Interpretations of the Aharonov-Bohm effect

[martinbn]

Unless the vector potential is there. That's the main idea of this whole thread as I see it.

Again, what do you mean by the vector potential? There is just one? And what do you mean that it is there? Where? In the Platonic world of ideas?

 

[Fra]

Well, that's why experiments must be reproducible to be taken serious, i.e., it must be possible to check each experimnt .

Sure, but my implicit but subtle point was that a real observer or reasearcher needs to take actions based on incomplete information that is at hand here and now, and decide in finite time. You refer to asymptotic procedures. How do we envison that nature enforce the laws in similar situations? So which comes first, the trial and error that may lead to perfection at infinity unless the subject matter changes too fast, or the constraint of perfection? I think this is influenced by how we understand causality in nature.

/Fredrik

 

[vanhees71]

Of course all knowledge in the natural sciences is always preliminary. If we discover new phenomena, they may well contradict our present models or theories. Of course, you have to first analyze whether there's some mistake in the experimental setup or in the theoretical description of the experiment using the present theories:

E.g., take the OPERA experiment, claiming some years ago there were "faster-than light neutrinos". It is, of course, extremely likely that there was some error in the experimental setup, because of all the highly accurate tests of the relativistic spacetime structure and relativistic QFT as a description being consistent with this spacetime structure. It's of course also not completely impossible that maybe OPERA has really discovered some really new physics, and that's why it was investigated so vigorously, also by independent other experiments. Finally the error in the experimental setup has been found (a bad junction of glass fibers or something like that, if I remember right).

That's in no way some political/democratic process but just hard scientific empirical work.

 

[Fra]

Of course all knowledge in the natural sciences is always preliminary. If we discover new phenomena, they may well contradict our present models or theories.
...
That's in no way some political/democratic process but just hard scientific empirical work.

My choice of words here causes misunderstanding sorry. I though it was a good choice but maybe not. While scienctific work, resources planning etc, does contain political and social components to a certain extent, it was NOT my intention to bring this up here and it was not my point at all. That has also been discussed elsewhere.

With observer democracy let's go back to the constructing principes of relativity:

The guiding principle of relativity (special as well as general) is that nature can not distinguish between observers. Ie. whatever anyone observer sees, must be an equally valid description of nature as that of another one. This is the essentially the origin of the "observer democracy".

There are paths forward from this

1) Strong version (adds consistency requirement)
Presume that the different views(observer-gauges) must be consistent and form a strict equivalence relation. And that the set of all "views" from the set of all possible observers, form a transformation group with some invariants that we can consider to be "physical". This is the traditional choice, and this also gives us a powerful tool for theorymaking. This principle is paramount to most modern physics.

2) Weak version(original version)
Maintain that the voice of any observer will count as much as any other voice, but not necessarily presume the existence of an agreement. That two observer fail to agree, is not necesarily a problem per see for nature, why would it be? it just means that the two observers most certainly will get into conflict(read interaction). (This conflict is what in the strong version is countered by explicit fields that counter the transformation terms exactly. So consistent "requires" new fields.) But in the weak version can consider the negotiation between observers as a physical evolutionary process. A stable state is not a priori assumed, but certainly expected eventually, and these steady states will correspond to the same symmetries as the strong version, but with additional explanatory power, as it considers the process of forging the asymptotic laws of physics that we observe.

Not suprisingly I reject the strong version but accept and seek to develop the weak version. But in the context of physical agents.

/Fredrik

 

[JandeWandelaar]

Let me first answer you with the question. In the conventional view, what does the electric field correspond to?

A more direct answer is this. It corresponds to some continuous stuff filling the space, a stuff which is responsible for various phenomena such as accelerations of charges or the Aharonov-Bohm effect.

Do you make the comparison with virtual particles here. They are not observable too but certainly have effect. I don't believe they are mere aids for calculation.

 

[Demystifier]

Do you make the comparison with virtual particles here. They are not observable too but certainly have effect. I don't believe they are mere aids for calculation.

That's another topic, on which we already have several threads.

 

[Demystifier]

What do you mean by "the wave function interacts with the gauge potential"? How can two mathematical objects interact!

By having an interacting term in the equations that describe them.

What do you mean by the gauge field? Is there just one, or do you have one in mind?

Already answered. Hint: fixed gauge.

 

[Demystifier]

And what do you mean that it is there? Where? In the Platonic world of ideas?

Read again my paper! For me, interpreting something as "ontic" is a tool for thinking. So yes, it's akin to the Platonic world of ideas. Two questions are relevant here. First, is the idea of ontic useful? It is for some people, the others are not obliged to use it. Second, is the idea consistent? Nobody so far in this thread seriously attempted to show that it isn't.

 

[JandeWandelaar]

That's another topic, on which we already have several threads.

The A-field can be seen as build up from virtual photons. So can the change in phase.

 

[Demystifier]

The A-field can be seen as build up from virtual photons. So can the change in phase.

It's true in the Dirac interaction picture, but not in the Schrodinger and the Heisenberg picture. I don't see a reason to think that Dirac picture is anything more than a convenient mathematical trick. But if thinking in terms of virtual particles as being real makes things more intuitive for you, I'm fine with that. However, be prepared to revise your intuition when dealing with non-perturbative effects, where description in terms of virtual particles fails.

 

[JandeWandelaar]

It's true in the Dirac interaction picture, but not in the Schrodinger and the Heisenberg picture. I don't see a reason to think that Dirac picture is anything more than a convenient mathematical trick. But if thinking in terms of virtual particles as being real makes things more intuitive for you, I'm fine with that. However, be prepared to revise your intuition when dealing with non-perturbative effects, where description in terms of virtual particles fails.

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

 

[vanhees71]

Read again my paper! For me, interpreting something as "ontic" is a tool for thinking. So yes, it's akin to the Platonic world of ideas. Two questions are relevant here. First, is the idea of ontic useful? It is for some people, the others are not obliged to use it. Second, is the idea consistent? Nobody so far in this thread seriously attempted to show that it isn't.

There is no need to attempt to show that the idea that the em. potentials in some fixed gauge have a particular physical meaning, is flawed, because this is mathematical property. It has in this sense nothing to do with any kind of philosophical interpretational issue: Any other set of potentials differing from these potentials by a gauge transformation are describing exactly the same physics, and that's why observable quantities must be gauge-independent. You can call this "ontic" or however you want, it doesn't change the mathematical facts behind the formulation of a gauge theory.

 

[martinbn]

By having an interacting term in the equations that describe them.

Then why not be explicit about it? In a thread about existence and reality of thing, you need to be as clear as possible.

Already answered. Hint: fixed gauge.

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

Read again my paper! For me, interpreting something as "ontic" is a tool for thinking. So yes, it's akin to the Platonic world of ideas. Two questions are relevant here. First, is the idea of ontic useful? It is for some people, the others are not obliged to use it. Second, is the idea consistent? Nobody so far in this thread seriously attempted to show that it isn't.

I don't believe you. It is not just a tool for thinking. If it were you wouldn't have started this discussion. You claimed something more, that the AB effect implies that something is real, that there exist additional matter fields to the known ones, additional interactions/actions and so on.

 

[Fra]

interpreting something as "ontic" is a tool for thinking.
...
First, is the idea of ontic useful? It is for some people, the others are not obliged to use it. Second, is the idea consistent? Nobody so far in this thread seriously attempted to show that it isn't.

I do not connect with Bohmian thinking, but I would give you the benefit of doubt that this can be useful and consistent in principle. Especially because I see an analogy with this to my own thinking.

Given your occasional solipsist HV ideass, it seems natural to associate the gauge fixing to the observer fixing. I may sound strange as the it seems very alien to Bohmian logic to highlight the observer, but that actually can make sense.

From the qbist and agent stance, one always works in a fixed observer gauge. There simply is no way to observe nature from any other perspective than the inside. The illustion of unbiased observation are I think wishful thinking. Which means; choose an observer. Once chosen, it's her observations that matters and that are ontic, and this is in a way hidden from others.

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

But there is always a preferred frame - Mine. (no pun intended)

How I communicate and negotiate my preferred experiences with others, is another topic and an interesting one. But there is no outside view, and no "neutral" processing grounds for comparing views, where would that be? And it's the place where one compare the views, that the patternline like laws emerge.

What makes rejecting the observer as a mathematical gauge choice is that if one consider that the observer is a physical system, then the encoded information the observer has acquired must be encoded in matter, and thus be real. And what is certain gauges makes the encoding more efficient? would it then not at least be remotely possible that the reality of the "gauges" has a physical preferences in the chosen frame? I find it to actually be conceptually inconsistent to deny the physical basis of observer gauges.

I do not think we fully understand the full observer symmetry yet. Most physics is about spacetime symmetries, but a real observers should have more qualities, like internal structure, that also is a kind of observer gauge, right?

I can honsetly say that I do not like Bohmian mechanics, but after seeing some of Demystifiers ponderings it seems at least not out question that such ideas might meet up with other research fronts in the future.

/Fredrik

 

[Demystifier]

one always works in a fixed observer gauge

What is observer gauge?

 

[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.