Interpretations of the Aharonov-Bohm effect

[Demystifier]

I don't believe you. It is not just a tool for thinking. If it were you wouldn't have started this discussion.

Discussion is a tool for thinking too.

 

[Demystifier]

Isn't the BA effect a kind of interacting case.

Yes it is, but it doesn't mean that one must use the interaction picture.

 

[Demystifier]

Which one? Any? There is one true one, but we can never tell? This is similar to the notion of preferred frame.

Already said.

You claimed something more, that the AB effect implies that something is real,

When I say that something is real, I mean it's useful to think that it's real.

that there exist additional matter fields to the known ones, additional interactions/actions and so on.

I never said such things, that was only your misinterpretation of my words.

 

[Demystifier]

You can call this "ontic" or however you want, it doesn't change the mathematical facts behind the formulation of a gauge theory.

Of course, being ontic is not a mathematical property. Mathematics is a powerful tool that can describe a lot, but it cannot describe everything. Some questions require non-mathematical tools. One can choose to ignore such questions because they are not precise, but I choose not to ignore them.

 

[JandeWandelaar]

Yes it is, but it doesn't mean that one must use the interaction picture.

Yes it is, but it doesn't mean that one must use the interaction picture.

But you could view is as an interaction with zero energy- momentum transfer. Virtual particles .can have any combination, which makes then ideal to couple to for interaction, making sure the right energies and momenta are transferred (the Diract deltas at the vertices). Can't the transfer a phase difference only? Of course you have to consider the virtual particles as some real stuff. And why should non-observability make them unreal, virtual?

 

[Spinnor]

Reading Feynman lectures, vol. 2 starting at section 15-4 Feynman seems to argue yes, the vector potential is "real".

https://www.feynmanlectures.caltech.edu/II_15.html

 

[Demystifier]

Reading Feynman lectures, vol. 2 starting at section 15-4 Feynman seems to argue yes, the vector potential is "real".

https://www.feynmanlectures.caltech.edu/II_15.html

"What we mean here by a “real” field is this: a real field is a mathematical function we use for avoiding the idea of action at a distance. ... You may be wondering about the fact that the vector potential is not unique—that it can be changed by adding the gradient of any scalar with no change at all in the forces on particles. That has not, however, anything to do with the question of reality in the sense that we are talking about."

 

[JandeWandelaar]

"What we mean here by a “real” field is this: a real field is a mathematical function we use for avoiding the idea of action at a distance. ... You may be wondering about the fact that the vector potential is not unique—that it can be changed by adding the gradient of any scalar with no change at all in the forces on particles. That has not, however, anything to do with the question of reality in the sense that we are talking about."

In the case of the BA effect it IS real. The phase is globally changed without real changes in energies or momenta. There is a visible change in the interference pattern. Is the virtual field to which charged particles couple just that, virtual? Of course NOT. How else can it influence real particles?

 

[martinbn]

"What we mean here by a “real” field is this: a real field is a mathematical function we use for avoiding the idea of action at a distance.

Right in the beginning he also says "First we should say that the phrase “a real field” is not very meaningful". But also what you quoted shows that he is not talking about "real" in the ontological sense. If it is all game of words to you, then here you go. Everything can be completely understood by using real numbers, therefore the potential is real. Here by real we mean that only real numbers are used. Q.E.D.

... You may be wondering about the fact that the vector potential is not unique—that it can be changed by adding the gradient of any scalar with no change at all in the forces on particles. That has not, however, anything to do with the question of reality in the sense that we are talking about."

One also might be wondering that the vector potential does not exist (in the mathematical sense of the word) if the region is not simplyconnected. Here is a standard example let $\omega = \frac{-y}{x^2+y^2}dx+\frac{x}{x^2+y^2}dy$. There isn't a function $f$ such that $df=\omega$, although the necessary condition is satisfied. Is it usfull to think that there is such an $f$? Is such an $f$ (forget that it doesn't exist) real?

 

[martinbn]

Already said.

You could say it again, or point to the post that said it.

When I say that something is real, I mean it's useful to think that it's real.

So unicorns exist, because when I say exist I mean it is useful to think they exist!

I never said such things, that was only your misinterpretation of my words.

I repeatedly asked you to clarify and you either gave unclear answers or simply refused to asnwer! I could I possible be misintepreting your words!

 

[martinbn]

In the case of the BA effect it IS real.

Is there any reason to switch the name to BA from AB?

 

[JandeWandelaar]

Is there any reason to switch the name to BA from AB?

Ah! I didn't realize! I must say that I like Böhm! He was called a childish Trotskyan in his time! Imagine that. For introducing hidden variables...A hidden agenda!

 

[Demystifier]

So unicorns exist, because when I say exist I mean it is useful to think they exist!

How is it useful for you?

For me, if I watch a fantasy movie about unicorns, I can better enjoy the movie if, during the watching, I feel as if they exist. I have no idea how thinking that unicorns exist could help me to understand science, but if it could, I would embrace such a mode of thinking even in science.

 

[vanhees71]

Of course, being ontic is not a mathematical property. Mathematics is a powerful tool that can describe a lot, but it cannot describe everything. Some questions require non-mathematical tools. One can choose to ignore such questions because they are not precise, but I choose not to ignore them.

So "ontic" is an empty phrase to make some impression of erudition at a party? Well, yes, that's what philosophy is mostly good for. SCNR.

 

[Demystifier]

So "ontic" is an empty phrase to make some impression of erudition at a party? Well, yes, that's what philosophy is mostly good for. SCNR.

A dialogue on a party:
Young attractive girl: So, what do you do?
Me: I'm a theoretical physicist.
She: You mean like Sheldon? Sounds nerdish.
Me: No, I study ontology.
She: Oncology? So you are a doctor?
Me: No, ontology. I am a doctor, but not that kind of doctor.
She: OK, so what is this ontology thing?
Me: It's hard to explain, even my colleagues theoretical physicists don't understand it. Even Sheldon doesn't understand it.
She: So you are smarter than Sheldon, but not a nerd?
Me: Exactly.
She: And nobody understands what is this ontology thing you study?
Me: I didn't say that. Nerds don't understand it, but I think you could understand it.
She: So explain it to me!
Me: Not here, it's too loud here.
She: Shall we go to my place?
Me: OK.

 

[PeterDonis]

I study ontology.

I thought ontology was philosophy, not physics. Although I can see how it would be harder to get away with the play you're describing here if you led with "I'm a philosopher".

 

[WernerQH]

We are constantly being cautioned not to think of electrons and photons as waves or particles. We should rather talk about excitations of quantum fields. But the problem with quantum theory is the absence of a clear concept of what it is about. (Yes, its ontology!) It is not enough to point at the mathematics. Saying that quantum theory is about wave functions and field operators is as helpful as saying that classical mechanics is about differential equations.

 

[martinbn]

...
Me: No, I study ontology.
...

That's ironic. In this thread I made the assumption that you are talking about existence of things, only for you to object that it is not the case and I misinterpreted your words.

 

[Demystifier]

That's ironic.

She didn't see it that way, and that's all what matters in the context of the dialogue.

 

[vanhees71]

We are constantly being cautioned not to think of electrons and photons as waves or particles. We should rather talk about excitations of quantum fields. But the problem with quantum theory is the absence of a clear concept of what it is about. (Yes, its ontology!) It is not enough to point at the mathematics. Saying that quantum theory is about wave functions and field operators is as helpful as saying that classical mechanics is about differential equations.

But the physical part of QT is very clear, because it describes, as far as we know today, correctly all observations. It predicts the probabilities for the outcomes of measurements given the state of the measured system.

 

[Demystifier]

But the physical part of QT is very clear, because it describes, as far as we know today, correctly all observations. It predicts the probabilities for the outcomes of measurements given the state of the measured system.

Nobody denies that. But some people want to understand the non-physical part. Obviously, physics cannot answer all the questions that humans care about. Some physicists want a strict separation between physics and non-physics, and want to ban questions that combine insights from both sides. They are afraid that such combinations will ruin the purity of physics, and they certainly will. But too much purity is not a good thing, some mixture of physics with non-physics is welcome. Exactly how much of such a mixture is welcome, and how much is too much, there is no consensus on that.

 

[PeterDonis]

some people want to understand the non-physical part.

QT is a theory of physics. What "non-physical part" would such a theory have?

The issue that I see is that, at least for some, QT is an incomplete theory of physics. It allows you to predict probabilities for measurement results, but doesn't tell you "what is really going on" the way that classical theories did.

Obviously, physics cannot answer all the questions that humans care about.

This is not at all the same as claiming that a physical theory should have a "non-physical part".

In fact, it's not even the same as claiming that other things that humans care about are not ultimately dependent on physics. To most physicists, they are, since they are all ultimately made of the things that our theories of physics describe.

 

[Fra]

What is observer gauge?

The observer gauge I see it as a "thinking tool", and guiding principle for theory building to use your terminology.

It conceptually see it as corresponding to the choice of mathematical information structure that is associated with an observer, and which encodes the effective "hilbert space" for that observer, or whatever the generalization would be called. The corresponding "transformation" would generate all possible observers, and the gauges itself can be thought of as what gives distinguishes observers. What the explicit full emergent observer symmetry is like from the agent perspective that corresponds to our world is of course an open question, this is the million dollar question I guess.

But roughly speaking, this emergent symmetry would be expected to split off into a spacetime part and and internal structure part. But the thinking tool has the ambition to explain, why 4D, and what the symmetry groups of particle physics are like they are. And why no other symmetries are seen.

Traditionally by "observer" and observer invariance we only mean the reference/coordinate frames. ie. special and general relativity. But once you adopt the agent stance, it seems quote obvious that there is much more descriptors to an observer than it's motion in spacetime. It also has it’s internal degrees of freedom, and some mass or complexity limit with has the effect of a lossy retention of the full interaction history.

The difference in the thinking tool, is that the "freedom to choose" observer is not void of physical siginficance. Instead of thinking of it as a mathematical choice that makes not difference. Difference observers here - while all equally valid - have different fitness. And the set of observers is considered the real population in the real universe, not just a fictive ensemble.

/Fredrik

 

[Davephaelon]

An interesting paper i found today that might be relevant: https://journals.aps.org/pra/abstract/10.1103/PhysRevA.86.040101
(https://arxiv.org/abs/1110.6169)

and a reply to the above paper: https://arxiv.org/abs/1604.05748

This paper by Lev Vaidman I find very interesting. I'm only able to read the abstract for now, but what he seems to be saying, is that the Aharonov-Bohm (AB) effect is essentially the same thing as quantum entanglement, and there's no need to invoke the potential concept to explain the AB effect. This is appealing as it brings the AB effect under a common roof with other phenomena that are explained by entanglement yielding a simplification; sort of like when Maxwell united electricity and magnetism. I'll print out the paper at our local library tomorrow, though I suspect it will be quite technical and over my head.

 

[Davephaelon]

I should have read the rebuttal to Vaidman's paper, by Aharonov, Cohen, and Rohrlich, that is also linked above before making the above comment. It's actually not too hard to follow their analysis at the beginning, but I will have to do some deep thinking to follow their arguments all the way through to the end of the short paper.

 

[Demystifier]

What "non-physical part" would such a theory have?

I was using the terminology of @vanhees71, for whom "non-physical" part means interpretational aspects that do not affect measurable predictions. Each physical theory, in that sense, has a "non-physical" interpretational part. For example, in Newtonian celestial mechanics it is taken for granted that the planet Mars is there even when nobody observes it. Of course, if I was not replying to vanhees71, I would not call it "non-physical".

 

[Demystifier]

This is appealing as it brings ... under a common roof with other phenomena that are explained by entanglement yielding a simplification

Then you might be interested in my https://arxiv.org/abs/1203.1139

 

[vanhees71]

QT is a theory of physics. What "non-physical part" would such a theory have?

The issue that I see is that, at least for some, QT is an incomplete theory of physics. It allows you to predict probabilities for measurement results, but doesn't tell you "what is really going on" the way that classical theories did.

According to QT the probabilities are all there is, i.e., the observables only take determined values if the system is prepared in a corresponding state (in the most simple case described by an eigenstate of the self-adjoint operator presenting this observable). All other observables do not take determined values before measured. This were only incomplete a description if you could empirically demonstrate that this prediction of "indeterminacy" is wrong, but there are very strong hints that in fact QT is correct. All Bell text demonstrate at least that there is no local HV model that all observables take predetermined (but maybe unknown) values all the time. So people, who claim that QT were incomplete, should have some empirical evidence for it. Philosophical prejudices are not argument within the natural sciences!

This is not at all the same as claiming that a physical theory should have a "non-physical part".

In fact, it's not even the same as claiming that other things that humans care about are not ultimately dependent on physics. To most physicists, they are, since they are all ultimately made of the things that our theories of physics describe.

What should such a "non-physical part" be?

There is of course much more humans care about than the natural sciences investigate and describe, but of course the human condition as a whole depends on the objective natural laws described by the natural sciences.

 

[martinbn]

I was using the terminology of @vanhees71, for whom "non-physical" part means interpretational aspects that do not affect measurable predictions. Each physical theory, in that sense, has a "non-physical" interpretational part. For example, in Newtonian celestial mechanics it is taken for granted that the planet Mars is there even when nobody observes it. Of course, if I was not replying to vanhees71, I would not call it "non-physical".

This is not a good example. In Newtonian mechanics "Mars is there" is not an interpretation but part of the core theory. The observalbes, in this case position, have values at all times whether they are being measured or not.

 

[JandeWandelaar]

Is there any reason to switch the name to BA from AB?

QT is a theory of physics. What "non-physical part" would such a theory have?

The issue that I see is that, at least for some, QT is an incomplete theory of physics. It allows you to predict probabilities for measurement results, but doesn't tell you "what is really going on" the way that classical theories did.This is not at all the same as claiming that a physical theory should have a "non-physical part".

In fact, it's not even the same as claiming that other things that humans care about are not ultimately dependent on physics. To most physicists, they are, since they are all ultimately made of the things that our theories of physics describe.

Physical theories can't describe though what a particle is. You can say it's an excitation of a field, an operator valu8ed distribution, but they create or destroy states which refer to wavefunctions. A wavefunction gives the probabilities of finding particles, A particle is said to be a point-like 1D "structure". Or maybe a string or even something more exotic. But then again, what stuff is a string, or why does it vibrate? What is space made of? The content seems non-physical, and maybe lies at the root of consciousness.