Name: On the Holographic Foundation of Complexity: Experimental Evidence Suggesting NP=P by Alessandro Rizzo
Duration: 20 min 4 s
Description: Exploring the frontier of computational complexity, this paper presents a groundbreaking approach suggesting NP=P, inspired by Bohm's concept of implicit order. A concise, rigorous dive into a new computational paradigm grounded in holographic principles.

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 vortices by Fabrizio Tamburini and collaborators, we demonstrate how GS provides a robust framework for understanding the interplay between gravitational fields, electromagnetic structures, and high-energy particles. Our multi-messenger approach reveals that the interactions near black hole horizons, characterized by GS-induced torsion and electromagnetic vortices, can account for the observed absorption of gamma rays and the production of high-energy neutrinos. These findings suggest that GS offers significant insights beyond classical GR, potentially unifying gravitational and electromagnetic phenomena in extreme astrophysical environments.

http://dx.doi.org/10.13140/RG.2.2.32710.48966

Electromagnetic Vortices & Spacetime Torsion in High-Energy Phenomena Near Supermassive Black Holes

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 as elementary quantum vortices formed by two photons with spin-1 moving within the light cones of Lorentzian spacetime. Incorporating the concept of spacetime torsion, we analyze this connection within the framework of quantum field theory and quantum geometry, providing insights into the quantum structure of spacetime. Furthermore, we explore how processes such as cavitation, fission of spacetime, or polarization can lead to the formation of particle-antiparticle pairs, such as proton-positron pairs, in addition to gamma rays. We formulate the concept of an electromagnetic molecule of a quantum of spacetime, denoted as gamma2G, and discuss its implications for the unification of gravity and light.

On the Unification of Gravity and Light through Planck Mass and Spacetime Torsion

Zitterbewegung, a term introduced by Erwin Schrödinger in the early 1930s, refers to the rapid oscillatory motion of relativistic particles, particularly electrons, as predicted by the Dirac equation. Brownian motion, observed by Robert Brown in 1827, describes the erratic movement of particles suspended in a fluid due to collisions with molecules. While these phenomena arise from different physical contexts, they share similarities in representing underlying microscopic dynamics through observable macroscopic effects. In this paper, we explore the mathematical foundations of Zitterbewegung, its analogy with Brownian motion, and the zigzag picture of fermions, providing rigorous arguments and equations to support the idea that such motions reveal the quantum-atomic nature of spacetime. We integrate spacetime torsion into the analysis within the framework of General Singularity (GS), where spacetime torsion and electromagnetic vortices play central roles. By connecting these theories, we propose that particles and black holes share a vortical nature and that singularities can be understood as vortices in spacetime at every scale, drawing upon the holographic principle. We discuss how the scale invariance of vortices demonstrates the omnipresence of the golden spiral in nature as an expression of such vortices. This approach offers a new perspective on the quantum behavior of matter in curved, torsion-dominated spacetime

Zitterbewegung, Brownian Motion, and the Zigzag Picture of Fermions

We propose a novel theoretical framework to explain the optical invisibility of dark matter by modeling it as a topologically constrained liquid-like field characterized by a non-orientable topology, specifically analogous to a Klein bottle. Within the General Singularity (GS) γ 2 G framework, we demonstrate that this non-orientable structure inherently prevents electromagnetic waves from interacting with dark matter, providing a rigorous explanation for its lack of electromagnetic interaction despite its significant gravitational effects. We further show that dark matter can be modeled as a Majorana fermion in a liquid and topological electromagnetic state. The topological stability provided by the Klein bottle geometry offers new insights into dark matter's distribution, coherence, and its role in the large-scale structure of the universe. Additionally, we explore why dark matter interacts only gravitationally and not electromagnetically, and we demonstrate the fractal nature of spacetime resulting from its topological properties.

Why is Dark Matter Invisible?

Exploring the frontier of computational complexity, this paper presents a groundbreaking approach suggesting NP=P, inspired by Bohm's concept of implicit order. A concise, rigorous dive into a new computational paradigm grounded in holographic principles.

On the Holographic Foundation of Complexity: Experimental Evidence Suggesting NP=P

The Lorentz-Möbius Torsion Theorem presented in this paper establishes a rigorous connection between special relativity, spacetime torsion, and the hydrodynamic interpretation of quantum mechanics. By demonstrating that the integral of the Lorentz factor over all normalized velocities equals π/2, the theorem reveals an underlying angular normalization analogous to the quantization in spin fields. This result reflects the cumulative effects of relativistic transformations, where integrating over velocities yields a discrete angular measure akin to the quantized spin values in quantum mechanics. The theorem is explored in the context of Lorentz transformations and Möbius mappings, connecting these to physical phenomena such as rapidity, the behavior of spinors under boosts, and the intrinsic spin in quantum fields. Additionally, the discussion extends to the implications of spacetime torsion, as predicted by the Einstein-Cartan theory, and its unifying role in describing particles, black holes, and potential dark matter candidates through the lens of the holographic principle. This unified framework highlights how local spin-induced torsion can influence gravitational behavior, aligning with observations that suggest non-trivial topologies and quantum effects at cosmic scales.

On the Holographic Foundation of Complexity: Experimental Evidence Suggesting NP=P

Alessandro Rizzo

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