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Planck's Constant and Quantization
a Mechanical Explanation

by Miles Mathis

It has now been 108 years (since 1900) that quantum mechanics has existed without a mechanical explanation of the quantum. That is to say, we have lived 108 years with a misnomer. Quantum mechanics is not and never has been mechanical. By the same token, Quantum Electrodynamics has never been dynamical. Both are theoretical and heuristic.

For quantum mechanics to be mechanical would require that we have a mechanical explanation of quantization, but we don’t. We only have a mathematical explanation of quantization.

Max Planck—who discovered his own constant, of course—believed that the constant was only a useful device of problem solving. He did not believe in the actual quantization of energy. Or, to be more precise, he believed that quantization was an outcome only of absorption or emission: the energy could exist continuously, but only be emitted in steps. In a sense he was correct, as we will see. He was not altogether correct, in that there is a simple mechanical reason for quantization, and he never discovered or proposed that reason. To his credit, he resisted the Copenhagen Interpretation and all the fuzzy theory of “duality.” But because he could not show how the quantization was caused by emission, in a straightforward mechanical way, he lost the argument to the superior charm of Bohr and Heisenberg.

Bohr and Heisenberg defined the terms of quantum theory, and those terms still stand. Both Schrodinger and Einstein disagreed with these terms, but they have been outvoted. Today, top physicists either agree with Bohr and Heisenberg, or they don’t really care one way or the other. No prominent physicists now claim that quantum mechanics does or should have a mechanical basis. This mechanical foundation was ridiculed by Feynman, Pauli, Dirac, and is still ridiculed by Gell-Mann, Hawking, Weinberg, and the rest of the top names. For this reason, doubters have found it best to keep quiet.

As a matter of theory, we are stuck at the level of Bohr and Heisenberg. The foundations have not changed since the issuance of the Copenhagen Interpretation. What the Copenhagen Interpretation said, in short, is that electro-magnetic radiation (usually including both photons and electrons) has a dual nature. It is both particle and wave. This much is true, and I have nothing to say against it. But what was novel about the CI is that its authors went much further: they claimed that this duality was inherently mysterious and could not be understood in classical or mechanical terms. Bohr and Heisenberg couldn’t discover a mechanical explanation (and neither could anyone else at the time) so, to save face, they decided that the problem was categorically insoluble. It was a problem beyond classical understanding, beyond the reach of visualization or illustration. But they went even further. They decided that this decision of theirs was final, and they all but forbade anyone from seeking for a solution after that. They could not pass a law, of course, so they did the next best thing. They created a cult. Anyone who continued to seek a mechanical explanation was ridiculed and ostracized.

You wouldn’t think such a plan could work in the “upper reaches” of science, but Bohr and Heisenberg and the rest (Pauli, Born, etc.) knew how to create fear. They went right at their biggest foe, and his defeat was the defeat of the entire opposition. Yes, this cabal defeated Einstein, and after that no one wanted to end up like Einstein. Each doubter looked at the facts and said to himself, “Well, if Einstein couldn’t win that argument, what chance have I? Best specialize in something else and keep my mouth shut.”

This has been the way of it for 70 years, at least. Not one big-name physicist has attempted to explain quantization or duality in a mechanical or classical fashion. A few, like Bohm and Bell, have made small steps in this direction, but they have never questioned the groundwork itself. That is, they have questioned specific points of the theory, but not the theory itself. They have not started over from the beginning and tried to build a logical visualization. Like the rest, they have accepted that this could not be done.

And so, in the year 2008, quantum theory, as a theory, stands almost precisely where it stood in 1927. We still believe in the dual nature of light, but we have no clearer picture of this duality than we had then. How could we? We were forbidden by the CI to seek a clearer picture, and physicists have stuck fiercely to their Constitution.

Physicists certainly would like a clearer picture of quanta and of light. That is one reason that string theory was invented in 1984. But they will not do the logical thing and seek to explain duality directly, by ignoring Bohr’s rules. They will not seek a mechanical explanation of duality.

Ironically, it is the CI that has allowed someone like me to do foundational mechanics. No one else wanted to do it. No one else was allowed to do it. Being an outsider, I was free to ignore the CI. My career and reputation do not depend upon obeying 80 year old rules, made up by people now long dead. If I desired to seek a mechanical explanation of quantization and duality, I could do so without looking over my shoulder or worrying what my colleagues might think.

Now for the mechanics of quantum mechanics. I have already explained most of this in my paper on superposition, but I thought I needed to put the analysis under its own title, and link it directly to Planck and quantization. That other paper is about stacked spins on the photon, and using them to explain the various detector mysteries and paradoxes. But there I never get around to explaining to my reader that this must solve the problem of duality itself. I had thought it would be implicit, but I now see it is best to be explicit. It is best to drive the point home with all rigor and emphasis.

The standard model states that matter has a dual nature, showing characteristics of a particle in some experiments and characteristics of a wave in others. But it does not tell us how matter expresses these characteristics. It assumes that it is impossible to do so. But it is not impossible. In fact, it is embarrassingly simple. Matter is NOT both particle and wave. Matter is a particle with a wave. That is, the photon, like the electron and the proton and every other incorporation of matter, is a discrete particle, with a radius, a surface area, a mass, and a spin. Fundamentally, it is not a wave. It is a physical sphere, just as much as the Earth or the Moon or a marble or a bowling ball.

So all those smug little PhDs on the forums are wrong. To solve the problem of duality, we must not think of the photon or electron as a probability. We must think of it as a physical sphere. We must do so because doing so is the only way to solve the mysteries of quantum mechanics. I have already proved this in the most direct fashion possible: by solving problems that had stymied them for generations. I have solved problems Bohr could not solve, that Einstein could not solve, that Feynman could not solve, and I have done it by ignoring all the warnings from the physics police—ignoring the warnings of the cult groupies.

They have said there is no way to visualize superposition, but I have done it. They have said there is no way to illustrate wave motions or characteristics, but I have done it. They have said there is no way to explain duality in a physical, mechanical way, but I have done it.

I have done it by showing that a simple sphere, of any size, can have four stacked spins. The first spin is an axial spin, with a size of R (where R is the radius). The second spin cannot be axial, due to gyroscopic rules. It must be outside the influence of the axial spin. Therefore it must be an end-over-end spin, with a size of 2R.

If we give the particle a straight-line motion in any direction, the end-over-end spin will give it a wave. Just monitor the position of the center of the particle, relative to its initial position. On any graph, the motion must create a wave.

I call this first end-over-end spin the x-spin (the axial spin is not an x-spin, since an axial-spinning particle is not moving in the x,y,z field yet). Then we have a y-spin of 4R and a z-spin of 8R. Each spin is orthogonal to inner spins. And each spin creates another wave.

The z-spin creates the electrical field and the y-spin creates the magnetic field. These two outer spins are orthogonal, and the right hand rule applies to them. We achieve all this simply from a mechanical analysis of spin, without any other postulates or theory.

This shows the exact mechanical cause both of the wave and of the duality. Stacked spins cause the wave. The particle is not a wave: the particle moves as a wave against a background, due to stacked spins.

These spins may be caused simply by collisions. We may assume that particles collide all the time. If they survive collision, it is because the collision was indirect. An indirect collision would create a spin on any sphere of any size. Summed over a long period of time, these spins would tend to maximize in one direction or another. That is to say, simply as a statistical matter, we would expect all or most surviving particles to have all possible spins. This applies to photons and electrons as well as to free protons.

To see how this solves the mysteries of superposition and the various detector paradoxes, you will have to visit that paper. To see how this solves the mysteries of QCD, you will have to visit that paper. To see how this solves quantization, you only have to read on.

It turns out that Planck was right: no energy state is outlawed by quantum theory. A particle or system can have any possible energy value, over a continuum. But given a specific interaction, like an emission or absorption or an orbit, a particle or system must change in a quantized way. This is due to the stacked spins. It is due to the fact that each spin is an integer value of the radius of the particle itself. Not just an integer, but an even integer! Yes, we may have the number three in the wave equations, but at the foundational level, we don’t have any odd numbers. In this sense, not only is energy quantized, it is an exponent of 2. At the very lowest level of energy measurement, the wave cannot have an odd value (relative to the radius, I mean).

This is the root cause of quantization and of Planck’s constant. Planck’s equation is E = hν. Energy is quantized because frequency is quantized. Well, frequency is quantized because wavelength is quantized. Frequency and wavelength are straight functions of one another. The spin causes the wavelength directly. The electrical wavelength is 8 times the radius of the spinning particle. If the radius is 1, the electrical wavelength is 8.

Quantization is caused by simple rules of spin. Actually, just one rule: the rule of gyroscopic exclusion. You can’t have more than one spin about a given center. And this rule is not a bald postulate either. It is a logical outcome of motion and matter. That is to say, there is nothing mysterious about gyroscopic exclusion. To propose that two spins could happen simultaneously about the same center, you would have to propose that matter had no structure, at any level. To propose spinning the Earth around two separate axes that went through its center, you would have to propose that the Earth is structure-less sort of gas, with no interaction between particles. Likewise with any quantum. To apply gyroscopic exclusion to quanta we only have to assume that they are material, and that they are not points or point-like. This is the logical mechanical assumption, so I am not going to spend any time defending it. It is current theory that is illogical, in proposing that “matter” that expresses “energy” and causes real “motions” can fail to have “extension”. I simply return to classical assumptions, based on the definitions of all these words, in which matter must have extension. A point is a nothing, and you cannot propose that a nothing expresses energy, transmits force, or takes part in events.

The other problem this solves, of course, is the assignment of Schrodinger's waves. In the wave equations, we have four parameters that define every electron energy state. These four parameters are the four stacked spins, and my visualization is the first to explain the precise mechanical relationships of these spins. Of the four basic quantum numbers, one is already called angular, which is of course tied to spin. One is called spin. And one is called magnetic. This mirrors my assignments, except that my theory is strictly mechanical, assigning all four quantum numbers to real spins. One spin does indeed cause the magnetic field, but it is still a spin quantum number. All the numbers are spin numbers, as a matter of mechanics. Magnetism is not a quantum or mechanical quality. Magnetism is an outcome of the spin. Spin is the cause and magnetism is the field it causes, by bombardment and direct contact. Putting a mechanics under the wave equations also explains the Pauli exclusion principle in a direct fashion. We no longer need to rely on a mathematical interpretation, since we can see the physical reason. The reason is that electrons are actually positively charged. Meaning, according to my theory, that they are emitting a real field just like the proton. Although this field is both real and repulsive, it does not act like the proton field because it has a much smaller density. It adds little to the proton-electron repulsion, since, due only to surface area, it diminishes so quickly with distance from the electron. But it does act to repel other electrons. Electrons repel not because they have the same charge, but because they have the same size, or scaling. The electron emission field is not powerful enough to affect protons, but it is powerful enough to affect other electrons. This is the main cause of exclusion. An electron in an orbit actually excludes all other electrons from that orbit, but only electrons with the same four numbers try to inhabit the same states, so the first electron will only have to exclude electrons just like it. Imagine you are a rabbit in a hole. You may have the ability to bite any intruder, but you will only bite intruders that come into the hole. The hole is just the right size for a rabbit, so you only have to bite other rabbits. You could bite badgers and bears and elephants, but they see how small the hole is and don't try to climb into it. Now, any blind person monitoring your hole would hear only the squeals of the rabbits you were biting, and he might come to the conclusion that you only exclude other rabbits. But the truth is, you only have to exclude other rabbits.

Now, I don’t claim that my analysis instantly solves all the problems of QM or QED. But it certainly provides the method to do so. We must seek physical, mechanical causes for the motions and forces we see. That is what physics always was, and still is. If we are not going to seek physical causes for events and data, then we shouldn’t call the field physics.

My analysis does not solve all problems, but it is shocking how many major problems it does solve, very quickly and transparently. We do not need difficult fields, operators, or math. We do not need illogical rules and illogical exceptions to these rules (variances, violations, or symmetry breaking). We do not need cultish warnings, waving us away from looking closely at the world around us. We need rigor, logic, and the courage to go where the data leads us—even if it leads us away from the mainstream and the standard model.

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