Alessandro Rizzophysiks.net
Alessandro Rizzo
I’m working on a unified field equation:
(R^ - ∇K + K²)_ab = 0
About
77
Publications
40,695
Reads
How we measure 'reads'
A 'read' is counted each time someone views a publication summary (such as the title, abstract, and list of authors), clicks on a figure, or views or downloads the full-text. Learn more
1,220
Citations
Introduction
Standing before the stopped clock in Brescia’s Piazza della Loggia, I was struck by time's stillness, spurring my quest for a unified geometric framework weaving gravity, torsion, forces, and information into one field equation. Inspired by Einstein, Planck, Cartan, Kaluza, Klein, Bohm, Feynman, and Wheeler, I aim to reveal how matter, energy, and quantum information can arise from a single spacetime geometry.
Additional affiliations
September 1990 - September 1994
Education
September 1991 - September 1993
Publications
Publications (77)
**Abstract**
This paper targets students who want to build a thorough understanding of how General Relativity can be extended by allowing torsion in the spacetime connection. We first recap the key features and limitations of the usual Levi-Civita (symmetric) framework, underscoring why a purely metric-based approach struggles with high-curvature...
This document examines the angular size of the black hole shadow in M87 under two frameworks: General Relativity (GR) and a torsion-based extension often referred to as "General Singu-larity" (GS)[5]. The main goal is to determine how an effective torsion-induced modification to the Schwarzschild-like geometry might shift the photon-sphere radius a...
This letter proposes a conceptual framework in which the quantization of torsional fluxes in \((4+n)\)-dimensional gravity, imposed by integral topological constraints, leads to the emergence of a minimal length scale on the order of the Planck length. By connecting these discrete flux boundary conditions to the rank of an elliptic curve as formula...
Various high-precision experiments aiming to measure the universal gravita-tional constant G have reported values that differ by more than their claimed uncertainties, suggesting an anomalous dispersion among reported measurements. This text proposes that these discrepancies can be explained through the General Theory of Singularity (GS), where tor...
A derivation is presented for the origin of matter-antimatter asymmetry through a torsionful theory governed by a Unified Field Equation (UFE). The approach eliminates independent matter fields in favor of geometric fluxes, enabling both CP violation and baryon-number non-conservation in a single framework. The mathematical steps connect torsion-in...
Experimental evidence indicates that neutrinos possess nonzero masses, conflicting with the minimal Standard Model assumption of massless neutrinos. This text incorporates the General Theory of Singularity (GS), governed by a Unified Field Equation (UFE), to account for neutrino mass generation. Mathematical steps show how torsionful geometry can g...
This paper shows how the observed accelerated expansion of the Universe-commonly attributed to Dark Energy-naturally arises from the Unified Field Equation (UFE) in the General Theory of Singularity (GS). By incorporating torsion and integral topological constraints in a higher-dimensional geometry, the vacuum energy behaves effectively as a discre...
A comprehensive and unified presentation is provided here to demonstrate how the Theory of General Singularity (GS)-a torsionful extension of Einstein-Cartan-Kaluza-Klein (ECKK) geometry with integral topological fluxes-can explain flat or slowly declining galactic rotation curves without introducing new, non-baryonic matter. First, an expanded der...
“If you can’t explain it simply, you don’t understand it well enough.”
Albert Einstein
A derivation of a physical information theory is presented, grounded in a torsionful gravitational model based on the Unified Field Equation (UFE). By introducing torsion and integral topological fluxes in a (4 + n)-dimensional spacetime, the usual stress-energy tensor is replaced by geometric terms, leading to discrete spectra of classical and qua...
Paper Edition," published on 1st January 2025. Available at: https://www.amazon.com/dp/B0DRWVFYXL
© 1991-2025
This paper presents a unified geometric theory in which the DNA double-helix emerges from a single field equation with both local (chemical-mechanical) and global (topological flux) properties. Within the framework of the General Theory of Singularity (GS), an extended Einstein-Cartan-Kaluza-Klein geometry identifies geometric torsion fields as car...
We provide a detailed demonstration of how one starts from the unified field equation of the Theory of General Singularity[9, 3, 5, 14], R AB − 1 2ĝ ABR − ∇ C K C AB + K C D (A K B) C D = 0, and, via a dimensional reduction with anisotropic torsion, arrives at an effective low-energy Hamiltonian for semi-Dirac fermions, i.e. electronic quasiparticl...
Singularities in classical General Relativity have long been regarded as breakdown points where spacetime curvature diverges and predictive physics fails. In black holes, these singularities appear as inescapable fates for infalling matter, raising fundamental paradoxes regarding unitarity and information loss. The General Singularity (GS) framewor...
(Letter to the Research Community) December 22, 2024
This paper presents a mathematical derivation demonstrating that gravitational collapse into black holes and quantum wavefunction collapse can be rigorously described as equivalent, entropy-minimizing processes. Within the General Theory of Singularity (GS)-an integrative framework unifying geometry, torsion, integral topological constraints, and f...
This note provides a derivation, in a topological and geometric context, of how the unified field equation of the General Singularity (GS) framework emerges from a multiscale Feynman path integral construction. By integrating over all geometric configurations of spacetime, including torsional degrees of freedom and integral topological constraints,...
The minimal-entropy condition in the General Singularity (GS) framework operates similarly to the quantum wavefunction collapse, where the Shannon entropy serves as a measure of the complexity of quantum superpositions. Measurement-induced collapse minimizes this entropy, effectively reducing it to zero. In GS, a comparable minimal-entropy principl...
This paper presents the Theory of General Singularity (GS), a unified geometric framework that incorporates torsion, higher dimensions, and integral topological constraints into a single field equation. From this construction emerge discrete, quantized ring structures around black holes, analogous to atomic orbitals in quantum mechanics. By imposin...
The Theory of General Singularity (GS) is a torsionful Einstein-Cartan-Kaluza-Klein (ECKK) framework that incorporates integral topological conditions to unify matter fields, interactions, and the geometry of spacetime. It extends Einstein's equations by including torsion and topological constraints, leading to integral conditions that determine al...
Quarks, with their fractional electric charges, threefold color multiplicity, and confinement into hadrons, pose a profound conceptual challenge. While the Standard Model accommodates these phenomena empirically, it provides no underlying principle for their integral structure. Here, I present a framework in which quark properties arise naturally f...
The persistent discrepancy between the Standard Model (SM) prediction and experimental measurements of the muon anomalous magnetic moment (g − 2) is a longstanding puzzle in fundamental physics. While the SM calculation of a µ = (g − 2) µ /2 is extraordinarily precise, current experimental results suggest an anomaly at the level of several standard...
We introduce the ``Quantum Equivalence Principle'' (QEP) within the Theory of General Singularity (GS), which is built on a torsionful Einstein–Cartan–Kaluza–Klein (ECKK) framework. The QEP generalizes Einstein’s Equivalence Principle (EEP) to the quantum-geometric regime. In GS, all physical parameters—masses, charges, and coupling constants—arise...
A century ago, Einstein described gravity as a manifestation of geometry, encoding the gravitational field in the curvature of spacetime. We extend this geometric principle to all known fundamental interactions by formulating a framework—referred to here as the ``General Singularity'' scenario—based on Einstein–Cartan–Kaluza–Klein (ECKK) geometry w...
Africa is uniquely positioned to harness its abundant renewable energy resources to address global challenges. The pressing issues of climate change, resource scarcity, and economic disparities necessitate transformative solutions. Project Terra 2 envisions Africa leveraging its vast solar and wind energy potential to produce green hydrogen, propel...
This letter reflects on the extraordinary convergence of scientific minds in the early 1900s, which led to groundbreaking discoveries in physics and beyond. It examines the unique cultural and systemic conditions that fostered such creativity, contrasting them with the challenges faced by modern science, such as hyper-specialization and the dominan...
A unified, geometric perspective is presented in which the properties of fundamental particles—spin, mass, and charge—emerge from the geometry and topology of a higher-dimensional Einstein–Cartan–Kaluza–Klein (ECKK) framework augmented by a Higgs-like mechanism. Without arbitrary inputs, fermion and gauge boson masses, electric charges, and spins a...
We present the Lorentz-Möbius Torsion Theorem, establishing a novel connection between special relativity and quantum geometry. By demonstrating that the integral of the Lorentz factor over all normalized velocities equals \(\frac{\pi}{2}\), we reveal an underlying geometric significance associated with angular measures and conformal mappings. This...
We propose a succinct method for solving combinatorial problems—potentially including NP-hard tasks—by encoding constraints into wave interference and extracting solutions through \emph{minimal-entropy} collapse. In this holographic view, consistent partial configurations reinforce each other; mismatches cancel out. A fast transform (e.g.\ FFT) the...
A theoretical framework is presented that integrates quantum mechanics, general relativity extended to include torsion (Einstein-Cartan theory), extra dimensions (Kaluza-Klein), and nontrivial spacetime topologies (orientable and non-orientable) to provide a unified understanding of matter and energy. In this construction, spacetime is treated as a...
We explore a theoretical framework in which Majorana fermions, generated within topological crystalline materials, facilitate nuclear fusion at ambient temperatures through enhanced quantum tunneling effects. By creating topological tunneling pathways in specific materials, these quasiparticles may significantly lower the Coulomb barrier between nu...
We propose a geometric and topological scenario in which dark matter arises as a Majorana fermion mode from a higher-dimensional spacetime with torsion and non-orientable topology. These conditions yield stable, electrically neutral fermions that couple only to gravity and not to electromagnetism, explaining their invisibility. We connect these pro...
Zitterbewegung, originally predicted by Schrödinger in the solutions of the Dirac equation, has traditionally been viewed as a purely quantum mechanical curiosity associated with the interference of positive and negative energy states of spin-$\tfrac{1}{2}$ particles. In this work, we re-interpret Zitterbewegung within the framework of the General...
We present an analysis of the General Singularity (GS), which extends General Relativity (GR) by incorporating electromagnetic vortices and spacetime torsion. Focusing on observational data from the supermassive black hole (SMBH) in NGC 1068, high-energy neutrino detections by the IceCube Observatory, and recent experimental work on electromagnetic...
The Planck mass defines a fundamental scale where quantum gravitational effects become significant. By re-expressing the Planck mass equation, we derive a relation involving fundamental constants that connects gravitational and electromagnetic quantities. This relation suggests that gravitons, as quanta of spacetime with spin-2, can be understood a...
Albert Einstein's quest for a Unified Field Theory (UFT) sought to merge gravitation and electromagnetism into a single geometric framework. In this work, we revisit and refine these ideas by introducing an asymmetric metric tensor and a non-symmetric affine connection with torsion. By identifying the antisymmetric part of the metric with the elect...
Antimatter is the rarest and most valuable substance known, with immense potential for energy generation due to its complete mass-to-energy conversion upon annihilation. Traditional production methods are inefficient and prohibitively expensive , limiting practical applications. This paper presents a novel, energy-efficient approach for large-scale...
The concept of the empty set and its relation to the construction of natural numbers has profound implications in mathematics, physics, and philosophy. In this paper, we explore von Neumann's construction of natural numbers, particularly the fundamental relation 1 = {0}, and delve into its philosophical and physical implications. We draw parallels...
Richard Feynman famously asked: ``What is energy?'' Although energy stands at the heart of all physical theories, it is often treated as an abstract conserved scalar rather than a fundamental substance. This work proposes a paradigm shift: \emph{space and energy are equivalent manifestations of the same underlying entity.} We argue that space itsel...
This paper presents an analysis of negative mass phenomena, interpreting them as regions of lower energy density within a fluid-like vacuum. We develop a hydrodynamic model that accounts for the counterintuitive behavior observed in experiments with Bose-Einstein condensates, such as those conducted at Washington State University in 2017. Our appro...
This research introduces the Sono-Luminescence Emitting Device (S-LED), an innovative light source that harnesses sonoluminescence within a controlled, LED-like structure. Each S-LED functions as a highly efficient, precisely controlled light-emitting device, offering unprecedented energy density and control at the microscale. The S-LED generates l...
This paper presents a unified approach to multi-scale physics using Feynman's path integral formulation. We demonstrate the mathematical equivalence between the path integral and Schrödinger equation approaches, elucidating the advantages of the path integral method in handling systems with uncertain boundaries and probabilistic interactions. The f...
A framework is presented that unifies Large Concept Models (LCMs) with key insights from Special Singularity theory, General Theory of Singularity (GS), and a torsionful Einstein-Cartan-Kaluza-Klein (ECKK) geometry. Central to this approach is the notion of minimal-entropy functionals, which link discrete flux constraints in non-orientable spacetim...
This paper presents a novel theoretical framework that reinterprets inertia as a dynamic emergent property arising from second-order electromagnetic interactions between matter and the quantum vacuum. We develop a comprehensive mathematical formalism that unifies the concepts of inertia, vacuum energy, and quantum interactions, providing new insigh...
This paper presents a comprehensive theoretical framework for gravity control based on the Theory of General Singularity (TGS) and its applications to superconducting systems. We introduce explicit Einstein field equations that decompose the stress-energy tensor into visible and dark matter/energy components, and propose a quantum gravitational wav...
This paper presents a comprehensive theoretical framework for gravity control based on the Theory of General Singularity (TGS) and its applications to superconducting systems. We introduce modified Einstein field equations that incorporate both visible and dark matter/energy tensors, and propose a quantum gravitational wave function satisfying a no...
We present a derivation of the Prime Distribution Theorem within a higher-dimensional framework, where torsion fluxes are quantized as integer lumps. This improved approach strengthens mathematical proofs, highlights uniqueness arguments, and establishes deeper connections to analytic number theory, including links to the Riemann zeta function, its...
The Theory of Special Singularity (SS)} offers a framework in which consciousness and other complex phenomena unfold within \emph{near-zero–entropy} “conscious frames,” mirroring how inertial frames in Special Relativity preserve uniform motion. By positing that local pockets of high information-integration operate with minimal net entropy producti...
We present the Theory of General Singularity (TGS) within an Einstein-Cartan-Kaluza-Klein (ECKK) geometric framework that unifies quantum field theory, general relativity, and the standard model. In this approach, what were once described as “phonons” in a quantum vacuum modeled as a Bose-Einstein condensate (BEC) are now understood as emergent, lo...
This paper explores the concept of general covariance in natural laws using geometric intuition and tensor algebra. By introducing the notions of covariance and contravariance using intuitive examples from projections and the scalar product, we illustrate how the covariance of natural laws ensures their universality and objectivity. We also discuss...
Thia paper shows that the General Theory of Singularity (GS) necessarily entails a strictly positive mass gap for 4D Yang--Mills gauge bosons. By "mass gap," we mean the statement that no non-trivial Yang--Mills excitation can be massless, so all gauge bosons have masses bounded below by some strictly positive constant \(m_{\mathrm{min}}>0\). Our d...
The Navier–Stokes existence and smoothness problem in three dimensions is one of the well-known "Millennium Prize Problems" posed by the Clay Mathematics Institute, which remain unsolved in the standard 3D setting. In this work, we present a geometric–torsional framework wherein the Navier–Stokes equation (NS) emerges naturally from a Unified Field...
We present a simple, geometric picture of the universe in which gravity, electromagnetism, weak and strong nuclear forces, and even the masses and charges of particles all come from one underlying idea: the shape and structure of a higher-dimensional space. By carefully studying how extra dimensions and a property called “torsion” influence the geo...
We present the Quantum Gravity Theorem (QGT), a mathematically framework that unifies Quantum Mechanics (QM) and General Relativity (GR) in a torsionful Einstein – Cartan – Kaluza – Klein (ECKK) setting. By imposing integral topological conditions on a fractal internal manifold and holographic boundary conditions realized as topological quantum err...
This document provides a research-level demonstration, now extended with detailed proofs and expansions, that constructs a Dirac--Torsion operator D on a Lorentzian manifold M^4 with signature (3,1) and quantized torsion, and shows that its associated spectral zeta function zeta_T(s) coincides exactly with the classical Riemann zeta function zeta(s...
A fully rigorous proof of the Hodge Conjecture is provided by unifying two key components: the Torsion-Flux Realization Theorem (TFR) and the construction of a universal principal bundle with integral torsion data. First, the TFR ensures that any rational (p,p)-class whose pairing with a suitably chosen torsion-curvature form Q[R,T] is nonzero must...
This study examines the Gertsenshtein effect, which theorizes the conversion of electromagnetic waves into gravitational waves in the presence of a strong magnetic field. First proposed by Mikhail Gert-senshtein in 1962 and grounded in general relativity, this effect forms a bridge between electromagnetism and gravity, providing insights into the f...
The Theory of General Singularity (TGS) provides a unified framework for understanding the quantum origin of gravity and the nature of spacetime at microscopic scales. In this work, we rigorously derive the formulation of the $\gamma_2 G$ liquid spacetime, in which spacetime emerges as a Bose-Einstein condensate (BEC) of $\gamma_2 G$ quantum molecu...
This paper explores the concept of general covariance in natural laws using geometric intuition and tensor algebra. By introducing the notions of covariance and contravariance using intuitive examples from projections and the scalar product, we illustrate how the covariance of natural laws ensures their universality and objectivity. We also discuss...
Exploring the quantum vacuum as a dynamic Bose-Einstein Condensate (BEC), this study draws a parallel between phonons and photons to reveal how dark photons can be transformed into visible light. Through phonon-photon interactions, akin to sonoluminescence, we demonstrate the quantum vacuum's ability to illuminate dark matter phenomena. By adapting...
This study examines the Gertsenshtein effect, which theorizes the conversion of electromagnetic waves into gravitational waves in the presence of a strong magnetic field. First proposed by Mikhail Gertsenshtein in 1962 and grounded in general relativity, this effect forms a bridge between electromagnetism and gravity, providing insights into the fu...
Exploring the quantum vacuum as a dynamic Bose-Einstein Condensate (BEC), this study draws a parallel between phonons and photons to reveal how dark photons can be transformed into visible light. Through phonon-photon interactions, akin to sonoluminescence, we demonstrate the quantum vacuum's ability to illuminate dark matter phenomena. By adapting...
At the heart of mathematics lies a mysterious harmony, a connection between seemingly unrelated concepts that resonates with the beauty and complexity of nature itself. In this exploration, we venture into fascinating territory, where division, frequencies, imaginary exponents, and the Riemann zeta function intertwine to unveil a hidden symphony in...
We propose a unified geometric interpretation of sonoluminescence and Terrestrial Gamma-ray Flashes (TGFs) within a $(4+n)$-dimensional spacetime endowed with torsion. In this approach, gravity, gauge fields, scalar modes (including the Higgs), and fermionic masses emerge from the geometry alone, without ad hoc fields. Phonons, traditionally viewed...
The Golden Ratio Theorem, deeply rooted in fractal mathematics, presents a pioneering perspective on deciphering complex systems. It draws a profound connection between the principles of interchangeability, self-similarity, and the mathematical elegance of the Golden Ratio. This research unravels a unique methodological paradigm, emphasizing the om...
We propose a unified geometric interpretation of sonoluminescence and Terrestrial Gamma-ray Flashes (TGFs) within a $(4+n)$-dimensional spacetime endowed with torsion. In this approach, gravity, gauge fields, scalar modes (including the Higgs), and fermionic masses emerge from the geometry alone, without ad hoc fields. Phonons, traditionally viewed...
We present the Theory of General Singularity (TGS) within an Einstein-Cartan-Kaluza-Klein (ECKK) geometric framework that unifies quantum field theory, general relativity, and the standard model. In this approach, what were once described as “phonons” in a quantum vacuum modeled as a Bose-Einstein condensate (BEC) are now understood as emergent, lo...
The Golden Ratio Theorem, deeply rooted in fractal mathematics, presents a pioneering perspective on deciphering complex systems. It draws a profound connection between the principles of interchangeability, self-similarity, and the mathematical elegance of the Golden Ratio. This research unravels a unique methodological paradigm, emphasizing the om...
This paper explores the transformative potential of human-machine collaboration in scientific discovery. Drawing on historical precedents like the Einstein-Ricci dialogue and the Solvay Conferences, as well as contemporary examples like the author's work on general singularity theory, it argues that the symbiosis of human creativity and artificial...
This reflection invites the student to experience the joy of discovering nature’s truths in solitude, where true understanding transcends recognition and brings deep personal fulfillment.
In this letter, we explore the mechanism of local symmetry breaking in n-m dimensions and the conservation of global symmetry in (n)-dimensions. By analyzing the role of the potential (V(\phi)) and the gauge fields, we demonstrate how spontaneous symmetry breaking can occur without violating global conservation laws. This formalism provides insight...
This letter introduces the principles of Special Relativity, focusing on the concept of symmetry in physics. It explains the invariance of the speed of light and explores time dilation and length contraction through thought experiments with light clocks. The relationship between mass and energy is derived, culminating in the famous equation \(E = m...
This letter introduces the wave-particle duality in quantum mechanics, starting with how circular motion relates to wave patterns. It explores how this wave concept applies to particles, leading to de Broglie's idea that all particles have associated waves. The paper culminates in presenting Schrödinger's equation, which mathematically describes th...
In this letter, the Taylor series and its special case, the MacLaurin series, are presented as powerful mathematical tools used to approximate functions. Named after mathematicians Brook Taylor and Colin MacLaurin, these series allow complex functions to be represented as infinite sums of simpler polynomial terms. This approach is fundamental in ma...
In this letter, Euler's Identity is presented as often hailed as the most beautiful equation in mathematics. It elegantly connects five fundamental mathematical constants in a single, simple equation. This identity brings together concepts from complex numbers, trigonometry, and mathematical analysis, demonstrating the profound interconnectedness o...
Ciaoidea Lab - Sonoluminescence: Where Sound Meets Light. Experimental studies on single-bubble sonoluminescence in various liquids, focusing on light emission characteristics and bubble dynamics. Analysis of acoustic parameters influencing luminescence intensity and spectral distribution.
Mastering the Concept of Distance in Differential Geometry - An In-Depth Course on the Metric Tensor. (May 2005)
Questions
Questions (3)
I recall a fascinating lecture given by Professor Enrico Bellone. In a letter dated May 7th, 1952, addressed to his friend Maurice Solovine, Einstein shared a drawing that summarized his ideas on the subject: "What is science ?". The drawing features a horizontal line labeled E, which represents immediate experiences or the empirical basis, and a vertical line labeled A, which represents the axioms underlying theories. Einstein argued that there is no logical process that allows us to derive axioms from experiences; instead, it requires an intuitive, extralogical, and psychological leap. Once we have intuited the axioms, we can deduce special statements S1, S2... by assuming their truthfulness and then comparing them with experience. According to Einstein, the crucial level lies in the axioms, and therefore there is no distinction between science and philosophy, but rather a single set of concepts. He also maintained that the theoretical principles of scientific theories are fictional, and any attempt to deduce ideas and laws from elementary experiences is doomed to fail. So, what is science according to Albert Einstein? Einstein believed that all the games are played at the top of the drawing, where we jump from one idea to another, from one theory to another, and where we model nature because we have categories of ideas that are fairly standard. In this context, Einstein praised the great philosophers he admired.
