Physical reality is totally and completely one-dimensional. This simple conjecture is much easier said than it is proven. The two basic ingredients of one-dimensional topology are simply line and circle. These are generalized into opened-curves and closed-curves. All opened-curves have two ends, while every one of the closed-curves simply looped back continuously on itself. The study of one-dimensional topology, at the least, comprises the various minimal transformations of opened-curve into a line or closed-curve into a circle. Hence, line and circle represent the geodesics of one-dimensional Euclidean topology.
A ball of spaghetti and a ball of rubber bands are good examples of three-dimensional representations of open-curves and closed-curves. Sadly, there are no higher dimensional representations although by advanced mathematical abstractions there are. Fortunately, these are not important for the formulation of a quantum theory of the spacetime continuum. Furthermore, for this proposed quantum theory, opened-curves are extra baggage for the quantum travelers and they are much better left behind at the train of thought station. In the final analysis, the one and only ingredient of one-dimensional topology are special kinds of closed-curves called Hopf links. These subdivided into two distinct topologies called H-plus and H-minus. Both are represented by Hadamard matrices. Luckily, a unique algebra is constructed for the multiplicative, additive, and subtractive operations of these matrices in order to justify the quantitative science of mass and charge variability of physical reality and giving answers to the fundamental question why electric charge is a relativistic invariance while physical mass is not.


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