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One of the upvoted answers to Why don't electromagnetic waves require a medium? says that the electromagnetic field is the medium for electromagnetic waves. It went on to say that if the electromagnetic field does not oscillate, there will be no electromagnetic waves.

In real life light can be produced by simply burning wood. How does the action of burning wood produce an oscillating electromagnetic field which manifests itself as visible light?

Furthermore, in particle physics, in the creation of particles, one simply assume that if there is enough energy, a photon can pop out of vacuum. But since a photon will imply an oscillating electromagnetic field, what exactly is the mechanism that produces this oscillating electromagnetic field?

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Light or visible light produced while burning of wood is called incandescence. It is a special case of thermal radiation which only deals with visible light. However, we know, that any substance above 0K will emit radiation. However, the radiation may not be in visible range. To understand how this works consider this-

When a body is above 0K, there are oscillating charges and dipoles in the body. A static charge will produce an electric field, and a moving charge will produce a magnetic field. When the charges are oscillating, they produce electromagnetic field because the Electric field and magnetic field is not constant (velocity is not constant) and changing electric induces magnetic field and vice versa. So any body above 0K will radiate some em waves mostly microwaves or infrared.

For wood burning, it is actually a chemical reaction vigorously exothermic. But due to high energy release, the charges oscillate much faster releases visible light.

Coming to the second point, and I am not absolutely sire about this. Photons are just excitation of the EM field like an electron is an excitation of electron field. The field is always present, but when certain interactions take place (like pair annihilation), there are excitation in the EM field thus producing a photon.

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When a wood burns, exothermal chemical reactions occur, and energy is released as heat. Then gas molecules go faster, and they hit stronger, giving energy to peripheral electrons of atoms. Those electrons then go back to their unexcited energy level by creating a photon, or, if you prefer, the perturbation of their motion, which, since electrons have an electric charge, perturbates the electromagnetic field.

In QTF, let say that EM field is never really at rest, there is always an irreducible "noise", and so you can think, as a first approximation, that statistically, from time to time, noises add up to something more significant.

It is a very basic answer, since we would need quite some more technicality to be a bit more accurate.

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Anything with a temperature above 0 Kelvin emits EM radiation. In outer space a body will not receive a lot of EM radiation and will cool down very fast.
In our environment - because of the temperature around us of about 20° C -, things emit infrared radiation (in addition to reflection in the visible light range).
In the case of burning wood, chemical processes realize energy and the fire glow not only in the IR, but also emit EM radiation in the visible range.

How does the action of burning wood produce an oscillating electromagnetic field which manifests itself as visible light?

All EM radiation has its origin in the relaxation of subatomic particles to lower states. Mostly electrons are excited by incident radiation or chemical or physical processes and from excited states they fall back into lower states and emit photons.

It must be emphasized that all EM radiation has its origin in the emission of photons and that EM radiation is always a stream of photons.

Are these photons synchronized to possess the properties of periodic intensity that constitutes a wave? They're not. The excited electrons fall back at different times and intensities, so that the emitted photons are random in their energy and their emission time. Not every EM radiation has the properties of a wave.

Radio waves have the properties of a wave. Electrons on the skin of the antenna rod are accelerated almost synchronously and thus emit photons almost simultaneously and in a small range of EM radiation.

Since this acceleration is repeated periodically - otherwise the acceleration process will simply come to a standstill after electrons have been shifted to one end of the rod - the emission of photons also occurs periodically and with changing sign and leads to a wave characteristic of the EM radiation.

The radio wave has an electric and a magnetic field component, both oscillating perpendicular to the direction of propagation and both (strictly speaking only in vacuum) perpendicular on each other.

enter image description here The image from Wikipedia shows only the electric field component, the magnetic field oscillates up and down.

It is only one step to infer the fields of the contained photons from the (for the first time by Hertz) measured field components of a radio wave. Each photon propagates like a wave with its oscillating E and M field components.

Furthermore, in particle physics, in the creation of particles, one simply assume that if there is enough energy, a photon can pop out of vacuum. But since a photon will imply an oscillating electromagnetic field, what exactly is the mechanism that produces this oscillating electromagnetic field?

The reason and the mechanism behind the oscillating photons are unknown. But the phenomenon is consistent with respect to the emitting particles. Charges - electrons and protons - have an electric field and a magnetic dipole and an energy content. They release energy in the form of quanta. How these photons oscillate with their E and M field is unknown.

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