[hamdani yusuf (OP)]

My conclusion thus far regarding the title is because we can't make a transmitter with less than one electron, and we can't make a receiver with less than one electron either.

The receiver is irrelevant. And if you accelerate a single electron continuously, say with a sinusoidal electric field, you won't generate quantised photons, just a continuous em wave.

How would you generate sinusoidal electric field using less than 1 electron?

[hamdani yusuf (OP)]

Answer to If photons cannot interact with themselves, why is there an interference pattern in the double slit experiment? by Viktor T. Toth https://www.quora.com/If-photons-cannot-interact-with-themselves-why-is-there-an-interference-pattern-in-the-double-slit-experiment/answer/Viktor-T-Toth-1?ch=3&oid=309004362&share=a36eec57&srid=uvWW4&target_type=answer

If light consisted of miniature cannonballs, we would see no interference pattern.

But that?s not how things work. Photons are indeed the quanta of the electromagnetic field, but they?re not miniature cannonballs. They are units of energy that may or may not be localized (confined to a small, compact volume.)

Assuming that a photon is like a miniature cannonball only produce more confusion and even contradiction, rather than clarity. Unfortunately, that's how it's often depicted in many popular physics literatures.

[alancalverd]

How would you generate sinusoidal electric field using less than 1 electron?

Impossible and irrelevant!
Consider an oscilloscope tube, or a linear accelerator flight tube,  with electrostatic deflection plates. apply a sinusoidal voltage to the plates, and reduce the beam current to one electron at a time. What happens to that electron?

[alancalverd]

Assuming that a photon is like a miniature cannonball only produce more confusion and even contradiction, rather than clarity. Unfortunately, that's how it's often depicted in many popular physics literatures.

For the nth time: we need two models to describe the properties of EM radiation. At low energies a wave model is most useful but at high energies the generation of EMR and its interactions with a target are better described by a particle model. 

[varsigma]

Is radio wave also quantized?

All EM radiation is quantized. But there is a problem with measurement and it has to do with the wavelengths.

These days (and actually for all the days before) radio wavelengths mean you need a big enough (in terms of wavelength) transmitting or receiving device. We call them antennas, but that's our business. The need isn't something we can choose to ignore.

[alancalverd]

All EM radiation is quantized.

I can generate any frequency of radio waves, continuously, for as long as I like, by an entirely linear and continuous process. Reception is likewise continuous. No charged particles jump between excited states at either end of the system. What is the energy of the quantum of 100 kHz EMR generated and  emitted for 1 second? 1.01 seconds? 

[varsigma]

I can generate any frequency of radio waves, continuously, for as long as I like, by an entirely linear and continuous process.

Yes, but the process is continuous because you don't get to see individual, long-wavelength photons. Emission of photons by charged particles is still a hot topic in research labs.

We're talking about the electromagnetic field as if it's fully understood, done and dusted. It's not true, yet.

[hamdani yusuf (OP)]

How would you generate sinusoidal electric field using less than 1 electron?

Impossible and irrelevant!
Consider an oscilloscope tube, or a linear accelerator flight tube,  with electrostatic deflection plates. apply a sinusoidal voltage to the plates, and reduce the beam current to one electron at a time. What happens to that electron?

That's exactly why electromagnetic radiation is quantized. Because electric charge and it's mass are quantized.

[alancalverd]

But the electron in question follows a smooth sinusoidal path and therefore generates a continuous EM wave at whatever frequency we choose. The emitted radiation is not quantised.

[varsigma]

But the electron in question follows a smooth sinusoidal path

I have to say this: you're making an assumption that fits a classical description of electron motion.

[alancalverd]

I'm just looking at the electron beam in an oscilloscope. I can measure the beam current, and I can deflect it with a time-varying and/or distance-varying magnetic or electric  field. So I can make a single electron follow any path through space, and whenever it changes direction, it will emit em radiation thanks to Maxwell. Indeed that is the reason for the failure of the Bohr model of the atom, and the need for Heisenberg, Schrodinger, and quantum mechanics!

So if I subject the electron beam to  a spatially sinusoidal static field, what is the energy of the supposedly quantised em radiation it emits? Why is it not a continuum?   

AFAIK the spectrum of x-rays from an undulator or a wiggler is a continuum.

[hamdani yusuf (OP)]

So I can make a single electron follow any path through space, and whenever it changes direction, it will emit em radiation thanks to Maxwell.

Except if there are one or more electrons moving in such a way that cancels it out.

[hamdani yusuf (OP)]

So if I subject the electron beam to  a spatially sinusoidal static field, what is the energy of the supposedly quantised em radiation it emits?

How do you construct that spatially sinusoidal static field?

[hamdani yusuf (OP)]

These days (and actually for all the days before) radio wavelengths mean you need a big enough (in terms of wavelength) transmitting or receiving device. We call them antennas, but that's our business. The need isn't something we can choose to ignore.

Not really. Stub antenna can still work, albeit not as efficient as normal ones.

[hamdani yusuf (OP)]

But the electron in question follows a smooth sinusoidal path and therefore generates a continuous EM wave at whatever frequency we choose. The emitted radiation is not quantised.

It's quantized by the number of electrons you made to follow that path. You can't half it down.

[alancalverd]

How do you construct that spatially sinusoidal static field?

Look at any cathode-ray oscilloscope, electron microscope, or particle accelerator. Magnetic deflection is often easier but I built electrostatic deflectors about 60 years ago. 

[alancalverd]

It's quantized by the number of electrons you made to follow that path. You can't half it down.

The frequency of the emr is not quantised. I can give it any value I choose.

Incidentally, I have just bought "Quantum Mechanics for Babies", for my 2-year-old grandson. It's very good. 

[hamdani yusuf (OP)]

It's quantized by the number of electrons you made to follow that path. You can't half it down.

The frequency of the emr is not quantised. I can give it any value I choose.

Did anyone told you otherwise?

[alancalverd]

The question here is "where does quantisation of the energy  of emr come from". If you accept that it is possible to generate emr of any arbitrary frequency, then it is clear that the energy is not necessarily quantised and the answer is that in many but not all cases it is generated by a quantum process.

[paul cotter]

I would argue that all em is quantised but I have zero proof. A thought experiment: set up a standard black body radiator, ie small aperture in a spherical matt black furnace, and use the radiation to illuminate a photoelectric cell. As we increase the furnace temperature we see a smooth increase in frequency of the emitted radiation exactly the same as one would see if the frequency of a radio transmitter was swept up or down. The photocell however will only react when a specific frequency is reached, indicating quantisation. It may be the case that we simply do not have a suitable phenomenon to detect the quantisation of lower em frequencies, akin to the photoelectric cell for the higher frequencies.