return to homepage Schrodinger’s Wave Equations If this paper was useful to you in any way, please consider donating a dollar (or more) to the SAVE THE ARTISTS FOUNDATION. This will allow me to continue writing these "unpublishable" things. Don't be confused by paying Melisa Smith--that is just one of my many noms de plume. If you are a Paypal user, there is no fee; so it might be worth your while to become one. Otherwise they will rob us 33 cents for each transaction.
return to updates
Explained
How can electrons have more than three wave motions
in only three dimensions?
As usual, I will give the simplest possible explanation, one that anyone can understand. Of course there are complexities that I will not address, and by not addressing them I am not implying they do not exist. I only want to show my reader here that questions about quanta and dimensions do not need to be difficult or esoteric. Simple explanations do exist, and they should continue to be sought. We should never accept that Quantum Mechanics or QED is mystical, senseless, or fantastic. It is ultimately mechanics, and as such must resolve to visually comprehensible explanations and simple math.
In my paper on superposition, I showed that wave motion was easily explainable as stacked spins. I will gloss that argument in a moment. The problem is that, even if this explanation is accepted, it would appear at first glance that we still only have three possible spins, in the x, y and z planes. But Schrodinger finds more waves than that. How is that possible?
It is possible since a fourth wave motion may be shown to exist, contained in that simple stacking. And a fifth wave motion can also be shown, one that is not determined by the spin of the quantum itself.
Others have postulated that since space is now four-dimensional (since Minkowski), one of the extra wave motions or variables might be a function or expression of time. This must be false, since time is not a separate dimension. In studying motion, time is a useful concept, but it is not a dimension like x, y, or z. In fact, time is a second measurement of one of the other three dimensions, as I show in several of my other papers. Therefore we must throw it out as an explanation of the number of waves motions in the equations.
No, we have simpler explanations than that, ones that require no esoteric expressions of time at all. The first extra dimension comes from analyzing even more closely the mechanics of spin. We begin with a simple sphere spinning on its axis. Up to now, theoreticians have called that spin the x-spin, leaving them y and z. But a spin about an axis is not a motion in x, y, or z. Just look at our little sphere, spinning away. It is not moving in x, y, or z yet. The fact is, we have spin plus x, y, and z to work with, which is four total motions. We can call these motions dimensions if we want to, although I am not sure I would call spin a dimension. Regardless of what we choose to call spin, it is a basic motion that creates a wave or a variance. We can have a CW spin or a CCW spin, and then we can have three spins stacked on top of that.
These outer spins have to be outside the influence of the inner spins, as I show in my superposition paper, but they are quite easy to visualize. Start with the CW spin, for example. Due to gyroscopic rules, you can’t spin that sphere in any other direction. What I mean is, imagine that sphere is the earth and you are spinning it about the N/S axis. You can’t also spin it about the E/W axis. Gyroscopic rules prevent it with any real body, including the earth and including a quantum.
But you can spin it E/W if you make the spin end-over-end. If the CW spin radius is 1, you just make the E/W spin radius 2, so that it is outside the influence of the inner spin. Then the second spin does not affect the first.
Of course the center of this second spin is on the shell of the sphere, not the center. You might not want to call it a spin. But whatever you call it, it is another variation that can either be CW or CCW. And it will act like a wave in equations. It will also move the entire body in a line, filling or creating the x direction in space.
Obviously, we have two more directions to fill in the same way, making sure that our new end-over-end spins are beyond the influence of all inner spins. In this way, we fill the y and z directions.
Since we have no other directions, we cannot propose any more waves in this way. We seem to have topped out at 4, which is still less than we need.
To continue, we just look to my paper on the electron orbit, to find another wave motion. This wave motion is created by interaction with another body. The quantum cannot exhibit this wave by itself. There I show that, just as at the macro-level, the field is a compound of the gravitational and E/M field. The standard model has long believed that the quantum field is all E/M and the macro-field is all gravity, but that model is wrong. At all levels the interaction field of all particles and bodies is a compound of gravity and E/M. Gravity causes an apparent attraction, E/M causes a real repulsion, and the orbit is caused by the balancing of both with the tangential velocity of the orbiter.
Due to the mechanics of the orbit, an electron cannot possibly be captured at a perfect tangent. A perfect capture would only take place with an infinite velocity. In short, it must be captured in a less-than perfect landing, which creates a bounce. I show this in more detail in the other paper. This bounce becomes the wave, once it settles. This wave would become apparent in a graph of the main orbital motion. Since it is caused by a bounce and not by a spin (end-over-end or otherwise), it is not disallowed by any gyroscopic rules or other rules of dimensionality.
That gives us a total of five, without once going beyond a high-school textbook or beyond simple logic and math. It is possible we could find more wave or wavelike motions, but I think I have made my point. We don’t need to look at esoterica to solve problems in QED. We need to think mechanically and clearly.
I have shown the mechanical genesis of five separate wave motions, motions that may be expressed by Schrodinger’s equations. As you can see, this does not imply that space is now five-dimensional, in any strange or esoteric sense. We still have only three directional dimensions here. It is only a complex stacking of spins and linear motions that gives us the extra functions or variables (or whatever you want to call them in your math and equations). I believe it is a mistake to call every new variable or motion a dimension, since it is not a dimension in common usage. A dimension implies an independent direction in space, and we have only six of those, three if positive and negative are taken as one.
Time is not even a dimension, in this regard, since its direction is not independent of the other three. If you give time a direction, as a vector, it must be in the direction of either x, y, or z, for any given problem, and the velocities and accelerations always bear this out. You can use Minkowski’s shortcuts if you like, but his postulates are absurd. Time cannot "move" in the direction of i, of course, since "move" happens to have a precise and unalterable definition. Motion is either a velocity or acceleration, in which the time variable is necessarily in the denominator. A denominator that was orthogonal to its own numerator would not give you a velocity or an acceleration. Minkowski must ignore vectors and only play with numbers. You can use that fake symmetry if it appeals to you, but you always have to push your vectors back into line at the end by main force, a thing I find to be the opposite of elegant.