Exploring Electromagnetism & Quantum Mechanics

[sol47739]

TL;DR Summary

I have some questions about accelerating charges and how a radio antenna would be explained in quantum mechanical terms.

In classical electromagnetism I think I have understood the following(please correct me if something is wrong): A charge produces an electric field, a charge moving with constant velocity produces a magnetic field, an accelerating charge emits electromagnetic radiation. In radio antennas this is used to make electrons accelerate back and forth, this back and forth acceleration of electrons produces an electromagnetic wave, which propagates through space and when arriving to the receiver make the electrons move in a corresponding way in the receiver, and the motion of these electrons gets then converted into sound waves.


In quantum mechanics electrons can only emit photons, which are quantized packets of energy. An electron either emits or not, it is not a continuously electromagnetic wave that is emitted. I wonder how would a radio antenna that emits and a receiver be explained in quantum mechanical terms? What makes the signal still being so smooth, and exactly what is it in the antenna that emits photons giving the appearance of a smooth wave?


Also in quantum mechanics if an electron is accelerating, in which manner does it emit it’s photons? Like in a synchrotron does the electron emit photons continuously all the time or just a very frequently spontaneous emission process?


To summarize what I want to know: In which manner does an unbound accelerating electron emit photons? And how does a radio antenna work from a quantum mechanical perspective?

 

[WernerQH]

In classical electromagnetism I think I have understood the following(please correct me if something is wrong): A charge produces an electric field, a charge moving with constant velocity produces a magnetic field, an accelerating charge emits electromagnetic radiation. In radio antennas this is used to make electrons accelerate back and forth, this back and forth acceleration of electrons produces an electromagnetic wave, which propagates through space and when arriving to the receiver make the electrons move in a corresponding way in the receiver, and the motion of these electrons gets then converted into sound waves.

Correct.

In quantum mechanics electrons can only emit photons, which are quantized packets of energy. An electron either emits or not, it is not a continuously electromagnetic wave that is emitted. I wonder how would a radio antenna that emits and a receiver be explained in quantum mechanical terms? What makes the signal still being so smooth, and exactly what is it in the antenna that emits photons giving the appearance of a smooth wave?

The packets are very small. If you work out the numbers, a 100 W transmitter produces at a frequency of 100 MHz on the order of $10^{27}$ photons per second (each photon having an energy of $6.626 × 10^{-26}$J. The signal appears smooth for the same reason as water running from a tap looks smooth, even though it comes in packages of $\rm H_2O$ molecules.

Also in quantum mechanics if an electron is accelerating, in which manner does it emit it’s photons? Like in a synchrotron does the electron emit photons continuously all the time or just a very frequently spontaneous emission process?

It's not continuous, but an extremely rapid series of spontaneous emission processes.
If you replace the synchrotron by a current loop, you also have these emission events, but since the electrons are so numerous and are homogeneously distributed along the wire, the waves emitted by the electrons interfere destructively and you get a static magnetic field.

 

[sol47739]

The packets are very small. If you work out the numbers, a 100 W transmitter produces at a frequency of 100 MHz on the order of 1027 photons per second (each photon having an energy of 6.626×10−26J. The signal appears smooth for the same reason as water running from a tap looks smooth, even though it comes in packages of H2O molecules.

Yes, I understand, but how are the photons in the wire produced? Is it that the electrons get excited from the valence band in the conduction band and then they emit? Or is it rather that they always are present in the conduction band where they are able to move freely and when voltage is applied they start to move in one preferred direction? And then it becomes some harmonic oscillating motion and during the acceleration in this motion the electromagnetic waves are emitted? But what is it that makes the emission "ordered" in the right way as in classical electromagnetism?

It's not continuous, but an extremely rapid series of spontaneous emission processes.
If you replace the synchrotron by a current loop, you also have these emission events, but since the electrons are so numerous and are homogeneously distributed along the wire, the waves emitted by the electrons interfere destructively and you get a static magnetic field.

Okey, thanks for your answer, I see. So if I understand correctly no matter in what circumstances an electron is accelerated, in vacuum, synchrotron or within a metal it will emit photons? And these are originally due to spontaneous emission also in a non bound free state?

 

[WernerQH]

Or is it rather that they always are present in the conduction band where they are able to move freely and when voltage is applied they start to move in one preferred direction?

Yes.

But what is it that makes the emission "ordered" in the right way as in classical electromagnetism?

The electric field in matter is a complicated sum of the fields of the electrons and nuclei. In classical electrodynamics you use a "coarse grained" picture, i.e. you look at averages over the fields. And this average is ordered in the same sense as wind speed is a more "orderly" description of the motion of air molecules.

So if I understand correctly no matter in what circumstances an electron is accelerated, in vacuum, synchrotron or within a metal it will emit photons? And these are originally due to spontaneous emission also in a non bound free state?

Of course the environment has a strong influence. You never have a completely isolated electron. If it is in a waveguide, for example, emission at some frequencies cannot happen. There is some back-reaction from the electrons in the waveguide.

 

[Demystifier]

In quantum mechanics electrons can only emit photons, which are quantized packets of energy. An electron either emits or not, it is not a continuously electromagnetic wave that is emitted. I wonder how would a radio antenna that emits and a receiver be explained in quantum mechanical terms? What makes the signal still being so smooth, and exactly what is it in the antenna that emits photons giving the appearance of a smooth wave?

It's not exactly true that a photon is either emitted or not. A typical quantum state of EM field produced by the antenna is a superposition of the form: vacuum + 1 photon state + 2 photon state + ... . Usually such a state has the form of a coherent state, which has properties very similar to the classical radiation field. A definite number of photons can only be associated with it when the number of photons is explicitly measured, which in practice is rarely done. That's one reason for the appearance of smoothness. Another, more intuitive, reason is that the average number of photons is huge. Roughly, this is similar to the fact that the picture on your screen on which you read this looks smooth, even though the screen is made of discrete pixels.