# Connection between photons and EM waves

We learn about electric and magnetic fields and how they conform EM waves. Then we discover the photon and how there was a duality between this two ideas, sometimes radiation behaved like a wave and sometimes like a particle. Now with QED we know for sure that radiation is a particle, but exhibits a wave behabiour due to its quantum properties.

My doubt comes when, for example, we take a metal bar (aka: antenna) and we irradiate it with an EM wave, we know that the changing electric field will move the electrons up an down in the antenna creating an alternating current. This is obvious if we interpret the wave as a field with some certain direction. How can this phenomenon be explained if we think of radiation as photons? In which way can photons contain the direction information of the previous electric field?

Another experiment is putting an electron between two charged plates (i.e inside and electric field). How QED explain the interacction between the electrons and the photons so the electron moves in the opposite direction of the "field"?

• Most general connection between particles and waves is De Broglie relation $h=\lambda p$. Put wavelength - get momentum back, put momentum and get wavelength. Second experiment can be explained that field photons scatters electron to an average direction of movement. Dec 30, 2023 at 15:05
• But how do the photons know in which direction to push? If the electric field has a direction, in which way the photons carry that direction information? I assume maybe the wavefunction of the photons carry information about the field direction...? Dec 30, 2023 at 15:21
• They don't. Photon momentum is aligned with electric field lines or so to say is collinear to EM wave poynting vector. Dec 30, 2023 at 17:33
• These answers of mine to relevant questions may help physics.stackexchange.com/questions/750499/… , physics.stackexchange.com/questions/273032/… Dec 30, 2023 at 17:38
• What are photons, EM radiation and EM waves Jan 1 at 6:33

I am not sure that my answer will really answer your question. But I hope it helps. You might also check Anna V's answer to How do photons induce current in an antenna?. Or Relation between radio waves and photons generated by a classical current

The connection between photons and EM waves is like the connection between molecules and sound waves. In a microscopic view, interactions are discrete collisions. In a macroscopic view, you see the average of a large number of tiny collisions as a smooth pressure.

Of course for light, the quantum nature of photons is important to understand the collisions.

It is an approximation to say that a photon is a classical particle or that it is a classical wave. It is enough like both that thinking about them shows some similarities to photon behavior. But they are different enough to lead you to think about photons incorrectly.

Furthermore, the electromagnetic forces between charged particles are mediated by virtual photons. It is another approximation to say that virtual photons are photons that momentarily exist. The interaction when light scatters off a charged particle is complex. It is tractable as a perturbation expansion. There is a central term, and then many terms that add a little to the result. Virtual photons correspond to these additional terms. The effect of these terms is something like the effect of a photon. The best explanation might be Of Particular Significance .

My doubt comes when, for example, we take a metal bar (aka: antenna) and we irradiate it with an EM wave, we know that the changing electric field will move the electrons up an down in the antenna creating an alternating current. This is obvious if we interpret the wave as a field with some certain direction. How can this phenomenon be explained if we think of radiation as photons?

What is the origin of the EM wave that triggers an alternating current in a receiving conductor piece?
With the help of an AC generator, electrons are accelerated back and forth in an antenna conductor rod. Each acceleration allows the surface electrons of the rod to emit photons. Namely polarised photons, each half-period of the generator parallel to the rod and then again antiparallel.
The number of emitted photons occurs largely according to a sine function (increasing and then decreasing number of photons with upwardly directed electric field and than for the next half period increasing and decreasing number of photons with downward directed electric field).

There is a great error or misconception of the nature of light since Plancks days: When Einstein conjectured, that light comes quantized in particles in 1909, Planck replied, that the young man was a bit too fast with his theoretical projections.

Planck was right: he only assumed, that in the exchange process of energy-momentum-spin between a enumerable mechanical system, e.g. an electron bound to an atom, and the electromagnetic field in a box, occurs in integer packets in the purely geometric physical entities, energy, momentum and spin.

There is a fundamental difference between the enumerable massive charged particles and the assumed photons, the exchange quanta with the abstract quantized em-field of the environment.

Fermions obey the Pauli principle and therefore, even if identical and indiscernible, can be enumerated and there always will be a 1-1 map between occupied 1-particle states in an product representation and the enumeration particle list.

The electromagnetic field on the other hand, is present everywhere, acts as a whole on all massive charged particles as the same field and can be represented as an infinite sum over all classical modes $$(\omega=|k|,\vec k)$$ for any representation at hand and suitable to fit geoemetry.

The quantized Fourier mode in a basis, free for a choice to fit boundary conditions in a experimatally fixed geometry, have no reality during free time evolution, they do not interact and any of the denumerable modes can be created in an infinite integer ladder of energy steps of $$\bar \omega$$.

This property is the fundamental for the freedom of basis transforms of the mode space in a given geometry.

This picture, that light is a classical wave, acting as an environmental medium, with integer quantized energy and spin ladders, has been developed over time during the 1950ties, but never reached the high school physics.

Still up today you will find denumerably infinite web pages discussing particle-wave duality and the abstruse question which slit a photon is taking: If there is a slit, the fundamental modes of the field all have a this slit boundary condition with the geometric consequences observable at any harbour with a bulwark or two openings: The quantized modes all have to have a zero at the wall.

If one is using wrong, nonfitting boundary conditions, by the completness of any mode Hilbert space, its possible to expand a single eigen mode with slit into an infinite convergent sum eg of free waves. But that approximation is useless, it converges in theory only. There is a general theorem, that says that single mode expansion with wrong boundary conditons converge as 1/n only, which is useless for finite approximations.

The QED industry has invested billions of dollars during the last century to explain any classical em-wave-electron by exchange of photons, culiminating in all the nonsense published about Casimir forces.

So, for the interpretation of the Hertz dipol, write down the electron surface field in a conductor at the thermodynamic Fermi level on the antenna and set up the classical Maxwell electromagnetic field equations with a conducting cylinder in the center, that is: normal E is charge density, tangent B is current density.

Use elliptical coordinates, a fixed frequency $$\omega$$ and divide the field into incoming and outgoing waves their diffences in energy and spin will be coupled somhow to the vacuum impedance of the antenna.

After the classical part is done, the quantization of the two fields eventually can be broken down to the field of a single free electron on a semiconconductor antenna and a 1-photon intensity in the sense of an Aspect scattering experiment.

The Nobel price came for these experimens confirming Plancks original ideas. The one- particle antenna and the single photon exchange with the environmental em field is the theory of the H-atom from the beginning.