[humanbydefault]

Origins of Planck's constant and Dirac's constant

Planck's constant, , was proposed in reference to the problem of black-body radiation. The underlying assumption to Planck's law of black body radiation was that the electromagnetic radiation emitted by a black body could be modeled as a set of harmonic oscillators with quantized energy of the form:
is the quantized energy of the photons of radiation having frequency (Hz) of or angular frequency of (radian/sec).
This model proved extremely accurate, but it provided an intellectual stumbling block for theoreticians who did not understand where the quantization of energy arose — Planck himself only considered it "a purely formal assumption". This line of questioning helped lead to the formation of quantum mechanics.
Dirac's constant or the "reduced Planck's constant", , differs only from Planck's constant by a factor of 2π. The SI unit of measurement of Planck's constant is joule per hertz, or joule per (turn per second), while the unit of measurement of Dirac's constant is joule per (radian per second). The two constants are merely conversion factors between energy units and frequency units.

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Let's start our analysis based on the fact that "c" (speed of light) is a constant in the vacuum.

If that's so... Wouldn't the "COIL SHAPE" manifested by all type of radiation while porpagating across the vacuum be the obvious CONSEQUENCE derived from this particular speed-limitation?
I've posted above a coupple of conclusions from Plank's and Dirac's work in the beginnings of quantum mechanics formulation.
Take a close look at the original equation from Plank... please!
E=hf >>> If the primary condition provided by the constancy of the speed of light applied to every form of radiation ARE UNCHANGEABLE >>> As the energy (E) of a wave increases the same LIMIT will be impossed on its propagation and it CAUSES the RECOILLING process over its original structure (!)
I'm talking about the reasons for FREQUENCY to exist in the first place (!)
Now let's go to Dirac's "reduced h."
What he did was to substitute the original constant and refer it to the angular velocity "w" expressing it in radians... (Correct me if I'm wrong).
Well... I suposse he didn't have in mind the "COIL STRUCTURE" I've mentioned before to you... (?)
If an energy wave propagates according to a "COIL FORMAT" as I believe it does:
Q>>> Wouldn't be closer to the "real thing" assuming in a MATHEMATICAL FORMULISM the same geometrical reality?
I'm not a mathematician but I would imagine that if you were an ant and you were forced to "walk" upon the path of an extended COIL you won't be spinning in PERFECT circles no more!
It's true that you would be moving up and down in a sort of spiral (maybe getting pretty dizzy here and then) but the fact of the matter is that you won't be performing a close spin at all.
According to my analysis based on pure LOGIC I can see why frequency bears a linear relationship with a net increase of energy since its origin (as I see it) is provided by the constancy of the speed of light in the vacuum (!)
My problem here is with Mr. Dirac's assumption of a pure and perfect circle when assuming the angular velocity of a particle***.
The ROOT of the problem takes us back to the false assumption that electrons spin inside the atom as point particles with a wave function.
If electrons (according to some of us) are nothing more than the expresion of two entangled waves in their mutual interaction as they move across the vacuum THEN the original mathematical formulation of quantum mechanics is flawed... isn't it?
Plank was right. The rest of the "mathematical building" based on radians and perfect angular velocities was not. Take a closer look to what I posted below:

Thus, may be said to be the "quantum of angular momentum".
Planck's constant also occurs in statements of Heisenberg's uncertainty principle. The uncertainty (more precisely: the standard deviation) in any position measurement, Δx, and the uncertainty in a momentum measurement along the same direction, Δp, obeys

But what is the famous "standard deviation" or contradictory "uncertainty"?
Standard deviation
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In probability and statistics, the standard deviation is the most common measure of statistical dispersion. Simply put, standard deviation measures how spread out the values in a data set are. More precisely, it is a measure of the average difference between the values of the data in the set. If the data points are all similar, then the standard deviation will be low (closer to zero). If the data points are highly variable, then the standard variation is high (further from zero).
The standard deviation is defined as the square root of the variance. This means it is the root mean square (RMS) deviation from the average. The standard deviation is always a positive number (or zero) and is always measured in the same units as the original data. For example, if the data are distance measurements in meters, the standard deviation will also be measured in meters.
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Couldn't be the ONLY reason for a non-linear deviation observed in quatum mechanical systems the fruit of A SIMPLE flawed DESCRIPTION in A MISTAKEN IDENTITY with respect to PHYSICAL REALITY?
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Go back to the image of a COIL and follow the spiral as if you were moving on top of its ondulating shape. If the net E (energy) increases you'll be forced to move in spiral more times than before the energy was increased...
[Plank's results] The "variance" of the path you are trying to follow will be shrinking as an acordion does when playing a tango. The standard deviation will be a reflection of that specific "shrinking" or "expansion" of the original waves.

HUMANBYDEFAULT

*** The root of the problems goes back to the classical definition of frequency. In simple words frequency is thought to be the repetition of CYCLES in equal intervals of TIME. (seconds for example).
A pure sinosoidal wave could be translated into the path of a point moving in perfect circles... This is basic waves physics. There comes the concept of a radian and its application in quantum mechanics. The problem as I see it is that we are in the presence of a combination of two different nature of propagation. One is a displacement in one AXIS while the other is "trying" to PERFORM CIRCLES as it goes on (!)