Ballentine's Ensemble Interpretation Of QM

[Devils]

Mate the (minor) issues with Ballentine has been discussed before - they are well known.

And of course I am no Prof - like you I am simply a math graduate with an interest in physics.

Thanks
Bill

Meh I have always though of you as Prof Hobba since we met 30 years & 9 months ago.

 

[TrickyDicky]

I found this a valuable account of the ensemble interpretation:

http://statintquant.net/siq/siq.html#siqse5.html

 

[vanhees71]

I found this a valuable account of the ensemble interpretation:

http://statintquant.net/siq/siq.html#siqse5.html

Already the interpretation of the Heisenberg uncertainty relation is, as discussed in this forum, at least questionable. The Heisenberg uncertainty relation in this form is not the measurement-disturbance relation as it was first adovated by Heisenberg. It doesn't tell us something about simultaneous measurements of incompatible observables but about the possibility to prepare a system with regard to accuracy of two such incompatible observables (here position and momentum components in the same direction).

Taking the ensemble interpretation, it's no problem to interpret it in the correct way: You assign a (pure or mixed) state by some preparation procedure to the particle. Then preparing a lot of particles in this state (the ensemble), on each individual system you measure either the position component with high precision or the momentum component with high precision, determine the standard deviations of these measurements. Then the Heisenberg uncertainty relation tells you that, independtly from the prepared state,
\Delta x \Delta p \geq \hbar/2.
This relation, however doesn't tell you how the measurement of position affects the state of the system with respect to the precision of the momentum and vice versa. This is a much more difficult issue, and whether such an uncertainty relation holds in the sense of measurement-error-disturbance relations depends on how you define the corresponding measures for error and disturbance.

 

[atyy]

Yes. Indeed, dBB theory can be viewed as one particular realization of the ensemble interpretation. In fact, Ballentine discusses dBB theory in his textbook.

OK, maybe the book has some merit after all:)

But given that dBB is one realization of the ensemble interpretation, shouldn't we credit the ensemble interpretation to dBB (instead of Ballentine), ie. once dBB was discovered and rediscovered, the conceptual possibility of such a theory and the possibility that it is not unique showed that the impression conveyed by some textbooks (like Feynman's wonderful lectures) of there being no deeper reality to the wave function isn't necessarily true.

Ballentine only considers the version of Copenhagen that thinks the wavefunction is real. That has issues as pointed out by Ballentine - collapse is a very unnatural assumption if you think it actually real.

But most versions of Copenhagen aren't like that - they don't consider it as actually real - it represents purely a state of knowledge a theorist has about the outcomes of observations - it applies to individual systems which separates it from the Ensemble interpretation - but its not real so collapse is of zero concern.

Is collapse problematic if the wave function is real, but quantum mechanics an incomplete theory? Standard QM is incomplete because it requires classical apparatus to make a measurement and produce an outcome - so classical physics remains fundamental, and QM is only an effective theory which always requires a division of the universe into observer and observed. The big problems from a more fundamental viewpoint are - what is the classical measurement device, and why are there outcomes? Neither is solved by the ensemble interpretation.

Collapse is only problematic if one asks what is the fundamental theory under QM. Assuming unitary evolution of the wave function (let's call that MWI) is a very natural attempt from at least two areas in basic physics:

1) What is the origin of thermodynamic irreversibility? Is it wave function collapse? If we wish to answer no, then attempting to explain thermodynamic irreversibility as deterministic evolution of many-particle systems is natural. (But maybe a viable approach is that wave function collapse is partly involved, since the reduced density matrix, which assumes collapse, often shows an approach to thermality even though it is part of a system which evolves unitarily.)

2) What happens when we attempt to apply quantum theory to the universe, and there seems to be no observer left? (An answer may be that as long as we wish physics to be an experimental science, there will always be an observer left.)

In both cases, MWI has the advantage over dBB in that, if it works, it is unique. With dBB we don't know what the most natural underlying hidden variables and dynamics are (could be non-unique).

 

[Nugatory]

Is collapse problematic if the wave function is real, but quantum mechanics an incomplete theory?

It depends (as with all interpretations) on what you consider to be a problem. How do you feel about the faster-than-light propagation of the collapse? Or the notion that the wave function that collapses is real, it collapses simultaneously at two different points, but no information is conveyed by its collapsing?

(Come to think of it, I could parody some of the arguments in this thread by asserting that entanglement at a distance "falsifies" Copenhagen while denying the sea of unstated assumptions from which that assertion emerges).

 

[atyy]

It depends (as with all interpretations) on what you consider to be a problem. How do you feel about the faster-than-light propagation of the collapse? Or the notion that the wave function that collapses is real, it collapses simultaneously at two different points, but no information is conveyed by its collapsing?

(Come to think of it, I could parody some of the arguments in this thread by asserting that entanglement at a distance "falsifies" Copenhagen while denying the sea of unstated assumptions from which that assertion emerges).

If it is correct as I and Demystifier think, to consider the ensemble interpretation as equivalent to QM being an effective theory by ignoring the pilot wave and other hidden variables, then there is no problem (especially afer Bell, who was inspired by dBB).

It's also no problem if one does not exclude that special relativity may be emergent, eg. http://arxiv.org/abs/0808.2495 .

Actually, isn't the wave function real in dBB? For example, http://arxiv.org/abs/0706.2661 classifies the wave function as real but incomplete in dBB.

 

[kith]

IMHO when done right, Copenhagen and the Ensemble Interpretation are more similar than people generally think. I am also partial to Consistent/Decoherent Histories, which some say is Copenhagen done right, but its a bit more complex than I think is necessary. To me however it's closer to MW than Copenhagen.

The more I learned about interpretations, the more similar they seemed to me. If we sort them from classical to literal quantum mechanical, we only get gradual differences for adjacent ones. dBB could be viewed as underlying the ensemble interpretation. If we take a more empiricist viewpoint, the ensemble interpretation is very similar to Copenhagen which in turn is very similar to consistent histories if you are right. From there, it is only a minor step to the MWI. And since dBB could be considered a single branch of the MWI, we are back at the start.

 

[kith]

But given that dBB is one realization of the ensemble interpretation, shouldn't we credit the ensemble interpretation to dBB (instead of Ballentine)

As I and Ken G have written in some earlier posts, there are different motivations to stick to the ensemble interpretation. Many people use it because they think that theories cannot do better in principle than to relate experimental ensembles to models about these ensembles. For example, I don't think van Hees would agree with your statement and he is one of the most prominent advocates of the ensemble interpretation here.

 

[atyy]

As I and Ken G have written in some earlier posts, there are different motivations to stick to the ensemble interpretation. Many people use it because they think that theories cannot do better in principle than to relate experimental ensembles to models about these ensembles. For example, I don't think van Hees would agree with your statement and he is one of the most prominent advocates of the ensemble interpretation here.

But that point of view had no teeth against a claim that there is necessarily no more fundamental reality than the wave function, until dBB.

 

[kith]

But that point of view had no teeth against a claim that there is necessarily no more fundamental reality than the wave function, until dBB.

I don't understand. Why should it have "teeth" against something which it doesn't oppose?

 

[atyy]

I don't understand. Why should it have "teeth" against something which it doesn't oppose?

If we try an interpretation in which the wave function is everything, yet applies only to ensembles, we obtain a contradiction because we still need classical apparatus to perform measurements and cause state vector reduction. The existence of classical apparatus as fundamental in the ensemble interpretation prevents the wave function from being everything.

 

[vanhees71]

If dBB stands for de Broglie-Bohm, I disagree with the statement that it is a flavor of the ensemble interpretation, because it adds "trajectories" to the quantum-mechanical particle description in a fancy non-local way. However, this doesn't add anything to observable predictions compared to quantum theory in the other interpretations that just take the probabilistic view (particularly of course the minimal statistical interpretation).

On top, as far as I know, there is no proper de Broglie-Bohm interpretation for relativistic quantum-field theory. So I don't see any merit of the de Broglie-Bohm interpretation compared to the minimally interpreted QT but a lot of additional trouble introduced.

I've also seen that there are statements about the incompatibility of the minimal statistical interpretation with the (in my opinion clearly observed) quantum-Zeno effect. In interpretations with a collapse, the effect is explained that whenever an observable is measured, the system right after the measurement necessarily "collapses" to an eigenstate of the corresponding self-adjoint operator (which one in the case of degeneracy is determined by the state immediately before the measurement by the projection postulate of the collapse interpretation).

I don't think that this is a valid contradiction to the ensemble interpretation, because the collapse description is just an effective hand-waving way to describe the dynamics between the measurement apparatus and the measured system. There are papers on this that show that you can explain the quantum Zeno effect without taking recurse to the collapse assumption. It's explained by the standard quantum dynamics with time-dependent interaction Hamiltonians between the measured system and the measurement apparatus, e.g.,

Dynamical quantum Zeno effect
S Pascazio, M Namiki
PRA 50, 4582 (1994)
http://pra.aps.org/abstract/PRA/v50/i6/p4582_1

 

[atyy]

I've also seen that there are statements about the incompatibility of the minimal statistical interpretation with the (in my opinion clearly observed) quantum-Zeno effect.

I don't think so either. The question is not whether a correct ensemble interpretation exists with quantum Zeno effect, but whether Ballentine's 1998 exposition of the quantum Zeno effect with regards to the ensemble and Copenhagen interpretations is correct.

I don't think that this is a valid contradiction to the ensemble interpretation, because the collapse description is just an effective hand-waving way to describe the dynamics between the measurement apparatus and the measured system. There are papers on this that show that you can explain the quantum Zeno effect without taking recurse to the collapse assumption. It's explained by the standard quantum dynamics with time-dependent interaction Hamiltonians between the measured system and the measurement apparatus, e.g.,

Dynamical quantum Zeno effect
S Pascazio, M Namiki
PRA 50, 4582 (1994)
http://pra.aps.org/abstract/PRA/v50/i6/p4582_1

Yes, this is available also in Copenhagen, it just depends on how much of the universe one explicitly includes in the Hamiltonian. But in Copenhagen both explanations are correct. Does the ensemble interpretation really not allow wave packet reduction (defined within the ensemble interpretation) as the explanation? As I understand, the ensemble interpretation still has state vector reduction, and if everything (Hamiltonian, state, state vector reduction) applies to ensembles, shouldn't what is acceptable in Copenhagen just carry over to the ensemble interpretation?

 

[bohm2]

Actually, isn't the wave function real in dBB? For example, http://arxiv.org/abs/0706.2661 classifies the wave function as real but incomplete in dBB.

From my understanding there are at least 4-5 different varieties of BM with respect to the ontology of the wave function.

1. Durr/Goldstein/Zhingo/Maudlin: wave function is kind of "real" as it is nomological (a law of nature).
2. Valentini: wave function is a non-local field
3. Bohm/Hiley: wave function is an informational field that guides the particle?
4. David Albert: there is just a single 3N-dimensional wavefunction, and the division of reality into separate three-dimensional objects, including organisms, is just the product of our internal representation. Thus, for Albert objects exist as single points, evolving one way or another in this very high-dimensional space.

 

[kith]

If we try an interpretation in which the wave function is everything, yet applies only to ensembles, we obtain a contradiction because we still need classical apparatus to perform measurements and cause state vector reduction.

Why do we need state vector reduction if our description isn't about single runs of the experiment?

 

[stevendaryl]

If dBB stands for de Broglie-Bohm, I disagree with the statement that it is a flavor of the ensemble interpretation, because it adds "trajectories" to the quantum-mechanical particle description in a fancy non-local way.

I don't think that means it can't be a variety of the ensemble interpretation. The point of an ensemble approach (as I understand it) is to describe the statistics of an ensemble of systems that have the same macroscopic description (in terms of preparation). It doesn't rule out the possibility that there might be a more fine-grained description of what's going on for a single system, it's just agnostic about it.

 

[atyy]

An interesting treatment of the quantum Zeno effect may be that in Berthold-Georg Englert's http://books.google.com/books?id=OnSiIpIxorgC&source=gbs_navlinks_s (p32). Englert seems to hold a version of the ensemble interpretation in that book, as well as http://arxiv.org/abs/1308.5290 , yet describes the quantum Zeno effect as being due to control measurements.

 

[TrickyDicky]

Already the interpretation of the Heisenberg uncertainty relation is, as discussed in this forum, at least questionable.

Is there really a standard interpretation of the hup as discussed in this forum? (I assume you mean this PF quantum physics forum)

 

[atyy]

Why do we need state vector reduction if our description isn't about single runs of the experiment?

Take an ensemble and make a measurement. Then let it evolve and make another measurement.

Don't you need state vector reduction to handle this case?

 

[kith]

Take an ensemble and make a measurement. Then let it evolve and make another measurement. Don't you need state vector reduction to handle this case?

No, you would get wrong predictions. The ensemble is not in an eigenstate after the first experiment because you have measured different values in different runs. In order to get an eigenstate you have to filter the ensemble which means you have to implement a projective (unitary) time evolution.

 

[atyy]

No, you would get wrong predictions. The ensemble is not in an eigenstate after the first experiment because you have measured different values in different runs. In order to get an eigenstate you have to filter the ensemble which means you have to implement a projective (unitary) time evolution.

So is it the case that state vector reduction in the ensemble interpretation is not merely wave function collapse of Copenhagen, just renamed and reinterpreted? At least from a naive view of the wave function as one's subjective information, it would seem that something like state vector reduction should occur as an analogy to Bayesian updating.

 

[bhobba]

dBB could be viewed as underlying the ensemble interpretation.

That's true - but only if you want to hold to the much more natural view that what you observe is there prior to observation and the ensemble is independent of the actual observation. You need something like DBB, Nelson Stochastics or Primary State Diffusion to underlie it for that. The advantage over those interpretations is you can leave it up in the air exactly how its done - its just done - somehow.

That's why I hold to the ignorance ensemble interpretation with decoherence. It APPEARS to be like that - it isn't really like that - but you can hold to the fiction it is, and if anyone 'calls your bluff' so to speak you can say - observationaly its exactly the same - but really it isn't.

As the link I am won't to give on decoherence and the measurement problem states, decoherence does not touch the central issue (generally called the problem of outcomes) so does not solve the measurement problem. That's true - but what I would add is that's not really the claim of decpherence enthusiasts like myself - its that it APPEARS to solve the issue.

Thanks
Bill

 

[kith]

So is it the case that state vector reduction in the ensemble interpretation is not merely wave function collapse of Copenhagen, just renamed and reinterpreted?

State vector reduction and collapse are two names for the same thing. They refer to the "reduction" of a superposition to an eigenstate in a single run of the experiment. They are not part of the ensemble interpretation because individual outcomes are not associated with states there.

 

[atyy]

And is wave function collapse really not needed in the Ensemble interpretation? Isn't there also state vector reduction?

Yes, you have state vector reduction. However, if you do not consider the wave function as real, you also do not need to interpret state vector reduction as collapse.

State vector reduction and collapse are two names for the same thing. They refer to the "reduction" of a superposition to an eigenstate in a single run of the experiment. They are not part of the ensemble interpretation because individual outcomes are not associated with states there.

I see your point, but I think Cthugha said the opposite when he replied to me above.

 

[kith]

I see your point, but I think Cthugha said the opposite when he replied to me above.

Cthugha seems to use "state vector reduction" if we consider the wave function to be only a calculation tool and "collapse" if we are realistic about it. I agree that this distinction could be made but I don't agree that any of these notions is used in the ensemble interpretation.

 

[atyy]

Cthugha seems to use "state vector reduction" if we consider the wave function to be only a calculation tool and "collapse" if we are realistic about it. I agree that this distinction could be made but I don't agree that any of these notions is used in the ensemble interpretation.

That's interesting. I wonder whose version of the ensemble interpretation Cthugha is using. I looked briefly at Ballentine, and he really doesn't seems to have it.

But if there is no collapse, how is filtering possible as a method of state preparation?

 

[Cthugha]

Sorry, if I was misleading. There are two ways of how state vector reduction can enter.

One way is found when you consider the wave function as real and perform some measurement. Here state vector reduction is another name for collapse.

The second way is found, when one performs a conditional measurement, so you pick a subensemble out of a full ensemble. This can be referred to as state reduction, though I admit that there are people out there who find this terminology unacceptable and would insist that one should pick a different name and state reduction is reserved for changes due to the results of single measurements.

State reduction in the sense of collapse does not exist in the ensemble interpretation. Also, please note that I am personally not really adhering to the ensemble interpretation.

 

[strangerep]

But if there is no collapse, how is filtering possible as a method of state preparation?

Maybe take another look through Ballentine's chapters 8 and 9?

 

[atyy]

Maybe take another look through Ballentine's chapters 8 and 9?

OK, I will. But let me just make sure I understand you are disagreeing Cthugha's statement (ie. it's not just that I used the term "collapse" instead of "state reduction"):

The second way is found, when one performs a conditional measurement, so you pick a subensemble out of a full ensemble. This can be referred to as state reduction, though I admit that there are people out there who find this terminology unacceptable and would insist that one should pick a different name and state reduction is reserved for changes due to the results of single measurements.

 

[Ken G]

well, nonlinear quantum mechanics make different predictions than standard quantum mechanics (a linear one), then is another model.

Yes, one important service that the various interpretations could provide is guidance toward the next theory. Here we would have to let nature adjudicate what works, so there would be no purpose in "preferring" one interpretation over another, except for personal guidance in our own efforts to find the next theory if we were ambitious enough to try. A key role of theory is not just to explain what we've already seen, but also to help us know what we might want to look for next. I think that's the place where the interpretations have the most value, and who knows which one will be the most helpful there. Thus we see both the advantages and disadvantages of a "minimal" interpretation like the ensemble approach-- it keeps us from going too far out on a limb, but it also provides minimal opportunity to jump to the next branch.