Missed analytical opportunities in Bohmian mechanics

[martinbn]

Thank you for pointing this out! The purpose of interpretation is not the truth, the purpose is intuition. Intuition is a thinking tool. Tools are practical, for those who know how to use them.

Can give an example of how they are practicle?

Different interpretations are like different martial arts. Someone likes judo, someone karate, etc. Some of them may carry some esoteric philosophy with it, but what counts at the end of the day is how well you can use your martial art in practice.

And some are fake and completly useless.

 

[Demystifier]

Can give an example of how they are practicle?

Yes I can.

Ah, you want me to give an actual example? Fine. The classic example is the Bell's theorem, who got inspired by the Bohmian way of thinking. In my own case, I solved a practical problem in https://arxiv.org/abs/2010.07575 , the solution is presented with standard QM, while the Bohmian point of view is presented as secondary, but in reality I first solved the problem from the Bohmian point of view, because it was conceptually easier for me, and then translated the results to the standard QM language.

And of course, all interpretations may be useful, not just Bohmian. Deutch, for instance, used many world way of thinking to develop important practical ideas in quantum computing.

And some are fake and completly useless.

Capoeira?

 

[Demystifier]

No. So what?

So how can you call it "standard"?

 

[vanhees71]

Well, the question is, where the collapse conjecture is ever used in the application of QM. Usually you have a system somehow prepared (particle beams in an accelerator) and then the outcomes are measured (particle detectors of different kinds) and then analyzed using statistical methods. That's all that's needed and that's indeed the typical "standard" procedure.

 

[gentzen]

Do you, like Ballentine, reject any form of wave function collapse in statistical interpretation?

I see the collapse more as a mixture between gauge freedom and "approximation accuracy" vs "model complexity and computational effort" tradeoff. However, it is Ballentine, not me, who favors (and defends) the statistical interpretation. So I should better read what he himself has written, for example in his book, in his 1970 paper, and in his 1972 paper, before I make non-sensical or non-defendable claims about the statistical interpretation. (At least I have just now read chapter "11.2 Ensemble interpretations" in "Do we really understand quantum mechanics" by Franck Laloë. I have read Ballentine's 1972 paper on Einstein before, and a bit of what Einstein himself wrote.)

If so, how do you explain the quantum Zeno effect with statistical interpretation?

I don't think that this is really a problem. Remember that the statistical interpretation makes the same predictions as the other interpretations. If it really interests you, I can point you to discussions in the context of quantum error correction (where the quantum Zeno effect has to play its part in the magic), and give indications of my own opinions on which assumptions are uncritical and which may "fail" in an actual quantum computer.

You may like that fact that Franck Laloë pointed out that in Ballentine's 1970 paper:

Ballentine remarks that “the introduction of hidden variables is fully compatible with the statistical predictions of quantum theory”, and discusses the properties of these variables at the end of his article.

and that in Ballentine's 1972 paper it is expained how Einstein put forward the statistical interpretation as part of his conviction that the quantum state is not a complete description of individual quantum systems.

 

[Demystifier]

Well, the question is, where the collapse conjecture is ever used in the application of QM. Usually you have a system somehow prepared (particle beams in an accelerator) and then the outcomes are measured (particle detectors of different kinds) and then analyzed using statistical methods. That's all that's needed and that's indeed the typical "standard" procedure.

In most applications, you are right. But in some applications you measure the same system more than once, at different times. In such applications, the collapse rule is used in a practical sense.

 

[Demystifier]

I don't think that this is really a problem.

Ballentine on the quantum Zeno effect, in his book:
"... we have been led to the conclusion that a continuously observed system never changes its state! This conclusion is, of course, false."

 

[gentzen]

Ballentine on the quantum Zeno effect, in his book:
"... we have been led to the conclusion that a continuously observed system never changes its state! This conclusion is, of course, false."

Oh, so you want me to review Ballentine's "analysis" of the quantum Zeno effect, and either confirm that you are right and he made a "mistake" here, or else defend his "analysis"? But even if Ballentine should have made a mistake here, that doesn't disprove his statistical interpretation. My guess would be that Ballentine is indeed wrong here, because of his telltale remark at the end of that subsection:

It is sometimes claimed that the rival interpretations of quantum mechanics differ only in philosophy, and cannot be experimentally distinguished. That claim is not always true, as this example proves.

In this case, I should better review what other people have written about his specific opinion on the quantum Zeno effect. I guess the following thread should be a good starting point for me:
https://www.physicsforums.com/threads/errors-in-ballentine-qm-textbook.998385/

 

[vanhees71]

In most applications, you are right. But in some applications you measure the same system more than once, at different times. In such applications, the collapse rule is used in a practical sense.

But this should then be also describable by quantum dynamics. It's also rare that the collapse assumption really holds, even in a FAPP sense.

 

[vanhees71]

Ballentine on the quantum Zeno effect, in his book:
"... we have been led to the conclusion that a continuously observed system never changes its state! This conclusion is, of course, false."

And what do you think is wrong with this?

 

[Morbert]

Re/ the QZE: An ideal physicist would write down a suitable model Hamiltonian for the unstable atom + detector + EM field + environment, and then compute the relevant decay rates/probabilities for some time of interest. This "shut up and calculate" procedure isn't contingent on the acceptance or rejection of any interpretation, statistical, minimalist, or otherwise.

What makes QZE interesting is the challenge of shutting up and calculating: the construction of the model Hamiltonian and the computation of decay rates etc. From https://arxiv.org/pdf/quant-ph/0307075.pdf:

The latter condition explains why the QZE was not obtained for exponentially decaying systems by theories based on the projection hypothesis. By applying the projection operator, the quantum coherences between |x, 0〉 and |g, k〉’s are destroyed regardlessly of the energy of the emitted photon. Therefore, the projection-based theory corresponds to ∆ → ∞ [20]. In such a limit, however, inequality (10) cannot be satisfied and the QZE never occurs. Since ∆ of any real detector is finite, such a limit is rather unphysical.

Naively projecting here and there is not a feature of an interpretation. It's a feature of poor application of a theory.

 

[PeterDonis]

The purpose of interpretation is not the truth, the purpose is intuition. Intuition is a thinking tool.

I agree with this, but I'm not sure all physicists who are proponents of particular interpretations do. Many of them appear to think that their preferred interpretations are "true", not just useful thinking tools.

 

[Demystifier]

I agree with this, but I'm not sure all physicists who are proponents of particular interpretations do. Many of them appear to think that their preferred interpretations are "true", not just useful thinking tools.

Yes, and I believe I can explain why is that. At the beginning, when one hears about a particular interpretation for the first time, nobody thinks it's "true". At best, it looks like "OK, maybe there is some truth in it". But with this state of mind, the tool is not yet fully efficient, one must create a stronger bond with it to exploit its full potential. For many people, the thinking tool may work the best when one imagines that it is "really true". But when one comes to that psychological state of imagination, the problem is then to later step out from this state of mind. So after a while the imagination may start to look like reality. The map may start to look like the territory.

My own way to cope with this is changing the roles. For example, when I speak with very strong proponents of the Bohmian interpretation, I often present them the counterarguments, some of which I've learned in this forum.

 

[Demystifier]

And what do you think is wrong with this?

Let me put it this way. Do you know a reference where the real quantum Zeno effect (which is a measured effect) is explained theoretically without reference to any kind of collapse? I would really like to see how one can avoid it, in actual calculation.

 

[vanhees71]

Can you refer to a reference, where "the real quantum Zeno effect" is demonstrated? I could imagine it's some atom in a cavity with a laser kicking it somehow to stay (maybe in principle for ever) in an excited/metastable state. I'm not sure, whether one can treat the full quantum-time evolution of this exactly.

The main objection against the hand-waving arguments using 1st-order perturbation theory for the transition rate for "infinitesimal times" and then treat the process as if it were Markovian is at least misleading.

The more we think about open quantum systems in our research work the more we come to the conclusion that Markovian approximations are making more trouble than good. Particularly it's not clear, how to ensure proper thermalization in the long-time limit, but that's a different topic.

 

[Demystifier]

Can you refer to a reference, where "the real quantum Zeno effect" is demonstrated?

https://arxiv.org/abs/quant-ph/0104035

 

[martinbn]

Let me put it this way. Do you know a reference where the real quantum Zeno effect (which is a measured effect) is explained theoretically without reference to any kind of collapse? I would really like to see how one can avoid it, in actual calculation.

Does collapse make sense in an ensemble interpretation?

 

[Demystifier]

Does collapse make sense in an ensemble interpretation?

It depends on who you ask. In my opinion, yes.
https://www.physicsforums.com/threa...on-is-neither-minimal-nor-statistical.998661/

 

[martinbn]

It depends on who you ask. In my opinion, yes.
https://www.physicsforums.com/threa...on-is-neither-minimal-nor-statistical.998661/

Then what is collapse in an ensemble interprwtatoon?

 

[vanhees71]

Does collapse make sense in an ensemble interpretation?

Collapse doesn't make sense to me, because it claims that there is dynamics not described by QT and then you ad hoc assume some magic that violates relativistic causality. I have no clue, what the collapse postulate is needed for.

 

[martinbn]

Collapse doesn't make sense to me, because it claims that there is dynamics not described by QT and then you ad hoc assume some magic that violates relativistic causality. I have no clue, what the collapse postulate is needed for.

That is not what i am asking. In a non ensemble interpretation it is clear what collapse is, whether it is needed or not is a separate question. But my question is what is it in the ensemble case?

 

[Demystifier]

Then what is collapse in an ensemble interprwtatoon?

Information updwatee.

 

[vanhees71]

But your information update should relate to what you look at. You cannot say that whenever you measure an observable the correct information update is that then the system is in an eigenstate of the measured observable with the eigenvalue given by the measured value. It depends on, how the system interacts with the measurement device, how to describe its state after the measurement. Sometimes the very object you were measuring is destroyed in the measurement process (like a photon hitting a photoplate). What sense then does the collapse postulate make?

 

[martinbn]

Information updwatee.

No, i mean how is it formulated if we have ensembles and the wave function describes them, not the idividual system?

 

[Demystifier]

But your information update should relate to what you look at. You cannot say that whenever you measure an observable the correct information update is that then the system is in an eigenstate of the measured observable with the eigenvalue given by the measured value. It depends on, how the system interacts with the measurement device, how to describe its state after the measurement. Sometimes the very object you were measuring is destroyed in the measurement process (like a photon hitting a photoplate). What sense then does the collapse postulate make?

https://www.physicsforums.com/threads/difference-between-collapse-and-projection.998545/post-6445809

 

[Morbert]

That is not what i am asking. In a non ensemble interpretation it is clear what collapse is, whether it is needed or not is a separate question. But my question is what is it in the ensemble case?

If you have some experiment involving a sequence of measurements, then an example of a "collapse" would be a partitioning of the ensemble of experimental runs into subensembles in accordance with the outcome of one of the measurements.

 

[vanhees71]

What has this to do with the collapse postulate?

 

[Demystifier]

No, i mean how is it formulated if we have ensembles and the wave function describes them, not the idividual system?

Then the collapsed wave function describes a subensemble, in which all members show the same measurement outcome.

 

[martinbn]

Then the collapsed wave function describes a subensemble, in which all members show the same measurement outcome.

How is it a subensemble? In any case it is a different ensemble, so what is collapse exactly?

 

[Demystifier]

What has this to do with the collapse postulate?

If you ask me, the last formula describes a generalized collapse rule for general POVM measurements.