[hamdani yusuf]

So the problem starts with the way the question was phrased.

Can you suggest a better way?

[hamdani yusuf]

So, in QFT, there is a photon field but there is NOT any fundamental Electric field or Magnetic field.

So, we might imagine that an e-m wave is a collection of many photons or that an experiment involving one photon has been done many times and the e-m wave we observe is the combined average of all of these.

How does it explain electrostatic and magnetostatic fields?

[hamdani yusuf]

If you could fire just one photon through the usual double-slit experiment apparatus,   then you probably won't get an interference pattern on the screen at the end.   Instead we think you'll get just one spot to glow on the screen.

You seem to interpret one glowing spot on the screen as an event of a single photon being detected. Have you considered some alternative interpretations or explanations?

Have you considered that a single slit experiment, when the width of the slit is equal to the distance between the slits in double slit experiment, will also produce interference pattern on the screen with comparable size?

[hamdani yusuf]

However, this demonstration gets close and claims to be using such a thin and dim stream of light that only "a few" photons per second will be produced.
https://sciencedemonstrations.fas.harvard.edu/presentations/single-photon-interference

Here's a comment by the author of the article.

In our previous paper1 we pointed out that, strictly speak-
ing, we are not detecting single photons of light but rather
single photoelectrons liberated by the light impinging on the
detector; this is still true in the present experiment.
Furthermore, the detection of a photoelectron does not neces-
sarily imply that a single photon arrived.

[hamdani yusuf]

many different versions of Quantum Mechanics.

By the name only, we already get quantum mechanics, quantum electrodynamics, quantum chromodynamics, quantum field theory.

[alancalverd]

Can quantum mechanics explain the generation, propagation, and reception of radio waves?

It doesn't need to. Continuum physics does the job adequately below the terahertz region.

[hamdani yusuf]

Can quantum mechanics explain the generation, propagation, and reception of radio waves?

It doesn't need to. Continuum physics does the job adequately below the terahertz region.

Can we use quantum mechanics to explain it?

[Eternal Student]

Hi.

[ES said]  So the problem starts with the way the question was phrased.
[Hamdani replied]  Can you suggest a better way?

     Obviously it's up to you to create your own question.   You can ask whatever you want.

      However, Gemini will be lead by the question you asked.  It rarely considers that the user has some faults or misconceptions (other than just spelling errors) in the question they ask.

     I am also going to be lead by the question but I am able to recognise that the question involves a classical phenomena while you seek an explanation involving quantum or discrete phenomena.
So the question is a special case of a more general question:
    Can Quantum Mechanics recreate or explain ALL classical phenomena?
    --->  I don't know and possibly we (physicists) haven't tested them all and nobody knows  BUT  it seems that it does recreate a great many of them very sucessfully.   Since the early development of QM one standard "test" or criteria for establishing the reasonableness of any new piece of quantum theory has been that it will reduce to a well established classical theory under suitable conditions  (for example, in the limit  ħ --> 0 ).
[Reference:  See https://en.wikipedia.org/wiki/Correspondence_principle  for some more discussion ].   It (Quantum Mechanics) also models or predicts some things which classical physics would not adequately model or explain.

How does it explain electrostatic and magnetostatic fields?

         With various pieces of mathematics which I would struggle to explain here in a short amount of time.    Typically you build (or propose) a Lagrangian that you believe describes the system.  There are some commonly used models that fit with observations well, so you don't just have to dream up a new Lagrangian every time.   It is then common to apply what is often called "Propagator Theory" and identify a suitable "propagator".

- - - - - - - -
An extract of some notes from the Physics module "Theoretical Elementary Particle Physics" by Nottingham University, United Kingdom.

Propagator theory.jpg (118.58 kB . 868x539 - viewed 38 times)

- - - - - - - - -
    It is possible to construct Feynman rules and suitable Feynman diagrams from these expressions.   With these sorts of diagrams, it is common to imagine that a pair of interacting particles (say two electrons with the usual negative charge) would be seen to move along for a short while and then exchange a virtual photon and end up moving slightly differently.   That is understood as the electrostatic repulsion between the electrons.    However, these Feynman diagrams are really just for convenience and provide a simple way to "visualise" and describe what is happening.   It is just the mathematics, the evolution of the wave function(s) we would obtain as an approximate solution using propagator theory that is really being shown in those diagrams.   The "virtual particles" are not something concrete that we could actually find or detect.

Let's paraphrase or summarise this again:  So how does this QM theory explain electrostatic interactions?   Well, it doesn't even attempt to "explain" these interactions.  It just provides an abiltiy to calculate the results.   It (the theory) just shows how the wave functions should evolve.   We (human beings) add a layer of interpretation on the top of this, we use terminology like "virtual particles" and build a useable and more intuitive way of thinking about or "explaining" the interaction to our satisfaction.

Concerning the double slit experiment with a single photon,  Hamdani said:  You seem to interpret one glowing spot on the screen as an event of a single photon being detected. Have you considered some alternative interpretations or explanations?

     Yes and it is very much as you described in a later post.

In our previous paper1 we pointed out that, strictly speak-
ing, we are not detecting single photons of light but rather
single photoelectrons liberated by the light impinging on the
detector; this is still true in the present experiment.
Furthermore, the detection of a photoelectron does not neces-
sarily imply that a single photon arrived.

    I don't know if we can ever be sure that we will detect a single photon in the sense of a small packet of light hitting only one spot.   No matter how much we think that only a single particle of light has been created and sent into the apparatus, it could still be a spread out wave of stuff that actually arrives at the detector screen.   Due to some properties of the screen all the energy is collected and deposited into just one small bit of the screen so that only that bit of that screen will glow.   
     It's interesting.  Is there a particle of light to be found and detected or is that just an object of convenience?  I don't know.  It's not necessarily important.   Simple Quantum Mechanics would quite like to have a particle of light, a photon, but provided the end result is an interaction that looks like a single particle interaction then "a photon" could just be an object of mathematical convenience.      With just a minor change in semantics, the popular phrase about light would still apply and the same Mechanics can be used to predict results:  "it travels as a wave and interacts as a particle".

...By the name only,...

     I didn't really understand what you meant here.    QED  ,  QCD,  QFT   and what I have tended to call simple QM differ by more than just their names.    For example, Simple QM is based on the original Schrodinger Equation which is non-relativistic in nature.   QFT is a relativistic quantum theory and was motivated by alternatives to the Schrodinger equation such as the Klein-Gordon and Dirac equations.

Best Wishes.

[hamdani yusuf]

 I didn't really understand what you meant here.    QED  ,  QCD,  QFT   and what I have tended to call simple QM differ by more than just their names.    For example, Simple QM is based on the original Schrodinger Equation which is non-relativistic in nature.   QFT is a relativistic quantum theory and was motivated by alternatives to the Schrodinger equation such as the Klein-Gordon and Dirac equations.

I meant that even if we only consider the names, we get many versions of quantum theories. If we also consider the different interpretation, we get even more.

[hamdani yusuf]

I asked ChatGPT if Maxwell's equations can be derived from quantum mechanics.

Maxwell's equations, which describe classical electromagnetism, are not directly derived from quantum mechanics. Instead, they emerge as a limit or approximation in the classical regime of quantum field theory, specifically quantum electrodynamics (QED).

Here?s an overview of how the two are related:

### 1. **Quantum Electrodynamics (QED) and Gauge Symmetry**:
   - In QED, the electromagnetic field is described by the photon, which is a quantum particle associated with the electromagnetic field. The interactions between charged particles, such as electrons, and photons are governed by the principles of QED.
   - QED is based on the principle of gauge symmetry, specifically U(1) gauge symmetry. This gauge symmetry is directly related to the structure of Maxwell's equations. Imposing U(1) gauge invariance leads to the field equations that resemble Maxwell's equations in the classical limit.

### 2. **Classical Limit of Quantum Field Theory**:
   - When the quantum aspects (like particle-wave duality and uncertainty) of the electromagnetic field are ignored, or when considering the behavior of large numbers of photons, the quantum fields reduce to classical fields. In this classical limit, Maxwell's equations naturally emerge.
   - For example, the classical electric and magnetic fields are interpreted as the expectation values of the quantum field operators in certain states (such as coherent states).

### 3. **Relation to Quantum Mechanics**:
   - Although Maxwell's equations arise from QED, they cannot be directly derived from non-relativistic quantum mechanics. In quantum mechanics, the interaction of charged particles with an electromagnetic field is incorporated via the minimal coupling of the electromagnetic potential A_\mu to the particle's wavefunction. However, this coupling is taken as a given, and the dynamics of the electromagnetic field itself is still described classically by Maxwell's equations.
   - The full quantum treatment of the electromagnetic field requires quantum field theory, not just quantum mechanics.

In summary, while Maxwell's equations emerge from the more fundamental framework of quantum electrodynamics, they are not directly derivable from quantum mechanics itself. Instead, they correspond to the classical limit of the quantum field describing electromagnetism.

[hamdani yusuf]

Have you considered that a single slit experiment, when the width of the slit is equal to the distance between the slits in double slit experiment, will also produce interference pattern on the screen with comparable size?

Interpretation of the double slit experiment with dim light source and polarizers as a result of observer effect on which way detection has created more confusions than the explanation it had to offer. It lead to the introduction of quantum eraser, and subsequently, delayed choice quantum eraser paradox.
https://en.m.wikipedia.org/wiki/Delayed-choice_quantum_eraser

They don't seem to have considered that a double slit apparatus has 4 edges, nor that a single slit experiment with comparable slit width as the distance between the double slits would produce a similar result of diffraction-interference pattern, although with different positions of bright and dark fringes.

[alancalverd]

I don't know if we can ever be sure that we will detect a single photon in the sense of a small packet of light hitting only one spot. 

Consider a gamma ray emitted from the nucleus of an atom.

We know that nuclei are "quantised" - atoms are individual and the nuclei in any state of matter are very small and a long way apart compared with the constituents of the electron cloud.

We know that nuclear disintegrations are quantised - each gamma ray has a unique energy and the residual nucleus cannot emit another of the same energy because it is transformed by the first emission.

We know how many nuclei there are in a gamma source, and knowing the half life of the material we can calculate the probability of two photons  arriving at the same point in space within any time interval.

Now set up a weak gamma source at such a distance from a small detector that the probability of more than one photon arriving within the time resolution of the detector is negligible. Every gamma event that we detect is the result of a single photon interaction with the detector.

[paul cotter]

I disagree, Alan, specifically with your last sentence. I would say there is a high probability that such events are single photon events but we cannot say absolutely that it is a single photon interaction. Disintegrations are random events as I am quite sure you know. Yours sincerely, pedantic engineer.

[alancalverd]

Let's propose an entirely feasible experiment.

Consider a source of radius 1 mm  and activity 1MBq, i.e. 1,000,000 disintegrations/second

The probability of two disintegrations occurring within Δt of each other is 0.5 x 1,000,000 x Δt

Use a small (1 cm²) detector with resolution Δt = 1 μs at 1 m from the source.

The photons will be emitted in random directions but symmetrically from the source so the number reaching the detector at 1 m will be about 8 per second. 

And the probability of two photons emitted within 1 μs of each other and both striking the detector is 4 x 10^-6

I think you will agree that the probability of any recorded event being the product of more than one photon is negligible, and if you record several events with the same energy transfer (the pedantic bit), I think you can reasonably conclude that you are recording single photon events.

I'm not sure what the modern equivalent of a GeLi detector is, but we used to do this sort of thing with buckets of liquid nitrogen and a rack of single-transistor electronics.

So to return to the question, yes, quantum mechanics could be wrong, but in my humble experience it has been a damn good approximation!

[paul cotter]

Agreed. You know my obsession with pedanticism(pedantry?). I think we can now close this question with your last sentence.

[alancalverd]

I've just increased the source activity and put some numbers into my "feasible experiment". It turns out to be really feasible! 

[paul cotter]

Enclose the whole gizmo with a thick blanket of lead, please. We don't want to lose you prematurely.

[alancalverd]

Since I already contain 5 kBq of natural and essential potassium, I'm probably in greater danger from myself than from a 1 MBq point source a meter away!

[paul cotter]

I have not a clue how to come up with a Sievert or rem figure for your experiment. 1000Mhz was the highest I worked with, obviously non ionising.

[hamdani yusuf]

Have you considered that a single slit experiment, when the width of the slit is equal to the distance between the slits in double slit experiment, will also produce interference pattern on the screen with comparable size?

Interpretation of the double slit experiment with dim light source and polarizers as a result of observer effect on which way detection has created more confusions than the explanation it had to offer. It lead to the introduction of quantum eraser, and subsequently, delayed choice quantum eraser paradox.
https://en.m.wikipedia.org/wiki/Delayed-choice_quantum_eraser

They don't seem to have considered that a double slit apparatus has 4 edges, nor that a single slit experiment with comparable slit width as the distance between the double slits would produce a similar result of diffraction-interference pattern, although with different positions of bright and dark fringes.

So, instead of closing one of the slit, you can just simply remove the middle part of opaque material in the double slit apparatus, and see the changes in the diffraction-interference pattern on the screen. There's now only one path, but it still produces diffraction-interference pattern on the screen.