If people are interested in the historical developments of EM theory and the various physical analogies maxwell used, I'd highly recommend "Faraday, Maxwell, and the Electromagnetic Field" by Forbes and Mahon. It has a interesting description of these, and also emphasizes the insights Faraday had - he wrote about the potential of EM waves ~30 years before maxwell came up with the mathematics.
And if you want to know what kind of thinking Einstein used to move from Maxwell equations to light being quanta I recommend: Einstein lecture by Douglas Hofstadter (Feb 4, 2018) https://www.youtube.com/watch?v=NXdQfPrU64g
I have a quick question: is the modern understanding that "the electromagnetic field itself quantized" OR is it just shorthand for "light emitted specifically by atomic electron orbitals changing is produced in discrete energy levels because the energy levels between orbitals are discrete"?
To me, it always felt like the latter, but I've never seen that written down explicitly, and everyone seems to talk like it's the former. I mean sure, 99.99% of the time experiments that emit or absorb photons are performed using atoms (and hence discrete electron orbitals) but that's certainly not the only way to create or or absorb photons. There's Cherenkov radiation, Bremsstrahlung, etc...
The EM field itself is quantized. You start with the classical electromagnetic field and you try to quantize it. The rules for this are not precise nor formal.
That means something a little different to "photons can only have specific energies" (that applies only to very specific atoms or atoms with certain structure; in many materials, electrons can exist in bands of continuous energy).
No. Absolutely not. This is where physicists get their history wrong and what the lecture explains.
When Planck described black-body radiation, he wrote that it was "as if" there were resonators in the walls that can oscillate at certain discrete frequencies. He did believe that light was a wave.
Even after Einstein published his paper much later, Planck and everyone else thought he was silly for almost twenty years. They accepted the photoelectric effect explanation but not how Einstein came to the result (photons).
OK, but it is worth mentioning, then, that the quantum theory as it has developed in the later years has, in fact, rejected the idea of the light quanta as Einstein thought of them, being "particles of light," i.e. something that is localized in space, whereas Planck's notion of energy quanta (or energy quantization, of the light wave or in general) has remained in force.
We are interested how the thinking and ideas behind physics historically proceeded.
The important historical lesson is that Einstein had the correct idea and framework to think about light __at that time__ and advance physical theory, he wrote it down and people refused to accept it.
* 1900 Plank describes black-body radiation in a way where energy is quantized.
* 1905 Einstein describes light as having “corpuscular” nature and uses it to describe photoelectric effect.
* 1923 Compton effect discovered. Einsteins ideas about light quanta explain them perfectly. Everybody accepts that light is also a particle and Gilbert Lewis coins the word photon.
Isn't this somewhat simplified? The modern "proper" understanding/mechanistic explanation of the Quantization of (spin-1/2, massless - or symmetry groups etc.)fields resulting in photons came later still.
You have to think how the ideas proceeded historically, not to try to retrofit current understanding backwards in time. For example, Isaac Newton believed light was composed of a stream of corpuscles, but he lost his case in 1801 when Young presented his double slit experiment.
Einstein's idea at that time was more correct and provided better explanations and predictions.
Kinda hard to beat Whittaker's "A History of the Theories of Aether & Electricity" -the more recent things tell a rather more linear story than the actual history. There were some crazy ideas, most of which were quasi-mechanical or fluid mechanical.
The book I referenced discusses both the early hydrodynamic model maxwell used for electrostatics and a rather bizarre (and intriguing) mechanical model involving flywheels and gears.
Can't comment on whether it linearizes the history though.
These ideas were not original to Maxwell; virtually ALL of the pre-Maxwell theories of electricity and magnetism looked like that. The first chunk of Whittaker's book is all about these mostly forgotten ideas and the cool people who tought them up. It's really a classic.
