# How is electric field arising from photons? [duplicate]

This question has nothing in common with the question it is proposed to be duplicate e.g about virtual photons. The question is about a real radiation field where is known that no virtual photons exist.

The electric field E moving up and down (in its value) as a sinusoidal wave, which has been regularly shown in EM books should move a probe electron up and down (in space). How does a photon picture make this pattern, as the photon is moving forward (not up and down) its momentum is perpendicular to E? Of course there is also magnetic momentum but it is too faints. If one uses Feynman diagrams (as is proposed in the answer of Lubos in the proposed duplicate question) for electron photon scattering the momentum of the electron should also be in the photon's direction and not perpendicular as the EM picture suggests.

• The em wave diagrams you see, are oscillating electric and magnetic fields , on a single line, these are not spacial oscillations , they are the oscillations of the EM field associated with a particular POINT in space. Mar 13, 2022 at 17:39
• Does this answer your question? Virtual photon description of $B$ and $E$ fields Mar 13, 2022 at 20:00
• @jensenpaull i didn't say that E is oscillating in time and space. The oscillation are of the electron in the E field. The electron is oscillating because the force is F=eE. Mar 13, 2022 at 20:44
• @JohnRennie well I never thought that the E filed is comprised of virtual photons. Is the E field also virtual? I will look at your link definitely. Mar 13, 2022 at 20:47
• You are talking about an oscillating charge, this oscillating charge causes electromagnetic waves, which are oscillating Electric and magnetic fields. The "wave diagram" of an EM wave are field oscillations, not spacial ones. Mar 13, 2022 at 21:09

A photon is not a particle in the classical sense of the word.

A photon is a quanta of the radiation field.

Suppose you've got your sinusoidal Electric field, Suppose as you fix the energy say, hv, then the phase is maximally unknown.(Quantum Mechanics)

In a way a photon is much more similar to a field than a particle.

The emergence of the classical Electric field from photons can be understood in the "coherent state" representation of the Hilbert space.(The point is that, the field becomes classical in the limit where the average number of photons of a favored mode goes to infinity and the field becomes similar to a classical sinusoidal wave in the favored mode)

• It is well known that a photon has momentum forward. Where it is is also known at the moment of the interaction (electron accepts it). The question is why the electron should move up-down when the momentum is forward. Mathematics just makes the things obscured. Mar 14, 2022 at 8:29
• Well it's a good question. For wavelengths below the Compton wavelength of the target, the wave like behavior of the photon is dominant, and when the Compton wavelength of the target is greater than the wavelength of the incoming photon then the particle like nature of the photon is dominant. That's the very cocept of particle-wave duality that can be unified in the context of any QFT including QED. Mar 14, 2022 at 8:44

Photons in mainstream physics, are quantum mechanical entities which in great numbers build up the classical electromagnetic radiation, which is what you are describing with the changing fields.

This picture for circularly polarized light gives an intuition how the classical wave is built up from a quantum mechanical substrate of photons.

One needs the mathematics of quantum mechanics in order to really understand this.

Also this double slit experiment can give an intuition how photons, when detected one by one leave a footprint of a particle on the screen,

Figure 1. Single-photon camera recording of photons from a double slit illuminated by very weak laser light. Left to right: single frame, superposition of 200, 1’000, and 500’000 frames.

but in a large accumulation the classical interference pattern of the wave nature appears on the right, connected with the probabilistic nature of quantum mechanics.

One needs to study quantum mechanics to master this.

• Do you know why the photon which is hitting forward is causing an electron to move up-down e.g. perpendicular to the push F=eE. Do really the field jiggle up-down as represented (because of the mass of the electron it is quite impossible to follow the speed c of EM wave)? Maybe the picture of EM is illusion. Electron can not follow it. Mar 14, 2022 at 8:38
• You need quantum mechanics for electron photon interactions . for beam of electrons and laser beam see uspas.fnal.gov/materials/08UMD/Lecture5.pdf Mar 14, 2022 at 9:41
• In QM the electron is not afaik free but in atom and there are transitions li>-> lj>. I think you mean QED but it is also not useful because there only Feynman diagrams and the momentum is forward, which is not what EM is pictured. I'm not interested in dense fields and electron jets, but a single electron + monochromatic asap EM wave. Mar 14, 2022 at 12:18
• google "feynman diagram electron photon scattering" and you will see how many QED diagrams exist depending on the energies involve between free electrons and free photons. Mar 14, 2022 at 12:44
• "perpendicular to the push F=eE." at the level of photons there is no push, as the photon has no electric field, just photon electron scattering quantum mechanically, only the probability of scattering is predicted, and is seen in the data of the double slits on the right. Mar 16, 2022 at 5:51