Geometric Phase Patterns generated by Holography and Diffraction characterizing Charge and Spin

"It is a miracle that curiosity survives formal education." Albert Einstein

Concepts

Geometric phases play a central role in Maxwell-Coulomb interaction. It is proposed that spiral Fresnel patterns or zones carrying topological charges can represent the holographic encoding of spin and charge, where the monopole charges emerge from a linear spin-precession coupling producing anholonomy. In this situation Berry phase patterns can be assigned to the non-spiralling neutral Fresnel zones (Fresnel diffraction) that can be found in the overlapping or interfering region between spiral patterns, see the images below.

Current Interests

Geometric Phase Patterns and Holography - the Nature of Charge beyond the Effect

"Geometric Phase Patterns and Holography- Encoding Model for Charge and Spin", invited poster (below are computer-generated toy patterns, "charged" with a little thought provocation), presented at the "Aharonov-Bohm Effect and Berry Phase Anniversary 50/25 2009, Dec., 14-15, University Bristol", GB (2009) .

Geometric phases arise from interference, where the interference of spatial separated interference patterns shows a characteristic correlation or interaction. Consider overlapping holographic interference patterns of topological charges (local twists and phase singularities). The local interference patterns of these topological patterns arising in the overlap region are proposed to be neutral Berry's phase patterns related to strong interaction. It seems that a stable configuration requires that all neutral patterns connecting charged patterns are in phase.
Look at the phase difference in the neutral/spiral Fresnel patterns between 4-Be-8 (0%, totally unstable) and 4-Be-9 (100%, extremely stable). With the charged and not the neutral patterns in phase in 4-Be-8, the coherent overlap neutral pattern in the center -responsible for the energy decrease- is missing. The same effect can be found with 5-B-10 (19.9%) and 5-B-11 (80.1%), where the effect becomes weaker with increasing ring diameter since the overlap region in the center has decreased. Adding more charges the overlap region at the center becomes too small to prefer an extra neutral pattern in the center. This can be seen at 6-C-12 (98.9%) and 6-C-13 (1.1%) or 7-N-14 (99.6%) and 7-N-15 (0.4%):
4-Be-8 Beryllium

It was a great pleasure to celebrate with, listen and talk to Sir Michael Berry, Sandu Popescu, John Hannay, Sir Michael Atiyah, Yakir Aharonov, Joseph Avron and many others ... and to learn about the charming history around the Bristol physics department. At the poster session in Bristol it was for me highly interesting to note that John Hannay presented a relation between Kirchhof diffraction and the AB phase, while I was presenting a relation between the Fresnel diffraction and the Berry phase. From private talks I got the impression that indeed most of the people think or feel that the deviation of the fine structure constant from 1/137 in measurement could be assigned to a geometric phase. But making such a statement in public without a super strong verification background could quickly kill a good reputation and career. In 2002 I would have said that the chance is about 80% that this new proposal could ever be verified, two years ago with the classical and quantum chaotic model 90%. Now, with the direct relations to the Schroedinger equation, stereographic projection, topological charges, spintronics, and the diffraction picture I would say 99%. The last 1% is connected to the uncertainty regarding the origin of the values 137 and the proton-to-electron mass ratio. So I can now recommend to make some investements into this direction - the years before I rather pointed to the risks.

Propulsion by Geometric Phases

SPESIF 2010, Washington, JHU
(Rolling oscillators. Geometrically Induced Interactions and Bifurcations)

Anholonomy Attractor - Generating Strong Geodesic Flows and Pumps

"Geodesic Holonomy Attractor between Surfaces of Different Curvature Signs relevant to Spin Transport", CHAOS2009, Chania, Crete (2009).
Nonlinear holonomy effects -especially the spin dissipation dynamics- arising in the transport of a linear rotator between metric spaces with different curvature (positive, zero, negative) are considered, where an extra 3D spin vector current induced by curvature or metric distortion provides for a holonomic attractor called "Magic Angle Precession" (MAP). Limitations and instabilities of the spin current exchange are assigned to bifurcations at high precession loads as the driving gauge potential. Transporting vector currents composed by spin and precession is treated by Schwarz-Christoffel triangle conformal maps with constant Schwarzian derivative and hypergeometric monodromy. Handling both curvatures simultaneously as a metric distortion is possible by hypergeometric functions related by inversion and can be described by the well known Schroedinger hypergeometric quantum mechanical solution providing for Poeschl-Teller type potentials, quantization, factorization, and ladder operators. By pull-back we get the generalized Gauss linking number density differential form. In the classical range the correspondence to the quantum chaotic dynamics can be verified with a mechanical toy gyroscope with built-in spin-precession coupling that could also be modeled by a Chua-type electronic circuit.

Recommendations

At the CHAOS2009 conference I met Alfred Inselberg who recently published the book "Parallel Coordinates" at Springer This highly recommendable book is about visualization, systematically incorporating the fantastic human pattern recognition into the problem-solving. I got interested in his visualization of a higher-dimensional rotation-translation duality (surely part of MAP) and other dualities (btw, he "immensely enjoyed" the poster/paper above).

Selected Publications

Harvard SAO/NASA Astrophysics Data System (ADS)

"Magic Angle Chaotic Precession", in "Topics on Chaotic Systems: Selected Papers from CHAOS 2008 International Conference", Editor Ch. Skiadas, Singapore, World Scientific Books, p.31-42 (2008), (Amazon).

"Berry's Phase and Fine Structure", preprint (2002), (PhilSci archive).

"Friedmann Propulsion in a Flat Holographic Universe" (Advanced Gauss Unit Scale Flux Normalization), STAIF 2008, New Mexico. In "Space Technology and Applications International Forum-STAIF 2008", Editor M. S. El Genk, AIP Conference Series 969, p.1146-1153 (2008).

older

Conferences with Contributions

STAIF 2007 Albuquerque (New Mexico, USA), QUANTUM MIND 2007 Salzburg (Austria), STAIF 2008 Albuquerque (New Mexico, USA), CHAOS2008 Chania (Crete, Greece), SPESIF 2009 Huntsville (Alabama, USA), CHAOS2009 Chania (Crete, Greece), Aharonov-Bohm Effect and Berry Phase Anniversary 50/25 2009 (Bristol, UK), SPESIF 2010 John Hopkins University (Washington, USA)

Simulations

Berry's Phase & Fine Structure Constant Java simulation, some screenshots

Geometric Phase Bifurcation near Z=115

Parallel Transport and Precession

Quantum Precession or Quantum Gyroscope with Magic Angle Precession (MAP)

Quark Model: Three Space-like Cones Rolling on a Common Time-like Cone

MAP part of a Chua oscillator showing "charged" bifurcation singularities