High School What Is Surprising About Wave Function Collapse?

[Jimster41]

Now comes my presonal opinion on the interpretation/measurement issue in connection with this experiment:

The SG experiment is one of the very few, which can (on this most simple level) be fully understood by nearly analytic solution of the appropriate wave equation (the Pauli equation, which generalizes the Schrödinger equation to an equation for particles with spin). As it turns out, just taking the probability interpretation of the wave function a la Born in the sense of the minimal interpretation, no mystery remains: You expect two distinct lines of silver atoms, and the silver atoms are sorted in (nearly) perfectly prepared spin-$z$-component eigenstates with $\sigma_z \in \{-\hbar/2,\hbar/2 \}$. The macroscopic measure for the spin-$z$ component is thus the location of the silver atoms itself, and there's a 100% correlation between this position and the spin-$z$ value because here we have an example for a perfect entanglement between this spin-$z$ component (microscopic variable) and the position of the silver atom (macroscopic variable). Nowhere do you have to envoke any classical process called "collapse" or other esoterics. In this sense, it's a paradigmatic example for an ideal von Neumann filter measurement.

I'm, however, pretty sure that other physicists reading this thread have a different opinion concerning this interpretation. My only excuse is that the minimal interpretation is the simplest one, sticking clearly to the physics content of the quantum theoretical formalism without adding metaphysical or philosophical additions to it.

What is controlling the shape of the probability wave, and how? Why isn't it just a Gaussian distribution in the z direction?

 

[vanhees71]

Once again, this is simply wrong. Here you only refer to one measurement.

I don't understand what you mean by this. Of course, here I measure $\sigma_z$ of silver atoms, nothing else. It's one measurement. So what?

 

[vanhees71]

What is controlling the shape of the probability wave, and how? Why isn't it just a Gaussian distribution in the z direction?

The shape of the probability wave is determined by its initial condition and the quantum dynamics, described by the Pauli equation. The solution is unique.

 

[atyy]

I agree. All I want is to provoke you to say: "Yes, I think there are hidden variables, and I don't care if I someone will think that I sound as a philosopher."
But you are tough. You don't want to say it explicitly, even though it is obvious that you think so.
(By the way, I also think that there are hidden variables. But I don't have a problem with saying it explicitly.)

It is very hard to undo the damage of Ballentine. It has been noticed that some who claim to use a minimal interpretation are secretly using another interpretation like MWI or hidden variables. http://arxiv.org/abs/quant-ph/0209123: "In fact, experience shows that defenders of the correlation point of view, when pressed hard in a discussion to describe their point of view with more accuracy, often express themselves in terms that come very close to the Everett interpretation (see § 6.5); in fact, they may sometimes be proponents of this interpretation without realizing it!" [bolding mine]

 

[atyy]

I don't understand what you mean by this. Of course, here I measure $\sigma_z$ of silver atoms, nothing else. It's one measurement. So what?

Collapse requires two measurements, because collapse is what one needs to calculate the conditional probability - the probability of an outcome B given poutcome A. So there are two outcomes, and two measurements.

 

[vanhees71]

Well, to check my claims, you only need one measurement: put another Stern-Gerlach apparatus into one of the partial beams to verify that these particles have a definite spin-$z$ component. So you have a preparation procedure (first SG apparatus). For collapse proponents the collapse has appeared here. For me it's simply not looking at particles in one of the partial beams but only in the other. So for me there's no collapse. The measurement of $\sigma_z$ (2nd SG apparatus) then confirms that the particles in that beam have a definite $\sigma_z$ component. You can of course measure any other $\sigma_z$ component with an accordingly directed SG apparatus, which doesn't have a determined value, and all QT predicts is the probability to find $\pm \hbar/2$ for the measured component. Again separating out one of the two beams prepared in that way, you have particles prepared such that the corresponding spin-component has a definite value, again just due to quantum dynamics but no collapse mechanism outside of that dynamics.

Whether or not this qualifies as being a hidden proponent of the Everett interpretation I cannot say, because I've never understood what makes this idea different from the minimal interpretation. At least as far as I understand it, there's no difference in the prediction of observable probabilistic statements about the outcome of measurements. So I don't see a difference between Everet's and the minimal interpretation from a physical point of view. You may believe or not that the universe splits in different branches at each measurement act (whatever this might be); it doesn't change any testable prediction of QT concerning objective observations.

 

[Jimster41]

The shape of the probability wave is determined by its initial condition and the quantum dynamics, described by the Pauli equation. The solution is unique.

I get that it is a solution to the wave equation. The part that seems surprising to me is that the solution (a specifically symmetrical periodic solution) is enforced by nature, for each silver thingy.

To the point about one experiment vs many. If it was one, and the silver thingy was classical, wouldn't it be a randomly curved path? If many, then a normal distribution of randomly curved paths? But what is seen are specific "eigenvalues", as I think you said. What is enforcing that?

 

[rubi]

I agree. All I want is to provoke you to say: "Yes, I think there are hidden variables, and I don't care if I someone will think that I sound as a philosopher."
But you are tough. You don't want to say it explicitly, even though it is obvious that you think so.
(By the way, I also think that there are hidden variables. But I don't have a problem with saying it explicitly.)

Why should we make ontological commitments as long as we aren't forced to? Why not just stay agnostic about it?

For an experiment such as the Stern-Gerlach experiment to be a matter of "filtering", then doesn't the quantity have to exist in order to filter based on its value?

I would say the word "filtering" is just a metaphor and one shouldn't take it too seriously.

 

[Demystifier]

I don't think that there are hidden variables. How do you come to this conclusion? To the contrary, I'm a "minimalist", i.e., there is the quantum-theoretical formalism including Born's rule and the operational definition of states as preparation processes and measurements linking the formal objects of the theory with the observations in the real world. I don't think that physics is about ontology but just about the description of the (objectively comprehensible part of the) world.

So when you say e.g. "the atoms in the remaining beam", you don't really think that there are really atoms there in the ontological sense? For you, atoms are merely an abstract operational description of observations?

I could understand such a view too. But then I could not understand why are you so much against collapse, not in the ontological sense, but also in the sense of an abstract operational description of observations. Therefore I think you really think atoms are there, and that's, by definition, is a belief in hidden variables.

 

[Jimster41]

Well, to check my claims, you only need one measurement: put another Stern-Gerlach apparatus into one of the partial beams to verify that these particles have a definite spin-$z$ component. So you have a preparation procedure (first SG apparatus). For collapse proponents the collapse has appeared here. For me it's simply not looking at particles in one of the partial beams but only in the other. So for me there's no collapse. The measurement of $\sigma_z$ (2nd SG apparatus) then confirms that the particles in that beam have a definite $\sigma_z$ component. You can of course measure any other $\sigma_z$ component with an accordingly directed SG apparatus, which doesn't have a determined value, and all QT predicts is the probability to find $\pm \hbar/2$ for the measured component. Again separating out one of the two beams prepared in that way, you have particles prepared such that the corresponding spin-component has a definite value, again just due to quantum dynamics but no collapse mechanism outside of that dynamics.

Whether or not this qualifies as being a hidden proponent of the Everett interpretation I cannot say, because I've never understood what makes this idea different from the minimal interpretation. At least as far as I understand it, there's no difference in the prediction of observable probabilistic statements about the outcome of measurements. So I don't see a difference between Everet's and the minimal interpretation from a physical point of view. You may believe or not that the universe splits in different branches at each measurement act (whatever this might be); it doesn't change any testable prediction of QT concerning objective observations.

I think I agree that at one level, the fact that fundamental things have always been observed to be something specific, and not random, or changing, is not mysterious or surprising. How else could it be? What is interesting to me is the way the mechanism that enforces that factitious fact is sitting there in the future, which surely is a thing in the world, though not precisely observable, doing a bunch of apparently non-local work - dictating eigenvalues across space-time, organizing the Lie group, maintaining the wave-equation.

 

[Demystifier]

Why should we make ontological commitments as long as we aren't forced to? Why not just stay agnostic about it?

I answered it in post #99. I cannot understand how can someone simultaneously be both a) agnostic about ontology and b) non-agnostic about collapse.

 

[atyy]

Why should we make ontological commitments as long as we aren't forced to? Why not just stay agnostic about it?

Exactly what Demystifier said - if we do not make an ontological commitment, then we do have collapse. It is percisely because the wave function is not real, that collapse is needed. Also, vanhees71's philosophy is not very coherent, as Matt Leifer says, "given that we are not assigning ontological status to anything, let alone the state-vector, then you are free to collapse it, uncollapse it, evolve it, swing it around your head or do anything else you like with it. After all, if it is not supposed to represent anything existing in reality then there need not be any physical consequences for reality of any mathematical manipulation, such as a projection, that you might care to do." http://mattleifer.info/2007/01/24/what-can-decoherence-do-for-us/

Collapse is a standard part of the minimal interpretation. As we discussed before, one does not need it if one does not do successive measurements. However, vanhees71 has not yet rejected successive measurements.

Once again, I stress that vanhees71 is making a technical error, so this debate is not a matter of taste. He is rejecting the textbook formulation of quantum mechanics, eg. Nielsen and Chuang or Holevo or Weinberg.

 

[atyy]

Well, to check my claims, you only need one measurement: put another Stern-Gerlach apparatus into one of the partial beams to verify that these particles have a definite spin-$z$ component. So you have a preparation procedure (first SG apparatus). For collapse proponents the collapse has appeared here. For me it's simply not looking at particles in one of the partial beams but only in the other. So for me there's no collapse. The measurement of $\sigma_z$ (2nd SG apparatus) then confirms that the particles in that beam have a definite $\sigma_z$ component. You can of course measure any other $\sigma_z$ component with an accordingly directed SG apparatus, which doesn't have a determined value, and all QT predicts is the probability to find $\pm \hbar/2$ for the measured component. Again separating out one of the two beams prepared in that way, you have particles prepared such that the corresponding spin-component has a definite value, again just due to quantum dynamics but no collapse mechanism outside of that dynamics.

How can there be partial beams? That is assigning a definite trajectory to particles.

And again, I stress that in the minimal interpretation it is wrong to use a one measurement procedure to argue against collapse. In the minimal interpretation, there is no need for collapse if one does one measurement.

Whether or not this qualifies as being a hidden proponent of the Everett interpretation I cannot say, because I've never understood what makes this idea different from the minimal interpretation. At least as far as I understand it, there's no difference in the prediction of observable probabilistic statements about the outcome of measurements. So I don't see a difference between Everet's and the minimal interpretation from a physical point of view. You may believe or not that the universe splits in different branches at each measurement act (whatever this might be); it doesn't change any testable prediction of QT concerning objective observations.

The difference is that in Everett's view, it makes sense to talk about the "wave function of the universe". In the minimal interpretation, we don't know what the "wave function of the universe" means.

 

[Demystifier]

Collapse is a standard part of the minimal interpretation. As we discussed before, one does not need it if one does not do successive measurements. However, vanhees71 has not yet rejected successive measurements.

Exactly!

 

[vanhees71]

How can there be partial beams? That is assigning a definite trajectory to particles.

And again, I stress that in the minimal interpretation it is wrong to use a one measurement procedure to argue against collapse. In the minimal interpretation, there is no need for collapse if one does one measurement.
The difference is that in Everett's view, it makes sense to talk about the "wave function of the universe". In the minimal interpretation, we don't know what the "wave function of the universe" means.

No, beams are not trajectories of particles in a classical sense. That's the whole point of this example! After the magnet of a properly constructed SG apparatus, you have a sufficiently good separation of beam-like regions of space, where only silver atoms in FAPP pure $\sigma_z=+\hbar/2$ states are found. I wrote FAPP, because in fact there's always a tiny probability to find a silver atom at such a place with $\sigma_z=-\hbar/2$, but you can make this tiny probability as tiny as you wish. That's why I wrote FAPP. Just looking at silver atoms in this region of space is the only thing you need to have an ensemble of silver atoms prepared in a (FAPP) pure $\sigma_z=+1/2$ state. No collapse argument is necessary to make this preparation. Note that a collapse is necessary only for state preparations, not for measurements, which usually destroy the object observed (like a photon hitting a photo/CCD plate, a particle being absorbed in ALICES calorimeter, and so on), and you don't need to bother about what state it might be into be described for later measurements ;-).

In this example I don't need a "wave function of the universe", and in my opinion it is very hard to make sense of such a notion in a physical sense. Whatever I tell this wave function might be, you'll never be able to think about an experiment in the real world that can verify or falsify my claim of such a wave function. It's not even possible in principle to observe the entire universe! Here, I'm humbly talking about a SG apparatus as found in many labs for physics students around the world :-).

 

[atyy]

No, beams are not trajectories of particles in a classical sense. That's the whole point of this example! After the magnet of a properly constructed SG apparatus, you have a sufficiently good separation of beam-like regions of space, where only silver atoms in FAPP pure $\sigma_z=+\hbar/2$ states are found. I wrote FAPP, because in fact there's always a tiny probability to find a silver atom at such a place with $\sigma_z=-\hbar/2$, but you can make this tiny probability as tiny as you wish. That's why I wrote FAPP. Just looking at silver atoms in this region of space is the only thing you need to have an ensemble of silver atoms prepared in a (FAPP) pure $\sigma_z=+1/2$ state. No collapse argument is necessary to make this preparation. Note that a collapse is necessary only for state preparations, not for measurements, which usually destroy the object observed (like a photon hitting a photo/CCD plate, a particle being absorbed in ALICES calorimeter, and so on), and you don't need to bother about what state it might be into be described for later measurements ;-).

So you reject that it is possible to do preparation, measurement A followed by measurement B?

 

[rubi]

I answered it in post #99. I cannot understand how can someone simultaneously be both a) agnostic about ontology and b) non-agnostic about collapse.

I think the point it not to be non-agnostic about collapse, but rather not to apply it in situations, where it isn't needed. The Stern-Gerlach experiment is one such situation and vanhees71 is arguing (if i understood him correctly) that any other possible experiment is also such a situation. Now this may be correct or not, but I can't think of a situation, where it is not the case. However, I agree to stay agnostic about it.

Exactly what Demystifier said - if we do not make an ontological commitment, then we do have collapse. It is percisely because the wave function is not real, that collapse is needed.

I don't find this argument convincing. The wave function may or may not be real, but it certainly contains information about "what is going on". There may be situations, where a collapse would discard too much of this information. We usually collapse the wave-function in situations, where we are fairly certain that the information we loose is not relevant for the further description of the system. But then again, it can't hurt to carry around the irrelevant information. It just complicates the description, so we usually don't do it.

"given that we are not assigning ontological status to anything, let alone the state-vector, then you are free to collapse it, uncollapse it, evolve it, swing it around your head or do anything else you like with it. After all, if it is not supposed to represent anything existing in reality then there need not be any physical consequences for reality of any mathematical manipulation, such as a projection, that you might care to do."

Well, as I said, the wave function contains information about "what is going on", so you better only apply manipulations that don't discard relevant information, if you want to end up with something that can still be used to describe physics. But apart from that, I agree with Matt Leifer.

Collapse is a standard part of the minimal interpretation. As we discussed before, one does not need it is one does not do successive measurements. However, vanhees71 has not yet rejected successive measurements.

If you want to describe successive measurements using the filtering framework, you need to include the apparatus in the description. The information that is usually lost during collapse is then just hidden in the description of the apparatus and we may or may not discard it. Since the information has become irrelevant for the further description, the predictions of the theory aren't influenced by our decision.

Once again, I stress that vanhees71 is making a technical error, so this debate is not a matter of taste. He is rejecting the textbook formulation of quantum mechanics, eg. Nielsen and Chuang or Holevo or Weinberg.

I think vanhees71 is still using textbook QM. He's just using a more sophisticated description of the system that doesn't discard irrelevant information.

 

[Demystifier]

Note that a collapse is necessary only for state preparations, not for measurements, which usually destroy the object observed

1) Now you finally admit that a collapse is necessary for something. That's a progress.
2) As I already explained in another post, the "destruction" in the one-particle Hilbert space can be described as a collapse in a larger Hilbert space of full quantum field theory.

 

[atyy]

I think vanhees71 is still using textbook QM. He's just using a more sophisticated description of the system that doesn't discard irrelevant information.

As we have agreed (I think), one can do without collapse if one rejects successive measurements. However, vanhees71 has not yet articulated this assumption, and I would like to see it clearly articulated before collapse is rejected.

 

[Demystifier]

He's just using a more sophisticated description of the system that doesn't discard irrelevant information.

If so, then why is he not using an even more sophisticated description, which does not discard the irrelevant information associated with state preparation?

 

[vanhees71]

1) Now you finally admit that a collapse is necessary for something. That's good.
2) As I already explained in another post, the "destruction" in the one-particle Hilbert space can be described as a collapse in a larger Hilbert space of full quantum field theory.

Argh! I should have said

"Note that a collapse is assumed to be necessary by collapse proponents only for state preparations, not for measurements, which usually destroy the object observed..." I still don't consider it a necessary part of QT nor one that can be defined in an unambiguous and consistent way!

What do you mean by "destruction" in the one-particle Hilbert space? My arguments about the SG experiment work fully in the realm of non-relatistic single-particle quantum mechanics for a spin-1/2 particle desribed by the Pauli equation. Perhaps, you can understand enough of my corresponding section in my German QM 2 manuscript. It's all pretty simple textbook QM:

http://theory.gsi.de/~vanhees/faq/quant/node102.html#potel2005quantum

for a more complete (numerical) investigation of the "spin-flip probability", leading to (practically arbitrarily small) contaminations of the "spin-up beam" with spin-down silver atoms, see

G. Potel, F. Barranco, S. Cruz-Barrios, J. Gómez-Camacho, Quantum mechanical description of Stern-Gerlach experiments, Phys. Rev. A 71 (2005).
http://dx.doi.org/10.1103/PhysRevA.71.052106

 

[atyy]

Argh! I should have said

"Note that a collapse is assumed to be necessary by collapse proponents only for state preparations, not for measurements, which usually destroy the object observed..." I still don't consider it a necessary part of QT nor one that can be defined in an unambiguous and consistent way!

Of course. Collapse is only necessary for preparations that are a result of measurements. In other words, collapse is needed if one does preparation, then measurement A, then measurement B. In such a case, measurement A is the preparation procedure for measurement B, and that is where collapse is needed.

So if you reject collapse, you reject that it is possible to do successive measurements. It is fine to reject successive measurements, but it is non-standard, so you should state it explicitly, just as when other non-standard assumptions like hidden variables or MWI are used, one has to state them explicitly

 

[kith]

And again, I stress that in the minimal interpretation it is wrong to use a one measurement procedure to argue against collapse. In the minimal interpretation, there is no need for collapse if one does one measurement.

The definition of "measurement" is crucial here. If I remember your position correctly, you define it as the occurrence of an irreversible mark. But irreversibility is not fundamental, so how do you determine whether there's one or two measurements?

 

[Demystifier]

What do you mean by "destruction" in the one-particle Hilbert space?

I mean (for instance) the phenomenon of the destruction of a single photon in the measurement of photon, abstractly described in the language of states in the Hilbert space for that photon.

Let me be more specific. If |1> is the one-photon state, then the destruction can be described as a transition
|1> --> nothing
where "nothing" means that no state in the Hilbert space is associated with photon(s).

The same process can be more properly described as a collapse in a larger space spanned by |1> and the vacuum |0>, e.g. as a transition
c1 |1>+c0 |0> --> |0> ,
where |c0|^2 is the prior probability that photon will be detected (and consequently destroyed), while |c1|^2 is the prior probability that photon will not be detected (and consequently destroyed).

While "nothing" is not a state in the Hilbert space associated with photons, |0> is a state in the Hilbert space associated with photons. |0> is a state in which the number n of photons is precisely defined and equal to n=0.

 

[Demystifier]

But irreversibility is not fundamental, so how do you determine whether there's one or two measurements?

It's not fundamental, but it's usually well defined FAPP (for all practical purposes).

For instance, for the sake of definiteness, one can say that a process is considered FAPP irreversible when its Poincare recurrence time is larger than 1000 years.

 

[rubi]

As we have agreed (I think), one can do without collapse if one rejects successive measurements. However, vanhees71 has not yet articulated this assumption, and I would like to see it clearly articulated before collapse is rejected.

I don't want to speak on behalf of vanhees71, but I don't reject successive measurements. I just say that one needs a way more complicated model if one wants to describe them in such a way that the predictions agree with the collapse description. I also don't reject collapse. I just can't think of a situation, where I couldn't come up with a (potentially much more complicated) model that doesn't rely on collapse.

If so, then why is he not using an even more sophisticated description, which does not discard the irrelevant information associated with state preparation?

Because he doesn't have the necessary information available. If he did, he might as well use an even more sophisticated description.

 

[Derek Potter]

No, it's not assuming that the silver atom starts off in a certain spin-$z$ state. The incoming beam is rather in a thermal state given that the beam is extracted from a little oven of hot silver vapor!

My understanding of spin is horribly shaky, but doesn't the x-up,x-down basis span the entire spin state space (not just x-spin)? If I'm right, interaction with the thermal bath leaves the atom in an improper mixed state. Its spin is not merely undefined but is FAPP random: up or down in any direction you care to choose.

 

[Demystifier]

Because he doesn't have the necessary information available. If he did, he might as well use an even more sophisticated description.

That would make sense, if only he could confirm this.

 

[atyy]

I don't want to speak on behalf of vanhees71, but I don't reject successive measurements. I just say that one needs a way more complicated model if one wants to describe them in such a way that the predictions agree with the collapse description. I also don't reject collapse. I just can't think of a situation, where I couldn't come up with a (potentially much more complicated) model that doesn't rely on collapse.

Coming up with the more complicated model is what I mean by rejecting successive measurements. In the more complicated model, one uses something similar to the deferred measurement principle. Anyway, I think we agree apart from slight differences in terminology.

The only difference might be one of taste. To me, as long as one does not solve the measurement problem and there is no sense to the "wave function of the univers", if quantum mechanics is just a tool to predict measurement outcome, then it is more convenient to take collapse as a postulate, rather than operating in a very much larger Hilbert space, especially in cases where the successive measurements are time stamped, and one would have to include the measurement apparatus as well as a clock in the Hilbert space. In other words, if quantum mechanics is a tool, then collapse is a powerful tool in that it allows you to take a small Hilbert space. This of course is religion http://mattleifer.info/wordpress/wp-content/uploads/2008/11/commandments.pdf :)

 

[atyy]

The definition of "measurement" is crucial here. If I remember your position correctly, you define it as the occurrence of an irreversible mark. But irreversibility is not fundamental, so how do you determine whether there's one or two measurements?

Irreversibility is fundamental, because we are operating in a minimal interpretation. There is no unitarily evolving wave function of the universe. After you have made your last measurement, the wave function is discarded.