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"Magic Angle Chaotic Precession" pdf 329kb first submitted and accepted draft 10.3.2008, first release 11.06.2008

Abstract: This paper explores the properties of a precessing rotor or a coupled system of precessing rotors (gyroscopes), where a special chaotic behavior in the precession angle can be found if the change of rotor angular velocity is linearly coupled by (an)holonomy to the precession angular velocity and angle. The linear coupling provides for rolling cone paths and allows spinning up and controlling the rotor simply by forcing precession at special quantum magic precession angles. This linear relation models a recurrent chaotic holonomy, where the cause of holonomy (precession) is also a generator of holonomy. The geometric phase induced by the curved path of the rotor or external curvature and part of the coupling increases with precession angle. This leads to bifurcations in coupling strength resulting in chaotic precession. As an alternative to the SO(3) matrix or quaternion representation the treatment of the three coupled rotations is here based on Euler’s dynamical equations. First, the classical Magic Angle Precession (MAP) dynamics is realized by a geometric or mechanical condition (type I, transcendental solutions), where it can be experimentally demonstrated how MAP can “slave” angular degrees of freedom allowing the external control of high-frequent spin by slow oscillations. MAP can be found in a commercial fitness device and conceptually approached via Chua’s electric circuit. Second, the quantum-gravitational MAP (type II, rational solutions) with discrete precession angles is analyzed on a deeper level requiring intrinsic curvature/relativistic effects adjusting holonomy to topological numbers. Third, a macroscopic network of MAP elements is presented as a discrete-time recurrent neural network synchronizing to one common MAP I/II dynamics under special pairing and symmetry conditions (type III). In all three cases MAP can be treated as a time-discrete chaotic system with singularities given by the cosine map with several possible links to interesting applications on all scales.

CHAOS 2008 Chania Grete Greece, Conference Proceedings, (2008)

Friedmann Propulsion in an Flat Holographic Universe pdf 189kb 2.12.2007

Abstract: Because of inversion symmetries in holographic systems, the spatial compression of lower-dimensional holographic memory leads to an expansion of the holographic image and vice versa (scaling duality), where the geometric mean between the small quantum memory and cosmic image scale defines the inversion scale, the unit scale to normalize the global holographic currents of momentum exchange. Assigning to the cosmic image (bulk) a 4d, to the quantum memory (baryon) a 2d, and to the inversion scale a 3d spherical topology, the cosmic critical density in the flat FRW cosmic test model corresponds to 1 memory unit (baryon). Otherwise, if we expect expansion driven by 3d Einstein gravity on all scales, we get the well known cosmic “dark matter” deficit of 96% or 0.04 baryons per unit volume. The cosmic deficit or quantum excess is assigned by Gauss law to the topological ratio 4d bulk surface S3 to 2d quantum surface S1, which dilutes gravity or the mass density by the dimensionless factor 0.04 ~ S3/2/S1^3 = 1/(8p) leading to a theoretical Hubble parameter of 73.2 kms^-1Mpc^-1. Regarding propulsion based on fractional linear transforms mapping the quantum compression by inversion to a cosmic expansion, the anisotropic transform resembles the Alcubierre mechanism if expansion is behind and the compression ahead of the spaceship.

Copyright (2008) American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics.
The following article appeared in SPACE TECHNOLOGY AND APPLICATIONS INTERNATIONAL FORUM-STAIF 2008: 5th Symp New Frontrs & Future Con. AIP Conference Proceedings, Volume 969, pp. 1146-1153 (2008)

"Magic Angle Precession" pdf 310kb 15.11.2007

Abstract: An advanced and exact geometric description of nonlinear precession dynamics modeling very accurately natural and artificial couplings showing Lorentz symmetry is derived. In the linear description it is usually ignored that the geometric phase of relativistic motion couples back to the orbital motion providing for a non-linear recursive precession dynamics. The high coupling strength in the nonlinear case is found to be a gravitomagnetic charge proportional to the precession angle and angular velocity generated by geometric phases, which are induced by high-speed relativistic rotations and are relevant to propulsion technologies but also to basic interactions. In the quantum range some magic precession angles indicating strong coupling in a phase-locked chaotic system are identified, emerging from a discrete time dynamical system known as the cosine map showing bifurcations at special precession angles relevant to heavy nuclei stability. The “Magic Angle Precession” (MAP) dynamics can be simulated and visualized by cones rolling in or on each other, where the apex and precession angles are indexed by spin, charge or precession quantum numbers, and corresponding magic angles. The most extreme relativistic warping and twisting effect is given by the Dirac spinor half spin constellation with “Hyperdiamond” MAP, which resembles quark confinement.

Towards a Self-Consistent and Controllable Graviton Flux pdf 188kb 22.11.2006

Abstract: The long standing hierarchy problem in particle physics addresses the 19 orders of magnitudes difference in interaction between electromagnetic forces and gravitation. Referring to string and conformal field theories it is commonly agreed that the weakness of gravity can in general be assigned to extra dimensions. To access and control the extra-dimensional flux for propulsion purposes, it is important to understand the graviton flux topology on the microscopic and macroscopic scale. Regarding the flux volume there is a characteristic power-law scaling between length and time or mass scales with exponent proportional to the number of spatial dimensions. Power-laws with different exponents intersect at the unit scale since any power of 1 is 1. Therefore, comparing forces with different dimensionality and topology the unit scale has a special and important role not only for practical purposes. By defining the gravitational unit scale Kepler dynamics (unit radius and angular velocity) that is generated by the unit field generating bulk mass |m_G|= |4p/G| we can be sure that any geometric radial power law flux and mass-energy scaling with or without extra-dimensions will intersect at this scale. A scaling number N_G µ c⁴ connecting microscopic and macroscopic scales can be found by dividing m_G into baryons or quantum mass units µ, where the Planck scale limit is obtained by dividing the unit length by N_G. The unit scale intersection method can be applied to all kind of quantum (spin) network systems exchanging topological fluxes and reveals that some microscopic scales (like the Planck scale) emerge from a macroscopic reference dynamics by inversion symmetry. Possible fields of application could be time scale, length scale, and dimensional adjustments improving the coupling of fields with different dimensionality, i.e. between a lower-dimensional quantum-electromagnetic and a higher-dimensional gravitational field relevant for space propulsion. One of the applications could be the adjustment of gravitational flux in solid state superconductors or neuronal networks with holographic interaction or backreaction.

Copyright (2007) American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics.
The following article appeared in SPACE TECHNOLOGY AND APPLICATIONS INTERNATIONAL FORUM-STAIF 2007: 4th Symp New Frontrs & Future Con. AIP Conference Proceedings, Volume 880, pp. 1181-1188 (2007)

Human Artificial versus Natural Conceptualization of Spacetime Units pdf 186kb, PS, 31.12.2003

Abstract: The human international system of units (SI) is an artificial conceptualization. At this stage general relativistic and quantum concepts are not fully integrated, i.e. the geometric structure of fundamental mass quanta. A natural conceptualization of spacetime units can only be found if hidden human artificial specifications are identified. Example: compressing a special number N \approx 10^{38} of neutrons into a black hole, the resulting Schwarzschild photon sphere radius is mathematically (a priori without physical meaning) identical to the Compton wavelength of one neutron. It is not surprising and can be easily shown by a scaling analysis that N is not a fundamental number but an extensive property of our system of units. But it is probably surprising that the square root of this artificial number of neutrons is the celebrated Planck mass.

Self-Consistent Quantum-Gravitational Quadrupole Fluctuations pdf 186kb, PS, 31.01.2003

Abstract: To establish a self-consistent system of mutually interacting gravitational quadrupoles, a characteristic number N of quantum masses µ are related to a characteristic velocity scaling. For this purpose a critical reference is defined by the flux and flux number of mass quanta constituting a confining unit field generating mass m_{G}=Nµ. In the field of m_{G} any small test mass orbits at unit distance r_{u} with unit velocity u (human artificial units). The velocity limit c with angular momentum quantum h is assigned to the Schwarzschild black hole photon sphere with radius given by the Compton wavelength. For this quantum mass we find the constitutional scaling relation N \approx 3m_{G}/µ \propto (c/u)^5 which indicates a quadrupole exchange. The corresponding coupling strength can be exactly related to previous results confirming the quantum mass µ hidden in the action quantum related at the Planck scale to the gravitational coupling constant G by µ^4 G=1. The coupling deficits can be assigned to a duality of coupling and non-coupling fluxes with 4th power flux scaling. This fits very well to existing models assuming a non-gravitating vacuum energy to give a satisfactory answer to the cosmological constant problem.

Natural Nonlinear Quantum Units and Human Artificial Linear System of Units pdf 108kb, PS, 12-15.01.2003

Abstract: Diving into the nonlinear massive range of nuclear physics, the quark model already indicates that the linearized massless length scales break down. Although we are often confronted with nonlinear and relativistic dynamics, we obtain our fundamental values with the classical linear system of units SI by linear extrapolation. Ignoring the correspondent nonlinear relations while extrapolating to the Planck scale h=c=µ=1 based on linear massless relations leads to pseudo-scales equivalent to geometrized mass units. This paper shows that one of the fundamental dimensions length, time, mass becomes redundant approaching the Planck scale. The hidden information can be assigned to a geometrized natural quantum mass unit µ part of the Planck constant h. In other words: c, h, and µ are interrelated.

A Natural Mass Unit Hidden in the Planck Action Quantum pdf 116kb, PS, PS, philsci-archive, 7.01.2003

Abstract: 0.138% above the neutron and 0.276% above the proton baryon mass a natural mass unit µ can be identified by extrapolating dimensionless Planck units h=c=1 to the System of Units (SI). Similar to quantum measurements that determine h it is only necessary to relate the unit kinetic particle energy to the quantum energy of a photon having a unit wavelength. Connecting both energies and shifting the units, the inverse ratio of length units evolves proportional to the square of velocity units since both are proportional to the energy unit. With this connection the measurement of h becomes an indirect light velocity measurement and measurement of µ and shows that nonzero action and mass quanta corresponds to a finite light velocity c. As already shown, these sequential baryon mass differences (typical mass deficits of strong interaction) including the electron mass can be recovered within measurement error (some ppm) by simple relations obtained from bosonizing a massive Dirac equation.

With Iterative and Bosonized Coupling towards Fundamental Particle Properties pdf 206kb, PS, latex, PS, philsci-archive, 31.12.2002, 5.1.2003 update

Abstract: Previous results have shown that the linear topological potential-to-phase relationship (well known from Josephson junctions) is the key to iterative coupling and non-perturbative bosonization of the 2 two-spinor Dirac equation. In this paper those results are combined to approach the nature of proton, neutron, and electron via extrapolations from Planck units to the System of Units (SI). The electron acts as a bosonizing bridge between opposite parity topological currents. The resulting potentials and masses are based on a fundamental soliton mass limit and two iteratively obtained coupling constants, where one is the fine structure constant. The simple non-perturbative and relativistic results are within measurement uncertainty and show a very high significance. The deviation for the proton and electron masses are approximately 1 ppb (10^-9), for the neutron 4 ppb.

Bosonization and Iterative Relations Beyond Field Theories pdf 220kb, PS, philsci-archive, 24.12.2002

Abstract: Solitons can be well described by the Lagrange formalism of effective field theories. But usually mass and coupling constants constitute phenomenological dimensions without any relation to the topological processes. This paper starts with a two-spinor Dirac equation in radial symmetry including vector Coulomb and scalar Lorentz potentials, and arrives after bosonization at the sine-Gordon equation. The keys of non-perturbative bosonization are in this case topological phase gradients (topological currents) that can be balanced in iterative processes providing for coupling constants driven by phase averaging and ``noise reduction'' in closed--loops and autoparametric resonance. A fundamental iterative spin-parity-asymmetry and dimensional shift quite near to the electron to proton mass ratio is found that can only be balanced by bosonization including Coulomb interaction.

Higher-Dimensional Solitons Stabilized by Opposite Charge pdf 146kb, PS, PS, tex 23kb mp_arc, 30.11.2002, update 9.12.2002

Abstract: In this paper it is shown how higher-dimensional solitons can be stabilized by a topological phase gradient, a field-induced shift in effective dimensionality. As a prototype, two instable 2-dimensional radial symmetric Sine-Gordon extensions (pulsons) are coupled by a sink/source term such, that one becomes a stable 1d and the other a 3d wave equation. The corresponding physical process is identified as a polarization that fits perfectly to preliminary considerations regarding the nature of electric charge and background of 1/137. The coupling is iterative with convergence limit and bifurcation at high charge. It is driven by the topological phase gradient or non-local Gauge potential that can be mapped to a local oscillator potential under PSL(2,R).

Soliton Compton Mass from Auto-Parametric Wave-Soliton Coupling pdf 138kb, PS, PS, tex 20kb mp_arc, 20.11.-2.12.2002, update 9.12.2002

Abstract: In this paper a self-excited Rayleigh-type system models the auto-parametric wave-soliton coupling via phase fluctuations. The parameter of dissipative terms determine not only the most likely quantum coupling between solitons and linear waves but also the most likely mass of the solitons. Phase fluctuations are mediated by virtual photons coupling at light-velocity in a permanent Compton scattering process. With a reference to the SI-units and proper scaling relations in length and velocity, the final result shows a highly interesting sequence: the likely soliton Compton mass is about 1.00138 times the neutron and 1.00276 times the proton mass.

Soliton Coupling Driven by Phase Fluctuations in Auto-Parametric Resonance pdf 132kb, PS, PS, tex 19kb mp_arc, 13-19.11.2002, update 9.12.2002

Abstract: In this paper the interaction of sine-Gordon solitons and mediating linear waves is modelled by a special case of auto-parametric resonance, the Rayleigh-type self-excited non-linear autonomous system driven by a statistical phase gradient related to the soliton energy. Spherical symmetry can stimulate "whispering gallery modes" (WGM) with integral coupling number M=137.

Josephson Effect, Baecklund Transformations, and Fine Structure Coupling pdf 144kb, PS, 25-29.10, revised 2.11.2002

Abstract: It is shown, that the geometric phase evolution within M circularly and toroidally arranged virtual Josephson junctions (coupled discrete impedance system) can be described by the integrable case of Baecklund transformations. The phase gradient of a junction is induced by a pseudospherical curvature. The internal phase difference and external bias is mediated by sine-Gordon solitons that provide for internal and external coupling. The idealized soliton resonance or feedback condition corresponds to an oscillator potential (Long Josephson Junction LJJ condition) that can be mapped by projective geometry to Coulomb coupling. The effective coupling strength is a generalized fine structure constant that can be iteratively determined, for M = 137 extremely close to measured values of the Sommerfeld fine structure.

Topological Phase Fields, Baecklund Transformations, and Fine Structure pdf 138kb, PS, 14.10.2002

Abstract: Quantum coupling is defined by comparing the evolution of an input to an output phase, where the phase is evolving on a curved pseudospherical surface. The difference given by interference obeys a single-valuedness condition since the output phase is coupling back to the input phase. We arrive at Bäcklund transforms and corresponding sine-Gordon soliton equation. The idealized resonance or feedback condition corresponds to an oscillator potential that can be mapped by projective geometry to Coulomb coupling, where the effective coupling strength can be iteratively determined.

Topological Phase Field Gradients on Pseudospheres as a Model for Nonlinear Electromagnetic Coupling pdf 153kb, PS, 1.10.2002

Abstract: This paper tries to answer the question: "what happens, if a spatially extended geometric phase pattern (the scattered field) couples back to the scattering field?" To approach an adequate answer it requires to generalize from linear to nonlinear topological phase fields, where the coordinate vector field is parallel transported along the soliton field on pseudospheres. There are also some small corrections to the previous paper.

Charge as the Stereographic Projection of Geometric Precession on Pseudospherespdf 167kb, philsci-archive, PS, tex 20kb mp_arc, 30.9.2002

Abstract: In this paper geometric phases (Berry and Aharonov-Bohm) are generalized to nonlinear topological phase fields on pseudospheres, where the coordinate vector field is parallel transported along the signal/soliton vector field with Levi--Civita connection. Projective PSL(2,R) symmetry describes the relativistic self-interacting bosonic sine-Gordon field. A Coulomb potential can be induced as the stereographic projection of a harmonic oscillator potential mapping angles or phases to distances and vice versa resulting in mutual coupling with a generalized coupling constant given by a nonlinear iteration. With single-valuedness requirement in 137-gonal symmetry it fits within a few ppb uncertainty to the Sommerfeld fine structure constant.

+PS Iterative Interplay between Aharonov-Bohm Deficit Angle and Berry Phasepdf 210kb, ps 349kb, 14.9.2002, 7.10.2002

Abstract: Geometric phases can be observed by interference as preferred scattering directions in the Aharonov-Bohm (AB) effect or as Berry phase shifts leading to precession on cyclic paths. Without curvature single-valuedness is lost in both case. It is shown how the deficit angle of the AB conic metric and the geometric precession cone vertex angle of the Berry phase can be adjusted to restore single-valuedness. The resulting interplay between both phases confirms the non--linear iterative system providing for generalized fine structure constants obtained in the preliminary work. Topological solitons of the scalar coupling field emerge as localized, non-dispersive and non-singular solutions of the (complex) sine-Gordon equation with a relation to the Thirring coupling constant and non-linear optics. This confirms the non-linear iterative system Ma = cos(pa) obtained in the preliminary work.

Spacetime Memory: Phase-Locked Geometric Phases pdf 136kb, philsci-archive, PS, tex 18kb mp_arc, 29.8.-1.9.2002

Abstract: Spacetime memory is defined with a holonomic approach to information processing, where multi-state stability is introduced by a non-linear phase-locked loop. Geometric phases serve as the carrier of physical information and geometric memory (of orientation) given by a path integral measure of curvature that is periodically refreshed. Regarding the resulting spin-orbit coupling and gauge field, the geometric nature of spacetime memory suggests to assign intrinsic computational properties to the electromagnetic field.

Geometric Phase Locked in Fine Structure pdf 200kb, philsci-archive, 16.8.2002, update 1.9.2002

Abstract: Berry's phase carries physical information coded as topological and geometrical objects that can be directly verified in measurements. In some cases the situation can be reduced to an irrational phase shift, that can be usually obtained by an iterative process. Take the Berry phase as the geometric object and let the iterative process be a non-linear phase-locked feedback mechanism defined by spin-orbit coupling and precession, a coupling of fast and slow rotating vectors. For spin-orbit coupling the realization provides for characteristic irrational and rational numbers.

Geometric Phase Locked in the Nucleus pdf 279kb, 26.8.2002, update 1.9.2002, preprint

Abstract: In this paper it is proposed, that nuclear interaction and charge quantization could be modelled by a low-dimensional non-linear iterative system, where instability induced by chaotic dynamics and bifurcations increase with charge or feedback strength. The system could be balanced by a generalized geometric phase part of the electromagnetic coupling strength and Sommerfeld fine structure constant carrying a screening Berry phase component.

Berry's Phase and Fine Structure pdf 334kb, philsci-archive, 25.7.2002, last update 1.9.2002

Abstract: Irrational numbers can be assigned to physical entities based on iterative processes of geometric objects. It is likely that iterative round trips of vector signals include a geometric phase component. If so, this component will couple back to the round trip frequency or path length generating an non-linear feedback loop (i.e. induced by precession). In this paper such a quantum feedback mechanism is defined including generalized fine structure constants in accordance with the fundamental gravitomagnetic relation of spin-orbit coupling. Supported by measurements, the general relativistic and topological background allows to propose, that the deviation of the fine structure constant from 1/137 could be assigned to Berry's phase. The interpretation is straightforward: spacetime curvature effects can be greatly amplified by non-linear phase-locked feedback-loops adjusted to single-valued phase relationships in the quantum regime.

Book from 2003

(conceptual work, has not been peer reviewed, but central messages are retrospectively correct)

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References (c) Bernd Binder 2002-2008