Not driven by observations, this paper digs into the “internal workings” of spacetime. Through logical deductions, micro dimensions appear to be uncovered, with possible SU(4) or SU(5): 1. It is thought that special relativity merely initiated the definition of spacetime,
but more scales are yet to be defined. 2. In the definition of spacetime, EM (electromagnetism) played another critical role, i.e., the six circular magnetic and electric field lines (running on the six planes) cross and “define equivalencies” between the four linear scales. Without
this definition, light would not be measured at the same speed in different directions. Being a gauge theory, EM defines two things: Linear scales and “equivalencies” between linear scales. 3. For any scale (and their equivalencies), there could be no or many arbitrarily assumed
definitions, or a concrete definition based on relevant physics. Nature would conform with but the one based on relevant physics, because Nature itself is consisted of that relevant physics. Thus, the principle: No scale and their equivalencies are meaningful unless defined by relevant physics.
4. Then, what are those fields running (and defining equivalencies between the six “angle scales”) on the six planes of the 4D spacetime? It is believed to be the “classical” weak fields which run in solid angles (or “3D angles”) between the six planes.
(The only suspicion is that this rotation does not preserve vector length, which is not a problem ultimately.) 5. If the six angle scales are drawn as six axes of a 6D superspace, then the “3D angle” rotations look like “plane angle” rotations and cause SO(6)∼SU(4)
[or SO(10)∼SU(5) for 5D spacetime], which appears to match baryon spectrum without quarks. 6. Since this rotation is between “planes” of the “external” spacetime, no linear dimension is visible, yet causing P-violations. 7. Similarly, fields running in 4D and 5D
angle rotations (between 3D and 4D surfaces) must also exist, which may be responsible for CP-violation and strong interactions. 8. The 5D angle rotations may be generating Baryon and Lepton numbers and hence explaining their conservation behaviors, e.g., no proton decay. 9. It can be inferred,
if 3D, 4D (and 5D) angle rotation fields did not exist, the 4D (and 5D) spacetime would be warped and the four (or five) linear axes would not be perpendicular to each other. 10. EM was simplified and turned elegant “only” after redefinition of spacetime by special relativity.
Likewise, weak, CP-violation and strong interactions are expected to simplify and turn as elegant as EM when 2D (plane), 3D, and 4D angle scales are defined by weak, CP-violation, and strong forces, respectively. 11. Verifications as accurate as EM are expected too. 12. Mathematically, higher
angle rotations thought to be inexistent only because it does not conserve vector length. Actually, they did not vanish and their symmetries would surface in particle classifications when linear momentum is not concerned. Micro dimensions being invisible is because symmetries do not have to
happen between linear axes, but can happen between 2-, 3- or 4-surfaces. These geometries together generate the complete particles spectrum.
Consequences of the order of the limit of infinite spacetime volume and the sum over topological sectors for CP violation in the strong interactions
