Riktare wrote:
The non-trivial exceptions to CPT consistency arise because EM and other manifestations and behaviors of matter are not merely described in the simple case by U(1) topology (as mathematically described by Heaviside's rendition of the Maxwell Equations), but by SU(2) topology in more complex cases. Maxwell began to understand this and incorporated such a description into his work (via his quaternion versions of his own equations - not those that were simplified and modified later). Quantum mechanics requires (in general) SU(2) descriptions.
Thanks for chiming in Steve. I see the confusion in the math of QM. If one is to consider the exponential of a Pauli vector the result is an expression analogous to Euler's formula. Recall that many times before I had mentioned that y=e^x is has no derivative but itself, therefore, calculation ceases once one realizes that the determinant of the exponential itself is 1, which makes it the generic group element of SU(2).
Riktare wrote:
SU(2) topology accounts for the fact that rotations have direction and that introduces particular configurational dependencies between particles or particle and field. Backwards running time is not required, but the concept might possibly be useful as an intellectual short cut or simplification.
Rotations have direction but a particle does not simply rotate. A particle has primary and secondary motion just as space moves. A particle breathes as it rotates. This fact changes everything! This is a revelation from TUB. This composite motion can be described as spiral motion. SU(2) topology cannot account for this. This motion has no direction at all. The reason for this is that spiral motion is motion in infinite directions, simultaneously.
Let's take the example of a perfectly spherical particle that rotates and breathes (expands and contracts). No matter what is its spin, the particle counter-rotates by virtue of an equator. Above the equator, clockwise, below, counter-clockwise. And this is visa versa as well. This is balanced motion. As the particle expands, it moves out from its center in the direction of infinite radii. As it contracts, it moves towards it center from infinite directions (a sphere has infinite radii). All vectors originate from a center and return to the center, origin and destiny.
I see this as insurmountably complex.
As you say, backward running time is not required but must be a possibility for CPT symmetry. This brings up the question of linear time vs circular time. Minkowski always depicted time as linear and orthogonal to space and placed time in the imaginary plane, i. He , therefore, had to depict space as a plane in his light cone diagram. Obviously, if time were to be treated as a line, it could only be perpendicular to a plane. He must have thought that we were all gullible since a space has to be at least three dimensional. And he was correct. All of physics swallowed this whole. Now we are choking on it. In addition, a moving space must be 4 dimensional.
TUB reveals time to be circular. TUB reveals space to be in motion, primary and secondary (spiral). Only a hyperbolic space can move thusly.
Fortunately, this fact is consistent with the geometric fact that only circles can be perpendicular to hyperbolas. This is a perfect fit that is only revealed in TUB.
BTW, a line is not symmetric yet a circle is perfectly symmetrical. A line is infinite and cannot be bisected. A circle is infinite but can be bisected.
Time is discrete and perfectly symmetric and , therefore, the CPT theorem cannot be descriptive of any physical reality.
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