I QFT made Bohmian mechanics a non-starter: missed opportunities?

[Demystifier]

a microscopic system's angular momentum obtaining some value, even if no measurement is made.

Consistent histories seems to better capture convention here

But consistent history depends on the choice of framework. We cannot say that the microscopic angular momentum obtains some value, period. Instead, we say that the microscopic angular momentum obtains some value in one framework, and does not obtain any value in another framework. Different frameworks, in my understanding, are just different modes of thinking. In this sense the CH interpretation is not one interpretation, but a large class of interpretations. Each framework can be thought of as another interpretation. The frameworks do not exist out there in nature itself, without physicists who apply them as their way of thinking. Does it make sense to you?

 

[Demystifier]

Sure, you can use different words for observables, and call them events. What does this change?

Are there microscopic events, which do not involve any macroscopic apparatuses or macroscopic environments? Is it possible to have an event in a system with only two particles, completely isolated from the environment?

 

[Demystifier]

This is more belief than what you addmitted initially.

Only a little bit more. Bohmians assume that a mathematical description of nature in the absence of measurement is possible (as I said before), and they also assume that measurement is not primitive (i.e. they assume that measurement can be explained in terms of something more fundamental).

 

[vanhees71]

Are there microscopic events, which do not involve any macroscopic apparatuses or macroscopic environments? Is it possible to have an event in a system with only two particles, completely isolated from the environment?

You can detect single particles/quanta, but of course it involves "macroscopic" equipment. The detection events are due to local interactions of the quanta with a small part of the macroscopic device, and the rest of it you can describe as "environment".

 

[martinbn]

Only a little bit more. Bohmians assume that a mathematical description of nature in the absence of measurement is possible (as I said before), and they also assume that measurement is not primitive (i.e. they assume that measurement can be explained in terms of something more fundamental).

And how does it follow from this that there are point particles, trajectories, preferred frame and so on?

 

[vanhees71]

Hm, are there point particles, trajectories or even a preferred frame? For me from Faraday on, physics teaches us that at the most fundamental level Nature is described by (local) quantum field theories rather than Newtonian point-particle mechanics. That we prefer point-particle pictures so much is most probably, because any systematic physics teaching starts with Newtonian point-particle mechanics, because it's the conceptually most simple and most "intuitive" picture. Also it has an amazing realm of applicability.

Then usually, we don't treat the trouble of the point-particle picture in much detail. At best you mention in passing that the radiation-reaction problem in classical point-particle electrodynamics (Lorentz's classical "electron theory") is plagued by inconsistencies and problems. The best one can do at this level is to use the 1st order perturbative implementation of radiation reaction/self-energies, aka the Landau-Lifhitz approximation of the Lorentz-Abraham-Dirac equation. I think a the classical level that's the best you can do, and it's not too bad in comparison with continuum-mechanical treatments (magneto-hydrodynamics, transport theory), which are much better suited, because more in the spirit of continuum/field descriptions, which seem to be more appropriate already at the classical level of relativsitic physics than the point-particle paradigm.

Finally, the best we have is local relativistic QFT, and even that it's not completely satisfactory from a mathematical point of view ("axiomatic QFT" in 1+3 dimensions hasn't delivered much more than a rigorous description of free quantum fields) as well as a physics point of view since it still lacks a satisfactory quantum description of the gravitational field/aka spacetime geometrodynamics.

 

[Demystifier]

You can detect single particles/quanta, but of course it involves "macroscopic" equipment. The detection events are due to local interactions of the quanta with a small part of the macroscopic device, and the rest of it you can describe as "environment".

I guess it means that the answer to my question is no. There are no events if the small part above is isolated from the rest of the environment. Right?

 

[vanhees71]

Yes, or do you have a counter example?

 

[Demystifier]

And how does it follow from this that there are point particles, trajectories, preferred frame and so on?

It doesn't follow. The point particles, trajectories, preferred frames and so on are just the simplest model that Bohmians found, which satisfies the mentioned assumptions. And of course, the notion of simplicity is subjective. If you have another model, which seems simpler to you, I would be truly happy to learn about that model.

 

[Demystifier]

Yes, or do you have a counter example?

I don't, I just wanted to be sure that I understood what you mean by "event". It's now clear that event, in your understanding of that word, cannot be purely microscopic. By contrast, @Morbert had a different meaning of the word "event" in mind, as something that can be purely microscopic.

 

[martinbn]

It doesn't follow. The point particles, trajectories, preferred frames and so on are just the simplest model that Bohmians found, which satisfies the mentioned assumptions. And of course, the notion of simplicity is subjective. If you have another model, which seems simpler to you, I would be truly happy to learn about that model.

But you believe in the model, right? Otherwise you would say "well, it goes against a lot of the understanding we have gained so far, so lets search for another model"

 

[Morbert]

I don't, I just wanted to be sure that I understood what you mean by "event". It's now clear that event, in your understanding of that word, cannot be purely microscopic. By contrast, @Morbert had a different meaning of the word "event" in mind, as something that can be purely microscopic.

Yes, a microscopic event can be constructed with a projective decomposition of the identity the state space of a microscopic system $I = \sum_i \Pi_i$. An event would then be a projector of the form $E = \sum_i \pi_i \Pi_i$ where $\pi_i$ is 0 or 1. I am assuming a similar procedure is possible in BM, where you can partition the state space in to a set of disjoint domains a la the partitioning of a classical phase space, and build the corresponding event algebra from that.

 

[Demystifier]

But you believe in the model, right?

No, I don't believe in the model the way you think I do. See in particular my recent https://arxiv.org/abs/2308.10500 Sec. 4.3.

Otherwise you would say "well, it goes against a lot of the understanding we have gained so far, so lets search for another model"

I'm searching, much more than you think. I even asked you to present your model if you have one, it was not purely rhetorical.

To me, Bohmian mechanics is like democracy. It sucks in many ways, but any known alternative sucks even more.

 

[vanhees71]

What do you have against the minimal interpretation, which works very well also in the relativistic domain and comes without unnecessary balast?

 

[Demystifier]

What do you have against the minimal interpretation, which works very well also in the relativistic domain and comes without unnecessary balast?

You should know by now what I have against it, I've explained it to you hundred times. By now, you should know why people need the "unnecessary balast". Even you need some "unnecessary balast", but you don't want to admit it. Do you want me to make a list of your unnecessary balasts?

 

[vanhees71]

No, thanks.

 

[martinbn]

No, I don't believe in the model the way you think I do. See in particular my recent https://arxiv.org/abs/2308.10500 Sec. 4.3.

This confirms my impression. By the way this is an example of the wishfull thinking i was talking about?

I'm searching, much more than you think. I even asked you to present your model if you have one, it was not purely rhetorical.

You mean a model where measurement is not a primitive notion? Then, no. But i dont know any models of.euclidean geometry where points are not primitive.

To me, Bohmian mechanics is like democracy. It sucks in many ways, but any known alternative sucks even more.

How so!!! QM ala von Neuman Dirac is waaay better.

 

[Demystifier]

This confirms my impression. By the way this is an example of the wishfull thinking i was talking about?

How? Support your claim with a quote from Sec. 4.3.

 

[Demystifier]

QM ala von Neuman Dirac is waaay better.

Both von Neumann and Dirac were fully aware that there is the measurement problem that their form of QM does not solve.

 

[Demystifier]

You mean a model where measurement is not a primitive notion? Then, no.

So you confirm that the Bohmian model is the best model you know in which measurement is not primitive. I rest my case!

But i dont know any models of.euclidean geometry where points are not primitive.

So, I believe that particles are pointlike, while you believe that measurements are pointlike. I can't compete with that, you are a much stronger believer than I will ever be.

 

[gentzen]

You mean a model where measurement is not a primitive notion? Then, no. But i dont know any models of.euclidean geometry where points are not primitive.

Maybe the core of your disagreement has less to do with the notion of "measurement" and more to do with the notion of "primitive notion"? For Descartes' model of Euclidean geometry, the "primitive notion" is given by real numbers, and a point is simply a pair (or n-tupple in general) of real numbers.

I brought up Descartes and his importance for the revolution in mathematics earlier in this thread:

With respect to Descartes, his dualism was a huge part of the revolution in mathematics and the sciences more general. But in the end, his dualism is probably not correct, and at some point it started to limit further scientific progress.

Descartes' move to give-up on points as being a "primitive notion", and instead reduce it to a pair of real numbers, was important for the revolution he triggered. Also note how Descartes' model seems to break a whole bunch of symmetries.

I can't decide what is harder, to imagine that point is not primitive, or to imagine that measurement is primitive. If you can think so abstractly that a measurement is analogous to a point, then maybe you have been reading Grothendieck too much.

Grothendieck too was responsible for another revolution in mathematics. To come back to points, part of that revolution was that sometimes non-abstract points are not enough, and you need to additionally consider generalized-points.

 

[vanhees71]

So you confirm that the Bohmian model is the best model you know in which measurement is not primitive. I rest my case!So, I believe that particles are pointlike, while you believe that measurements are pointlike. I can't compete with that, you are a much stronger believer than I will ever be.

That's what our best models and observations say. Of course, with a classical point-particle picture the double-slit experiments with what's in pre-quantum theories were thought to be particles (like electrons) must be mysterious, while for objects that were in pre-quantum theories thought to be "waves" (like photons) particle aspects must appear mysterious.

The aim of the natural sciences since the renaissance has always been to find descriptions which take mysticism away and find a rational one instead. That's what finally modern Q(F)T has achieved. In its minimal interpretation it describes both the "wave" and "particle" aspects of matter correctly and without any mystics involved. There is no wave-particle dualism but only quantum dynamics. There's no measurement problem but accurate descriptions of what's observed.

 

[WernerQH]

The aim of the natural sciences since the renaissance has always been to find descriptions which take mysticism away and find a rational one instead. That's what finally modern Q(F)T has achieved. In its minimal interpretation it describes both the "wave" and "particle" aspects of matter correctly and without any mystics involved. There is no wave-particle dualism but only quantum dynamics. There's no measurement problem but accurate descriptions of what's observed.

If rationality is on your side, why is it so difficult to convince others that your view is the only "reasonable" one?

 

[vanhees71]

Good question! I've the impression that many people love the mysterious.

 

[martinbn]

If rationality is on your side, why is it so difficult to convince others that your view is the only "reasonable" one?

Doesn't this apply to all?

 

[WernerQH]

Good question! I've the impression that many people love the mysterious.

Shouldn't thousands of posts have dispelled the mysteries?
How is this possible for a theory that, after almost a century, must be called mature?

Sure, Bohr contributed greatly to the mystery by insisting that quantum theory (which should contain classical physics as a limiting case) must be formulated using classical physics, and 'measurement' must play a special role. Somehow humans cannot possibly conceive of appropriate concepts to describe the microworld, and Q(F)T must necessarily have an air of transcendence? That it cannot be fully understood by mere mortals?
You have indicated that you "understand" quantum theory (in contrast to Feynman ), but why is it so difficult to share your understanding? Replacing "wave particle duality" with a term like "quantum dynamics" doesn't really remove the obstacles.

My impression is that we are still lacking a clear idea of how quantum mechanics meshes with classical mechanics. I think the situation is not unlike that of Maxwell's electrodynamics before 1905: It was a highly successful theory, but its clash with classical (Newtonian) mechanics wasn't clearly perceived. We may be witnessing a crisis in physics (in the sense used by Thomas Kuhn), and another revolution like the one in 1905 is still awaiting us.

 

[Demystifier]

I've the impression that many people love the mysterious.

I love the mysterious but not the mystical. The mysterious refers to a question that can be answered rationally, while the mystical refers to a question that can't be answered rationally. The mysterious is typical for science, while the mystical is typical for religion. For example, if someone believes that humans can't rationally understand God, or that humans can't rationally understand what is the world like when it's not observed, that's mystical. It looks as if you are saying that you don't like the mysterious, but like the mystical.

 

[martinbn]

I love the mysterious but not the mystical. The mysterious refers to a question that can be answered rationally, while the mystical refers to a question that can't be answered rationally. The mysterious is typical for science, while the mystical is typical for religion. For example, if someone believes that humans can't rationally understand God, or that humans can't rationally understand what is the world like when it's not observed, that's mystical. It looks as if you are saying that you don't like the mysterious, but like the mystical.

Hm, but you like BM, which has instantanious magic at a distance.

 

[Demystifier]

Doesn't this apply to all?

No. Those who prefer the standard/minimal/orthodox interpretation usually don't seriously think about other interpretations (unless they make new predictions, in which case we usually don't speak of interpretations) and can't understand why someone even considers them. By contrast, those who prefer some other interpretation, spend a lot of time by carefully thinking about relative advantages and disadvantageous of various interpretations. They are much more open to various points of view, and don't think that everyone should accept their point of view.

 

[Demystifier]

Hm, but you like BM, which has instantanious magic at a distance.

I don't see it as magic, you do.

 

[Structure seeker]

Good question! I've the impression that many people love the mysterious.

I like both the mysterious and the mystical. The latter is not to be sought when verifying or falsifying results, but also Pauli for instance was considered a mystic according to wikipedia. Of course reality (or nature) is the matter that science is about, yet how can I get to know anything new about laws of physics (which apparently are above and independent of nature) without some mystical process? Only when trying to solidify results, any mysterious or mystical ideas should be ignored.

 

[Morbert]

Both von Neumann and Dirac were fully aware that there is the measurement problem that their form of QM does not solve.

I think the measurement problem has been picked clean, and objections have a subjective character nowadays: Instrumentalism is rejected because we don't want preparation and measurement to play foundational roles. Consistent histories is rejected because we don't want protean event algebras. Bohmian mechanics is rejected because we don't want action at a distance etc etc

 

[gentzen]

If rationality is on your side, why is it so difficult to convince others that your view is the only "reasonable" one?

Good question! I've the impression that many people love the mysterious.

Good answer! In the poll A Snapshot of Foundational Attitudes Toward Quantum Mechanics (by Maximilian Schlosshauer, Johannes Kofler, and Anton Zeilinger, 2013) among 33 participants of a conference on the foundations of quantum mechanics, for Question 12: What is your favorite interpretation of quantum mechanics? the following options received no vote at all:
a. Consistent histories
c. De Broglie–Bohm
f. Modal interpretation
j. Statistical (ensemble) interpretation
k. Transactional interpretation
Both c. and j. are pretty non-mysterious. They both disappoint the "hope for more". Even if they vanhees71 would be right, and j. actually offered everything you wanted and more, it feels too straighforward and easy to understand so that nobody will believe that this "more" could be true. And the same applies for c. and Demystifier's efforts to put it to practical use.

 

[gentzen]

What do you have against the minimal interpretation, which works very well also in the relativistic domain and comes without unnecessary balast?

If feels so straightforward and easy to understand, that I quickly come to believe that my understanding of it must be correct. So I happily agree with the "beforehand approach" explained by Craig Gidney:

Although I think of my approach as "beforehand instead of in-the-moment" thinking, as opposed to "density matrices".
...
Pop science articles are basically always written from the in-the-moment view, which is unfortunate because that makes it very difficult to explain or integrate before-hand concepts such as the no communication theorem.

So I "feel" that this "beforehand approach" expresses the core of the statistical interpretation.

But if I adopt this beforehand perspective, how can I reply to a remark like this:

As for what changes, my opinion is that probably not much changes. Instrumentalism is a defensible position for a quantum physicist even if it is not for a paleontologist. As a foundational project, it is probably the most complete.

At the same time it's also my opinion that it doesn't fully capture the modes of thinking quantum chemists and applied quantum physicists use in their day-to-day.

As a paleontologist, how can I reasonably have statistics beforehand of what artifacts I will find? I cannot, i.e. there is no reasonable way to fix the context beforehand. And putting my model into the past before my artifacts got burried feels at odd with a "beforehand" perspective too. But here I should better be careful, it may well be that this perspective is perfectly consistent. I may just be blind to this, because the statistical interpretation feels so straighforward and easy to understand to me.

 

[Quantum Waver]

That's what our best models and observations say. Of course, with a classical point-particle picture the double-slit experiments with what's in pre-quantum theories were thought to be particles (like electrons) must be mysterious, while for objects that were in pre-quantum theories thought to be "waves" (like photons) particle aspects must appear mysterious.

The aim of the natural sciences since the renaissance has always been to find descriptions which take mysticism away and find a rational one instead. That's what finally modern Q(F)T has achieved. In its minimal interpretation it describes both the "wave" and "particle" aspects of matter correctly and without any mystics involved. There is no wave-particle dualism but only quantum dynamics. There's no measurement problem but accurate descriptions of what's observed.

That leaves the unobserved as mystical. Whereas realist approaches think science is attempting to remove mysticism from nature by providing full explanations, not just for observation. Most of nature goes unobserved by us and our equipment. Yet it manages to carry on somehow and produce what is observed. The wave-particle properties are produced by something in nature. Maybe there's a dynamical collapse that goes on, which is fundamentally stochastic. Or maybe there are hidden variables. Or maybe decoherence puts everything into superposition.

At any rate, it's a scientific question as to what's going on. It's just that so far, there's no empirical way to decide what that is. But it's interesting that quantum phenomenon can be scaled up to macroscopic sizes under certain conditions, where we can observe it behaving quantum mechanically, like with superfluids. David Deustch suggested that quantum computers could help decide the matter:

To those who still cling to a single-universe world-view, I issue this challenge: explain how Shor’s algorithm works. I do not merely mean predict that it will work, which is merely a matter of solving a few uncontroversial equations. I mean provide an explanation. When Shor’s algorithm has factorized a number, using 10^500 or so times the computational resources than can be seen to be present, where was the number factorized? There are only about 10^80 atoms in the entire visible universe, an utterly minuscule number compared with 10^500. So if the visible universe were the extent of physical reality, physical reality would not even remotely contain the resources required to factorize such a large number. Who did factorize it, then? How, and where, was the computation performed?

https://www.newyorker.com/magazine/2011/05/02/dream-machine

 

[Demystifier]

the statistical interpretation feels so straighforward and easy to understand to me.

Do you, like Ballentine, reject any form of wave function collapse in statistical interpretation? If so, how do you explain the quantum Zeno effect with statistical interpretation?

 

[Demystifier]

Demystifier's efforts to put it to practical use

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.

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.

 

[vanhees71]

Do you, like Ballentine, reject any form of wave function collapse in statistical interpretation? If so, how do you explain the quantum Zeno effect with statistical interpretation?

There is no wave-function collapse in standard QT. To introduce one means to invent a new theory (e.g., like stochastic collapse models like Ghirardi-Rimini-Weber (GRW) theory.

The quantum zeno effect is of course explained by standard quantum dynamics through the interaction of the measured system with the measurement device (+environment). No need for collapse!

 

[Demystifier]

There is no wave-function collapse in standard QT.

Do you know any standard textbook, in addition to Ballentine, that says so?

 

[vanhees71]

No. So what?

 

[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?