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Why Schrodinger's Wave Equations
move in Q-space
by Miles Mathis
Soon after Schrodinger's wave equations were published in 1926, critics began complaining that the waves moved in q-space. Q-space is the configuration space, an abstract structure, rather than physical space. Heisenberg used this fact as a reason to dismiss wave mechanics; while Einstein, who was delighted by the equations, also found the movement in q-space "strange." Several explanations for this were offered at the time, including one by Schrodinger himself, but none were or are convincing. While the "dual" nature of light was misunderstood, the movement of the waves in q-space could not be understood. Since the standard model still misunderstands the dual nature of light, it still misunderstands the cause of wave motion in q-space. I will briefly solve the mystery.
Two of my other papers contain information sufficient to solve this mystery. In the first, my paper on the calculus, I show that there is always a definite mathematical difference between physical space and any conceptual space postulated to represent the physical. We can call our conceptual space "phase space", the manifold, configuration space, or anything else; we can title it Lorentzian or Riemannian or Minkowskian or Euclidean or Galilean or Newtonian; it does not matter—in no case can this conceptual space match physical space precisely. Real objects move in physical space, but the functions or variables or differentials or operators or what have you that we create to represent them cannot travel in physical space. Mathematical terms can travel only in mathematical spaces, and these mathematical spaces are never equivalent to physical spaces. I showed that mathematical spaces—most of which can be diagrammed and all of which yield to equations of some form—are always at least one dimension away from physical space. For example, if your conceptual space is defined as R2, then the physical space you are representing must be at least R3. If you try to correct for this by defining your conceptual space as R3, then your physical space will switch to R4. You cannot catch up, no matter what you do axiomatically or definitionally.
The reason for this is very simple, and hinges on the ancient definition of point and number. A physical point, by definition, has zero dimensions. Logically, this means it cannot be represented on any possible graph or diagram, since representation on a graph or diagram automatically gives it at least one dimension. To exist on a graph or diagram is to have at least one dimension, by definition of the word "dimension". There is no way around this. But even if you give up graphs and diagrams as not pure enough for you mathematically, you still will not be able to outrun this problem, since variable or function or operator assignment does the same thing. You cannot assign a variable or function or operator to a point, since a point is a zero. Variables and functions and operators stand for potential numbers, and the only number that can potentially be assigned to a point is the number zero. Any other assignment or potential assignment to a point is simply false. It is not a paradox, it is a contradiction. A mathematical mistake.
Now, you can use mathematical points in math, it is true. One such point is a point on a Cartesian graph. That is a mathematical point, since you can draw it without making a line, and since it represents a non-extended place on both the x and y axes. But a point on a common Cartesian graph has two dimensions, not zero dimensions. As you see from the previous sentence, it has an x-dimension and a y-dimension.
The second paper that contributes to solving the mystery of Schrodinger’s waves traveling in the q-space is my paper on Superposition. There I first showed the solution of wave-particle duality, and through that the solution of the mysteries of superposition. Both mysteries are solved by recognizing that the wave is internal to the photon. Meaning, it is a characteristic of the photon itself, not of space or any medium. I showed the mechanical cause of the wave, which is simply the stacking of the various spins. For instance, if we imagine the x-spin to be about a central axis—giving the spin a radius of 1—then the y-spin must have a radius of 2, and the z-spin a radius of 4. This numerical progression is caused by gyroscopic rules, specifically the rule of precession, by which rotation is allowed in only one plane at a time. If you stack the spins in this way, the x-pin will be axial, but the y-spin will be end-over-end. These two motions alone are enough to create a wave pattern, and if you add a z-spin, you create an inner and outer wave, one orthogonal to the other. This is the basis not only for the wave motion of light; it is also the basis of electro-magnetism and the right angle relationship of electricity and magnetism.
But the reason this solves the current mystery is that it shows the precise relationship of the wave to the particle. We no longer have a mysterious undefined duality, we have a clear mechanical relationship. The particle is not the wave, nor the wave the particle. Rather, the particle creates the wave as a shape in any configuration field.
Think of it this way: a man walks by moving his legs in a method of locomotion we call "stride". The man is not the stride; nor the stride, the man. Rather, the man creates the stride as a shape that we may see in a continuous line of walking. In a single instant, we cannot see a stride. Over a series of continuous or nearly continuous intervals, we see his stride as a sort of wave: a pattern on a background. The man creates a wavelike pattern because his body is differentiated into two legs. Were the man a single sphere, undifferentiated (and not spinning), he could not create any pattern. But as an object with parts, he is able to create a pattern. It is the same with the photon, though the photon is in fact (we assume) a single undifferentiated sphere. It creates a stride by wobbling in a periodic manner, and the wobble is caused by multiple spins, each spin outside the gyroscopic influence of the other.
Now that we have these two major facts in hand, we are in a position to solve the mystery of Schrodinger’s wave equations. Up until 1926, indeed up until the present hour, it had and has been common usage to assign the representations of material particles to the physical field. I have shown that this was and is incorrect, but it was and is done this way regardless. Whatever mathematical field or space or manifold was being used at the time was assigned to the physical world—that is to reality directly—without any rigorous attempt to defend that assignment logically. Physicists, and sometimes mathematicians, wanted to apply their equations to the physical world, so they just did so, by a sort of unconscious fiat: "I have created a space (or manifold, or whatever) and I assert that the motion of material objects may be represented directly in this space, by a set of internally consistent rules." The problem is that, although the rules might or might not be internally consistent, the creator of the space must also externally tie his space to physical space, in a consistent mathematical way, and almost no creators of spaces have done this.
In the 20th century, the whole idea of a logic external to the mathematical field was considered to be metaphysical. It is not metaphysical, since what is meant by metaphysical in this case is a sort of useless and formless bickering over trivialities. Contemporary scientists and mathematicians also use the term "semantics" as another catch-all epithet to describe nitpicky questions that are a waste of time for them. But, as I have shown in many places, it is not a question of metaphysics or semantics, nor a waste of time, to ask how a given space or manifold represents the material world. It is a strict question of mathematics, since mathematics must include the axioms and definitions that act as a foundation for the functions, operators, and fields. These axioms and definitions are not metaphysical. Metaphysics is the philosophical foundation of physics. An example would be the "scientific method", which is a foundational rule that underlies the daily work of physics. But mathematical definitions and axioms are not metaphysical, they are logical. Mathematics is a field of logic, and whatever is mathematical is also logical. So that connecting a space or a manifold or a field to the objects it is meant to represent is itself a mathematical requirement. If you are doing applied math and you have failed to logically or definitionally or axiomatically connect your space to the physical world, you have failed mathematically. You have made a mathematical error. A physicist or mathematician who refuses to do this work is not a purist, he or she is simply a poor mathematician.
I have done the mathematical work in this case, and it is a fact that mathematical spaces cannot be assigned directly to the real world. Mathematical spaces are only representations of the real world, and, depending on the mathematical space, may be dimensionally close to the real world or not. A good mathematical space will not only be close dimensionally to the real world, it will define how close it is. It will define how many dimensions separate it from the world, and it will state how to logically make the transfer, with as little loss of information as possible. In this way it will be able to support the claim that its representations really represent what they are intended to represent.
The amazing thing about Schrodinger's wave equations, in this case, is that Schrodinger went to the trouble of building a space in which different conceptual levels could be differentiated. He didn’t bother to notice that his photons or electrons weren’t really traveling in physical space—no, his photons and electrons, like everyone else’s photons and electrons, are only mathematical representations of real photons and electrons, and therefore they travel in conceptual space only. But he did bother to create a logical space, in which particles and the waves those particles make travel in different spaces.
To show this, let us return to the man and his stride. Although the stride is not a material thing like the man, it can certainly be said to exist. As I said above, it exists as a shape on a background. It is a sort of waveform. You will say that the stride is made up of molecules, just as the man’s legs are made up of molecules, since a stride requires legs. Therefore it exists in the same way as the legs and the man. But there is a difference. The stride is actually the pattern made by the motion of the legs. The stride is not the molecules or the legs, it is the waveform created by the motion. Molecules may create the legs that create the shape, but the shape is mainly the pattern created on the background. To have a mathematical representation of stride, on any possible diagram, space, or manifold, you have to have a series of intervals, and you must connect those intervals. Your mind can do that, in a way, just by watching someone walk. But the pattern that we call stride cannot be created without a series. On the other hand, the man or his legs do not depend on a series for their existence. Any physical object, from an electron to a man, is more than a pattern. A man has a shape, but a man is not a shape. A man creates a shape, but a shape cannot create a man. A man can create a stride, but a stride cannot create a man.
Even more to the point, in this case, is the fact that the man and the stride move in different conceptual spaces. Graphing the motion of the man and graphing the motion of the stride are two different things. The motion of the man creates a nearly straight line; the motion of the stride creates a sort of wave. But even more important than the line or the wave is the background. The man creates a nearly straight line on the ground or through the air. Our representation of the man creates a nearly straight line through our space that (imperfectly) represents the ground or the air. But the stride moves through a different space altogether. Its background is both the man and the air, so that the stride exists in a dependent space. The motion of the stride might be called a subsidiary of the motion of the man. Conceptually, it is one step removed. The stride is one step more abstract than the man.
All this is analogous to the photon or electron in Schrodinger's wave equations. The photon moves in the primary space, which space is defined entirely by c. The wave is created by this primary motion, and is therefore a secondary motion. It is a shape created by the primary motion. It moves through a space defined both by c and by the wobble of the photon. The photon creates the wave, but the wave does not create the photon. The waveform is dependent upon the motion of the photon, but the motion of the photon is not dependent on the waveform. The primary motions or events are the forward motion of the photon, at c, and the wobble of the photon, caused by the stacked spins. The waveform is only an outcome of these primary motions. It is an effect, whereas the photon itself is the cause. Therefore there is no duality. There is a mechanical dependence, a definite hierarchy, and easily demonstrable levels of abstraction.
And that is why the wave moves in the q-field. The q-field is, and always has been, a dependent field. It is therefore one more feather in Schrodinger's cap that his waves move in a dependent field. It is a sign of distinction, not a demerit. Without being aware of the exact mechanical cause of the wave, nor of the relationship of the particle and the wave, Schrodinger nevertheless achieved the correct dependency and abstraction. All we have to do is downgrade both his spaces. It is said that his wave moved in the configuration field, whereas physical entities were supposed to move in the physical field; but we must move physical entities into a conceptual field, and waves into a subordinate conceptual field. Math and equations cannot be done in the physical field. At best they can be done in the first conceptual field.
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