Understanding "photons" from electron spin and dimensional analysis

Historically, the way quantum mechanics evolved seems to be something of the following:

1. Discovery of blackbody radiation and the photoelectric effect leads to the corpuscular theory of light, that is, light consists of particles called ”photons”.

2. Bohr derives the hydrogen spectra assuming quantization of angular momentum.

3. The electron double slit experiment leads De Broglie to assume wave-like properties of matter, which in turn leads to the Schrödinger equation.

4. Oh yes, and then we have the discovery that electrons have spin which also happens to be quantized.

No shade should fall upon the pioneers of quantum mechanics that these discoveries might not have come in the correct epistemological order. But now we have the opportunity to take some steps back and revise what we have discovered. Previously, I have advocated the idea of taking the quantized angular momentum of the electron as the starting point of the analysis. If so, would it then be wisest to assume that all other quantized phenomena in nature exist independently of this first assumption or would it be wiser to try to derive other quantization phenomena based on the first assumption?

Here we will try to understand the quantized energy packets o flight, also called ”photons”, based on the quantized electronic spin. First off, what is the dimension of angular momentum?

[angular momentum] = [energy] x [time]

You could imagine the electron saying to the light:

- I can only accept or give away angular momentum in integral packets of h_bar. If it does not have this size I have to give it back to you.

Now, from a dimensional point of view there are various ways this could be accomplished, a greater amount of energy could be provided on a smaller time scale or a smaller amount of energy could be provided on a larger time scale.

Now think for a moment, does light have a natural energy scale or a natural time scale? I would say it has a natural time scale. What is that time scale? Well, the period of one oscillation T. Recall that the frequency f is given by

f = 1/T

Now we get immediately

[quantized energy] = [quantized angular momentum]/T

or with properly scaled quantities

E = h/T = hf