Arbitrarily changing EM fields and their photons

[rumborak]

This started with me trying to read up how static electric/magnetic fields are described with photons, but it quickly evolved into the realization that I don't really know how the photonic viewpoint describes *any* changing EM field that isn't a neat monochromatic wave.
Some sites mention virtual photons being used to describe static fields, but the description sounded really shoehorned, since they were assumed to be a special kind of photon that doesn't carry any momentum.

Can anyone outline how arbitrarily varying EM fields, e.g. a step function, are described with photons? (Or is it just a Fourier transform of the signal, and the spectrum describes the distribution of the virtual photons?)

 

[sophiecentaur]

Can anyone outline how arbitrarily varying EM fields, e.g. a step function, are described with photons?

Not easily. Trying to include photons in explanations of 'classical' events, involving fields, is fraught with problems and seldom leads anywhere useful. Hence, the necessity of introducing ideas involving virtual photons.
From your very first sentence, I get the impression that you are anxious to have all the ideas involving photons being sewn up in classical terms. I would say that you should try to avoid going in that direction. Photons are just not that kind of entity.

 

[rumborak]

No offense sophiecentaur, but that looks like "sweeping it under the rug" to me.
I really don't see how an arbitrarily shaped EM field, meaning the overwhelming number of EM fields in this universe, is a "classical" event and thus shouldn't be considered to be described through photons.
Besides, there *does* seem to be a description of static fields through virtual photons, at least several places on the web suggested that. At the very least I would like to understand how that works.

 

[sophiecentaur]

No offence taken. The classical treatment of EM fields, static or time dependent, works fine. The Fourier transform of a time dependent function will produce its spectrum, which will give a measure of the probability of a photon being present or not in a given place and at a given time. The word "overwhelming" is not particularly appropriate when dealing with the concept of a continuous distribution; the Maths is not overwhelming.
On the subject of 'static fields' we can (certainly?) say that there is no such thing because any 'static' situation has, actually, a beginning and an end, even if that involved hours, years or centuries. So that means we are always dealing with a finite spectral bounds and non-zero frequencies. As the photon energy is inversely proportional to the frequency, we are dealing with lower and lower photon energies and approaching closer and closer to a continuous energy flow.
IF you really want to understand about this stuff, I would say that you really need to get very familiar with the situation 'without' virtual photons and to come to terms with the divisions between classical theory, QM and QED. It may be a step too far, to expect any useful explanation about virtual photons and where they fit in. They are at the end of quite a long line, I think.

 

[rumborak]

Found this very good Wikipedia article:

https://en.m.wikipedia.org/wiki/Static_forces_and_virtual-particle_exchange

I think what particular didn't make sense to me was, while I am aware of the existence of virtual particles as a consequence of the uncertainty principle, to my understanding they are always constrained to short distances and life times, since otherwise they would violate energy conservation.
So, I couldn't see how these effervescent particles could mediate at the far distances and (essentially infinite) lifetime of a static field.
The way I understand this article though, and please correct me if I'm wrong, it's essentially the point charges that perturb the vacuum in their vicinity to create virtual photons. What I'm not sure is, is the idea that those virtual photons create other virtual photons next to them (thus increasing the distance of mediation), or do they actually extend for such long distances because maybe some other variable (the energy?) is known very precisely?

 

[Nugatory]

I really don't see how an arbitrarily shaped EM field, meaning the overwhelming number of EM fields in this universe, is a "classical" event and thus shouldn't be considered to be described through photons.

You're going about it backwards. Every possible EM field, whether static or time-varying, can be described in classical terms by applying Maxwell's equations. Photons, whether virtual or real, come into the picture when we want to describe the interaction of that EM field with matter at a particular point in space.

 

[rumborak]

You're going about it backwards. Every possible EM field, whether static or time-varying, can be described in classical terms by applying Maxwell's equations.

Preeetty sure that that's an inaccurate statement. To my understanding, Maxwell's equations are the low-energy limit to QFT, which involves those very virtual particles we are talking about once you go above a certain energy limit. Maxwell's equations are *not* universally applicable.

So, the question here is really: QFT attempts to be a more accurate understanding of fields; given how it is a QM theory and thus deals with quanta, how does QFT describe static fields in its framework?

 

[blue_leaf77]

Can anyone outline how arbitrarily varying EM fields, e.g. a step function, are described with photons? (Or is it just a Fourier transform of the signal, and the spectrum describes the distribution of the virtual photons?)

My understanding about quantized EM field is based on Quantum Optics, there the fields are described as operators (which turn out to be quite similar to the quantum harmonic raising and lowering operators), I don't know if similar thing can also be found in QFT. Consequently many treatments in quantum optics find its analog in the harmonic oscillator problem, one of which is the so-called coherent state. It turns out that using single mode coherent state to describe the quantized version of light, the expectation value of E field looks just like the classical stationary field, the one which oscillates infinitely both way to the left and right along the time axis. In a more involved case involving multimode coherent state, one can also build the average of the field intensity operator to be of arbitrary form, such as your desired step function. I suggest that you take a peek in the book The Quantum Theory of Light by Loudon, the chapters on the multimode quantum optics.

 

[sophiecentaur]

Found this very good Wikipedia article:

https://en.m.wikipedia.org/wiki/Static_forces_and_virtual-particle_exchange

I think what particular didn't make sense to me was, while I am aware of the existence of virtual particles as a consequence of the uncertainty principle, to my understanding they are always constrained to short distances and life times, since otherwise they would violate energy conservation.
So, I couldn't see how these effervescent particles could mediate at the far distances and (essentially infinite) lifetime of a static field.
The way I understand this article though, and please correct me if I'm wrong, it's essentially the point charges that perturb the vacuum in their vicinity to create virtual photons. What I'm not sure is, is the idea that those virtual photons create other virtual photons next to them (thus increasing the distance of mediation), or do they actually extend for such long distances because maybe some other variable (the energy?) is known very precisely?

How worth while this, depends upon your / our understanding of the things it involves. I can be pretty sure that there is a wide range of knowledge of this in the readers and contributors to this thread. As I read through the wiki article, my eyes fell on the statement
"There are limits to the validity of the virtual particle picture."
Enough said, I think, as far as most people are concerned. Without some contributions with very good authority, this discussion could end up as an 'angels on a pinhead' conversation.

 

[insightful]

As the photon energy is inversely proportional to the frequency

Did you mean "directly proportional" as in E=hf?