Abstract
The purpose of the paper is to elucidate by global-dual contact holonomy why one might expect the Foucault spherical pendulum’s spin echo-stabilized, symplectic swing-plane through the rotation axis of the spinning earth to follow a parallel vector field as time passes at a velocity depending on the latitude of the swivel’s location. The spinor geometric foundations of the paradigmatic Foucault spherical pendulum experiment of global-local contact holonomy exploit Hopf–Rinow type minimizing geodesic trajectories which appear as inertial traces designed by swing-planes on the terrestrial circular floor panel which is situated beneath the covariant motion of the oscillating pendulum device and where the linear traces are designing diameters of the spin structure induced Poincaré conformal hyperbolic open disc model. The quantum field theoretical evidence of the existence and uniqueness of categorizing parallel vector fields around smooth loops follows in terms of the open-book foliation with Hilbert space structures placed on the covariant pages.
Highlights
1 Dynamic quantization and kinematic relativization. It is a highly remarkable feature of the Copernican lecture on the physical world that the diurnal rotation of the spinning earth, in contrast to its annual motion around the central body, which it shares with the orbits of the other planets of the system and in which it merely takes over what had previously been the mobile sun’s central position, is a novelty in the Copernican heliocentric reform idea of physical astronomy
In the context of the dual contact holonomy of Foucault’s spherical pendulum experiment, the Witt spinor norm group WS(R) and the proof of Hopf’s Umlaufsatz for the rotation index {±1} ∼= Z2 of a simple plane loop [61] give rise to the concept of real-valued angular gauge function t θ (t), which is unique up to an additive constant and defines a horizontal parametrization of the parallel transport dynamics of the spin echo-stabilized, symplectic swing-planes caused by the spinning earth and the reduced covariance of the oscillating spherical pendulum device
As a pulsar astrophysical application, the recording of the post-Kepplerian driving spinor warping within the open-book foliation, supplementary to the inversive geometry of the Kepplerian planetary contact holonomy, deals with the relativistic measurement protocol of the cumulative period shift of periastron time in seconds
Summary
It is a highly remarkable feature of the Copernican lecture on the physical world that the diurnal rotation of the spinning earth, in contrast to its annual motion around the central body, which it shares with the orbits of the other planets of the system and in which it merely takes over what had previously been the mobile sun’s central position, is a novelty in the Copernican heliocentric reform idea of physical astronomy. It is related to the second supplementary theorem of the famous quadratic reciprocity law [46] There is hardly another event in the history of science about which such mutually exclusive theses have been set up as the transformation of astrophysics into a form that did not block the Copernican heliocentric reform idea and the quantum field theoretic development of an inclinatio contact geometry of inertia consisting of supporting two-sided tangent planes. The underlying principle of circular inertia derives from the geodesics with respect to the Poincaré metric of the open disc model It is based on the mathematical concept of spinor which permits a transition from gravitation physics to the non-invasive imaging modality of nuclear spin magnetic resonance tomography with its own specific vocabulary [9,44,45]. One has to look with a certain pair of spectacles in order to see the very diversity of the topics on the list of different applications as being united via a single phenomenological structure
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