Areas of Research

It is clear from a mathematical viewpoint that unit scales have generally no special meaning. The scale of units or standards are usually defined such that they can easily be handled by humans. But there exist no such units for extra-dimensional phenomena like gravity. Referring to string and conformal field theories it is commonly agreed that the weakness of gravity (hierarchy problem) can in general be assigned to extra dimensions. There have been a lot of efforts (recently Arkani-Hamed, Dimopoulos - Dvali, Randall-Sundrum,  ...) to rescale the Planck scale ("diluting" gravity by extra dimensions or "warping" gravity into extra dimensions) but without realizing the role of the unit scale. If different-dimensional volumetric flow or flux rates are properly normalized they should all intersect at radial distance 1, the unit scale. This is because of the power-law flux scaling where the exponent is proportional to the dimension and any power of 1 is 1. Taking human artificial geometric units of length (meter) and time (second) and defining the correspondent unit fields and unit scale dynamics properly (i.e. by introducing the unit field generating bulk mass |m_G|= |4p/G| ), insures that any radial power law with or without extra-dimension will intersect at this scale. Properly means, that there is also a number scaling involved, especially comparing an interaction on the quantum level (i.e. the  electromagnetic flux quantum) with a higher-dimensional interaction on the macroscopic level (i.e. the gravitational flux of a bulk mass). Doing so, the common unit scale can build a bridge or scaling intersection between scaling laws of different fields. As a result we can show that the unit scale intersection constraint reduces the number of independent fundamental constants from three to two. Consequently, we can verify that i.e. the proton mass, the Newton constant, and/or the Planck length can be calculated from the unit intersection of quantum gravitational and electromagnetic fluxes knowing the action quantum and light velocity. 

The second area of research is about the local quantum geometric algebra involved to couple topologically different fluxes. To compactify the extra-dimension of gravitational flux to get a lower-dimensional electromagnetic flux, I suppose that curvature, parallel-transport, and consequently geometric phases are necessarily involved. Therefore, I suggest that geometric phases play a key role in every type of electromagnetic flux, i.e. as part of the fine structure constant. Consequently, traces of geometric phases should be found in many type of electromagnetic fluxes involving spin-orbit coupling, fine structure shifts, and corresponding spin anomalies and may be simulated by magic angle precession in curved space-time. Geometric phases appear typically while parallel-transporting vectors (conserved vector manifolds like spin) in curved space-time and are connected with the names of Berry, Pancharatnam, Aharonov, Bohm, Anandan, Focault, Casher, Thomas, Wilczek, Hannay, Ishlinskii, Rashba ... As a result, I can show with increasing number of arguments that the small difference between the fine structure constant and the rational number 1/137 can be assigned to a geometric phase. Therefore, I encourage measurements to identify the geometric phase component. In the H-atom I expect a geometric phase contribution of about 1/3806 part of the electromagnetic charge (about 1/3806^2 in energy), that should manifest itself in spin resonance anomalies/shifts subject to correspondent modulations of external magnetic fields that are not part of the standard Dirac equation.

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