How to talk about interpretations

[tzimie]

What is a correct way to answer (here, on PhysicsForums) interpretation-dependent questions?
I mean, without confusing people, but providing different points of view, but without starting "interpretation wars"?

 

[bhobba]

What is a correct way to answer (here, on PhysicsForums) interpretation-dependent questions?
I mean, without confusing people, but providing different points of view, but without starting "interpretation wars"?

I don't think there is any real way to answer that - all I can do is say how I approach it.

First understand what an interpretation is - it means a way of looking at it that leads to exactly the same results. Since science is correspondence with experiment that makes no interpretation better than any other.

The second thing is, because of the first point, the choice of interpretation is purely one of psychological preference - its not science.

Finally, while I hold to a particular interpretation, I try to understand the strengths and weaknesses of different interpretations and, as far as possible, if asked, explain what's going on.

For example, to me, MW is beauty and elegance incarnate, but it just doesn't gell with me. I try and explain what I have learned about it, and why it doesn't appeal - but the final acceptance/rejection must be each persons choice.

Thanks
Bill

 

[tzimie]

but the final acceptance/rejection must be each persons choice.

I agree with you, but what's about newcomers/layman questions?
These people don't have enough knowledge to chose the interpretation.
Giving them an answer "it is interpretation-depended" is confusing and looks like avoiding giving an answer.
Providing an answer based on any particular interpretation is not fair and hides part of the truth from them. It is like the "Big Bang as explosion" thing popular on TV/youtube which makes more harm than good.

 

[bhobba]

Answering newcomers/layman questions is difficult overall.

The reason is you have the correct answer - which is usually advanced, highly mathematical, and requires considerable background. Or you can give the usual answer as found in beginning books which is often, unfortunately, wrong - even though its very common in beginning texts. One example is the so called wave/particle duality - which is wrong - simple as that. Yet it's used so often you can see people have a hard time when its pointed out what a crock it is.

I have a paper I link to on that for people with a bit of background:
http://cds.cern.ch/record/1024152/files/0703126.pdf

Trouble is, while that does break down misconceptions - it also is wrong - but only from an advanced stand-point - meaning a beginner student wouldn't likely spot it:
http://arxiv.org/pdf/1009.2408.pdf

Feynman too commented on this and basically said he has no answer exept to look at it on a case by case basis.

This is basically what I do. I try and get an idea of their level and I have a number of links and standard explanations depending on the level.

Thanks
Bill

 

[atyy]

I have a paper I link to on that for people with a bit of background:
http://cds.cern.ch/record/1024152/files/0703126.pdf

Trouble is, while that does break down misconceptions - it also is wrong - but only from an advanced stand-point - meaning a beginner student wouldn't likely spot it:
http://arxiv.org/pdf/1009.2408.pdf

Actually, apart from Rothman and Boughn's objections, and vanhees71's objection in a previous thread about the use of a delta function, which is not a physical wave function, I don't like Marcella's article because it doesn't seem to state that he only gives the solution for a screen at infinity. He just says the observable measured is momentum, which is correct for a screen at large distance. However, people do use setups with the screen at finite distance, eg. http://www.atomwave.org/rmparticle/ao%20refs/aifm%20refs%20sorted%20by%20topic/ungrouped%20papers/wigner%20function/KPM97.pdf

 

[atyy]

I agree with you, but what's about newcomers/layman questions?
These people don't have enough knowledge to chose the interpretation.
Giving them an answer "it is interpretation-depended" is confusing and looks like avoiding giving an answer.
Providing an answer based on any particular interpretation is not fair and hides part of the truth from them. It is like the "Big Bang as explosion" thing popular on TV/youtube which makes more harm than good.

I don't know if there is an official policy, but I would imagine that one can answer using any interpretation that is correct (ie. is experimentally indistinguishable from quantum mechanics in the Copenhagen interpretation), provided one clearly states its limitations and allows that other interpretations are possible. I usually state my answers using Copenhagen (which is basically the same as bhobba's Ensemble interpretation). However, I try to make clear its limitations, for example, Copenhagen has a measurement problem. Also, historically some forms of Copenhagen have wrongly asserted that hidden variables are impossible, an assertion based on von Neumann's flawed proof.

In practice, the statement I try to be careful about while using Copenhagen is not to say that quantum mechanics says that particles do not have trajectories, which is not true, since a de Broglie-Bohm type interpretation is possible. Rather, I say that in quantum mechanics, particles do not have simultaneously well-defined position and momentum at all times, which is true in all interpretations (I think). The informal way to see this is that the Wigner function in general has negative portions. Looking at the Wigner function also allows you to see the special cases in which a particle can have definite position and momentum, even in Copenhagen.

 

[tzimie]

Rather, I say that in quantum mechanics, particles do not have simultaneously well-defined position and momentum at all times, which is true in all interpretations (I think).

In MWI there are no particles at all, they are just an illusion given by quantum decoherence

 

[bhobba]

In MWI there are no particles at all, they are just an illusion given by quantum decoherence

Don't agree with that.

In each world they certainly exist.

Your issue may be exactly what is a particle in QM - which is usually left up in the air. The real answer lies in QFT, but in QM, if you look at it carefully, it means position is an observable, which any interpretation of QM has.

That's all that's necessary to derive Schroedinger's equation etc as per chapter 3 Ballentine.

Thanks
Bill

 

[Demystifier]

Rather, I say that in quantum mechanics, particles do not have simultaneously well-defined position and momentum at all times, which is true in all interpretations (I think)

This is both true and wrong, depending on what exactly do you mean by a "particle". The meaning of the word "particle" in Bohmian interpretation is very different from that in Copenhagen interpretation. The Copenhagen "particle" is nothing but a click in a detector. In the Bohmian interpretation there are detector clicks too, but the word "particle" is reserved for something else: the well-localized object with a continuous deterministic trajectory existing even in the absence of measurement. In that sense, the Bohmian "particle" does have a simultaneously well-defined position and momentum at all times.

 

[Demystifier]

In MWI there are no particles at all, they are just an illusion given by quantum decoherence

Don't agree with that.
In each world they certainly exist.

As I explained in the post above, it depends on the definition of the word "particle". If by "particle" one means "detector clicks", then they exist in all interpretations, including MWI. But with a different definition of "particle" this doesn't need to be the case.

And this is a very important message for the topic "how to talk about interpretations". Different interpretations often use different languages, so one must be very careful in any attempt to compare them by using a single language.

 

[tzimie]

I wanted to provide yet another example.

Q: What is a difference between real and virtual particles?
(traditional) A: Virtual particles are just math to <blah blah>

I am layman, but I see it confusing for several reasons:
1. It implicitly uses CI where "reality" of particles is well-defined because they are "detected", or "measured"
2. Even in CI, it is valid in inertial frames only. In accelerated frames (Unruh effect) different observers don't agree on the number of "particles"
3. For macroscopic objectivist, both 'real" and "virtual" particles are "just math" to calculate probabilities of macroscopic events.
4. In MUH *everything* is "just math", and there is no difference, by definition, between "being real" and "being just math"

So can PhysicsForums mentors create a interpretation-neutral FAQ, like we have for Cosmology forum, or it is not possible?

 

[bhobba]

I am layman, but I see it confusing for several reasons:
1. It implicitly uses CI where "reality" of particles is well-defined because they are "detected", or "measured"

They have never been observed, nor does the theory allow them to be observed. CI is silent on things when not observed - but they can be observed - virtual particles can't be observed and it is thought they are simply an artefact of the perturbation methods used. But using those methods they have very real effects such as the Lamb shift.

However I have to say this is part of QFT, which is a very advanced and notoriously difficult area eg perturbation theory was taught in my degree as a second year university subject in numerical analysis and requires an understanding of calculus, particularly power series expansions to explain - and that's just the mathematical part devoid of the physics:
http://www.cims.nyu.edu/~eve2/reg_pert.pdf

Me throwing a word like perturbation around is completely unilluminateing to the layman - unless they have a good background in math.

Recall what I said above - 'The reason is you have the correct answer - which is usually advanced, highly mathematical, and requires considerable background.' Sorry - the jig is up with QFT.

Basically the issue is perturbation theory is a method to get successively better approximations to otherwise intractable mathematical problems. That the only way we know to get answers from QFT.

Trouble is, if you don't use it, and solve the problem directly using a computer (that's known as Lattice QFT) virtual particles never appear. This makes people think it simply an artefact of perturbation theory.

That said, if you know basic QM, or are willing to learn it, I have come across a very good book that explains QFT at an approachable level:
https://www.amazon.com/dp/019969933X/?tag=pfamazon01-20

Sorry - but that's the best I can do. Others may be able to explain it to the lay person - but I cant.

Regarding the other stuff - remember QM is simply a mathematical model - but its a model of things that occur in the real world. What the FORMALISM of QM is about (as opposed to interpretations) is observations that actually occur - they are very real. That's what makes it more than just math. Particles etc exist as observations such as the clicks that Demistifyer mentions. Virtual particles do not exist in that sense.

Thanks
Bill

 

[atyy]

This is both true and wrong, depending on what exactly do you mean by a "particle". The meaning of the word "particle" in Bohmian interpretation is very different from that in Copenhagen interpretation. The Copenhagen "particle" is nothing but a click in a detector. In the Bohmian interpretation there are detector clicks too, but the word "particle" is reserved for something else: the well-localized object with a continuous deterministic trajectory existing even in the absence of measurement. In that sense, the Bohmian "particle" does have a simultaneously well-defined position and momentum at all times.

But in BM, position and momentum are not canonically conjugate, so the BM momentum is not momentum, which is why it is true that particles in BM do not have simultaneously well-defined position and momentum.

 

[bohm2]

But in BM, position and momentum are not canonically conjugate, so the BM momentum is not momentum, which is why it is true that particles in BM do not have simultaneously well-defined position and momentum.

So you are saying that while position is more basic /"real", momentum must be contextual in BM?

 

[Demystifier]

But in BM, position and momentum are not canonically conjugate, so the BM momentum is not momentum, which is why it is true that particles in BM do not have simultaneously well-defined position and momentum.

That's wrong. In BM position and momentum of a particle are canonically conjugate, in the same sense in which they are conjugate in classical mechanics. You can see that by formulating BM in terms of a quantum Hamiltonian, which is the classical Hamiltonian plus the quantum potential. Note also that position and momentum of a Bohmian particle are c-numbers, not operators, so they commute.

 

[Demystifier]

So you are saying that while position is more basic /"real", momentum must be contextual in BM?

The momentum of a Bohmian particle is not contextual, but that quantity is not directly measurable. On the other hand, the measurable momentum (essentially, the pointer of a macroscopic apparatus that measures "momentum") does not differ from momentum in the Copenhagen interpretation, and is, of course, contextual.

But it does not mean that Bohmian momentum and Copenhagen momentum are unrelated. When Copenhagen momentum is measured with a perfect accuracy, then Copenhagen momentum is numerically equal to the Bohmian momentum.

 

[bohm2]

The momentum of a Bohmian particle is not contextual, but that quantity is not directly measurable. On the other hand, the measurable momentum (essentially, the pointer of a macroscopic apparatus that measures "momentum") does not differ from momentum in the Copenhagen interpretation, and is, of course, contextual.

I guess my confusion (and misinterpretation?) is these sentences by Durr et al.

We would now like to argue that with most observables, for example energy and momentum, something much more dramatic occurs: In the transition from classical mechanics they cease to remain properties at all.

http://arxiv.org/pdf/quant-ph/9511016v1.pdf

And then Myrvold:

It is this asymmetry—the fact that the Bohm theory singles out position as the basic quantity whose statistical distribution is to be recovered, at the price of contextualizing momentum...

http://publish.uwo.ca/~wmyrvold/Bohm.pdf

 

[tzimie]

Obviously these highly respected members of the forum don't have a consensus on even basic (which doesn't mean simple) questions, so can we say that it is not possible to write interpretation-neutral FAQ for QM section?

 

[Demystifier]

I guess my confusion (and misinterpretation?) is these sentences by Durr et al.

And then Myrvold:

I would say that Durr et al and Myrvold did not make the best choice of words in these particular sentences. Energy and momentum are properties of a Bohmian particle (unlike spin, which is not a property of a Bohmian particle). However, as Durr et al better expressed themselves in several other places, energy and momentum are not primitive properties of a Bohmian particle.

 

[Demystifier]

Obviously these highly respected members of the forum don't have a consensus on even basic (which doesn't mean simple) questions, so can we say that it is not possible to write interpretation-neutral FAQ for QM section?

That's true, because many of the most-frequently asked questions about QM are not interpretation-neutral. Of course, one can always write a truncated FAQ in which such interpretation-dependent questions are ignored, but is that something what one really wants?

 

[atyy]

That's wrong. In BM position and momentum of a particle are canonically conjugate, in the same sense in which they are conjugate in classical mechanics. You can see that by formulating BM in terms of a quantum Hamiltonian, which is the classical Hamiltonian plus the quantum potential. Note also that position and momentum of a Bohmian particle are c-numbers, not operators, so they commute.

OK, that's interesting. Can you give a reference? What goes wrong with the argument that position and momentum cannot simultaneously exist because if you take the Wigner function which is the quantum analogue of the classical joint probability distribution for position and momentum, the Wigner function is in general not a probability distribution?

 

[Demystifier]

OK, that's interesting. Can you give a reference? What goes wrong with the argument that position and momentum cannot simultaneously exist because if you take the Wigner function which is the quantum analogue of the classical joint probability distribution for position and momentum, the Wigner function is in general not a probability distribution?

Unlike Wigner function, BM does define a joint probability density for position and momentum. But in general, the corresponding marginal probability density of momentum is different from the momentum probability density in QM. Indeed, some amateur critiques of BM use this fact as an argument against BM. But it is an invalid argument, because it turns out that in the case of measurement, the two probability densities coincide. For more details see e.g. the Appendix in
http://lanl.arxiv.org/abs/quant-ph/0208185

 

[atyy]

Unlike Wigner function, BM does define a joint probability density for position and momentum. But in general, the corresponding marginal probability density of momentum is different from the momentum probability density in QM. Indeed, some amateur critiques of BM use this fact as an argument against BM. But it is an invalid argument, because it turns out that in the case of measurement, the two probability densities coincide. For more details see e.g. the Appendix in
http://lanl.arxiv.org/abs/quant-ph/0208185

Thanks, let me read the paper. But the general picture is ok, since what I mean is the Wigner function is negative, which is what I am taking as a "no-go theorem". So to be more careful can I say: "In quantum mechanics, in all interpretations, the measured canonically conjugate position and momentum do not simultaneously exist"?

 

[atyy]

Obviously these highly respected members of the forum don't have a consensus on even basic (which doesn't mean simple) questions, so can we say that it is not possible to write interpretation-neutral FAQ for QM section?

That's true, because many of the most-frequently asked questions about QM are not interpretation-neutral. Of course, one can always write a truncated FAQ in which such interpretation-dependent questions are ignored, but is that something what one really wants?

Hang on, let's see if Demystifier and I can sort out this position and momentum thing. My aim is that Copenhagen should be interpretation neutral :) I mean this in the sense that one should be able to simultaneously (!) believe in Copenhagen and any other valid interpretation, such as Bohmian mechanics, ie. Copenhagen and Bohmian mechanics should commute

I think there is hope here since we agree on the equation - the Wigner function is in general not a probability distribution. So if we can put that in simple words, then it would be interpretation neutral. I think there are interpretation neutral things like Bell's theorem, but putting it in clear simple English is usually a bit problematic ("local realism", "local determinism", "local physical"?), but it should be doable.

 

[bhobba]

That's true, because many of the most-frequently asked questions about QM are not interpretation-neutral. Of course, one can always write a truncated FAQ in which such interpretation-dependent questions are ignored, but is that something what one really wants?

I just want to emphasise the importance of what Demytifyer said.

Many, probably even the vast majority, of people into QM couldn't care a hoot about interpretive questions. When I started I wasn't really either - I was interested in mathematical subtleties associated with things such as Rigged Hilbert spaces and the like as well as exactly what is the most elegant mathematical formulation. I only became interested in interpretive things later - especially the role of dehoerence.

Now the lay person is entirely different. They hear on TV, and read about, all this crazy stuff about QM such as particles being in two places at once etc etc. This goes right to the heart of interpretation, the exact area there is the greatest debate amongst those professions that are into it - like I said most probably don't even care.

So they come here hoping to be enlightened, often not even understanding much of the highly technical discussion, and find people arguing about what interests them most.

The rock bottom truth is this - science doesn't have all the answers - and that is especially true on fundamental issues that interest laypersons. In fact what many laypersons are interested in is basically philosophy eg the OP wrote 'In MUH *everything* is "just math", and there is no difference, by definition, between "being real" and "being just math"'. That is really philosophy - although does lead to an important non-philosophy discussion on exactly what a mathematical model is. This again raises another issue - in physics and applied math in general - at university you are not taught what a mathematical model is - you learn it by doing. It actually requires a bit of thought, if you haven't done it before, to answer the just math question. I have answered that one many times from hanging around forums like this so have thought carefully about it - but its something that's not generally taught - you have to nut it out yourself. BTW the answer is its basically the same as good old Euclidean geometry you learned about at school - it mentions things that actually exist like points and lines - physical theories also do that - pure math doesn't - its usually couched in the application neutral language of set theory.

I also want to add, while science doesn't have all the answers, it does have some. The most striking and important is the role of symmetry. It is incredulous that nature is really governed by such an abstract highly mathematical idea - but its true and is one of the truly great discoveries of modern physics that's not generally discussed eg check out Noethers Theorem:
http://www.physics.ucla.edu/~cwp/articles/noether.asg/noether.html

Thanks
Bill

 

[Demystifier]

So to be more careful can I say: "In quantum mechanics, in all interpretations, the measured canonically conjugate position and momentum do not simultaneously exist"?

Define "canonically"!

 

[tzimie]

many laypersons are interested in is basically philosophy eg the OP wrote 'In MUH *everything* is "just math", and there is no difference, by definition, between "being real" and "being just math"'. That is really philosophy

So how do you qualify this article (I am sure you had read it):
http://arxiv.org/abs/0704.0646

1. Science or not?
2. Physics or Philosophy?
3. Useful or Useless?

Do you think that there are some cases where Philosophy can play some role in physics, for example, the eternal inflation/baby universes with different constants is driven mostly by AP, and AP is Philosophy, right?

Do you agree that the observed reality is unfairly "sampled" to an extreme extent - can physics ignore this fact?

 

[Demystifier]

So how do you qualify this article (I am sure you had read it):
http://arxiv.org/abs/0704.0646

1. Science or not?
2. Physics or Philosophy?
3. Useful or Useless?

1. Not.
2. Philosophy.
3. Useful only as a thought provoking.

 

[jtbell]

What is a correct way to answer (here, on PhysicsForums) interpretation-dependent questions?

I would say, "There is no generally-accepted answer to this question. QM proper (the mathematical theory that makes predictions about the results of experiments) simply does not address it, and there is no way (as far as we know) to address it experimentally. Physicists have come up with a variety of possible answers, called "interpretations of QM." However, they all produce the same answers for things that we can test experimentally, therefore one's choice among them has to be based on personal philosophical preferences about the way the universe should work."

 

[Dadface]

I would say, "There is no generally-accepted answer to this question. QM proper (the mathematical theory that makes predictions about the results of experiments) simply does not address it, and there is no way (as far as we know) to address it experimentally. Physicists have come up with a variety of possible answers, called "interpretations of QM." However, they all produce the same answers for things that we can test experimentally, therefore one's choice among them has to be based on personal philosophical preferences about the way the universe should work."

 

[atyy]

Define "canonically"!

How about $[X,P]=i\hbar$?

 

[Demystifier]

How about $[X,P]=i\hbar$?

In this case, the answer is - yes.

 

[atyy]

In this case, the answer is - yes.

I guess the trickly thing is that the other definition of canonically is via the classical Poisson brackets, and the classical Hamilton's equations. Would you have said "no" if I used that definition?

 

[bhobba]

So how do you qualify this article (I am sure you had read it):

It's philosophy pure and simple.

Do you think that there are some cases where Philosophy can play some role in physics, for example, the eternal inflation/baby universes with different constants is driven mostly by AP, and AP is Philosophy, right?

No. My view is the same as Wienberg:
http://www.phys.washington.edu/users/vladi/phys216/Weinberg_Against_philosophy.doc&ei=hqM-VMHiFKnHigKhzYFQ&usg=AFQjCNHg_elaIirwh-1Q7Al_kVaI8Fz8YA&sig2=XoTG_VPG0EcoweZDOisRCw

Do you agree that the observed reality is unfairly "sampled" to an extreme extent - can physics ignore this fact?

I think you need to define reality first and its unlikely your view will, how to put it, meet with the same kind of widespread acceptance scientific facts are.. My view is the best we can do is describe reality, and mathematical models are the best language to do that at the fundamental level.

Thanks
Bill

 

[bohm2]

My view is the same as Wienberg:
http://www.phys.washington.edu/users/vladi/phys216/Weinberg_Against_philosophy.doc&ei=hqM-VMHiFKnHigKhzYFQ&usg=AFQjCNHg_elaIirwh-1Q7Al_kVaI8Fz8YA&sig2=XoTG_VPG0EcoweZDOisRCw

Thanks, that was an excellent piece. But I wonder how accurate this sentence by Weinberg is:

Physicists do of course carry around with them a working philosophy. For most of us, it is a rough-and-ready realism, a belief in the objective reality of the ingredients of our scientific theories.

 

[bhobba]

But I wonder how accurate this sentence by Weinberg is

I think its true.

Simply think back to Euclidean Geometry. It talks about points having no size and lines no width so they don't really exist. But after a while it becomes such second nature you believe they do, by which I mean the point and lines you apply it to are the points and lines the theory talks about.

This goes right to the heart of the issue. Such simple ideas are all that's required to do the physics - questions like what reality, is it just math etc etc are basically of no relevance in actually doing the physics. Laypersons often worry about it - but very few physicists do.

And that view has led to the very striking discovery, no amount of philosophising could have possibly arrived at, that at rock bottom, symmetry is the key. That too is written in the language of math ie group theory.

Thanks
Bill

 

[Demystifier]

I guess the trickly thing is that the other definition of canonically is via the classical Poisson brackets, and the classical Hamilton's equations. Would you have said "no" if I used that definition?

Yes I would.

 

[tzimie]

It's philosophy pure and simple.
No. My view is the same as Wienberg:
http://www.phys.washington.edu/users/vladi/phys216/Weinberg_Against_philosophy.doc&ei=hqM-VMHiFKnHigKhzYFQ&usg=AFQjCNHg_elaIirwh-1Q7Al_kVaI8Fz8YA&sig2=XoTG_VPG0EcoweZDOisRCw

Good article, thank you.
However, it is pure philosophy too :)
So in some sense it is recursive

 

[bhobba]

Good article, thank you. However, it is pure philosophy too :) So in some sense it is recursive

Of course being 'anti' philosophy is itself a philosophy.

But I think most people get the gist.

Thanks
Bill

 

[atyy]

Yes I would.

Thanks a lot for your replies! One reason it's a bit confusing to think of a Hamiltonian version of Bohmian mechanics is that I typically think of the equation of motion for the particles as being first order, whereas Hamiltonian mechanics comes from Newton's laws which is second order. Am I getting confused between de Broglie's and Bohm's examples of possible dynamics?

 

[bohm2]

Thanks a lot for your replies! One reason it's a bit confusing to think of a Hamiltonian version of Bohmian mechanics is that I typically think of the equation of motion for the particles as being first order, whereas Hamiltonian mechanics comes from Newton's laws which is second order. Am I getting confused between de Broglie's and Bohm's examples of possible dynamics?

You might find the papers linked in this thread interesting:
https://www.physicsforums.com/threads/de-broglie-dynamics-fine-bohmian-dynamics-untenable.696231/

 

[Demystifier]

Thanks a lot for your replies! One reason it's a bit confusing to think of a Hamiltonian version of Bohmian mechanics is that I typically think of the equation of motion for the particles as being first order, whereas Hamiltonian mechanics comes from Newton's laws which is second order. Am I getting confused between de Broglie's and Bohm's examples of possible dynamics?

When I speak about Hamiltonian in BM, what I have in mind is a quantum variant of the Hamilton-Jacobi formulation of mechanics, which is a first-order formulation.

 

[atyy]

When I speak about Hamiltonian in BM, what I have in mind is a quantum variant of the Hamilton-Jacobi formulation of mechanics, which is a first-order formulation.

How about in the strictly Hamiltonian framework? In dBB, is it possible to write $\dot{q} = \frac{\partial H(p,q)}{\partial p}, \dot{p} = - \frac{\partial H(p,q)}{\partial q}$ where $q$ is the dBB position, and $p$ is the dBB momentum?

 

[Demystifier]

How about in the strictly Hamiltonian framework? In dBB, is it possible to write $\dot{q} = \frac{\partial H(p,q)}{\partial p}, \dot{p} = - \frac{\partial H(p,q)}{\partial q}$ where $q$ is the dBB position, and $p$ is the dBB momentum?

It is possible and not wrong to write it, but it is misleading. That's because in a strictly Hamiltonian framework the initial conditions q(0) and p(0) are independent, while in BM there is an additional constraint saying that p(0) is a function of q(0).

 

[atyy]

It is possible and not wrong to write it, but it is misleading. That's because in a strictly Hamiltonian framework the initial conditions q(0) and p(0) are independent, while in BM there is an additional constraint saying that p(0) is a function of q(0).

Does the constraint go away in the classical limit ($\hbar \to 0$) of Bohmian mechanics?

 

[Demystifier]

Does the constraint go away in the classical limit ($\hbar \to 0$) of Bohmian mechanics?

Excellent question! The constraint does not go away in the classical limit. Instead, in this limit you get classical mechanics in the Hamilton-Jacobi form, which also has a velocity constraint. I never thought about it this way before, but one can use it to argue that Hamilton-Jacobi formulation of classical mechanics is more fundamental than other formulations.

 

[Sugdub]

The Copenhagen "particle" is nothing but a click in a detector.

In this case, there should exist some description of an SG experiment dealing with a physical process producing a flow of events, analysing the variation of the statistical characteristics of this flow in response to a change of the relative orientation of two devices in the experimental setup. This would be rather different than discussing the behaviour of physical entities moving or propagating from a "source" to a "detector" according to their individual "spin" properties. Can you propose any reference?

 

[bhobba]

dealing with a physical process producing a flow of events

Hmmmm. Flow of events?

Can you give a detailed concrete example?

Thanks
Bill

 

[Sugdub]

Hmmmm. Flow of events?

Can you give a detailed concrete example?

A “click on a detector” as referred to by Demystifier is an event. An SG experiment run in an iterative mode produces a flow of such events distributed over a set of so-called “detectors”. This is a fact. Whether such events can be considered as the “measure” of a property of “something” in the world (e.g. the “spin” of a “particle” moving from a “source” to a “detector”) remains part of an interpretation of the SG experiment. It is not a fact.
If a “particle” is nothing else than a “click on a detector” in the “Copenhagen interpretation”, then I wish to know what gets “filtered” according to this interpretation. How does it describe the SG experiment if it refers to “events” (which is a concept inherent to phenomenology, i.e. what we observe) instead of referring to “particles” (which is a concept relevant to what might happen inside the experimental device, i.e. something we can't observe)?

It should be quite clear that reading the quantum formalism as a formalisation of a phenomenology or reading it as a formalisation of a “simulation of the world” are two different and exclusive paradigms. On which side falls the “Copenhagen interpretation”?
Thanks.

 

[bhobba]

If a “particle” is nothing else than a “click on a detector” in the “Copenhagen interpretation”, then I wish to know what gets “filtered” according to this interpretation.

Nothing - because the particle gets destroyed by the observation - as it is in virtually every observation that occurs in practice.

Only with what are called filtering observations are the objects not destroyed. In that case these days it is generally viewed as a different state preparation procedure. That is true in any interpretation, but the interpretation of what a state is varies between interpretations.

In CI a state is viewed, in most variants (yes CI has a number of variants) simply as a conceptual aid in calculating the probabilities of the outcomes of observation. It's a state of knowledge residing in the head of a theorist, similar to the Bayesian view of probabilities.

It should be quite clear that reading the quantum formalism as a formalisation of a phenomenology or reading it as a formalisation of a “simulation of the world” are two different and exclusive paradigms. On which side falls the “Copenhagen interpretation”?

For me its simply a variant of probability theory that allows continuous transformations between pure states.

Suppose we have a system in 2 states represented by the vectors [0,1] and [1,0]. These states are called pure. These can be randomly presented for observation and you get the vector [p1, p2] where p1 and p2 give the probabilities of observing the pure state. Such states are called mixed. Now consider the matrix A that say after 1 second transforms one pure state to another with rows [0, 1] and [1, 0]. But what happens when A is applied for half a second. Well that would be a matrix U^2 = A. You can work this out and low and behold U is complex. Apply it to a pure state and you get a complex vector. This is something new. Its not a mixed state - but you are forced to it if you want continuous transformations between pure states.

QM is basically the theory that makes sense out of such weird complex probabilities - it does so by the Born rule.

Here is a much more careful development of that view:
http://arxiv.org/pdf/quantph/0101012.pdf

CI is a minimalist interpretation of that formalism where probabilities are viewed the Baysian way. The other common interpretation is the ensemble where the frequentest view is taken.

CI is phenomenology pure and simple.

BM, Many Worlds, Nelson Stochastic's and Primary State Diffusion are examples of 'simulation' type interpretations, although that's not the terminology I would use, nor have I ever seen it in the literature. I would use real.

Thanks
Bill