I am digging deep into the details of how an R3+I unitary vector field behaves. I study this field because I’m hypothesizing that it is a good candidate for an underlying field that will produce the particle zoo of reality. I’m not trying to figure out gravity or dark matter or any of that–I just want to find a workable underlying structure that could explain why there are stable and unstable particles, and why quantum creation operators evolve particle/antiparticle pairs. If you take a look at some of my recent prior posts, you’ll see the thinking I used to come up with this field concept.
I really like this study, because it avoids the handwaving problem of trying to prove that some new idea represents actual reality. Every amateur (and I’m sure most real-life physicists) have their pet idea of how things work, and the central problem in promoting that idea is not discovering new science, but rather the socio-political problem of convincing others, and in particular, professional researchers, that your idea is right. That is a really hard problem that doesn’t involve actual science research. I have attempted to publish papers in the past and have discovered that that activity is an exercise in futility. What I love about my study of the R3+I unitary rotation field is that I leave that all behind–I’m just exploring how this field behaves, all the while keeping an eye out for something that might invalidate the field as a candidate for reality.
And to this end, I have discovered some great properties of this field. The field so far shows the right degrees of freedom to produce linear and closed loop particles, shows why quantization occurs (the lowest energy state of the field is the +I rotation direction, confining twists to integer multiples of complete cycles) and clearly shows how the two types must interact. Since (see previous posts) the field is blocking, a linearly propagating twist rotation through +I will propagate until it encounters a closed loop twist in this field. Non-unitary fields such as an EM field permit varying vector magnitudes, including regions with zero magnitude. In that type of field, there is no possible way that a linearly propagating twist can intercept and be absorbed by a closed loop through the center (think photon striking an electron). But a unitary twist field, as shown in previous posts, has a very specific stable configuration of rotations that must exist in the center of the loop. When a linearly propagating twist tries to collide with the closed loop, it cannot pass through (remember that unitary rotations cannot linearly combine, there is no magnitude other than 1). It will pass its momentum components to the rotations in the loop, but cannot dissolve the loop unless the momentum of the linear particle approaches the momentum of the loop components and breaks the loop. I know this sounds like handwaving, but I think if you do your own analysis of this field you will find this to be true.
Now on to the new findings: as I dug deeper into the specifics of this interaction, I had to define exactly how rotation momentum would propagate through the rotation field, and in so doing discovered a very important principle, shown in the figure. I described how momentum translates in spacetime with a single rule as follows–a delta rotation in R3+I propagates in the direction of rotation. Quantization says that there must also be a background state restoration force (note that the momentum itself is not unitary, it can be zero or even infinite, and everything in between. It’s only the vector magnitude that has to be unitary in the R3+I unitary vector field). When looking at the geometry of this, I discovered something very important about the unitary rotation field R3+I–geometrically, if conservation of momentum is to hold, in certain circumstances, the momentum path must curve.
Normally, if a quantized rotation twist propagates through the +I background rotation state, there is no reason why the momentum propagation rule wouldn’t ensure a straight line path. However, suppose the twist passes through a region where the field is not at +I (the low energy state). If this region is pointing orthogonal to the twist path, the resulting sum of the propagated twist rotation direction and the existing field direction would be linear and momentum magnitude and direction would be conserved. But you cannot sum vector directions in this field–it is unitary, only rotations are allowed. The only way the incoming momentum magnitude could be conserved is if the rotation follows a curved path (see illustration).
What this means is that in most circumstances, linear twists will propagate in a straight line since the default state for the path will be at the +I rotation direction. But if it passes through a field region where there is an angle offset from +I (for example, in the neighborhood of a closed loop particle), it will curve in the plane of the angle offset and the direction of travel. Two adjacent twists will curve antiparallel to each other and produce a sustained closed loop path, thus forming a field soliton.
In earlier posts, I hypothesized that quantum interference in an R3+I system would redirect a particle’s linear path and form a soliton–we know that to be true from experiments like the two-slit experiment, but I didn’t know why the curvature would happen. I was on the right path with quantum interference, but by breaking down how rotations must propagate, now I know geometrically that if we assume a unitary rotation vector field, then closed loop particles must occur. Even better–the effect is contravariant. That is, higher twist momentums lead to smaller closed loops. In Newtonian physics’ descriptions of orbiting particles, the larger the momentum, the larger the resulting orbit. The effect on path is covariant. But you should be able to see (reference the figure) that in the R3+I unitary rotation vector space, the larger the momentum, the greater the curvature must be to conserve momentum magnitude, and the smaller the resulting path must be. This field clearly provides the means for the contravariant relation between particle energy and particle wavelength–something no other theory that I know of has been able to explain.
Agemoz
Agemoz's Physics Blog 