# Exploring Electromagnetism & Quantum Mechanics

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• sol47739
In summary, the conversation discusses the principles of classical electromagnetism and how it relates to quantum mechanics, specifically in terms of electron acceleration and photon emission. It is explained that in classical electromagnetism, an accelerating charge emits electromagnetic radiation, whereas in quantum mechanics, electrons can only emit photons in quantized packets of energy. The conversation also delves into the workings of a radio antenna and receiver in quantum mechanical terms, and how the emission of photons is responsible for the smooth appearance of a wave signal. Finally, the conversation touches on the continuous versus spontaneous emission of photons in different scenarios, such as in a synchrotron or a current loop.
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?

sol47739 said:
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.
sol47739 said:
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.
sol47739 said:
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.

Twigg
WernerQH said:
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?

WernerQH said:
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?

sol47739 said:
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.
sol47739 said:
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.
sol47739 said:
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.

Twigg and sol47739
sol47739 said:
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.

vanhees71 and PeroK

## What is electromagnetism?

Electromagnetism is a branch of physics that deals with the interactions between electrically charged particles. It explains how electricity and magnetism are related and how they affect each other.

## What is quantum mechanics?

Quantum mechanics is a branch of physics that studies the behavior of matter and energy at a very small scale, such as atoms and subatomic particles. It explains how particles behave and interact with each other at the quantum level.

## How are electromagnetism and quantum mechanics related?

Electromagnetism and quantum mechanics are closely related because both theories explain the fundamental forces and interactions between particles at a subatomic level. In fact, quantum mechanics is used to explain the behavior of electromagnetic fields and particles.

## What are some real-world applications of electromagnetism and quantum mechanics?

Electromagnetism and quantum mechanics have numerous practical applications in our daily lives. Some examples include electronic devices such as computers and smartphones, medical imaging technologies like MRI machines, and energy production through nuclear power plants.

## What are some current research topics in electromagnetism and quantum mechanics?

Scientists are currently researching various topics related to electromagnetism and quantum mechanics, such as quantum computing, quantum entanglement, and the development of new materials for energy storage and transmission. Other areas of interest include the exploration of dark matter and dark energy, as well as the search for a unified theory that combines electromagnetism and quantum mechanics with gravity.

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