Teaching Bohmian QM before standard QM

[Demystifier]

In many physics curricula, some elements of the so called "old" (Bohr-Sommerfeld) QM are taught before teaching the actual QM. The pedagogic value of such teaching may be doubtful, but for someone without prior knowledge of QM, the old QM is more intuitive than the actual QM. That's because the conceptual difference between "old" QM and classical mechanics is not so big, while the conceptual difference between actual QM and classical mechanics is much bigger.

Bohmian mechanics, as one of interpretations of the actual QM, is conceptually also quite close to classical mechanics, much closer than the actual QM in the standard form. So perhaps, for pedagogic purposes, it would make sense to teach some elements of Bohmian mechanics before teaching QM in the standard form. What do you think of that?

Those who think that Bohmian interpretation is conceptually misleading may be afraid that such teaching would make more harm than good. But the "old" QM is also misleading, yet it doesn't seem that teaching it makes much harm. So why would Bohmian mechanics be different? Just the opposite, even if Bohmian interpretation is not how the nature actually works, I believe that it can be helpful as an intuitive thinking tool in the process of learning QM.

 

[Minnesota Joe]

In many physics curricula, some elements of the so called "old" (Bohr-Sommerfeld) QM are taught before teaching the actual QM. The pedagogic value of such teaching may be doubtful, but for someone without prior knowledge of QM, the old QM is more intuitive than the actual QM. That's because the conceptual difference between "old" QM and classical mechanics is not so big, while the conceptual difference between actual QM and classical mechanics is much bigger.

Bohmian mechanics, as one of interpretations of the actual QM, is conceptually also quite close to classical mechanics, much closer than the actual QM in the standard form. So perhaps, for pedagogic purposes, it would make sense to teach some elements of Bohmian mechanics before teaching QM in the standard form. What do you think of that?

Introducing a particle and a wave after talking about the apparent wave nature of the electron particle seems like a natural transition to me. It would give de Broglie and Bohm their due!

Imagine discussing Bohmian mechanics before reading Richard Feynman's somewhat defeatist take on the double-slit experiment,

In this chapter we shall tackle immediately the basic element of the mysterious behavior in its most strange form. We choose to examine a phenomenon which is impossible, absolutely impossible, to explain in any classical way, and which has in it the heart of quantum mechanics. In reality, it contains the only mystery. We cannot make the mystery go away by “explaining” how it works. We will just tell you how it works. In telling you how it works we will have told you about the basic peculiarities of all quantum mechanics.

https://www.feynmanlectures.caltech.edu/III_01.html#Ch1-S3

I'd be interested to learn how you would start and what topics you would cover in such a course. The Schrodinger equation, the guidance equation, and the free particle? Would you introduce decoherence? I can't remember even discussing that in my first QM course (but that was a long time ago).

 

[anuttarasammyak]

Physical constants $c$ in relativity and $\hbar$ in QM are not agreeable with mechanics hitherto. Progress of science history, which might be described with Hegelian dialectic of thesis-antithesis-synthesis if you like, would be interesting and nourishing for established scientists. For QM native young students it would be efficient and also economic in time to get thus attained fruits first, history later. I am not qualified at all to prepare such a leaning course program but imagine it could be
1. introduce QM fundamentals e.g. state vector, operator, eigenvalue, commutation relation, path integral and QFT including vacuum state, annihilation and creation
2. show thus introduced quantities correspond those of classical mechanics ( if they have correspondence in classical mechanics ) in formal limit of $\hbar\rightarrow 0$. Ehlenfest's theorem would be a part of it.

 

[Demystifier]

I'd be interested to learn how you would start and what topics you would cover in such a course. The Schrodinger equation, the guidance equation, and the free particle?

Most certainly yes.

Would you introduce decoherence?

In an introductory course I would not introduce density matrices, so decoherence in a technical sense would not be explained. But I would explain the von Neumann theory of quantum measurement, which is technically very simple and is essential for understanding how Bohmian mechanics explains the results of measurements.

I can't remember even discussing that in my first QM course (but that was a long time ago).

Unfortunately, QM first courses (as well as most advanced QM courses) don't explain even the simple von Neumann theory. I think they should.

 

[Minnesota Joe]

In an introductory course I would not introduce density matrices, so decoherence in a technical sense would not be explained. But I would explain the von Neumann theory of quantum measurement, which is technically very simple and is essential for understanding how Bohmian mechanics explains the results of measurements.

That explanation is what I would hope for, good!

Unfortunately, QM first courses (as well as most advanced QM courses) don't explain even the simple von Neumann theory. I think they should.

Do you know I wracked my brain and I'm embarrassed to say that I don't recognize "von Neumann theory of quantum measurement" by name, so you may be right at least for the courses I've taken. I mean I don't recognize it as something that would have been presented to me under that name and searching through textbooks hasn't helped. (Density matrices I have encountered some). Google searching was ambiguous. Given that you say it is essential for understanding measurements in Bohmian mechanics (BM) , the high level descriptions I've read about BM and the measurement problems must be leaning on it. Do you have a good introduction you could recommend?

 

[EPR]

How does an electron with a definite position at all times tunnel through a barrier in the Bohmian interpretation? How is it able to overcome the repulsion forces of like charges?

 

[PeterDonis]

How does an electron with a definite position at all times tunnel through a barrier in the Bohmian interpretation?

By following the trajectory that the Bohmian equation of motion says it does, which takes it through the barrier. The Bohmian equation of motion is not the same as the classical equation of motion, so particles can have definite positions at all times in Bohmian mechanics and still not exhibit classical behavior.

 

[EPR]

By following the trajectory that the Bohmian equation of motion says it does, which takes it through the barrier. The Bohmian equation of motion is not the same as the classical equation of motion, so particles can have definite positions at all times in Bohmian mechanics and still not exhibit classical behavior.

What about the repulsion forces of like charges?

 

[PeterDonis]

What about the repulsion forces of like charges?

What about it? It's included in the equation of motion. But because the equation of motion is not the same as the classical one, you cannot assume that the electron will exhibit classical behavior.

 

[PeroK]

Imagine discussing Bohmian mechanics before reading Richard Feynman's somewhat defeatist take on the double-slit experiment,

It depends what you mean by defeatist. You could say that Goedel's theorem is defeatist, in the sense that it destroyed any hope of a "perfect" mathematical system. Goedel's theorem, of course, could itself be proved, so there was no real argument from mathematicians who didn't want to accept it.

You could see an unwillingness to accept what nature is telling us through QM as defeatist. If QM is correct, then a pursuit of determinism is defeatist.

 

[EPR]

What about it? It's included in the equation of motion. But because the equation of motion is not the same as the classical one, you cannot assume that the electron will exhibit classical behavior.

By 'non-classical behavior' you don't mean the electron has no definite position at all times, do you? Does it have a definite position within the barrier as it traverses over it?

 

[Minnesota Joe]

You could see an unwillingness to accept what nature is telling us through QM as defeatist. If QM is correct, then a pursuit of determinism is defeatist.

What nature is telling us through QM is the very thing at issue. Also, indeterminism isn't what I find somewhat defeatist about the Feynman quote. If the universe is indeterministic, so be it. Some physical theories of QM rely on it.

 

[PeterDonis]

By 'non-classical behavior' you don't mean the electron has no definite position at all times, do you?

Not in the Bohmian interpretation, no.

Does it have a definite position within the barrier as it traverses over it?

In the Bohmian interpretation, yes.

 

[EPR]

Not in the Bohmian interpretation, no.
In the Bohmian interpretation, yes.

I thought so. So, in a sense, there's no classical trajectory for single particles, even in DeBB. It's Hilbert space and the fundamental quantum rules. There is no classical realism to speak of. The DeBB should not be taken to extremes to mean a restoration of classical realism where single particles behave as little particles subject to classical mechanics. In classical electrodynamics the electron would immediately be repelled by the electrons of the barrier. In DeBB it's a Hilbert space-mandated realism subject to the rules of quantum probabilities. Classical realism can be said to be emergent in DeBB as well?

 

[kith]

In classical electrodynamics the electron would immediately be repelled by the electrons of the barrier. In DeBB it's a Hilbert space-mandated realism subject to the rules of quantum probabilities.

No. In DBB, classical realism holds (albeit a nonlocal variant of it). Particles have definite positions at all times. The dBB equation of motion of particles can be written in a form which is very similar to the corresponding equation of motion of classical mechanics. There's an additional term, the so-called quantum potential, which -speaking in Newtonian terms- leads to an additional force which acts on the particle. So tunneling happens when this "quantum force" is bigger than the electromagnetic repulsion.

 

[kith]

@Demystifier: Would you use the quantum potential in your porposal or would you use another formulation of Bohmian mechanics?

 

[atyy]

Standard QM should definitely be taught first. It is more original and beautiful. Or some would say - it is more romantic

Besides, if you use the analogy with old quantum physics, then Bohmian Mechanics should be taught first, in order to be discarded.

 

[PeterDonis]

in a sense, there's no classical trajectory for single particles, even in DeBB

There is no trajectory that obeys a classical equation of motion. But there certainly is a definite trajectory from a given initial position of the particle. Saying "there is no classical trajectory" invites confusion between these two things, which are not the same. You appear to be suffering from that confusion.

There is no classical realism to speak of.

Having trajectories be "real" does not require that they satisfy classical equations of motion.

In DeBB it's a Hilbert space-mandated realism subject to the rules of quantum probabilities.

No, it isn't. In the Bohmian interpretation probabilities are classical probabilities, solely due to our ignorance of the exact initial state of the system (the exact initial position of the particle). There are no "quantum probabilities" in Bohmian mechanics in the sense you mean.

 

[Demystifier]

What about the repulsion forces of like charges?

They are overcame by the quantum force generated by the quantum potential.

 

[Demystifier]

esides, if you use the analogy with old quantum physics, then Bohmian Mechanics should be taught first, in order to be discarded.

Why first?

 

[Demystifier]

@Demystifier: Would you use the quantum potential in your porposal or would you use another formulation of Bohmian mechanics?

Good question. In a serious treatment of BM quantum potential should be avoided, but in an introductory course it's useful.

 

[Demystifier]

I'm embarrassed to say that I don't recognize "von Neumann theory of quantum measurement" by name, so you may be right at least for the courses I've taken.

For a brief review in a non-Bohmian context see e.g. Sec. 6.1 of http://de.arxiv.org/abs/1406.5535

 

[atyy]

Why first?

Well, I was taught old QM first. I have to say though, that we got to the traditional Hilbert space formalism in 3 lessons.

 

[Minnesota Joe]

For a brief review in a non-Bohmian context see e.g. Sec. 6.1 of http://de.arxiv.org/abs/1406.5535

Interesting, thank you! That seems to be the same thing that Bohm and Hiley do in Chapter 2 and Chapter 6 of The Undivided Universe. They even associate it with von Neumann. I don't know why on Earth I didn't think to look there first, but your reference explains it better in my opinion.

 

[Minnesota Joe]

For a brief review in a non-Bohmian context see e.g. Sec. 6.1 of http://de.arxiv.org/abs/1406.5535

This seems like a really neat argument to get what is essentially decoherence just by thinking about what makes a good measurement device. If you just stop there, it demonstrates the measurement problem as well (since you have a super-position but don't observe one). What we see is a Bohmian particle interacting with the measurement device in one of the "channels" of the quantum potential to paraphrase Bohm.

(For anyone that is interested here is another good review of von Neumann measurement theory. This one uses Dirac notation: see Section VIII, page 21 in https://arxiv.org/pdf/1908.03949.pdf. That paper also references one of Bohm's first treatments of it: Quantum Theory (1951) by David Bohm, Chapter 22: Quantum Theory of the Measurement Process. There is a Dover reprint of this that I remember a lot of people having on their shelves. So I probably have encountered this in the past, but not in enough detail to remember it by name apparently.)

@Demystifier Would you discuss non-locality and EPR /GHZ in an undergraduate QM course?

 

[Demystifier]

@Demystifier Would you discuss non-locality and EPR /GHZ in an undergraduate QM course?

Sure. In particular, GHZ (or Hardy) is a much better way than Bell to prove nonlocality.