| viXra.org > Mathematical Physics > 2412 |
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| viXra.org > Mathematical Physics > 2412 |
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[5] viXra:2412.0063 [pdf] submitted on 2024-12-10 07:35:58
Authors: Sourangshu Ghosh
Comments: 48 Pages.
In this article, we mathematically rigorously derive the expressions for the Del Operator ∇, Divergence ∇ ·u20d7v, Curl ∇ ×u20d7v, Vector gradient∇u20d7v of Vector Fields u20d7v, Laplacian ∇2f ≡ ∆f of Scalar Fields f and Divergence ∇ · T of 2nd order Tensor Fields T in both Cylindricaland Spherical Coordinates. We also derive the Directional Derivative (A · ∇)u20d7v and Vector Laplacian ∇2u20d7v ≡ ∆u20d7v of Vector Fields u20d7v usingmetric coefficients in Rectangular, Cylindrical and Spherical Coordinates. We then generalized the concept of gradient, divergence and curlto Tensor Fields in any Curvilinear Coordinates. After that we rigorously discuss the concepts of Christoffel Symbols, Parallel Transport inRiemann Space, Covariant Derivative of Tensor Fields and Various Applications of Tensor Derivatives in Curvilinear Coordinates (Geodesic Equation, Riemann Curvature Tensor, Ricci Tensor and Ricci Scalar).
Category: Mathematical Physics
[4] viXra:2412.0062 [pdf] submitted on 2024-12-10 22:00:36
Authors: Marco Maccarrone
Comments: 4 Pages. (Note by viXra Admin: Please cite and list scientific references)
This paper proposes an extension of the equivalence principle to unify relativity,quantum mechanics, and energy dynamics under a single geometric framework. Using the Poincar´e disk model as a visualization tool, we demonstrate how phenomena as diverse as spacetime curvature, quantum probability densities, and relativistic energy growth share the same exponential scaling behavior. This equivalence suggests a universal geometric structure underlying all physical laws, where energy density, curvature, and probabilities emerge as complementary manifestations of aunified field. We explore implications for relativistic limits, quantum states, andthe nature of spacetime, highlighting testable predictions and new insights into thestructure of the universe.
Category: Mathematical Physics
[3] viXra:2412.0055 [pdf] submitted on 2024-12-09 21:50:03
Authors: Nick Navid Yazdani
Comments: 36 Pages. (Correction made by viXra Admin to conform with the requirements of viXra.org - Please cite and list scientific references)
In this [] work, we introduce a universal framework that re-imagines the fabric of reality through the lens of waves. By positioning waves as the fundamental entity underlying all physical phenomena, this paradigm challenges long-standing constructs like particles, fields, and singularities, offering a unified and deterministic alternative. We derive a novel partial differential equation (PDE) operator that encodes infinite complexity expansions, capable of describing phenomena across quantum and classical regimes. This operator resolves inconsistencies in traditional physics, including the quantum-classical divide and the anomalies of singularities, while ensuring convergence and stability. This work lays the mathematical foundation for a transformative understanding of physics, setting the stage for applications ranging from quantum mechanics to cosmology. It invites the scientific community to explore a universe where waves, not particles or fields, are the fundamental building blocks of reality.
Category: Mathematical Physics
[2] viXra:2412.0054 [pdf] submitted on 2024-12-09 21:54:36
Authors: Nick Navid Yazdani
Comments: 36 Pages. (Correction made by viXra Admin to conform with the requirements of viXra.org - Please cite and list scientific references)
This second installment of The Wave Paradigm advances the quest for unified physics by addressing the long-standing divide between quantum mechanics and classical physics. It reinterprets quantum phenomena - superposition, entanglement, and measurement - as finite complexity illusions, resolving paradoxes with deterministic elegance. By embracing infinite complexity as the natural state of the universe, this work eliminates the need for probabilistic interpretations, replacing them with deterministic wave dynamics. Classical physics emerges seamlessly as a limit of this framework, demonstrating how the same universal wave equation governs phenomena across all scales. This chapter builds on the foundation of Part I, offering profound insights into the true nature of reality and setting the stage for future applications in cosmology, chemistry, and technology.
Category: Mathematical Physics
[1] viXra:2412.0030 [pdf] submitted on 2024-12-06 21:46:16
Authors: Bjørn Leon Søren Riedel
Comments: 6 Pages. In English & Japanese (Correction made by viXra Admin to conform with the requirements of viXra.org; also please cite and list scientific references and don't use author's name to name any formula/method etc.!)
The Infinite Tree Branch Hypothesis explores the transformation of infinitely branching trees across dimensions. In 2D, infinite branches converge into a circle, while in 3D and 4D, they form a sphere and hypersphere, respectively, with growth dictated by dimensional scaling. Using a what I think is novel Tree(n-branch)funtion, although agreebly this could have been invented before in fractal geometry or graph theory (but I could not find such a function).this hypothesis mathematically formalizes the convergence of such structures, leveraging properties of spherical coordinates and Gaussian integrals to define their limits. Novel implications include a reinterpretation of infinite branching within quantum mechanics, suggesting that seemingly independent "branches" in the Many-Worlds Interpretation may converge into a unified hyper continuum in higher dimensions. This hypothesis introduces a unique perspective on infinite systems, connecting fractal geometry, graph theory, and quantum cosmology.
Category: Mathematical Physics
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