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Series on knots and everything

Implications of Multidimensional Geometries and Measurement

Published Jul 1, 2009• 0 citations
Publisher

Abstract

Complexification of Maxwell’s equations with an extension of the gauge condition to non-Abelian algebras, yields a putative metrical unification of relativity, electromagnetism and quantum theory. This unique new approach also yields a universal nonlocality with implications for Bell’s Theorem and the possibility of instantaneous quantum connections because spatial separation can vanish by utilizing the complex space.

DOI
10.1142/9789812839312_0008

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Complexification of Maxwell’s equations with an extension of the gauge condition to non-Abelian algebras, yields a putative metrical unification of relativity, electromagnetism and quantum theory. This unique new approach also yields a universal nonlocality with implications for Bell’s Theorem and the possibility of instantaneous quantum connections because spatial separation can vanish by utilizing the complex space.
We outline the relativistic formalism which gives a more comprehensive explanation of the complexification scheme. Such issues as considering the Higgs Boson as a soliton depends on Lorentz invariance and relativistic causality constraints. We relate the complexification of Maxwell's equations to models of nonlocal micro and macro phenomena. In this chapter we relate the electromagnetic fields, F and A , the potentials to the gravitational field, G . We examine, for example, the manner in which advanced potentials may explain the remote connectedness which is indicated by the Clauser test of Bell's theorem. Similar arguments apply to Young's double slit experiment. The collective coherent phenomena of superconductivity is also explainable by considering the relativistic field theoretic approach in which wave equations are solved in the complex Minkowski space.
Abstract In considering models of reality we must consider the fundamental nature of quantum mechanics, which has had great success in describing the spectrum of light from distant stars and galaxies, formulating the properties of the strong, electro-weak or electromagnetic and weak decay forces, and explaining atomic order formulated as the atomic periodic table and atomic spectra. A vast array of technologies has resulted from quantum theory, from semiconductors to NMR machines, nuclear reactors and possibly encryption secured, fast quantum computers. Quantum theory, however, has yet to fully engage with the gravitational force. With the advent of quantum theory, several major issues stand out, leaving us with major philosophical questions on the nature of physics and reality, and our ability to comprehend them. The issues involve the interpretation of quantum measurement, the Heisenberg uncertainty principle on the completeness of quantum theory and nonlocality. The frontiers of science continue to open new concepts based on a multidimensional reality which we use to address these issues, including solving the Schrödinger and Dirac equations in complex Minkowski eight space. We also formulate Bell’s theorem and the Young’s double slit experiment in Rauscher’s complex eight-space. We formulate an interpretation of the quantum that yields locality in a hyper-dimensional complex space and that maintains the completeness of quantum theory and nonlocality in usual four space, with local connectivity and the Lorentz invariant conditions, where subluminal and luminal signaling are maintained. Are we really forced to choose between two alternate views of reality? One view that external reality exists independent of the observer, and the other that the observer somehow is a participator or an integral part of all of nature. Must we choose between these or is there another way out? We find our way out and we satisfy both Bohr (Copenhagen) and Einstein (determinism) in bringing about a practical outcome of the debate. By developing and applying complex eight space, we can accommodate locality or local realism in terms of contiguous event connections in complex eight space. In four space, nonlocality dominates and also can be considered locality in eight space. The determination of the state of a system naturally collapses to its final state where quantum mechanics is functioning completely in four and in eight dimensional spaces.
In order to prevent ``unavoidable'' break-down of the ``peaceful coexistence'' between foundations of quantum theory and relativity I propose a new type of a quantum gauge theory (superrelativity). This differs from ordinary gauge theories in the sense that the affine connection of this theory is constructed from first derivatives of the Fubini-Study metric tensor in the projective Hilbert space of the pure quantum states CP(N). That is we have not merely analogy with general relativity but this construction should presumably provide a unification of general relativity and quantum theory.
The Theory of Temporal Relativity proposes a unified theoretical framework that extends Special and General Relativity into the complex domain, integrating aspects of Quantum Mechanics within a single geometrical structure. The theory introduces a generalized Hilbert-space geometry and interprets quantum states as observer-dependent, arising from complex temporal relations between reference frames. Theory of Temporal Relativity is a theoretical framework proposing a unified extension of Special and General Relativity into the complex domain, with the goal of incorporating aspects of Quantum Mechanics within a consistent geometrical model. The theory generalizes Hilbert-space geometry and relativistic invariance to complex coordinates, introducing observer-dependent descriptions of physical quantities and a reinterpretation of quantum states as complex-phase relations between reference frames. Within this model, fundamental constants such as c, G, and h are not strictly universal but can exhibit apparent local variations arising from the observer’s position in the complex spacetime manifold. These variations preserve global covariance and CPT symmetry while reconciling quantum non-locality with relativistic kinematics. The framework predicts experimentally testable effects, including measurable phase shifts in interferometric experiments, possible frequency modulations in non-inertial systems, and small local deviations of physical constants detectable in condensed-matter and gravitational contexts. The supplementary work, “Quantum Uncertainty, Planck’s Constant, and Ontological Insights from Complex Spacetime Geometry and Local Metric Deformations”, develops the principle of Temporal Relativity as a foundational element of the theory. It formalizes the connection between quantum uncertainty, metric deformations, and complex temporal structures, within an alternative logical framework (AU). This extension provides both an ontological interpretation of the wavefunction and a basis for the emergence of quantum indeterminacy from geometric causes. Together, these works present a coherent attempt to unify the relativistic and quantum domains under a single complex-geometric view of spacetime, maintaining mathematical rigor while providing clear experimental pathways for empirical validation.