Interpretations of the Aharonov-Bohm effect

[Davephaelon]

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

Thanks for referring me to your paper, which I just brought up on my screen.

 

[PeterDonis]

it should be clear that all physical theories are complete as long as there is no reproducible phenomenon that proves them wrong.

Complete as far as their predictions go, yes. But not everyone uses that definition of "complete".

 

[Fra]

To add to the old post:

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".

While these ideas are not yet a set of homogenous ideas, but ideas in such a direction exists, that puts what I meant in a better perspective than sociology, for example here in a reasonably recent papers from Smolin:

Views, variety and quantum mechanics
"Also, without space, what is a reference system? What is the purpose of a symmetry? Einstein had several different motivations in his search for general relativity. Rather late in the process, he understood the role of gauge invariance under active diffeomorphisms. It took a good think through the hole experiment-which he initially misunderstood. Once he had that he was essentally done. But another motivation was to relativize the concept of inertia so that there was an expansion of the relativity principle from an equivalence of inertial frames to a general principle of relativity underwhich all frameswould be equivalent. In this he failed,which is good because the premise is wrong.
...
There seems to be no equivalence between inertial and accelerating motion. But if space takes a walk that distinction also disappears and there is a path to start with a general equivalence of observers. This is the motivation for what follows.
...
We democratize and universalize the notion of a frame of reference by replacing it with the notion of a view of an event."
-- Lee Smolin, https://arxiv.org/abs/2105.03539v1

And this related one...
The dynamics of difference
"A proposal is made for a fundamental theory, in which the history of the universe
is constituted of views of itself. Views are attributes of events, and the theory’s only
be-ables; they comprise information about energy and momentum transferred to an
event fromits causal past. A dynamics is proposed for a universe constituted of views
of events, which combines the energetic causal set dynamics with a potential energy
based on a measure of the distinctiveness of the views, called the variety[14]. As in
the real ensemble formulation of quantum mechanics[11], quantum pure states are
associated to ensembles of similar events; the quantum potential of Bohm then arises
from the variety."
-- Smolin, https://arxiv.org/abs/1712.04799v3

/Fredrik

 

[JandeWandelaar]

Depends on the theory. QM doesn't, but classical physics did. That's why some people think QM is an incomplete theory.

Is that the incompleteness of QM? Isn't the hidden variable interpretation solving that? Which, by the way, wouldn't answer the question what exactly a particle is. I mean, you can assign properties, like charge, but what then is charge exactly? Can physics ever tell?

 

[PeterDonis]

Is that the incompleteness of QM? Isn't the hidden variable interpretation solving that?

No interpretation can "solve" anything since all QM interpretations make the same experimental predictions, and in any case, as I said, we currently can't experimentally test whether macroscopic objects exhibit quantum effects or not. Interpretations of QM at this point are just forms of speculation or personal opinions about how our future knowledge might develop--but none of those developments have happened yet.

 

[PeterDonis]

Can physics ever tell?

Physics can never answer all possible questions. Any physical theory will eventually "bottom out" in statements that cannot be analyzed further.

 

[JandeWandelaar]

No interpretation can "solve" anything since all QM interpretations make the same experimental predictions, and in any case, as I said, we currently can't experimentally test whether macroscopic objects exhibit quantum effects or not. Interpretations of QM at this point are just forms of speculation or personal opinions about how our future knowledge might develop--but none of those developments have happened yet.

I think though that an interpretation that offers a mechanism for chance is to be preferred. I find "empty" chance hard to imagine.

 

[JandeWandelaar]

Fine, but it should be clear that all physical theories are complete as long as there is no reproducible phenomenon that proves them wrong. Then you need to refine the theory or even find a completely new one. The old theory then doesn't become completely obsolete but you learn about the constraints of their applicability. There's no constraint yet known concerning quantum theory.

It's also clear that there's still no satisfactory quantum theory of the gravitational interaction. In this sense QT is also incomplete, but as far as particle physics is concerned, quantum gravity effects are very hard to observe, so that at least FAPP concerning particles QT is complete.

I think a non-pointlike structure of gravitons eliminates singularities. How can a black hole singularity (or divergence of integrals) form if particles are non-pointlike? (Just an aside, I know its not mainstream, but strings are not point-like either).

 

[JandeWandelaar]

Not everywhere. If you have a region of space where there is no magnetic field anywhere (for example, a double slit experiment with no solenoid placed between the slits), there will be no Aharonov-Bohm effect.

Is it the B-field inside the solenoid that induces the phaseshift of the electron field? Isn't a gauge on the electron field performed?

 

[PeterDonis]

I think though that an interpretation that offers a mechanism for chance is to be preferred.

Which is your personal opinion. Maybe some day we'll be able to test such things. But we can't now, so it all comes down to people's opinions. There's no way to settle such questions unless and until we can do so by experiment.

 

[PeterDonis]

Is it the B-field inside the solenoid that induces the phaseshift of the electron field?

What do you think? If the B field inside the solenoid is not there, there is no effect. If the B field inside the solenoid is there, there is an effect. What does that tell you?

Isn't a gauge on the electron field performed?

How would you do such a thing? What does "performing a gauge on the electron field" mean experimentally? Experimentally, the thing that makes the difference is whether the solenoid with its B field is there or not.

 

[JandeWandelaar]

What do you think? If the B field inside the solenoid is not there, there is no effect. If the B field inside the solenoid is there, there is an effect. What does that tell you?How would you do such a thing? What does "performing a gauge on the electron field" mean experimentally? Experimentally, the thing that makes the difference is whether the solenoid with its B field is there or not.

There is a B-field in the thin solenoid only. But no B-field outside it. An example of non-locality?

Isn't the phase of the electron field changed globally on both sides of the solenoid? If you reverse the current, the pattern shifts to the opposite side. Isn't a gauge performed on the field?

 

[PeterDonis]

There is a B-field in the thin solenoid only. But no B-field outside it. An example of non-locality?

Possibly. Some physicists seem to think so.

Isn't the phase of the electron field changed globally on both sides of the solenoid?

How would you tell? You can't measure the phase of the electron directly.

If you reverse the current, the pattern shifts to the opposite side.

Yes.

Isn't a gauge performed on the field?

Again, what would this mean experimentally? How would you experimentally "perform a gauge on the field"? If that is just another word for "putting a solenoid in" or "reversing the current", why not just say plainly what you're doing in the experiment?

 

[JandeWandelaar]

Again, what would this mean experimentally?

Isn't the shifted pattern proof of the phase changes of the electron field on both sides of the solenoid?

 

[PeterDonis]

Isn't the shifted pattern proof of the phase changes of the electron field on both sides of the solenoid?

Why would it be, since you can't measure the phase change?

Of course in a particular theoretical model the shifted pattern indicates a phase change, but that's in the theoretical model. The model is not reality.

 

[JandeWandelaar]

What if you send an AC current through the solenoid, or introduce an ordinary "thick" solenoid? Will you see, resp., the pattern go to and fro, or being destroyed by the B-field?

 

[JandeWandelaar]

Why would it be, since you can't measure the phase change?

Of course in a particular theoretical model the shifted pattern indicates a phase change, but that's in the theoretical model. The model is not reality.

But isn't the pattern a measurement of the phase change?

 

[PeterDonis]

But isn't the pattern a measurement of the phase change?

It's a measurement of relative phase, but not absolute phase. Perhaps that is where we have a disconnect. You can't measure absolute phase, but yes, you can measure relative phase with things like interference patterns.

 

[JandeWandelaar]

It's a measurement of relative phase, but not absolute phase. Perhaps that is where we have a disconnect. You can't measure absolute phase, but yes, you can measure relative phase with things like interference patterns.

So it is like potential energy? Only differences that count?

 

[PeterDonis]

So it is like potential energy? Only differences that count?

As far as measurements go, yes.

 

[JandeWandelaar]

As far as measurements go, yes.

Which means the A-field is a real thing?

 

[hutchphd]

I have not reviewed the entire colloquy (my apologies in advance), but

You can't measure absolute phase, but yes, you can measure relative phase with things like interference patterns.

I thought the interesting part of the Bohm-Aharonov was the vanishingly small overlap of the B field producing very large changes in measured particle flux. Not an absolute phase change.
So I do not understand the thrust of your argument.

 

[JandeWandelaar]

It's a measurement of relative phase, but not absolute phase. Perhaps that is where we have a disconnect. You can't measure absolute phase, but yes, you can measure relative phase with things like interference patterns.

But both with and without the solenoid you measure relative phases. The solenoid induces a global phase change on both sides of it.

 

[PeterDonis]

Which means the A-field is a real thing?

The A-field is not the same thing as relative phase, so I don't see why a measurement of relative phase would indicate that the A-field "is a real thing".

both with and without the solenoid you measure relative phases.

Yes, and the relative phase change is different in the two cases.

The solenoid induces a global phase change on both sides of it.

What does "global phase change" mean? If it's just another way of saying "the relative phase changes with the solenoid present", why not just say the latter?

 

[PeterDonis]

I thought the interesting part of the Bohm-Aharonov was the vanishingly small overlap of the B field producing very large changes in measured particle flux.

In the subthread you responded to, we are talking about the effect in a double slit experiment, where the observable is the interference pattern at the detector. The pattern changes when a solenoid is present. The pattern is basically a measurement of relative phase (beween the "paths" coming from the two slits).

 

[Demystifier]

I think that BM is a different theory.

But it makes the same measurable predictions as standard QM. Or do you think that it doesn't?

Or if you think that it does, why then Bohmian mechanics is a different theory, while interpretation of gauge field as real isn't?

 

[hutchphd]

In the subthread you responded to, we are talking about the effect in a double slit experiment, where the observable is the interference pattern at the detector. The pattern changes when a solenoid is present. The pattern is basically a measurement of relative phase (beween the "paths" coming from the two slits).

Yes I know that. As usual with these discussions I have lost track of what the damned question on the table is. And everyone is answering a slightly different question vociferously (using QM written in dogma speak). No mas.

 

[JandeWandelaar]

What does "global phase change" mean? If it's just another way of saying "the relative phase changes with the solenoid present", why not just say the latter?

I means that the phase of the electron wave is changed non-arbitrarily over the whole region between the double slit and the screen. Not everywhere the same, which would have no effect, but neither locally, which would have caused photons.

 

[PeterDonis]

I means that the phase of the electron wave is changed non-arbitrarily over the whole region between the double slit and the screen.

But we aren't measuring everywhere. We're only measuring relative phase at the detector screen, and observing how it changes when we add a solenoid. So how do we know what the phase is everywhere?

Not everywhere the same, which would have no effect, but neither locally, which would have caused photons.

I don't understand this. Why would changing the phase "locally" "cause photons"?

 

[JandeWandelaar]

Depends on the theory. QM doesn't, but classical physics did. That's why some people think QM is an incomplete theory.

What the is a particle according to classical physics? A localized mass or charge with a momentum? Which leaves the question what charge is. If you consider mass an interaction effect, there is a connection between mass and charge. If charge is defined as the coupling to the associated gauge field (say electric charge and the photon field), then maybe the wavefunction is a means to let the particle "explore" space (within the confines of that wavefunction) to be able to interact with other particles. Still, what charge IS will still be a mystery. Maybe a "longing" to interact, but now I truly stray into a weird domain...

 

[JandeWandelaar]

I don't understand this. Why would changing the phase "locally" "cause photons"?

Isn't the A-field caused by local gauge transformations, i.e., interaction by means of photons which "make up" for the gauge changes?

 

[PeterDonis]

Isn't the A-field caused by local gauge transformations, i.e., interaction by means of photons which "make up" for the gauge changes?

The A-field can be changed in the math by local gauge transformations, but most physicists view that as solely a mathematical convenience, not corresponding to anything physical.

It might help if you gave a reference for where you are getting the understanding you describe here.

 

[JandeWandelaar]

The A-field can be changed in the math by local gauge transformations, but most physicists view that as solely a mathematical convenience, not corresponding to anything physical.

It might help if you gave a reference for where you are getting the understanding you describe here.

I think this question is basically the same as asking if virtual particles are real. There is an interaction between the solenoid and the electron field between the slits and the screen. You can see this as mediated by virtual photons. Are they real? The pattern shift is real for sure. But if virtual photons are not, how then can they influence the pattern?

 

[PeterDonis]

I think this question is basically the same as asking if virtual particles are real.

We have multiple Insights articles on this (and plenty of previous threads); this one is probably the best one to start with:

https://www.physicsforums.com/insights/misconceptions-virtual-particles/

The pattern shift is real for sure. But if virtual photons are not, how then can they influence the pattern?

This is circular reasoning: you're assuming a particular model in which virtual particles are real and cause the pattern, and then you're trying to argue that because the pattern is real, the virtual particles must be real.

It's always a mistake to confuse models with reality. Virtual particles are part of one particular model--and even that is less than it appears, since that model is based on perturbation theory, which can't even be used to make predictions about many phenomena (and one of them, AFAIK, is in fact the Aharonov-Bohm effect). The fact that a certain observable phenomenon is real can never, by itself, prove that every entity in a particular theoretical model about that phenomenon is real.

 

[JandeWandelaar]

We have multiple Insights articles on this (and plenty of previous threads); this one is probably the best one to start with:

https://www.physicsforums.com/insights/misconceptions-virtual-particles/This is circular reasoning: you're assuming a particular model in which virtual particles are real and cause the pattern, and then you're trying to argue that because the pattern is real, the virtual particles must be real.

It's always a mistake to confuse models with reality. Virtual particles are part of one particular model--and even that is less than it appears, since that model is based on perturbation theory, which can't even be used to make predictions about many phenomena (and one of them, AFAIK, is in fact the Aharonov-Bohm effect). The fact that a certain observable phenomenon is real can never, by itself, prove that every entity in a particular theoretical model about that phenomenon is real.

I have had a lot of discussions about virtual particles. And they are involved here too. The standard, so I have experienced, is to consider them mathematical aid. I think you can consider them real. It can be considered an opinion though. It's my opinion that they are real, the opinion of others that they are not. You can leave them out in bootstrap or S-matrix approaches, but they still have effect. You can't observe them obviously, and what means a particle with zero energy and non-zero momentum? So it's simple. One considers them truly present in the vacuum, and others don't. Òne thing's sure. They are not exchanged, nor popping up as pairs.