Interpretations of the Aharonov-Bohm effect

[Demystifier]

I don't think we agree. You think of T2 as a different theory, I don't. At least this is how I understand your paper (the proof of concept). To me it is the same as saying let T1=classical mechanics and T2=classical mechanics using only cartesian coordinates. These are not two theories with the same predictions. It is just one theory and the theory with some arbitrary restrictions imposed on it.

But we agree that T1 and T2 make the same measurable predictions.

 

[Demystifier]

The Coulomb gauge is a nice example for why the potentials cannot be observables

Yes, but my point is that they can be ontic. Furthermore, if something is not an observable does not mean that it cannot be measured. For example, time in nonrelativistic QM is not an observable, but can be measured.

 

[martinbn]

But we agree that T1 and T2 make the same measurable predictions.

The same as what?

 

[WernerQH]

These are not two theories with the same predictions. It is just one theory and the theory with some arbitrary restrictions imposed on it.

I think the arbitrariness lies in the gauge theories. There is redundancy in the formalism in that many different potentials describe exactly the same physics. To make matters worse, any of these irrelevant, unobservable gauge transformations must be applied to photons and electrons at the same time. I prefer to think of photon and electron "fields" as derived from some common substructure.

 

[vanhees71]

But we agree that T1 and T2 make the same measurable predictions.

Yes, because you tacitly also stick to the fact that measurable quantities must be gauge invariant, claiming the contrary for some ununderstandable reason.

 

[vanhees71]

Yes, but my point is that they can be ontic. Furthermore, if something is not an observable does not mean that it cannot be measured. For example, time in nonrelativistic QM is not an observable, but can be measured.

Whatever ontic means for you, it then cannot be a useful concept of physics which is about reproducible objective quantitative observables of Nature.

Time in both relativistic and nonrelativistic QT is not an observable, but what has this to do with the errorneous attempt to make gauge-dependent quantities observables or "ontic" or whatever?

 

[Demystifier]

The same as what?

T2 makes the same measurable predictions as T1.

 

[Demystifier]

Yes, because you tacitly also stick to the fact that measurable quantities must be gauge invariant, claiming the contrary for some ununderstandable reason.

Gauge invariance is not an experimental fact. An experimentalist cannot change the gauge in her laboratory and then observe that the result of experiment is the same. A change of gauge is just an artefact of how theorists represent the laws of physics mathematically. All I'm saying is that the theorists can alternatively use a different mathematical representation, in which gauge transformations and gauge invariance are not even mentioned.

 

[Demystifier]

Whatever ontic means for you, it then cannot be a useful concept of physics which is about reproducible objective quantitative observables of Nature.

It's useful to me. It helps me understand things intuitively, after which I can more easily make actual measurable predictions.

In the last section of the paper I mentioned above, I have explained how Bohmian intuition helped me better understand the standard instrumental quantum theory which cares only about measurable predictions.

Time in both relativistic and nonrelativistic QT is not an observable, but what has this to do with the errorneous attempt to make gauge-dependent quantities observables or "ontic" or whatever?

How can you say that it is erroneous to make gauge-dependent quantities ontic, if you don't know what does "ontic" even mean?

 

[vanhees71]

Indeed, gauge invariance is not a physical property. It's the property of the description of observable facts, and it implies that only gauge-invariant quantities can represent observables. That precisely must be so, because (!) indeed "a change of gauge is just an artefact of how theorists represent the laws of physics mathematically." Nothing that depends on some arbitrary choice of a theorist can represent an observable.

Your last sentence is utterly errorneous: If you don't mention that you describe nature with a gauge theory you cannot even define, which empirically testable predictions you model indeed means.

Of course, you can formulate classical electrodynamics entirely without the potentials, dealing only with observable quantities, i.e., the em. field, $(\vec{E},\vec{B})$, as well as the sources, $(\rho,\vec{j})$. This is not possible for QED, because you need the potentials for a description in terms of a local QFT. Already for the free field, where you can use radiation gauge to fix the gauge entirely, the transverse vector potential cannot represent a local observable, because it does not fulfill the microcausality constraint, which is why you have to build the observables in terms of the field operators $(\vec{E},\vec{B})$, which fulfill it. Particularly the correct Hamilton density is $\mathcal{H}=(\vec{E}^2+\vec{B}^2)/2$.

 

[PeterDonis]

time in nonrelativistic QM is not an observable, but can be measured.

How? Your answer can't just be "look at a clock", because how do you know that what a clock measures is the "time" that appears as a parameter in the math?

 

[Demystifier]

Indeed, gauge invariance is not a physical property. ... only gauge-invariant quantities can represent observables.

So basically you are saying that observables must have a non-physical property.

But when I say that measurable things must have another non-physical property (they must be ontic), you complain that non-physical properties are not useful in physics.

Don't you think that you hold double standards?

 

[vanhees71]

No, I'm saying that quantities that have non-physical properties are non-physical. That's very consistent, while you are contradicting yourself in saying on the one hand that gauge invariance is unphysical and claim at the same time gauge-dependent quantities were physical.

 

[martinbn]

T2 makes the same measurable predictions as T1.

Yes, a theory makes the same predictions as itself!

 

[martinbn]

I think the arbitrariness lies in the gauge theories. There is redundancy in the formalism in that many different potentials describe exactly the same physics. To make matters worse, any of these irrelevant, unobservable gauge transformations must be applied to photons and electrons at the same time. I prefer to think of photon and electron "fields" as derived from some common substructure.

Nature is the way it is. It does not care what we prefer.

 

[Demystifier]

How? Your answer can't just be "look at a clock", because how do you know that what a clock measures is the "time" that appears as a parameter in the math?

I don't know it a priori. I make a hypothesis that those two "times" are the same, make a measurable prediction based on that hypothesis, compare the predictions with actual experimental results, and find that they match.

By the way, the same can be said about any other object in a physical theory. How do you know that the eigen-values of the momentum operator are the same thing as the measured momenta?

 

[vanhees71]

Since the eigenvalues (or rather the spectrum) of the momentum operator is entire $\mathbb{R}^3$, that's not too strong a prediction I'd say :-)).

 

[Demystifier]

No, I'm saying that quantities that have non-physical properties are non-physical.

Electric field has a property of gauge invariance. Gauge invariance is a non-physical property (you said it yourself). Ergo, electric field has a non-physical property. Q.E.D.

 

[Demystifier]

Since the eigenvalues (or rather the spectrum) of the momentum operator is entire $\mathbb{R}^3$, that's not too strong a prediction I'd say :-)).

That explains nothing, because the spectrum of the position operator is the same, and yet you will not say that position eigen-values are measured momenta. But if that was a joke, then OK.

 

[Demystifier]

Nature is the way it is. It does not care what we prefer.

We are part of that nature too, and we care what we prefer. Ergo, at least a part of nature cares what we prefer.

 

[WernerQH]

Nature is the way it is. It does not care what we prefer.

Nature may be different than you think.

 

[vanhees71]

Electric field has a property of gauge invariance. Gauge invariance is a non-physical property (you said it yourself). Ergo, electric field has a non-physical property. Q.E.D.

The electromagnetic field, $(\vec{E},\vec{B})$ is a gauge-invariant quantity and thus (can be) physical within the gauge theory.

What is you motivation behind your attempts to claim the opposite of the mathematically evident properties of gauge theories?

 

[martinbn]

We are part of that nature too, and we care what we prefer. Ergo, at least a part of nature cares what we prefer.

What i meant was that nature has the laws it does, and not the laws we want it to have.

 

[martinbn]

Nature may be different than you think.

Yes, and it may not be the way you want it to be.

 

[Fra]

physics which is about reproducible objective quantitative observables of Nature.

How much many repeats do we need to say that something is reproducuble?
How many observers must agree for objectivity?

Are single observations, from single observers not "real"? Or are only the asymptotic fictious concepts real? One can perhaps turn the argument around, and say that all the apparent convergent sequences are real, but are the limits real? Who has ever collected and processed an infinite amount of data in finite time?

And during this process, doesn't real interactions take place, that are not referring to asymptotics?

/Fredrik

 

[vanhees71]

Well, that depends on the definitions of the scientific community. E.g., in the HEP community a discovery must be significant at at least the $5\sigma$ level. Of course, you can never collect infinite amounts of data.

 

[Demystifier]

What is you motivation

The motivation is to explain the AB effect in terms of local beables, but a beable is a philosophical concept that doesn't make sense to you.

 

[Demystifier]

What i meant was that nature has the laws it does, and not the laws we want it to have.

My desires are determined by the laws of nature, so what I want cannot be in contradiction with the laws of nature.

 

[martinbn]

My desires are determined by the laws of nature, so what I want cannot be in contradiction with the laws of nature.

What about all those who want a perpetual motion machine?

 

[Demystifier]

Yes, a theory makes the same predictions as itself!

Yes, but the point of talking about T1 and T2 as different is a conceptual difference, not an observational difference. Indeed, @vanhees71 thinks that T1 is right and T2 wrong, so even for him non-observational differences are relevant, despite the fact that he often claims that only observational aspects are relevant.

 

[Demystifier]

What about all those who want a perpetual motion machine?

Those are made by nature too, so it can be said that a part of nature itself wants a perpetual motion machine.

 

[PeterDonis]

My desires are determined by the laws of nature, so what I want cannot be in contradiction with the laws of nature.

This is invalid reasoning. Suppose I write a computer program that does incorrect calculations of the predictions of the laws of nature. Its behavior is still determined by the laws of physics, but that doesn't mean what it calculates is not in contradiction with the laws of nature.

The disconnect between the two clauses of your sentence is that "contradiction" is not a matter of physics, it's a matter of what meanings humans assign to symbols. It is entirely possible for different strings of symbols to be assigned meanings by humans that are contradictory, even though all such behavior is determined by the laws of nature.

 

[vanhees71]

The motivation is to explain the AB effect in terms of local beables, but a beable is a philosophical concept that doesn't make sense to you.

I don't know, what's meant by "beables". If it's something physical, it cannot be the electromagnetic potentials, which are unphysical by definition. We argue in circles!

 

[Fra]

One attempt to illustrate what i tried to say before, relating to Bells book:

"The beables of the theory are those elements which might correspond to elements of reality, to things which exist. Their existence does not depend on 'observation'. Indeed observation and observers must be
made out of beables."
-- Speakable and Unspeakable in Quantum Mechanics, p174

These beables sounds much like what I consider to be encoded in the microstructure of the observer/agent. Indeed this just IS, but WHAT is it? I would say it might represents the agents physical knowledge(*) if it's environment, the the acquired, processed and encoded "facts". In a way one can call this the "evidence" in "classical terms" that Bohrs seems to put it. From the agent perspective, nothing gets more "ontic" or "real" as that. However, this information is be construction hidden from OTHER agents. So each agent/observer would have it's own set of beables. This is not a contradiction in any way. It is just a manifestation of the relativity of inference. The only way agents can query each other is by means of physical interaction or communication.

(*) If you consider the saying that what an observer "knows" is inseparable from what the observer "is", then observers are literally made out put what encodes what they now.

The difference is to acknowledge how the individual agents (not the community of agents) registers, recodes and stores the "empirical" data, from single interactions (not statistics).

/Fredrik

 

[Demystifier]

This is invalid reasoning.

I know, but I like to tease matinbn, just as he likes to do the same to me.