A Interpretations of the Aharonov-Bohm effect

[Demystifier]

That's the usual beginner's trap in not forgetting to think of particles as classical point particles as soon as quantum effects are important, and here you have a specific phenomenon that can only be understood in terms of quantum mechanics.

Even if I forget about point particles and think only in terms of wave functions, it's still true that the wave function is zero everywhere where the magnetic field is non-zero.

 

[vanhees71]

Great, so in this paper it's worked out that the AB effect is describable within local relativsitic QED, and the observable predictions are gauge invariant. I'm not too surprised ;-).

 

[Demystifier]

Great, so in this paper it's worked out that the AB effect is describable within local relativsitic QED, and the observable predictions are gauge invariant. I'm not too surprised ;-).

I am also not surprised, because the interaction (3) is expressed locally in terms of the potential, not magnetic field. They say explicitly that interaction expressed in terms of the magnetic field would be non-local.

Even if we put my interpretation (that potential in a fixed gauge is "ontic") aside, I think there should be no doubt that the potential is a more fundamental object than the electric and magnetic field.

More fundamental means that more can be derived from it, more fundamental does not mean more directly observable. Indeed, it is very common that things which are more directly observable are less fundamental. Consider e.g. gas vs atom, detector click vs wave function, etc.

 

[vanhees71]

Of course, that's all well known and in no way contradicting anything I said above. You need to express the Hamilton density in terms of the four-potential to get a local QFT. The observables can however only be represented by gauge-independent quantities, and the AB effect is no exception: The phase shift leading to the shift of the observable interference pattern is gauge-independent. Some people call the result that it depends on the magnetic flux, which is an integral over a surface as a "non-locality", but that comes from the errorneous intuitive picture of classical point particles, but electrons from the point of view of local (!) relativistic QFT, are no classical point particles but field quanta.

It's in the same sense "non-local" as the interference pattern in a double-slit experiment without any magnetic field involved. It's then often said "the electron goes through both slits", and this occurs to be weird only, because errorneously people think in terms of classical point particles rather than in terms of the here necessary quantum description. The correct wording rather is "the electron, hitting the double slits, is not localized" in the sense of quantum mechanics (as well as relativistic local quantum theory). All apparent "weirdness" disappears when being a bit more careful with the wording when describing the concise mathematical formulation of QM or QFT in words!

 

[Fra]

What do you guys consider more "fundamental", all the individual scientists and their actual observations, or the scientific community and the consensus they together negotiate by democratic procsesses?

/Fredrik

 

[vanhees71]

There is no democratic process deciding about succuess of failure of a model or theory. Only objective, experimental tests decide this, not some arbitrary social process to reach "consensus".

 

[Fra]

There is no democratic process deciding about succuess of failure of a model or theory. Only objective, experimental tests decide this, not some arbitrary social process to reach "consensus".

I didn't mean to focusg in sociology here. I was more thinking that what if some individual scientists are using biased or otherwith strange apparatous, or performing their experiments from odd labframes. All detector hits are real, and objective wether the inference-machinery is "optimal" or not. Marginalizing outliers can be thought of as democratic method. Or let's call it statistical process if that makes you more comfortable, but that misses the key mechanism that sometimes one researcher can point out to another one that, hey I think your apparatous is bad, it's part of the "democratic process", to either align or kick out the outliers.

/Fredrik

 

[Demystifier]

in no way contradicting anything I said above.

Except in post #84. The electron wave function interacts locally with the gauge potential, not with the magnetic field. You are right that the essence of the AB effect is interference, but it depends on the phase of the wave function, which is described by the potential. Sure, the result is gauge invariant, and can even be written down in terms of magnetic field, but the description in terms of magnetic field is not local. A local description requires the gauge field.

 

[gentzen]

What do you guys consider more "fundamental", all the individual scientists and their actual observations, or the scientific community and the consensus they together negotiate by democratic procsesses?

Your question might indicate that you don't "feel" just how compatible classical communication is with quantum mechanics. You don't need to invoke any dubious classical limit for that. At least I was first surprised when somebody explained that in a way that I really could "feel" it:

TL;DR: The ban on copying is not nearly as universal as it might seem. No-cloning theorem actually allows copying as long as it is limited to orthogonal states. Classical information is the type of information which is encoded in orthogonal states, so it may be copied.

An individual scientist can just read what other scientists have done in the past, and talk with still living scientist. And the observations of other scientists are often not significantly more dubious than his own observations. After all, his own observations are often not as well-controlled as they should be. On the other hand, neither are many published observations. Still, both provide valuable information about how things work.

 

[Davephaelon]

I honestly don't understand the AB effect, despite extensive reading and watching Youtube videos (granted these videos are not good sources for information, but do help in visualization). It's baffling that 'something' that is not there (the vector potential A) can affect electrons passing either side of the solenoid. In any case, reading Hans de Vries paper (http://www.physics-quest.org/Book_Lorentz_force_from_Klein_Gordon.pdf), which was linked in another thread on Physics Forums, I discovered a new wrinkle in the AB effect that I wasn't previously aware of. On page 4 of this paper he states: "A change in the current through the solenoid leads to a change in the phase difference which then causes a change of the interference pattern on the detector plate." Now I always thought that the magnetic AB effect entailed a constant current through the solenoid; an impression I got from earlier reading and the aforementioned videos. But Hans seems to be saying that for the AB effect to manifest the current in the solenoid must be changing.

 

[Davephaelon]

Oops, I goofed. I was referring to the magnetic field outside the solenoid for "something" that not physically in the space outside the solenoid, not the magnetic vector potential as I stated.

 

[Demystifier]

It's baffling that 'something' that is not there (the vector potential A) can affect electrons passing either side of the solenoid.

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

 

[Fra]

Your question might indicate that you don't "feel" just how compatible classical communication is with quantum mechanics. You don't need to invoke any dubious classical limit for that. At least I was first surprised when somebody explained that in a way that I really could "feel" it:An individual scientist can just read what other scientists have done in the past, and talk with still living scientist. And the observations of other scientists are often not significantly more dubious than his own observations. After all, his own observations are often not as well-controlled as they should be. On the other hand, neither are many published observations. Still, both provide valuable information about how things work.

Not sure what association you had here, but it sounds like something else than what I meant? Classical communication and information sharing is even a pre-requisute for formulating QM in it's current form as I see it. This is why I enjoy the copenhagen interpretation for the non-modified theory.

But the problem of that stance, is that it pushes the observer out to asymptotic scattering observations, the only solulutiuon is "more of the same". The opposite of what it takes transform the theory to an inside observer and consider interacting observers. We expect also quantum interactings betwee observers, not just classical interactions. We also expect a universal attraction betweeen observers, right?

This is why I think building off the classical backdrop, also limits the theory to subatomic physics, without insights into how interactions may unify at high energies, without the expected facing unnatural finetuning.

My train of thought to the subjective gauge choices is that certain gauges are "natural" from the perspective of actual agents, and that this thus MAYBE be more fundamental starting point, to explain which gauge transformations nature implements. Perhaps the reality in this is that the gauge transformations is the manifestation of how the parts(ie agents) relate to each other.

/Fredrik

 

[vanhees71]

I didn't mean to focusg in sociology here. I was more thinking that what if some individual scientists are using biased or otherwith strange apparatous, or performing their experiments from odd labframes. All detector hits are real, and objective wether the inference-machinery is "optimal" or not. Marginalizing outliers can be thought of as democratic method. Or let's call it statistical process if that makes you more comfortable, but that misses the key mechanism that sometimes one researcher can point out to another one that, hey I think your apparatous is bad, it's part of the "democratic process", to either align or kick out the outliers.

/Fredrik

Well, that's why experiments must be reproducible to be taken serious, i.e., it must be possible to check each experiment independently, in the best case by completely independent researchers. All this has nothing to do with a kind of political decision process, be it democratic or not.

 

[martinbn]

Except in post #84. The electron wave function interacts locally with the gauge potential, not with the magnetic field. You are right that the essence of the AB effect is interference, but it depends on the phase of the wave function, which is described by the potential. Sure, the result is gauge invariant, and can even be written down in terms of magnetic field, but the description in terms of magnetic field is not local. A local description requires the gauge field.

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

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

 

[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?