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I am trying to understand electromagnetic fields so I have two question related to them.

  1. What is a electromagnetic field made of? Is it made of photons / virtual photons?

  2. How about a static electric or magnetic field?

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4 Answers 4

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When thinking about fundamental entities, it's quite easy to ask a question that, upon reflection, is contradictory. The questions of this kind take the form: What is [some fundamental thing] made of?

The contradiction here is that there can only be an answer if the fundamental thing isn't fundamental!

The electromagnetic field is one such fundamental entity. It's not made of anything else, it just is what it is. In the context of QFT, photons (real and virtual) are, loosely speaking, "excitations" of this entity. Real photons are associated with the long range propagation of energy and momentum, i.e., electromagnetic waves. Virtual photons are associated with the electromagnetic force, i.e., the Lorentz force, as well as evanescent waves, and near field antenna radiation.

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I'd want to add "to our best current knowledge" the electromagnetic field is fundamental. Maybe in the end it's all strings... –  WIMP Jun 21 '12 at 14:45
    
in that sense it's still in spirit fundamental. It would mean that quantum fields in general are fundamental but the specific particles in the field, although they look distinct, are really just different vibrational modes of the same particle. I mean let me restate it this way. The fact that particles we thought were 0 dimensional are now 1 dimensional doesn't change the "fundementalness" of the fields that the particles were the quanta of. –  tachyonicbrane Jun 21 '12 at 14:54
    
@WIMP Actually I should have said that the Electromagnetic Field is not fundamental either way (it's sort of semantical) because regardless of the dimensionality of the particles the field would have quanta (photons) which may be 0 dimensional objects or 1 dimensional objects a priori. My original comment was making the point that the electromagnetic field would new a manifestation of the string field but I wouldn't say the string field is "more fundamental" since it's not like the electromagnetic field is "made of string fields" it's a particular aspect of the string field. –  tachyonicbrane Jun 21 '12 at 15:11
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@WIMP, it's a good point you make but let me point out that it will always be the case that the context is "our best current knowledge". After all, that's all we've got! :) –  Alfred Centauri Jun 21 '12 at 15:19
    
@WIMP: Maybe in the end everyone agrees that physics is just model building and refering to something in reality is a problem merely emerging from language and the observation that we can abstractly compute and thereby predict. I think all these rigid designators refer to constructions of the human mind (and these are not even mind independend). –  NikolajK Jun 21 '12 at 15:31

Electromagnetic fields, which include static electric and magnetic fields, are indeed made of photons. From a particle physics perspective the Quantum Electrodynamics as a model of particles carrying electric charge interacting via photons has a spectacular agreement with experiment. The thing is, those experiments are very special in that we are sending in 'free' particles with a ton of energy and treating the interactions with the electromagnetic field as a very small perturbation on the free particles. So the picture we draw in our heads of particles interacting via exchange of a single photon is a simplified case that works very well in this situation:

enter image description here

Now, to make the answer more precise for something like a static electric field, to my knowledge is pretty much impossible. To see this we can look at something much simpler, coherent states (see http://en.wikipedia.org/wiki/Coherent_states) . These states don't even have a well-defined photon number, so while they are clearly ' made' of photons as the state is a linear combination of states of well-defined photon number:

$ |\alpha \rangle = e^{ \frac{- |\alpha|^2}{2}} \displaystyle\sum\limits_{n=0}^\infty \frac{\alpha^n}{\sqrt{n!}}|n \rangle $

the the probability of detecting n photons is:

$ P(n) = e^{-|\alpha|^2} \frac{|\alpha|^{2n}}{n!}$

which clearly isn't a delta function for n, which it would be if n was always the same number. And as far as I can tell, a state which produces a Coulomb-type field ($\frac{k q}{r^2}$) is going to be even more complicated than the coherent states, so it seems hopeless to try and phrase it in these terms. Note that this is in stark contrast to say, the electron number, which is always well-defined. Thus thinking about an electromagnetic field as made up of photons as the same way a block of metal is made up of electrons and other particles is probably a bad analogy to stretch very far.

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I am not sure I really understand this. You are saying that both the electromagnetic field and a static electric electric field are made of photons (the charged particles interact trough the exchange of photons) and that this is a good simplified way of viewing things but we should not think of this in the same way as a solid block is made of particles? So for example if we have two charged particles the electric field around them is made of photons? They will interact by exchanging photons? Is this correct? –  Buzai Andras Jun 21 '12 at 19:41
    
Did I understand correctly your answer? –  Buzai Andras Jun 22 '12 at 12:55
    
Pretty much. Although I would caution that this is just my way of thinking about it. I sort of threw this out to see what other people and this answer hasn't received any up-votes so I might be incorrect. –  DJBunk Jun 22 '12 at 14:53

Fields are more fundamental compared with particles (as fundamental as string). Particles, such as electron, are the excitation of Dirac fields (sorry for that). Possible related discussion from M Strassler which may be helpful. http://profmattstrassler.com/articles-and-posts/the-higgs-particle/360-2/ Some points are the following :" A field is something that

1.is present everywhere in space and time,
2.can be, on average,  zero or not zero, and
3.can have waves in it.
4.And if it is a quantum field, its waves are made from particles.

So for example: the electric field is a part of nature that is found everywhere. At any given point in space, and at any particular time, you can measure it. If it’s non-zero on average in some region, it can have physical effects, such as making your hair stand on end or causing a spark. It can also have waves — visible light is such a wave, as are X-rays and radio waves.

Ok, so, what is a particle?

A quantum field’s waves cannot be of arbitrary intensity. The least-intense possible wave that a field can have is called a particle, and it often behave in rough accordance with your intuitive notion of “particle”, moving in a straight line and bouncing indivisibly off of things, etc., which is why we give it that name.

In the case of the electric field, its particles are called “photons”; they represent the dimmest possible flash. Your eye absorbs light one photon at a time (though it typically waits for several photons to arrive before sending a signal to your brain.) A laser produces very intense waves, but if you shield a laser with a screen so that only a tiny fraction of the light gets through, you will find, if you shield it enough, that the light passes through the screen in little blips — single photons — all of them equally dim."

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I am not sure I follow the second part of your comment. Are you saying that electrons are a result of the excitation of electromagnetic fields? Because I am pretty sure that is not true. –  Buzai Andras Jun 21 '12 at 14:12
    
They can be seen as excitations of an electronic-field, which is distinct from the electromagnetic field. –  Frédéric Grosshans Jun 21 '12 at 14:43
    
Yeah photons are the quanta of the electromagnetic field. It's also correct that photons are excitations of the electromagnetic field. –  tachyonicbrane Jun 21 '12 at 15:14
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Buzai, I believe he meant electron field, a fermionic field. In the context of the Standard Model, all fundamental particles are thought of as "excitations", i.e., quanta, of an associated fundamental field. So, for example, the Dirac equation for the electron is re-interpreted as an operator equation; the Dirac spinors become operators. These operators create and destroy electrons and positrons with spin up or spin down. Look at the Wikipedia article "Fermionic field". –  Alfred Centauri Jun 22 '12 at 2:55
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I am sorry for that. I mean the electron field, spin-$\frac{1}{2}$ Dirac field. –  Craig Thone Jun 22 '12 at 3:13

A magnetic field is a essentially a cloud of virtual photon "place-holders" in a state of flux; it's what the electrons that produce the field "owe" to other nearby electrons (which have gained real photons), for having their spin-charge moments aligned in the same direction.

A magnetic field is even more fundamental an entity than particles such as electrons, protons and neutrons.

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