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I have read these questions:

Virtual photon description of B and E fields

How do virtual photon cloud produce discrete magnetic field lines in bar magnet?

How virtual photons give rise to electric and/or magnetic field?

What are electromagnetic fields made of?

Where Alfred Centauri says:

The electromagnetic field is one such fundamental entity. It's not made of anything else, it just is what it is.

And where DJBunk says:

Electromagnetic fields, which include static electric and magnetic fields, are indeed made of photons.

So the question is what are they made of, photons or are they fundamental.

Question:

  1. Which one is right, are EM fields made of photons or are they fundamantal?
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In the modern view, the quantum electromagnetic field is the fundamental object. The elementary excitations of this field are called photons. Quantum fields are very complicated objects, but under certain circumstances where there are many photons, they may be approximately described by a classical field, called the classical electromagnetic field, which simply assigns a few numbers to every spacetime point. This is the field that Maxwell studied.

So there’s no contradiction here. There are two notions of “electromagnetic field” which have basically opposite status with respect to photons.

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Which one is right, are EM fields made of photons or are they fundamantal?

A classical "electromagnetic field" cannot be defined in the way an electric field or a magnetic field is defined classically (or a gravitational one). One needs a test particle to measure the strength of the field, and I cannot define a test particle that will measure the strength of electromagnetic radiation. One can define an electric field and magnetic field at a point in space-time , and Maxwell's equations connect them as one entity that behaves differently given the velocity of the observer.Two different kinds of test particles are necessary to test electric and magnetic fields, and that is part of the confusion.

To start with, since from our present knowledge, everything classical emerges from the underlying quantum mechanical level, fundamental are the photon particles represented in quantum field theory by a photon field, on which creation and annihilation operators generate the real photons.

Both classical Maxwell equations and the quantum mechanical ones are mathematical models. It has been demonstrated mathematically that the classical fields emerge from the quantum mechanical ones, and there is smooth continuity, going from particles ( photons) to electromagnetic waves(classical ). It can also be shown that at the limiting case of static behavior this continuity exists, and virtual photons can mathematically model static fields.

As physicists we accept what the rigorous mathematical models predict and describe, as long as there is no experimental falsification. So at this point in time, fundamental is the photon field with its creation and annihilation operators ( an operator field). Virtual photons are a price for using mathematics, as they cannot be measured, but as far as the theory goes, the whole thing hangs together with no experimental falsifications.

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  • $\begingroup$ Thank you. Can you please tell me about these two sentences? "Maxwell's equations connect them as one entity that behaves differently given the velocity of the observer.Two different kinds of test particles are necessary to test electric and magnetic fields, and that is part of the confusion." $\endgroup$
    – Árpád Szendrei
    Commented Jul 10, 2018 at 16:15
  • $\begingroup$ I wanted to know if the EM field is one entity that behaves differently given the velocity? And what are those two different kind of test particles? $\endgroup$
    – Árpád Szendrei
    Commented Jul 10, 2018 at 16:16
  • $\begingroup$ one needs a magnetic dipole as a test particle for a magnetic field, and a test charge for the electric field. The electromagnetic wave as modeled by classical maxwell's equation is made up of electric and magnetic fields, so two test particles are needed to measure the fields. The electromagnetic energy is different depending on the velocity of the observer, the effect of special relativity as the classical electromagnetic wave obeys it. $\endgroup$
    – anna v
    Commented Jul 10, 2018 at 17:02
  • $\begingroup$ Doesn't the electron have a magnetic dipole moment and an electric charge too? With the velocity I meant that at different velocities the E and M fields react differently? $\endgroup$
    – Árpád Szendrei
    Commented Jul 10, 2018 at 17:14
  • $\begingroup$ E and B fields follow the Lorentz transformation, Yes, the electron has a dipole moment. For an ideal test particle a magnetic dipole and a charge are assumed without admixtures. It works with the classical mathematics beautifully. $\endgroup$
    – anna v
    Commented Jul 10, 2018 at 17:25
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Well, you're walking edge of what could be counted as more of a philosophical edge of physics rather than absolute. A moving charge in space will indeed cause a field to radiate in one direction or the other and this is the electric field in its excited state, where photons are excitations of this field. A static electric field however, i myself tend to just accept as a potential gradient is space. It is a region where other charges placed inside it feels a force upon themselves.

A static electric field is the electric field in its ground state, its unexcited state, here the field does not produce any photons.

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