Quantum measurement of a Strontium ion

[Lord Jestocost]

The correlations described by entanglement are there from the very beginning due to the preparation of the photons in the entangled state, and...

You don't get it. The above statement is an ontological statement about an entangled system, and such a statement doesn't belong to the “instrumentalist minimal interpretation”.

 

[PeterDonis]

If this is MWI, so be it!

If you're going to take that position, that's fine, but then you need to stop claiming that you are using the "minimal statistical interpretation", since you're not. You can't have it both ways.

In a way I'm arguing within Friebe's minimal interpretation

No, you're not. At least, not if you're claiming that the particle + detector system evolves unitarily. You need to make up your mind what interpretation you are using.

 

[Lord Jestocost]

This forum is labeled “Quantum Interpretations and Foundations”. It would thus be helpful when the participants in discussions within this forum would clearly define and denote which kind of “interpretation” they follow. To my mind, this could save long and fruitless debates.

 

[vanhees71]

If you're going to take that position, that's fine, but then you need to stop claiming that you are using the "minimal statistical interpretation", since you're not. You can't have it both ways.
No, you're not. At least, not if you're claiming that the particle + detector system evolves unitarily. You need to make up your mind what interpretation you are using.

It is new to me that only because one part of a closed system is a "detector" it's not subject to unitary time evolution anymore. What makes a detector distinct from a usual piece of matter that you don't call a detector? Also a detector consists of the known particles of the standard model following the universal physical laws described by it.

Of course you are right when you say that a measurement involves also some irreversibility, i.e., you have to somehow "store the measurement result" to make it readable to us macroscopic human beings, and here you have to use some macroscopic description, involving coarse graining to effective macroscopic variables, leading to description in terms of non-unitary time evolution (which doesn't make sense to begin with for, e.g., describing something like macroscopic fluid flow in terms of fluid dynamics). All this doesn't contradict of course the validity of unitary time evolution for closed on the fundamental microscopic level. To the contrary, it's one of the most important principles guaranteeing the consistency of our macroscopic description, including the "arrow of time" in the sense of Boltzmann's H-theorem.

 

[PeterDonis]

It is new to me that only because one part of a closed system is a "detector" it's not subject to unitary time evolution anymore.

Again, if you want to claim that the particle + detector system is subject to unitary time evolution, that's fine--but then you need to admit that you are using the MWI, not the "minimal statistical interpretation". The latter does not claim that the particle + detector system is subject to unitary time evolution; it leaves that question open.

 

[vanhees71]

No, you make a very far-reaching claim, namely that unitary time evolution is invalid only because some piece of matter is used by human beings as a detector for measurement. I think this is not true, and I don't know any physicist who claims this. It may be part of some Copenhagen interpretation flavors, where a fundamental quantum-classical cut is assumed (I think Bohr himself never claimed it in this strong sense, I'm not sure about Heisenberg, who might have been more inclined to think about it in this way, because he's the one inventing this idea of a cut), but it's for sure not in the orthodox interpretation of textbooks and not in the minimal interpretation.

Also there are some decades of research about open quantum systems and decoherence and all that between Bohr and today, and this shows that the classical behavior of macroscopic systems has nothing to do with a fundamental cut but with a coarse grained view on macroscopic systems in terms of the relevant macroscopic observables, which tend to behave classical in almost all circumstances (there are of course some famous exceptions like BECs, superfluidity and superconductivity, where you have quantum-coherent behavior for macroscopic observables, but that's well understood either within standard QT without any fundamental quantum-classical cut). Also more and more experimental investigations indicate that there seems indeed to be no such cut, given that with proper preparations you can observe quantum behavior of very large (mesoscopic?) systems like in a recent experiment involving very large molecules with de Broglie wavelengths in the order of fm (nuclear scale!).

So far, nothing in the physical laws indicates the validity of a fundamental quantum-classical cut, let alone the necessity of "extra rules" for "detectors" or general "measurement devices", but I think I better give up on this topic once more. It's anyway hopeless to communicate about these vague philosophical issues in a coherent way. I'm only wondering, how one can avoid always falling in this trap when discussing very uncontroversial quantum physics in this forum. Maybe after all you were right in shifting this question about a (real-world not gedanken!) experiment to the Foundations Forum. This should have been warning enough for me :-((((.

 

[Lord Jestocost]

It's anyway hopeless to communicate about these vague philosophical issues in a coherent way.

@vanhees71
Nobody forces you to participate in such discussions!

 

[vanhees71]

No, indeed, but I answered a question which on the first indication for me had nothing to do with this quantum-philosophy business and immediately the discussion went into these philosophical issues, but you are right. I should have simply ignored the thread from then on. It was again a lack of self-disciplin on my side. I'm sorry.

 

[PeterDonis]

you make a very far-reaching claim

I haven't made any claims at all. I have only been pointing out the implications of your claims.

I think this is not true, and I don't know any physicist who claims this.

Any physicist who does not support the MWI is (at least implicitly) denying that unitary time evolution is always valid, because if you assume that unitary time evolution is always valid, the MWI is what you get.

I'm only wondering, how one can avoid always falling in this trap when discussing very uncontroversial quantum physics in this forum.

When we split off this foundations and interpretations forum from the main quantum physics forum, we were quite clear about the ground rules for what counts as "uncontroversial quantum physics" in the main quantum physics forum. For reference, the guidelines for the main QM forum are here:

https://www.physicsforums.com/threads/guidelines-for-quantum-physics-forum.978328/

There is also a link there to the Insights article where the "minimal" interpretation of QM that is to be used for discussion in the main QM forum is described. The way to avoid falling into a "trap" in the main QM forum is to stick to that minimal interpretation.

Maybe after all you were right in shifting this question about a (real-world not gedanken!) experiment to the Foundations Forum.

The criterion for a thread belonging in this forum instead of the main QM forum is not whether or not an experiment being discussed is "real". It is interpretation. The OP of this thread asked explicitly about "instant wave function collapse", which makes it an interpretation discussion since that goes beyond the minimal interpretation referred to above.

 

[Killtech]

Sure, but I could say the same thing about an electron's interaction with a Stern-Gerlach magnet. The "collapse" in collapse interpretations doesn't come when the electron interacts with the magnet; it comes when the electron hits the detector screen and makes a bright spot at a particular place.

Has this been experimentally verified or is this just a speculation on your part? A simple detection and counting of results itself is not able to distinguish between measuring a superposition of states and a stochastic distribution of states whenever the effective distributions are identical. So this has to be tested in a more sophisticated way than the Stern-Gerlach setup. But given a separation into two beams those could be brought back together to cause interference - if the interaction with the magnet did not already collapse the state. Otherwise no interference of the beams will be observed.

purely on an intuitive level i would have assumed that an interaction with a magnetic field is significantly more intrusive to a state then for example the interaction with an atomic grid of a mirror. i mean classically shooting a small permanent magnet in zero gravity through a big Stern-Gerlach device will render its original state highly unstable and it will have to decide one way or the other for every time it passes one of the magnetic fields. so if it had any means to get rid of the excess energy from its residual angular momentum (initial and from potential energy when entering the B field away from the stable equilibrium configuration) it should classically start to collapse into one of the two stable equilibriums in a dampened oscillation - while its remains in the field. Sure classic analogs don't usually count for much but i don't exactly see how a quantum state would be immune to this type of interaction.

 

[PeterDonis]

Has this been experimentally verified

Has what been experimentally verified? Remember I was talking about interpretations. All interpretations agree on the predicted and observed experimental results; the difference is in how to explain why those predicted and observed results are observed.

given a separation into two beams those could be brought back together to cause interference

Yes, and this has been observed, with photon polarization if not electron spin: the simplest example is a Mach-Zehnder interferometer. I don't know if the analogous experiment has been run with electrons, but I don't think anyone is in doubt about what result would be obtained.

 

[Killtech]

Has what been experimentally verified? Remember I was talking about interpretations. All interpretations agree on the predicted and observed experimental results; the difference is in how to explain why those predicted and observed results are observed.

an experimental yes or no question has nothing to do with interpretation. your assumption however makes for a different experimental expectation in the extended setup i described later. so in term of observing the interference it makes a big difference whether the wave function leaves the Stern-Gerlach device in a collapsed state or a superposition state. Its further time evolution before the actual measurement will simply be a distinguishably different one. I would generally consider any experimentally testable statement not an interpretation issue.

However, yeah. Where a measurement/collapse (or however one likes to call & describe the mechanic) happens is not well defined in QM... so i guess this leaves it up for interpretation of a different type exactly because it should be experimentally decidable. As in: Mach-Zahnder obviously shows that it never applies to a photon-mirror interaction.

Yes, and this has been observed, with photon polarization if not electron spin: the simplest example is a Mach-Zehnder interferometer. I don't know if the analogous experiment has been run with electrons, but I don't think anyone is in doubt about what result would be obtained.

But the Mach-Zahnder interferometer is a very different setup and i cannot find a reason why a photons interaction with the atomic grid (unless it's temporarily absorbed) would cause any instability promoting anything like a collapse. But for a spinning magnet the state it is hardly imaginable why it should remain stable. The circumstance that one should be able replicate Stern Gerlach using macroscopic permanent magnets in zero-g with random initial angular momentum if they were given enough travel time to lose their excess energy (e.g. via EM-radiation from their oscillation) should put that photon comparison at least under scrutiny.

 

[PeterDonis]

the Mach-Zahnder interferometer is a very different setup

Not as far as this discussion is concerned; as far as this discussion is concerned, it is the same as sending, say, a spin-x up an electron through one Stern-Gerlach device oriented in the z direction, then taking the two output beams and sending them back through a second Stern-Gerlach device that recombines them. In both cases you have a qubit whose spatial path gets split into two parts and then recombined, and you need to take interference into account to correctly predict what happens at the recombination.

or a spinning magnet the state it is hardly imaginable why it should remain stable

An electron is not a "spinning magnet". The spin-x up state (or indeed any eigenstate of one of the spin operators) of an electron is also an eigenstate of the free particle Hamiltonian, so it will be unchanged by time evolution. That is the same property that you correctly ascribe to the photon states in a Mach-Zehnder interferometer.

 

[PeterDonis]

using macroscopic permanent magnets in zero-g with random initial angular momentum

I don't know where you are getting that from since it's nothing like what I specified.

 

[Killtech]

An electron is not a "spinning magnet". The spin-x up state (or indeed any eigenstate of one of the spin operators) of an electron is also an eigenstate of the free particle Hamiltonian, so it will be unchanged by time evolution. That is the same property that you correctly ascribe to the photon states in a Mach-Zehnder interferometer.

yeah, except in simple QM the electron cannot radiate off energy because its coupling to the EM-field goes only one way. that makes the state artificially stable. same for classics: if the magnet goes through vacuum the only way to lose energy is via radiation. if you disable that process you suddenly make an unstable state into a stable periodic one. so you'd need QED to allow it to lose excess energy via a photon emission just like the classical magnet would do. for the atomic levels this doesn't need measurement to happen but should occur naturally.

As a QM analogue: Zeeman effect where the higher energy eigenstates aren't perfectly stable. if you are in a magnet field a state that isn't oriented along that field has a different energy value and should at some point fall down to the lower pure state, of which there are only two, no? okay, it is a fair point to ask how long that would take on average.

Therefore i would have expected QM follow a similar time evolution as the (indeed different but somewhat similar) classical process.

 

[PeterDonis]

in simple QM the electron cannot radiate off energy because its coupling to the EM-field goes only one way. that makes the state artificially stable

Sure, and in "simple QM" photons propagating through air don't interact with it, that makes the state artificially stable. So yes, both of these models are approximations; but in practice they are quite useful ones for real experiments.

As a QM analogue: Zeeman effect where the higher energy eigenstates aren't perfectly stable.

This is a bad analogy because the higher energy states in this case decay very quickly. Free electrons or photons propagating through an experimentalist's lab don't.

if you are in a magnet field a state that isn't oriented along that field has a different energy state and should at some point fall down to the lower pure state

What "magnet field" are we talking about in the case of a free electron propagating through a lab?

i would have expected QM follow a similar time evolution as the (indeed different but somewhat similar) classical process

Your naive expectation here fails to take crucial factors into account. See above.

 

[Killtech]

This is a bad analogy because the higher energy states in this case decay very quickly. Free electrons or photons propagating through an experimentalist's lab don't.
What "magnet field" are we talking about in the case of a free electron propagating through a lab?

When an electron enters the Stern-Gerlach magnet its Schrödinger equation changes from a simple free one to one within the presence of a magnetic field. indeed it still remains in an unbound state but this is still different from an entirely free electron traveling the lab experiencing no exterior force at all. EDIT: actually shouldn't be an classical orbit trajectory in a magnetic field be considered a bound state?? and anyway, sorry i meant an atom. doesn't make sense to put an electron through Stern-Gerlach. your mention of the electron just confused me.

And for the Atom: if it travels through a Stern Gerlach device you have for a short time an atom in a magnetic field (and Stern Gerlach is historically performed with atoms). Among other effects shouldn't the Zeeman effect be present? The B field won't be exactly static but on the atoms scale it might be close enough.

 

[PeterDonis]

When an electron enters the Stern-Gerlach magnet its Schrödinger equation changes from a simple free one to one within the presence of a magnetic field.

Yes, and we already know what that does to the electron: it splits its wave function into two components, one corresponding to an "up" result and the other corresponding to a "down" result, with the two components moving in different directions. Or, to put it another way, it entangles the electron's spin degree of freedom in the direction of the device's alignment, with the electron's momentum degree of freedom in the same direction.

But once the electron exits the device, it's a free electron again. And so there's nothing in principle preventing us from re-combining the two output beams by directing them into a second Stern-Gerlach device oriented in the same direction.

shouldn't be an classical orbit trajectory in a magnetic field be considered a bound state?

No.

sorry i meant an atom. doesn't make sense to put an electron through Stern-Gerlach

Sure, it does. The fact that it's very hard to do experimentally doesn't mean it doesn't make sense.

Among other effects shouldn't the Zeeman effect be present?

The Zeeman effect doesn't change anything I said above. It will slightly shift the energy of the unpaired electron in the atom (a silver atom in the most common case), but it won't affect its spin or the entanglement of the spin and momentum degrees of freedom by the interaction with the device.

 

[Killtech]

The Zeeman effect doesn't change anything I said above. It will slightly shift the energy of the unpaired electron in the atom (a silver atom in the most common case), but it won't affect its spin or the entanglement of the spin and momentum degrees of freedom by the interaction with the device.

Okay, my understanding was this: an atom enters a Stern-Gerlach device. in it's magnetic field it's energy levels change due to the Zeeman effect. So initially its wave function should be in some superposition of the different energy levels: specifically of energy levels now different due to the Zeeman effect. If a higher energy state would be sufficiently short lived then the corresponding electron would decay to a lower level losing a very small amount of energy. since it remains bound this should effect the entire atom.

now even if the energy amount is minimal turning the atom into another orientation doesn't take much energy either. i mean to classically change the orientation of a body in space takes a net 0 energy if final angular momentum is the same as the initial (acceleration to start turning takes energy but in order to stop that energy can be taken back theoretically). in a magnetic field the different orientations have slightly different potential energy so it would take the potential energy difference in ideal circumstance to make the orientation change.

So in the end i would expect the lower Zeeman energy state to also directly correspond to a pure spin up/down state of the entire atom: both are the energetically most convenient configurations after all. Also the electrons total angular momentum in the lower Zeeman level should align with the magnetic field and should differ from higher energy states (which due to being a basis must also have components in other less energy optimal directions) to minimize energy and therefore change $J$ and $J_z$ of the entire atom. as such the emission of energy from the higher Zeeman level would imply a mechanism that does just what the wave function collapse does - but already on entering the device long before hitting the detector. and also completely regardless of any interpretation stuff.

But fair enough, i haven't checked what the energy difference is between a pure spin up/down state and the spin state orthogonal to the magnetic field and how that corresponds to the energy between the Zeeman levels.

 

[PeterDonis]

my understanding was this

I don't know where you are getting all this from; it's nothing like the standard description of a Stern-Gerlach device. Do you have a reference? Or is it just speculation on your part?

 

[Killtech]

I don't know where you are getting all this from; it's nothing like the standard description of a Stern-Gerlach device. Do you have a reference? Or is it just speculation on your part?

sorry, this is just my intuition of QM. Am i so hopelessly wrong with that? For me this is kind of the canonical attempt to try explain the results. But it's just an idea/ansatz where i would start. Normally i try to google such stuff but it's usually not helpful in figuring out how good that intuition is... (Neither is working in insurance away from physics) so no, i haven't found a reference that tells either way how well this idea works. but aren't the forums a place to help with that out? i mean i wouldn't ask if i knew and i don't know where else to ask.

 

[PeterDonis]

this is just my intuition of QM. Am i so hopelessly wrong with that?

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.

Btw, since the Stern-Gerlach experiment was one of the classic experiments that showed that QM is necessary for describing how subatomic particles like electrons work (because the prediction of classical physics for the result was shown to be false), you have to be very careful not to use classical ideas when analyzing it.

 

[vanhees71]

Any physicist who does not support the MWI is (at least implicitly) denying that unitary time evolution is always valid, because if you assume that unitary time evolution is always valid, the MWI is what you get.

You should not put words in my mouth I didn't say! I said for any CLOSED SYSTEM unitary time-evolution is valid. It's analogous to classical mechanics, where the fundamental Hamilton canonical equations also hold for closed and/or non-dissipative systems only. When you treat open quantum or classical systems the time evolution is no longer unitary, and you describe among other things decoherence. There's no need for the assumption that there's a quantum-classical cut (including an instantaneous collapse). That's all I'm saying. I don't think that this is MWI, but I don't care how you call any interpretation, because it's anyway imprecise to name any interpretation by a single word.

In the SGE you send an Ag atom through a magnetic field taylored such that you prepare position-spin entangled states. This is indeed described by the unitary time evolution, i.e., by the time-dependent Pauli equation, which is a manifestation of unitary time evolution in the position-spin (or if you prefer momentum-spin) representation.

You are right in saying that, within collapse interpretations, the collapse occurs when the Ag atom hits the screen. Then it's stuck there and its position (a macroscopic variable!) can be measured (or rather the distribution of many Ag atoms hitting the screen) by observing it under a microscope (at least that's how it was done in 1921).

I don't see, how you can claim that here a collapse assumption is necessary. As well I can argut that the Ag atom interacts with the screen, and the apparent collapse simply comes from the very coarse-grained description and from looking at one (macroscopic) observable only, namely the single-Ag-atom distribution on the screen. Why do you think that's a non-orthodox interpretation? Only because I avoid the very problematic idea of an instantaneous collapse?

 

[Lord Jestocost]

When you treat open quantum or classical systems the time evolution is no longer unitary, and you describe among other things decoherence.

When quantum mechanics is applied uniformly at all levels, to the apparatus and its environment as well as to the system, the time evolution is always unitary as all entangles to each other. Decoherence changes nothing (see "Why Decoherence has not Solved the Measurement Problem: A Response to P.W. Anderson" by Stephen L. Adler).

 

[vanhees71]

Well, but the classical behavior of macroscopic systems is convincingly described by quantum statistical mechanics, at least FAPP. What's the physical (sic! I mean rather than philosophical) problem left concerning the so-called "measurement problem"? Can you point to the specific article you have in mind?

 

[Lord Jestocost]

Joos, E. (1999) ‘Elements of Environmental Decoherence’, in P. Blanchard, D. Giulini, E.
Joos, C. Kiefer and I.-O. Stamatescu (eds.), Decoherence: Theoretical, Experimental, and
Conceptual Problems (New York: Springer), pp. 1-17:

“Does decoherence solve the measurement problem? Clearly not. What decoherence tells us is that
certain objects appear classical when observed. But what is an observation? At some stage
we still have to apply the usual probability rules of quantum theory.”

And the probability rules represent nothing else but the non-unitary collapse.

You don't get the problem. Maybe, the following might help you:

"Basically, the quantum measurement paradox is that most interpretations of QM at the microscopic level do not allow definite outcomes to be realized, whereas at the level of our human consciousness it seems a matter of direct experience that such outcomes occur..."
(A. J. Leggett in "The Quantum Measurement Problem")

P.S.: To understand my position: For me there exists no "classical behaviour" as I regard classical concepts as folk science.

 

[vanhees71]

Indeed, I don't get the problem. The first quote by Joos is all I need. Of course QT tells us that nature is inherently probabilistic, and at "some stage we still have to apply the usual probability rules of quantum theory." What else should I apply, given that QT is the best theory we have?

The quote by Leggett is true too, of course, but so what? Human observations do not resolve the "microscopic level", and decoherence tells me satisfactorily why any observation is a definite outcome of macroscopic observables.

Of course, the "classical behavior" is only apparent and due to the necessarily coarse grained observation of macroscopic systems.

 

[PeterDonis]

I said for any CLOSED SYSTEM unitary time-evolution is valid.

But you also claimed that a particle + detector system is closed. It isn't. You even admit that:

When you treat open quantum or classical systems the time evolution is no longer unitary, and you describe among other things decoherence.

Unless you are going to claim that there is no decoherence when an Ag atom hits the detector in a Stern-Gerlach measurement?

Remember that in the Stern-Gerlach measurement, the magnet is not the detector. The detector is the screen that the Ag atoms hit after they have exited the magnetic field. You can treat the atom plus magnet system as closed and undergoing unitary time evolution. You cannot do the same for atom plus detector; that system is not closed, it is open, and undergoes decoherence.

I don't see, how you can claim that here a collapse assumption is necessary.

Now you're the one putting words in my mouth. I never made any such claim.

As well I can argut that the Ag atom interacts with the screen, and the apparent collapse simply comes from the very coarse-grained description and from looking at one (macroscopic) observable only, namely the single-Ag-atom distribution on the screen. Why do you think that's a non-orthodox interpretation?

I never said that this interpretation was non-orthodox. I have simply been trying to get you to explain clearly what interpretation you are actually using. The next question based on your description here is obvious: what happens when the human observer looks at the screen? Is there only an "apparent collapse" there as well? If your answer is "yes", you are describing the MWI. If your answer is "no", you are describing a collapse interpretation. Trying to waffle by saying things like "there's no need for a quantum-classical cut" won't do.

 

[vanhees71]

Ok, if you consider the meausurment device as external (which makes of course sense), then there's no unitary time evolution for the Ag atom alone, but it's also not a spontaneous collapse. It doesn't even make sense, because the Ag atom is for sure not in the "measured" spin state for long but it thermalizes rapidly with the matter making up the detector, where it is stuck after it hit the plate.

As always, it depends on how you split the complete system (Ag atom + detector) into an open quantum system, i.e., which "information you project out/or coarse-grain away". For a closed system, AFAIK there's no clear argument or experimental fact that indicates that the usual dynamical rules of QT were incomplete and some fundamental quantum-classical cut is necessesary. That's all I'm claiming.

 

[Lord Jestocost]

Indeed, I don't get the problem.

To understand my reasoning, there is a simple and fundamental question:

Does a measurement reveal a preexisting value of a measured property (hidden variable reasoning, ensemble interpretations) or is the outcome of a measurement brought into being by the act of measurement itself (Copenhagen interpretation)?

My point of view:

No observable has any value before a measurement: Measurements of an observable thus “create” their outcomes because all of an unmeasured systems‘ possibilities are live possibilities - potentially possible in the instant of a measurement’s onset, not randomly pre-existing just before the measurement.