LeandroMdO said:
The point here is that physicists like to use what are called 'natural units'. For example, if you measure distance in light years, the speed of light is 1 light year per year. When you look at it this way, it becomes almost silly to give a different name to the unit of distance, so you can just as well measure distance in "years", and say that the speed of light is 1 year/year, also known as "1". This is because the speed of light is just a conversion factor between meters and seconds, units we invented because they are convenient on a human scale, and the scales that are actually relevant for natural phenomena.
There are other constants like that, such as Planck's constant, the gravitational constant G, and the Boltzmann constant. You can just as well work in units where Planck's constant is 1, and particle physicists do. In the end you're left with only one unit to keep track of, which we typically choose to be energy. So for example we can measure masses in joules (related to kg via E=mc²), distances in 1/joules, electric fields in (joules)², and so on. For convenience we typically use some other unit more relevant for particle physics, such as mega electron-volts. Then the "size" of a proton, 10^(-15) m, can be written as 1/(180 MeV). The particle that is responsible for binding protons together is called the pion, and it has a mass of ~140 MeV. Interesting, huh?
Anyway, this type of system of units gets called "natural units", because it leaves most human prejudices aside. In natural units, hbar is 1, and the energy of the photon is E=f. Does it then make sense to attribute the meaning you gave to hbar, as a "unit of energy"? We can see that it doesn't: it's role is to translate between the units that nature likes and common units such as joules and seconds, that humans like.
This is a nice post! It's in my opinion a harmonic combination of logic, clarity and elegance. My compliments, for what they are worth.
I see the point, but probably not completely. I should like to explain why...
Fore sure, the unitary magnitude for hbar makes it more manageable in the calculations, but this is a technical consideration, not something about principles, meanings or even intuitions.
Instead, I have to confess that putting hbar=1, i.e adimensional, is to me a bit strange (*).
On the other hand, I have no difficulty to accept E=f, once the convention is established.
This indicates that in the world we are dealing with, every thing which shows a frequency is also expressing an energy and vice versa. And there is no room for errors, I guess, since there are after all only frequencies, i.e. exciteable field oscillators. But this doesn't shift my point of view.
The Planck's constant leads me back to the historical experiment with the blackbody emission and to the regularly avoided "Ultraviolet Catastrophe" (Rayleigh formula, classic electromagnetic eigenoscillations in a cavity). The equation E = n h f was then a ruse invented by Planck to describe the non divergent radiation behaviour, presuming a discrete behaviour. But as for the physical interpretation? Planck didn't give any. The constant remained just an arithmetic device.
The constant h is an action, the same type of physical magnitude that relates to Hamilton law. But what does this mean? I think here at Einstein, who was the first to give an answer, studying the photoelectric effect and taking account of Planck's arithmetic adjustment. The "escape energy" needed by the electrons to leave the metal illustrated better that discrete behaviour already seen but not really understood by Planck. Einstein postulated the existence of light's quanta, photons. The equations for the photon's energy and momentum are then a known consequence of the relativity (c= cost; E = mc2; rest mass = 0; and so on).
So, a photon implies a precise amount of action. A photon can't be divided. It's a physical entity all-or-nothing. In this sense, it's the smallest action that can be carried in space-time from a source to an interacting point. This is my interpretation. Since the word "action" is may be to classic, in this discussion I expressed the above in terms of energy, saying a quantum is the smallest energy amount that can be carried from a source to an interacting point in space-time "at a given frequency".
This doesn't rule out the fact that a photon can then exchange only a portion of the energy transportated to the interaction point, as in the Compton effect. Of course, it doesn't rule out the fact either that a photon can have any frequency value, so that energy itself can vary continuosly.
It's evident that I have a too little expertise in QM to try to depict drastic frameworks for this discipline (as it was written in relation to some of my posts, what is understandable). No way. I'm only referring to action and energy, not to perturbations, probabilities, paths. So, I'm not at all trying to reduce the QM to Planck's constant, even if it was the value through which a new world was discovered.
(*) Personal consideration: I guess this is only because I pretend to keep to myself a bridge that connects hbar to my day by day world of seconds, meters, kilojoules, kilograms. I'm born in a dimension where time, space and matter are primitive concepts and energy a derivate physical unit.
I know of course that my ordinary world is a consequence of quanta dynamics e not vice versa. But my understanding goes top-down and not bottom-up. This means, I have to reduce my macroscopic experience to the microcosm, before trying to reconstruct back the first on the basis of the latter. I don't see prejudices in this, but it's for sure more tiring than the one-way interpretation bottom-up. Tiring, but more intuitive. Ok, sorry for the detour...
That particular article looks OK to me for a start, but also note that I said to look at the references as well. Even Wikipedia articles that aren't very accurate by themselves can give useful references.
