How can electrostatic fields be composed of photons?

[fox26]

I know little about QED, QCD, and whatever the corresponding theory for the
weak force is, and of course virtually nothing about the quantized theory of the
gravitational force, which mostly doesn’t exist, so the following arguments and
questions may be somewhat wrongly based where they refer to such theories.

I will talk specifically about the quantized theory of the electromagnetic field, but
the considerations may generalize to the other three forces. A stationary,
non-time-varying electrostatic field was said, in my classical E&M course, to have
an energy of its own which was calculated, in the case of the field between the
plates of a capacitor, by determining the energy required to charge the capacitor
to create the field and assuming conservation of energy. The energy density at
each point turned out to be proportional to the square of the magnitude of the
field there. In the quantized theory of the E-M field, as I understand, there is
nothing similar to the continuous E-M field in classical theory. What is observed
macroscopically as a stationary electrostatic field, such as that of a stationary
electron, is popularly said according to QED to be due to photons, real or virtual.
My question is: How is this possible?

Julian Schwinger asked why people insist on the existence of theoretical objects,
such as atoms, electrons, and E-M fields or photons, and are not satisfied with
just the mathematics of physical theories, and the observable predictions it
makes, as a description of nature. Whatever the reason, most people, including
most physicists and myself, want a description that includes physical entities of
some sort. Quantum Field Theory provides this for such things as electrons, in a
way that is at least semi-satisfactory, as excitations of some quantum field. Is
there a corresponding description by Quantum Electrodynamics (QED) of the
electromagnetic field?

If, according to QED, an electrostatic field is somehow composed of photons,
are these real or virtual, or is this supposed question, according to QED,
meaningless? Even in QED, energy expectation value is conserved, so the
energy used in charging a capacitor must go somewhere, and would that not be
into the E field between the plates of the capacitor, or QED’s substitute for that?
Surely the E(r) field of a stationary electron must, as in the case of the field in a
capacitor, have an energy density expectation value at a point r proportional to
|E(r)|² (with E(r) being the classical field). The problem is, why don’t the photons
comprising the field, whether they are real or virtual, for an electron in otherwise
empty space, fly off to infinity? Even virtual photons, which some people writing
in PF or elsewhere, such as Arnold Neumaier in his PF article “The Physics of
Virtual Particles”, claim are unobservable (or nonexistent), surely (?) would fly
off to ∞. The electron couldn’t renew its supply of energetic photons, real or
virtual, which in this view its E field must be composed of, all of which would be
going to ∞, since that would cause its own mass to decrease.

It may be that the claim that a quantized E-M field is composed of photons, real
or virtual, is another case of misrepresentation by popularizers. If that is so, what
is a quantized (supposedly all are) E-M field composed of? Must we, according
to present theory, give up the picture of such a field as being made up of physical
entities?

 

[Vanadium 50]

How can electrostatic fields be composed of photons?

They can't. They aren't. Anywhere you have read this is just wrong.

 

[hilbert2]

Solving the ground state of the QFT system composed of an electron and the EM field it creates would probably not be possible analytically. I'm not sure if the ground state can even be an eigenstate of the electron number operator, though, so this may be a wrong way to state the problem (could some kind of very transient electron-positron pair formation occur at the high electric field very close to the electron?). Also, the electron in that solution would not be localized to any particular region in space so it wouldn't represent the physical situation of a static localized charge very accurately.

 

[DrDu]

What is strange, is the fact, that it is very easy to describe a static lattice deformation in terms of virtual phonons, while the analogous situation for photons in relativistic QFT is awkward.
That's one of the many indications that relativity and QFT do not harmonize too well.

 

[vanhees71]

The Coulomb field is not described by a single photon but by resumming the soft-photon ladder diagrams.

See Weinberg, Quantum Theory of Fields, vol. 1

for a very clear treatment of the soft-photon problems in QED.

You must not think about photons as being little billard balls. The are not localized little bullets but do not even allow to define a position observable in the usual sense. Photons are special, because they are, by definition, one-photon Fock states with precise photon number 1, i.e., particular states of a massless spin-1 quantum field.

 

[hilbert2]

Should the problem be approached by treating only the electric field quantum mechanically and modeling the static charge as a constant source term in the Maxwell equations? To me it seems that it becomes very difficult if some actual particle is taken to be the source of the static field.

 

[bhobba]

Here is the truth:
http://www.physics.usu.edu/torre/3700_Spring_2015/What_is_a_photon.pdf

Summary - a photon is an excitation of the quantum em-field that pervades all space. The technical meaning of excitation is explained in the above.

We now know all particles are described in a similar way - by quantum field theory.

Thanks
Bill

 

[vanhees71]

Should the problem be approached by treating only the electric field quantum mechanically and modeling the static charge as a constant source term in the Maxwell equations? To me it seems that it becomes very difficult if some actual particle is taken to be the source of the static field.

Of course, you get the correct result by using a "hemiclassical" approach: You treat the charge as infinitely heavy and simply as an external classical Coulomb field and then quantize the motion of the electron(s) around it, first solving the Dirac equation and then use perturbation theory to address "radiative corrections" (i.e., in this case the Lamb shift).

You can derive this result, however, systematically using QED and the correct power counting of diagrams, which is not the naive one by just counting the number of vertices. Due to the soft-photon poles you have to resum a class of diagrams to be consistent in leading order (ladder diagrams). For details, see the corresponding chapter in Weinberg, Quantum Theory of Fields.

 

[hilbert2]

Thanks for the replies, looks like I got the qualitative idea right.

I guess that to model actual emission of photons, I would create a time-dependent charge density

$\rho(\mathbf{r},t) = Ae^{-b(x+c\sin(\omega t))^2}e^{-by^2}$

and the corresponding current density $\mathbf{j}(\mathbf{r},t)$, and then quantize the electromagnetic field by adding this moving charge as a perturbation to the free EM field dynamics. Then it would be supposed to emit photons with the same frequency $\omega$ as that of the motion of the gaussian charge distribution, just like in the classical case.

EDIT: the problem wasn't about finding the QFT corrected ground state of an atom, it was just about finding the quantized electric field around a single electron, which is already an analytically unsolvable problem because the fermion-EM coupling works both ways and there will be an uncertain number of electron-positron pairs around the charged particle.

 

[Derek P]

Must we, according to present theory, give up the picture of such a field as being made up of physical entities?

Not according to someone I know on-line who does QFT for a living. The field is composed of particles taking all possible paths (actions?) simultaneously - very similar to the Feynman Path Integral Formulation. The fact that these paths are superposed means they are more succinctly described as a continuous field. As he is also an MWI advocate he is quite cheerful that quantum physics permits a pure particle picture which is local, causal and real (in the ordinary sense) - as long as you allow superposition. Unfortunately, he doesn't post here - probably because PF is locked into orthodox (homework-compatible) interpretations. So pending my getting to grips with QFT I'll take his word for it...

 

[Derek P]

Of course, you get the correct result by using a "hemiclassical" approach: You treat the charge as infinitely heavy and simply as an external classical Coulomb field and then quantize the motion of the electron(s) around it, first solving the Dirac equation and then use perturbation theory to address "radiative corrections" (i.e., in this case the Lamb shift).

You can derive this result, however, systematically using QED and the correct power counting of diagrams, which is not the naive one by just counting the number of vertices. Due to the soft-photon poles you have to resum a class of diagrams to be consistent in leading order (ladder diagrams). For details, see the corresponding chapter in Weinberg, Quantum Theory of Fields.

Thanks for the reference, I'll get a copy and bury myself in it for a year or so!

 

[PeterDonis]

The field is composed of particles taking all possible paths (actions?) simultaneously

This isn't what I've seen in a variety of QFT textbooks and papers. All of the references I've seen describe quantum fields as operators--usually operators that create and destroy particles (since the creation-annihilation operator representation is the most common one).

PF is locked into orthodox (homework-compatible) interpretations.

PF does not require or forbid any particular interpretation of QM. A better quick summary of PF's position would be that, since all interpretations use the same math and make the same predictions for all experimental results, questions about QM interpretations can't be settled by experiment and therefore aren't really questions about physics, they're questions about personal preferences.

 

[Derek P]

PF does not require or forbid any particular interpretation of QM. A better quick summary of PF's position would be that, since all interpretations use the same math and make the same predictions for all experimental results, questions about QM interpretations can't be settled by experiment and therefore aren't really questions about physics, they're questions about personal preferences.

I don't agree with that. Take, for instance, interpreting entanglement experiments. If we interpret the macroscopic state as "collapsing" when a measurement is taken, then the predicted correlations imply reverse causality. So we can test whether collapse occurs by seeing whether the experiment yields the predicted results. It does. Therefore: either causes can happen after their effects, which would be crazy, or collapse does not happen. Proved by experiment.

 

[PeterDonis]

either causes can happen after their effects, which would be crazy

Tell that to the proponents of the transactional interpretation, which makes precisely the claim that causes can happen after their effects.

The point is that, unless a claim, like "causes must happen after their effects", can be embodied in models that make different predictions depending on whether the claim is true or false, there is no way to test it by experiment. Nobody has a pair of models that make different predictions based on "causes must happen after their effects" being true vs. being false. So there's no way to test this claim by experiment.

That's not to say that someone might not come up with such a pair of models in the future. People used to think that there was no way to test the premises of Bell's Theorem by experiment, until Bell showed how to do it. But nobody yet has come up with a way to test "causes must happen after their effects" by experiment.

 

[Mentz114]

I don't agree with that. Take, for instance, interpreting entanglement experiments. If we interpret the macroscopic state as "collapsing" when a measurement is taken, then the predicted correlations imply reverse causality. So we can test whether collapse occurs by seeing whether the experiment yields the predicted results. It does. Therefore: either causes can happen after their effects, which would be crazy, or collapse does not happen. Proved by experiment.

This is interpretation dependent. In 'shut-up and calculate' we only use the information in the state ( entangled singlet) and it has nothing to say about the order in which events happen to entangled pairs. The concept of individual particle is absent from the state. It makes no difference which order is imposed.

 

[Derek P]

This is interpretation dependent. In 'shut-up and calculate' we only use the information in the state ( entangled singlet) and it has nothing to say about the order in which events happen to entangled pairs. The concept of individual particle is absent from the state. It makes no difference which order is imposed.

If you read what I said I was not talking about assigning events to particles. I was talking about observed events - which are what happens to the detectors.They have definite timings independent of any theory.

edit: Just to be clear I don't mean the events are definite. I mean that for any observation (in any history) the associated time is definite.

 

[Mentz114]

If you read what I said I was not talking about assigning events to particles. I was talking about observed events - which are what happens to the detectors.They have definite timings independent of any theory.

To be more specific - the DCQE experiment does not predict retrocausality in all interpretations. The disentangling events in the Kim experiment are when one of an entangled pair hits a detector. There is no way (or need) to define a time interval between the detector events because the correct prediction is made whatever order is assigned.

I'll leave it there because I think this is off-topic.

 

[PeterDonis]

They have definite timings independent of any theory.

Not if the detection events are spacelike separated, which is the scenario that's usually tested.

 

[Derek P]

Tell that to the proponents of the transactional interpretation, which makes precisely the claim that causes can happen after their effects.

The point is that, unless a claim, like "causes must happen after their effects", can be embodied in models that make different predictions depending on whether the claim is true or false, there is no way to test it by experiment. Nobody has a pair of models that make different predictions based on "causes must happen after their effects" being true vs. being false. So there's no way to test this claim by experiment.

That's not to say that someone might not come up with such a pair of models in the future. People used to think that there was no way to test the premises of Bell's Theorem by experiment, until Bell showed how to do it. But nobody yet has come up with a way to test "causes must happen after their effects" by experiment.

Yes, I was wondering about the TI. I am sure the maths works but - provisionally - I would say that the TI is crazy when taken to mean actual events in the "wrong" order and physically real time-travelling advanced waves. Nature could, of course be precisely that crazy so if that's what you're saying I'll plead guilty to preferring a sane theory, albeit a counter-intuitive one, over one riddled with grandfather paradoxes.

 

[PeterDonis]

I would say that the TI is crazy

Yes, and as a personal opinion, you would find lots of people to agree with you.

But that's not the same as saying it's ruled out by experiment. It can't be, because it makes the same experimental predictions as every other interpretation of QM.

 

[PeterDonis]

I'll plead guilty to preferring a sane theory, albeit a counter-intuitive one, over one riddled with grandfather paradoxes.

The transactional interpretation does not have any grandfather paradoxes, unless standard QM does. The TI uses the same math and makes the same predictions as standard QM. It tells a story about what's happening "behind the scenes" that many people find "crazy" (to use your term), but the same is true of every interpretation of QM.

 

[Derek P]

To be more specific - the DCQE experiment does not predict retrocausality in all interpretations. The disentangling events in the Kim experiment are when one of an entangled pair hits a detector. There is no way (or need) to define a time interval between the detector events because the correct prediction is made whatever order is assigned.

I'll leave it there because I think this is off-topic.

Well I'll drop it if you like but my last word is that making the correct prediction is irrelevant because the real or apparent reverse causality is a matter of the observed events, not the predicted ones.

 

[PeterDonis]

making the correct prediction is irrelevant

Not if you're trying to use experiments to decide between theories or interpretations.

the real or apparent reverse causality is a matter of the observed events

You don't directly observe causality. It has to be inferred, and any such inference will depend on the theory and interpretation you are using.

 

[Derek P]

The transactional interpretation does not have any grandfather paradoxes, unless standard QM does. The TI uses the same math and makes the same predictions as standard QM. It tells a story about what's happening "behind the scenes" that many people find "crazy" (to use your term), but the same is true of every interpretation of QM.

Not really. The stories have different ontologies. A priori you might assume that the human race - or an informed subset - would be equally divided between those who find reverse causality crazy, those who find superposed worlds crazy and those who find consciousness causing wavefunction collapse crazy. But gut reactions are not a good guide to what is plausible. One really must dig beneath the surface and say why each is crazy. If whole classes of interpretation violated traditional causality or traditional physicalism or traditional realism and between them left nothing we would be forced to adopt some "philosophical extravaganza born of despair in the face of a grave crisis". But that is not the case. There is a class of interpretation which keeps reality real, physical, causal, and local. So why resort to craziness? That's all I'm saying. Of course MWI does strike people as crazy but it doesn't require jettisoning local, causal realism. It just requires superposition which, as it is part of the theory we are trying to interpret is a zero-cost option :)

Do you want to leave it at that?

 

[Derek P]

Not if you're trying to use experiments to decide between theories or interpretations.

Well you're saying we cannot and I'm not trying to. So yes, it's irrelevant.

You don't directly observe causality. It has to be inferred, and any such inference will depend on the theory and interpretation you are using.

Well yes. That's what I'm saying. The events are observed by a straightforward i.e. classical, extension of our senses. People interpret the observation as indicating a unique detection event. That goes beyond the facts.

 

[PeterDonis]

The stories have different ontologies.

"Ontology" isn't something you can test by experiment.

There is a class of interpretation which keeps reality real, physical, causal, and local. So why resort to craziness?

"Craziness" is in the eye of the beholder. More precisely, which interpretation is more "crazy" is in the eye of the beholder. Many people (myself among them) find the MWI too crazy to accept, just as you find the TI too crazy to accept. Sure, MWI keeps locality, and "causality" for an appropriate interpretation of that term. But to say that it "keeps reality real" is IMO absurd, at least as absurd as you find the idea that causality can go "backwards" as the TI claims. The "reality" that MWI forces you to accept is nothing like the "reality" we observe every day.

My own personal view is that no interpretation of QM that we currently have is correct. They're all too crazy to accept. Fortunately, you don't need an interpretation in order to do physics. You just need a model that makes correct predictions.

 

[Derek P]

"Ontology" isn't something you can test by experiment.
"Craziness" is in the eye of the beholder. More precisely, which interpretation is more "crazy" is in the eye of the beholder. Many people (myself among them) find the MWI too crazy to accept, just as you find the TI too crazy to accept. Sure, MWI keeps locality, and "causality" for an appropriate interpretation of that term. But to say that it "keeps reality real" is IMO absurd, at least as absurd as you find the idea that causality can go "backwards" as the TI claims. The "reality" that MWI forces you to accept is nothing like the "reality" we observe every day.
My own personal view is that no interpretation of QM that we currently have is correct. They're all too crazy to accept. Fortunately, you don't need an interpretation in order to do physics. You just need a model that makes correct predictions.

Then we will have to agree to disagree.

 

[PeterDonis]

Then we will have to agree to disagree.

Yes, that's common in QM interpretation discussions.

 

[Derek P]

Yes, that's common in QM interpretation discussions.

Sometimes because the alternative is that one or more parties drop dead of exhaustion.
Cheers.

 

[Orodruin]

Yes, that's common in QM interpretation discussions.

And precisely why they are not about physics and, in my meaning, quite useless. Physics is an empirical science aiming to make predictions about what can be measured. Quibbling about different interpretations remains purely philosophical (or, worse, religious). A scientific question can be answered by experiments.

 

[Nugatory]

Then we will have to agree to disagree.

Yes, that's common in QM interpretation discussions.

Sometimes because the alternative is that one or more parties drop dead of exhaustion.

And that is why we generally close them when they reach the point of diminishing returns... As this one has.
Closed it is, although as usual if someone has something that hasn't already been said and that will bring the thread back from the point of diminishing returns, they can PM any mentor to ask that thread be reopened.