[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 (!)

[humanbydefault]

This is an interesting conclusion quoted from above:

"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."
Haven't we said that a quantum is the [intermitent] product of the mutual interference of two entangled waves as they propagate in the vacuum?
Its existence (quantum) depends in the actual state of the interference be that a constructive or destructive ones... Right?
Then wouldn't be logical to assume that as the "TWO-COIL-SYSTEM" shrinks or expands itself due to the particular STATE OF THAT PROCESS the actual POSITION of the "mass" and "charge" of the given quantum will also CHANGE with respect to space?
So! It wouldn't be ilogical to understand that there are in fact some variables that could influence the outcome of such PREDICTION would be?
If the inherent energy of the two entangled waves are higher or lower the whole "COIL STRUCTURE" will be forced to "respond" to it in a sort of "STANDARD DEVIATION" manner I would say...
THEREFORE if two electrons were MADE (scatterred) from two different "energetic entanglements" (actual physical atomic orbits) wouldn't be too difficult to assume that their relative structure had to be somewhat different too... right?
This could make pretty complicated the entire calculation procedure I guess... So manny uncertainties to handle at one time...(?)
I guess the easier shortcut was to renomalize the entire mathematical formulation and case closed!
What do you really think? Could our "SPIRAL MODEL" be of some help to reconsider once again Dirac's "reduced h" ?
Do you think you could do by yourselves?


HUMANBYDEFAULT

[mkirkpatrick]

I think thatyou have made some very valid points HBD,your many references
to the Spiral-model,remind of nothingmore than a vortex,if you want to
simplify this as you say you do.then all the maths and equations boil down to
a vortex within a vortex within a vortex,and so on add infinitum.the electron
for instance is no more than a vortex,with opposing rotations.



kind regards michael.

[dleviwing]

Hi hbd;
The spiral model is the result of 2 dimensional thinking; The universe and everything in it are 3 dimensional and thus its relation to the spiral model is limited to such. (worthless)

If you imagine the substance of one of the constructive interference patterns as a spherical volume then it can be viewed as a particle for a brief instant (the reciprocal of 2c). Possibly this is the virtual particle that is talked about so much. Our visualizations are very difficult to extract from the convoluted mathematical modeling of QM.

Excellent post hbd.

[humanbydefault]

Originally Posted by dleviwing Hi hbd; The spiral model is the result of 2 dimensional thinking; The universe and everything in it are 3 dimensional and thus its relation to the spiral model is limited to such. (worthless).

I was referring to the actual shape of the wave propagation across space. The spiral or coil model is obviously a 2D one and I agree on the 3D universe too. Take for example the DNA model. It follows the spiral shape in 3D does it?
The key is to understand why and when the absorption of external energy will produce the necessary wavy entanglement to be achieved inside the atom in the production of electrons once outside in the vacuum.
I am one that share the conclusion that what we see moving as a flow of charges in electrical and electronic circuits are not integral parts of the atomic structure... That's a given!
I can't accept the idea that even today in school they teach students in the belief that a proton is +1 positive charge and the electron -1 negative charge and that is the reason for current to flow in conductors.

First>>> Protons are no where near battery poles in the "making" of the so-called POTENTIAL (emf) (?)
SECOND>>> The necessary potential to promote the flow of electromagnetic energy is happening between two UNBONDED atoms [ex-component of a previous molecule]. The accumulation of those IONS in their corresponding side of the battery will produce the SOURCE for those waves to move, meet and as a result simultaneously create the POSIBILITY for those charges to be COLLAPSED into a circuit component, a measurement or its transformation into WORK.
It is precisely about this aspect of electrical charges what I want to dedicate this post.
When we talk about molecules we are referring to bondings between atoms and their specific atomic configuration that made that coupling possible. Chemistry replaced alchemy when those unexplicable compounds found in nature became less than a puzzle and more like a science. The "discovery" [production I'd rather say] of those corpuscles by J.J. Thompson (his "electrons") enabled those new generations of chemists to visualize a practical MODEL upon which they could based their observations.
Today we know that things were not as SIMPLE as they thought back then...
However most of the scientific community still consider electrons as the unit for charge inside atoms and the "exhange currency" between them in the making of molecules... I CAN'T DISAGREE MORE...(!)
I am convinced that BONDS between atoms is nothing more than a MAGNETIC-ENTANGLEMENT between the opposite strength of their fields (orbits).
The entanglement occurs because it is in the angle and corresponding magnitude of the field-strength where everything began.
It's not a coincidence the specific angle molecules adopt after a "chemical" bond. It's not a coincidence either the angle two magnets will adopt after they get suficiently close together.. Following me so far?
If it's true that we can not take appart the naturally-entangled poles of the magnet the situation with a molecule is entirely different.
We can make a bond to brake with an EXTERNAL application of ENERGY.
The same>external energy< we will get back when we power our alectrical or electronic appliances. The energy used could vary as we all know (heat, kinetic, light etc.) >>>The right amount required to separate the attraction between the orbits involved in the bond.

I'll come back with more of this in my next encounter.

HUMANBYDEFAULT

[dleviwing]

hbd;
I was referring to Michael's vortex spiral model as 2D thinking. You have got your thinking in the 3D mode and are doing very well with it.

[humanbydefault]

A holistic model of the atom is the only viable way to explain the mechanism behind the nature of a quantum entanglement between atoms>>> something we know as molecular bond. To get the right idea I'd ask you to consider the conclusions of my thought experiment back in special relativity posting. Two spheres with different radious serving as the path to a light beam made to move in circles around both of them. A logical conclusion to such hypothetical case could only be the presence of an increasing "LAG" as time elapsed due to the difference between the propagation of light in one circle with respect to the other. The case is not that hypothetical at all. It is precisely the structure assumed to spin around the core of the atom a similar phenomenon where a logical lag has been interpreted as relativity of space-time. Instead of the light beam of my thought experiment the atom is the "backbone" for a harmonic structure of energies (standing nuclear waves).

A chemical bond is a typical example of a NON-LINEAR coupling of orbits. The nature of the non-linearity includes space-time and the actual configuration of energies (its own scale responding to Pauli's Exclusion Principle).
Let's explain one by one:
1>>> What would happen if you try to put closer together two positive poles of two magnet?
The rejection will get stronger with the shrinking of the distance. A sort of a response with an inverse square of the (approaching) distance. The same picture but showing attraction will be to put two magnets facing opposite magnetic poles. This is a fact I suppose.
A chemical bond is just this. Two atomic orbits (harmonics) linked into an entangled spinning orbit "looking for" a net ENERGETIC COMPENSATION of the given orbit.
The problem arises with the FACT that the actual bond or link is only "perfect" at DISCONTINUED [intermitent] LAPSES OF TIME. To understand this point (which is not too abstract at all as you'll see) you need to visualize the actual non-linearity at which the entangled-spinning orbits belonging to each atom produce the bond. Go back to the "Two-circle-experiment" of mine for a second. Put those two circles one beside the other barely touching one another by a common point in the orbit. There has to be a RECURRENT INSTANT IN TIME where the magnetic interaction of both orbits are in perfect balance >>> a negative pole and a positive one close to each other. But as time goes on the NON-LINEAR speed of one orbit with respect to the other will increase*, reaching its maximum LAG [the point of maximum instability of the bond] to finally resuming the cycle with the initial state of equilibrium.
THIS PEFECTLY LOGICAL FEATURE OF EVERY EXISTENT CHEMICAL BOND BETWEEN ATOMS IN MOLECULES IS THE ONE RESPONSIBLE FOR THE OBSERVED VIBRATION OF ATOMS IN LATTICES OF SOLIDS, LIQUIDS AND GASES.
Bonds are conceived to reach a perfect magnetic balance between two atoms with place for enegy in their missing harmonics but the same REASON that conditiones their bond, namely the attraction between two complementing orbits (positive pole with negative pole) is the same reason that makes them so unstable together (!)
That's why atoms bond each other with incomplete harmonics. The actual distance between the core of the atom and its harmonic taking part in a bond (radius) has to be different in order to create the space-time effect I explained to you with my thought experiment in the past.
THIS COUPLING BETWEEN ORBITS WITH AN INHERENT "TIME LAG" MANIFESTED BY THE ENERGY CHANGING SPINNING POLARITY IN A NON-LINEAR CONFIGURATION IS ALSO THE SOURCE FOR THE PHYSICAL PHENOMENON KNOWN AS "ATOMIC OSCILLATOR" (!)

IT IS DURING THE EXACT PERIOD OF TIME WHERE A "POLARITY-INSTABILITY" OR IMBALANCE IS PRESENT INSIDE THE STRUCTURE OF THE BOND WHEN THE MOLECULE IS READY TO ACCEPT INCOMING EXTERNAL ENERGY TO PUT UP WITH THE MIS-ALIGNEMENT CREATED BY THE "LAG." (!)

Light or any other type of electromagnetic energy is actually pulled inside the molecular bond to account for the imbalance caused by the "LAG" BETWEEN THE ORBITS (HARMONICS) MAKING for the chemical bond >>> getting REMODULATED or TRANSFORMED inside the "micro-singularity" into a new type of quantum.

IT IS PRECISELY THIS FEATURE WHAT EXPLAINS WHY SOME ATOMIC STRUCTURES PRESENT A DIFERRENT PATTERN OF DELAY** AND BEHAVE WITHOUT A UNIQUE RULE WHEN IT COMES TO SCATTERRING ENERGY BACK INTO THE VACUUM.
It is thought that electrons (previously excited) inside atoms "take their time" to "jump down" in the ladder sometimes skiping one or more rungs in it. The truth is that no one has ever come up with a logical explanation to such weird feature of atomic scatterrings.
We could also explain under my assumptions the stubborness showed by atoms when it comes to accept inside them only certain "chunks" of energy and not any quantum we would like them to absorb. The reason as I see it comes from the length of the instability (intermitently) present in every single coupling at molecular levels. If the magnetic balance between atoms were optimally reached [at all times] then it wouldn't be any chance for abpsortion of any kind and therefore light wouldn't even exist in the first place (!)

*The difference of the two atomic radius involved in the chemical bond is simulateously responsible for the enegetic instability occuring as time elapses. If you like... This recurrent process could be seen as a race where one car is moving at twice the speed of the next spinning in the circle. The actual distance separating one from the other will uniformely increase and as it reaches the maximum value the instability will starting to decrease to zero... Omly those two "cars" are moving at light speed (!)
** The actual delay is proportional to the non-linearity involved in the mutual spin. In other words... Absorbed external energy will stay inside the bond until the magnetic balance is ultimately reached once again. Not before that moment any eventual scatterring of remodulated enegy has no chances to occur at all.
I'd like to hear the opinion of those who have read my thread.

HUMANBYDEFAULT

[humanbydefault]

"Phonons are a quantum mechanical version of a special type of vibrational motion, known as normal modes in classical mechanics, in which each part of a lattice oscillates with the same frequency. These normal modes are important because, according to a well-known result in classical mechanics, any arbitrary vibrational motion of a lattice can be considered as a superposition of normal modes with various frequencies; in this sense, the normal modes are the elementary vibrations of the lattice. Although normal modes are wave-like phenomena in classical mechanics, they acquire certain particle-like properties when the lattice is analysed using quantum mechanics (see wave-particle duality.) They are then known as phonons. Phonons are bosons possessing zero spin." [wikipedia].
Phonons are a direct result of my interpretation including a holistic model in atomic bonds. They are a quantized modulation of a previously (low-energy) absorption to compensate for the time-lag causing the magnetic imbalance inside the bond. The quantization factor is logically derived from the symmetrical configuration of the mentioned imbalance between the orbits involved.
It doesn't take a lot of brain to get the right picture of what's going on in superconductivity (physically speaking of course).
Lowering the temperature of the environment those atoms taking part inside the lattice will be forced to adopt a different structural shape to respond to the recurrent imbalance of magnetic equilibrium>>> (inside the chemical bond where they are linked). Remember that I said that atomic vibrations are a logical and natural feature in every bond (being that at molecular levels or even deeper levels inside the core of atoms). Atoms take advantage of the presence of energy in the environment to absorb what they need to compensate during the cycle where the explained "time-lag" caused the magnetic imbalance in the bond. Since energy is also remodulated and finally scatterred from the bond itself it looks to us as a quantized (particle-like) pattern.
For those still with some doubts about the nature of the magnetic imbalance I'm refferring here I reserved a simple analogy:
Try to visualize two atoms bonding to each other as two magnets with different size. One of them [the smallest one] will rotate faster that the bigger [being the bigger one weaker in strength]. This may sound weird but in fact it is just like this. The harmonic with greater radius is always the one with a lower energy density per unit of space carrying the lowest magnetic pull. As both magnets spin close to each other their own lines of force will interact in different fashion as time goes on. Since the short magnet spins faster than the big one (time-lag) we'll observe how the configuration of the bond will find itself transformed during the entire cycle. To simplify your visualization process I suggest you to pay attention only to the big magnet alone. Since the smallest will rotate faster it is up to the slower moving one to finally arrive at the initial point of equilibrium that promote the bond in the first place. During the repetitive process you'll find a recurrent symmetry in the pattern of imbalance causing the observed vibration around the bond as well as the rest of a bunch of unexplained quantum mechanical features orthodox physicists have a hard time explaining to themselves. Mathematics have gone a long way ahead of us but I feel that our physical interpretation of reality has a regretable "LAG" behind their mathematical colleagues.
Dave if you had read these past comments I'll ask you to give me your honest opinion about how you see it.

Thanks for your attention and your previous comments.

HUMANBYDEFAULT

[humanbydefault]

The point of these physical interpretations I'm trying to bring to your attention is to let you see that the problems with quantum mechanics arose right from the beginning of the theory.
Every time you read about the first steps of quantum mechanics in science you were "redirected back" in time to the years around 1900. Plank had a brilliant mathematical idea to avoid the theoretical outcome of something entirely impossible in all terms: The infinite emission of energy by a so-called black body in the state of thermal equilibrium. By the time he proposed his math solution it was clear that the energy of a system had a proportional relationship with frequency... Let's see it.
"The ultraviolet catastrophe results from the equipartition theorem of classical statistical mechanics which states that all modes (degrees of freedom) of a system at equilibrium have an average energy of kT / 2. According to classical electromagnetism, the number of electromagnetic modes in a 3-dimensional cavity, per unit frequency, is proportional to the square of the frequency. This therefore implies that the radiated power per unit frequency should follow the Rayleigh-Jeans law, and be proportional to frequency squared. Thus, both the power at a given frequency and the total radiated power go to infinity as higher and higher frequencies are considered: this is clearly an impossibility, a point that was made independently by Einstein and by Lord Rayleigh and Sir James Jeans in the year 1905." [wikipedia].
I want you to see that the physical interpretation drawn by Rayleigh-Jeans Law were not entirely wrong!
IF FREQUENCY COULD IN FACT BE INFINITE .>> AND I'LL GO RIGHT AWAY TO EXPLAIN WHAT THAT MEANS<<< THE POWER AND RADIATED ENERGY WOULD GO INTO INFINITE VALUES (!)
HERE IS MY POINT! "...as higher frequencies were considered..." [fragment of the quote above] But we were limited in our "considerations" by the fact of "c" being a constant so the whole physical conclusion was not entirely a flawed. It was our incomplete description of REALITY what was flawed once again!
I started this thread by saying that FREQUENCY is the direct [PROPORTIONAL] effect of the vacuum-impossed LIMITATION in the propagation of WAVES. The greater the inherent energy of the WAVE the greater will be the FREQUENCY of the WAVE. It was Maxwell who had the vision to propose that "c" was a universal constant and a also a LIMIT.
Having all this clear then...What would be the true PHYSICAL INTERPRETATION of an INFINITE FREQUENCY or what's the same thing an INFINITE ENERGY?
If you go back to the first post of this thread you will find the original Plank constant and beside that one the reduced Dirac version of it. They are assumed to be a merely "unit-equivalency" a simple mathematical transformation if you which...
The problem is that there are no automatic mathematical transformations without a clear understanding of what we attempt to express in other terms (!) An infinite frequency could only mean a "RECOILING" of the wave in such magnitude that the front and the end of the wavelength will coincide in the same point in space !!! It could resemble a propagation of perfectly shaped RINGS one behind the next>>> Not a WAVE as we have observed by out instruments but something a human being couldn't even imagine it to exist.
As I warned before a wave does not close the loop while moving in the vacuum. It follows a "coil" configuration due to "c" being a constant and a LIMIT too.

HUMANBYDEFAULT

[humanbydefault]

How many times have you read similar descriptions:

Quantum mechanics uses complex number wave functions (sometimes referred to as orbitals in the case of atomic electrons), and more generally, elements of a complex vector space to explain such effects. These are related to classical physics largely through probability. Probability in the context of quantum mechanics has to do with the likelihood of finding a system in a particular state at a certain time, for example, finding an electron, in a particular region around the nucleus at a particular time. Therefore, electrons cannot be pictured as localized particles in space but rather should be thought of as "clouds" of negative charge spread out over the entire orbit. These clouds represent the regions around the nucleus where the probability of "finding" an electron is the largest. This probability cloud obeys a quantum mechanical principle called Heisenberg's Uncertainty Principle, which states that there is an uncertainty in the classical position of any subatomic particle, including the electron; so instead of describing where an electron or other particle is, the entire range of possible values is used, describing a probability distribution. So in normal atoms with electrons in stationary states, the probability of the electron being within the nucleus (or somewhere else in atom within similarly small volume) is nearly zero according to the Uncertainty Principle (it is nearly zero as the nucleus has a volume and is not a point). Therefore, quantum mechanics, translated to Newton's equally deterministic description, leads to a probabilistic description of nature. [wikipedia]

Too many I guess...! However have you ever bumped into the actual WHY physicists have to rely on something called "Uncertainty Principle" to justify their inhability to "locate" anything inside the atom? I'll tell you the answer >>> Because we (humans) sometimes tend to forget the use of a very old and treasured intelectual "tool" >>> courtesy and legacy of our ancestors: LOGIC (!)
I assume that if you are reading this particular posting (right now) you have already gone through all the previous ones. Because the question I'm going to ask you next holds the key to unravel that "uncertain probabilistic notion of our REALITY."
In order to make my point the easier way I decided to number some important conclusions discussed before here in this thread:
1>>> "c" The speed of light is both a CONSTANT and a LIMIT speed for any type of wave in the vacuum.
2>>> As the energy of the WAVE increases, DUE precisely to the speed limitation "c," the configuration (shape) of the propagation will observe [what I chose to call it] a RECOILING PROCESS.
3>>> The relationship between energy-frequency (pay attention to it) will be a linear one.
What I meant to say with a LINEAR one is that its relationship is not QUANTIZED. For a given magnitude of ENERGY it will ALWAYS be a FREQUENCY. It might sound a little stupid but I assure you this... This is the KEY! Have you ever realize that sometimes the most complex questions require the simplest answer? Well this is one example of it!
It is true and a physical fact also that ENERGY is quantized... BUT!
IT COMES THE TRICK