in nature, but it's very hard to realize since you'd have to construct a global initial condition for the field precisely such as to radiate backwards and precisely being absorbed by the source.

I am kind of curios how that kind of effects may be related to the wave function collapse in general and which is why i was asking my initial question about when the collapse happens in SG case, just so to gain a little more clarity and ideas from there.

 

[vanhees71]

In my opinion, there's no collapse happening ever, but as you see on the example of this thread, this opens rather a can of worms than helping to answer this question. I think there are at least as many answers as there are physicists trying to answer them, and this indicates that it's not a well-posed scientific question, having a theortical or experimental resolution. All one can say are the probabilities for finding a particle in the one or the other partial beam behind the SG magnet, and since here for a good experimental setup the spin component in direction of the magnetic field is almost exactly entangled with the position (particle being in the one or the other partial-beam location) this implies the probabilities for finding the particle in the one or the other spin state. If you define "collapse" as just fixing the measurement result by the detector, then it occurs when the particle hits the detector and the detector stores the result somehow (as a spot on a photoplate or in a computer file for a CCD cam, etc.).

 

[PeterDonis]

if you force and electron into a curved trajectory it will radiate photons (e.g. synchrotron radiation)

Remember we are talking about QM. In QM, the electron will have an amplitude to radiate photons. One then has to set up the experiment to make this amplitude as small as possible during the experiment. Then one makes a large number of runs of the experiment, and one expects that during some appreciable fraction of these runs, no photon was emitted so no information is irreversibly lost.

Your apparent belief that photons are somehow immune from this is mistaken, btw. One has the issue of maintaining coherence with photons as well. Passing a photon through a beam splitter has a nonzero amplitude for the photon being absorbed in the splitter instead of passing through into the output beams. This is a nonzero amplitude for irreversible loss of information.

Due to Zeeman spin up and down states should differ in energy levels, no?

Not once they are recombined. The Zeeman effect, by itself, is unitary and reversible.

i am looking for the experimental cases where this is done for any charged or neutral particles with a magnetic moment and where the beam is split via a magnetic field (i.e. Zeeman applies)

I believe I have already said several times that I do not know of any experiments which attempt to recombine SG beams or anything equivalent.

 

[PeterDonis]

if i want to know if a particular collapse type has occurred (defined by its observable/eigenstates) i just have to do interferometry with those states and see the results

You are confusing two different meanings of "interferometry". One meaning is "putting a bunch of devices in the experiment that can produce interference", like beam splitters in an MZI. The second meaning is "putting detectors in the experiment that register irreversible results, and then using those results to infer whether interference has occurred".

The first meaning above, in itself, does not cause collapse under any interpretation. You can put a hundred beam splitters in your experiment and no collapse will happen under any interpretation just because of the beam splitters.

The second meaning above, combined with the first kind of experimental configuration, can indeed tell you whether interference has occurred; but that's not the same as telling you whether collapse has occurred inside the apparatus. You already know that collapse never occurs inside the apparatus according to any interpretation, as I said just above.

Plus, even having irreversible results recorded at the detectors doesn't tell you that collapse has occurred, because not all interpretations have collapse in them at all. According to the MWI, there is never any collapse, even when detectors register irreversible results.

 

[Killtech]

You are confusing two different meanings of "interferometry". One meaning is "putting a bunch of devices in the experiment that can produce interference", like beam splitters in an MZI. The second meaning is "putting detectors in the experiment that register irreversible results, and then using those results to infer whether interference has occurred".

The first meaning above, in itself, does not cause collapse under any interpretation. You can put a hundred beam splitters in your experiment and no collapse will happen under any interpretation just because of the beam splitters.

The second meaning above, combined with the first kind of experimental configuration, can indeed tell you whether interference has occurred; but that's not the same as telling you whether collapse has occurred inside the apparatus. You already know that collapse never occurs inside the apparatus according to any interpretation, as I said just above.

I know quite well how interferometry is normally performed. And I work on an extension to what you called the "first meaning".

Okay, maybe exchange the word "collapse" for decoherence and I think it should be quite clear how an interferometry setup is usable to check if coherence was lost or not. A possible decoherence could collapse the superposition into a corresponding ensemble. Which means that this acts about the same as a "measurement collapse" (minus the instantaneous and now-well defined aspect) which however does not consume the particle like a detector would but allows it to travel on in the collapsed state.

Plus, even having irreversible results recorded at the detectors doesn't tell you that collapse has occurred, because not all interpretations have collapse in them at all. According to the MWI, there is never any collapse, even when detectors register irreversible results.

In my opinion, there's no collapse happening ever, but as you see on the example of this thread, this opens rather a can of worms than helping to answer this question.

So to clarify: whenever I talk about a collapse I always mean an objective event which can be experimentally verified in principle and never about the "interpretation" thing. It just so happens that these two quite often overlap in an extended framework whenever the prior gains the capacity to describe physics that are part of the measurement process.

In a more general context I was trying to understand what impact full QED time evolution might have for various states. In terms of decoherence QED takes away the idea of an isolated system as any particle now always interacts with the other fields around it. And with simple proxy calculation I made it seems that any system composed of anything electrically charged, every superposition of states with different energy levels will swiftly lose their energy to the EM-field and thus decay into pure states and where on the other hand energy eigenstates would seem stable. Ironically enough this works just along the lines of the instability in Bohrs old atom model from Larmor frequency. Or in other words: the system undergoes a reversed Rabi oscillation - reversed because it becomes itself the source of the oscillatory field to which it loses energy. Well, okay a superposition becomes stable if the right oscillatory field is applied externally. And interestingly trying to spatially separate the superposition won't help but may even make things worse - that's where calculation get the most messy as it approaches a division by zero.

In any case this is why it did go against my intuition that a superposition in SG would be able to maintain coherence while it is in the magnetic field - and once lost it cannot be regained upon recombination.

 

[PeterDonis]

maybe exchange the word "collapse" for decoherence

Which makes a huge difference. Decoherence is part of the "minimal" math of QM, it is there regardless of what interpretation you choose. So testing for decoherence is interpretation independent. Testing for collapse is not.

Also, as I've already noted, testing for decoherence does not test for any kind of "collapse", whether the interpretation dependent one of standard QM or some alternative theory that is different from standard QM (see below). So "collapse" is not a good term to use if what you mean is "decoherence".

whenever I talk about a collapse I always mean an objective event which can be experimentally verified in principle and never about the "interpretation" thing

Then you are either talking about decoherence (as above), or you are talking about some different theory from standard QM, such as the GRW "spontaneous collapse" theory. In either case, just using the term "collapse" without qualification is not a good way to communicate what you are talking about. We could have avoided this whole fruitless discussion if you had been clearer about this at the outset.

I talked about testing for decoherence above. Obviously you can also test a theory that is different from standard QM by finding a situation where it makes different predictions from standard QM and then running the experiment. But first you have to decide what different theory you are talking about. Are you trying to investigate the GRW theory? Or some other theory? That is the crucial missing piece. Without a specific alternative theory there is no way to know where it will make different predictions from standard QM.

It just so happens that these two quite often overlap

No, they don't "overlap", they just can both be talked about in the context of the same experiment--but that doesn't make them the same or excuse confusing one with the other.

 

[vanhees71]

So to clarify: whenever I talk about a collapse I always mean an objective event which can be experimentally verified in principle and never about the "interpretation" thing. It just so happens that these two quite often overlap in an extended framework whenever the prior gains the capacity to describe physics that are part of the measurement process.

I've not a single example for the observation of a collapse. All measurements I know of are well describable by local interactions between measured objects and measurement devices.

 

[PeterDonis]

I've not a single example for the observation of a collapse.

It turns out he doesn't mean what we thought he meant by "collapse". See my post #124 just now.

 

[PeterDonis]

Since the OP is long gone and it turns out most of the discussion since was based on a miscommunication, this thread is now closed.