Strings and Things

                                                                              Black Hole Simulation                                                                                                                  This simulation demonstrates quantum spacetime fluctuations under extreme conditions , simulating a  black hole-like scenario with the following dynamics: Localized High Energy Density : The central regio...

  🚀 Developing a Quantum Tensor Model for Hawking Radiation Modification We now construct a Quantum Tensor Gravity (QTG) model to modify Hawking radiation , integrating: Quantum Tensor Oscillations into Black Hole Radiation Theory. Derivation of a Modified Hawking Temperature from Tensor Fields. Quantum Corrections to Black Hole Evaporation. Implications for the Black Hole Information Paradox. Numerical Simulation of Modified Hawking Radiation Over Time. 📖 Step 1: Standard Hawking Radiation & the Information Paradox 1.1 Classical Hawking Radiation Formula In standard General Relativity, black holes radiate energy via Hawking radiation , given by: T H = ℏ c 3 8 π G M T_H = \frac{\hbar c^3}{8\pi G M} where: T H T_H is the Hawking temperature. M M is the mass of the black hole. G G is Newton’s gravitational constant. ℏ \hbar is the reduced Planck constant. ➡ Problem: This process suggests complete evaporation , leading to information loss , which contr...

  📖 Formulating a Quantum Field Theory for Quantum Tensor Gravity (QTG) Now, we construct a Quantum Field Theory (QFT) for Quantum Tensor Gravity (QTG) , based on the oscillatory energy coupling of tensor fields that we previously developed. This framework: Defines the Fundamental Fields of Quantum Tensor Gravity. Constructs the QTG Lagrangian & Action. Derives the Field Equations for Quantum Tensor Gravity. Explores Quantum Corrections to General Relativity. Predicts New Physical Phenomena, Including Possible Observables. Numerically Simulates Quantum Tensor Field Evolution. 📖 Step 1: Defining the Fundamental Fields of Quantum Tensor Gravity We introduce a quantum tensor field T μ ν \mathcal{T}^{\mu\nu} , which oscillates in spacetime and governs gravity at quantum scales. 1.1 The Tensor Field T μ ν \mathcal{T}^{\mu\nu} The metric tensor g μ ν g_{\mu\nu} is now an emergent classical limit of a more fundamental quantum tensor field T μ ν \mathcal{T}^{\mu\n...

  Relating Hofstadter’s Butterfly to Spin Network Entanglement Spectra Hofstadter’s Butterfly is a fractal energy spectrum that emerges from quantum systems with periodic magnetic fields . Interestingly, spin networks also exhibit self-similarity and entanglement scaling , suggesting a deeper connection. Key Insights Hofstadter’s Butterfly is not just a fractal energy spectrum, but also exhibits fractal entanglement scaling. Entanglement entropy follows a self-similar structure , similar to spin networks in quantum gravity . This connects fractal quantum systems to entanglement-based holography , potentially linking quantum condensed matter physics to quantum gravity . The connection between quantum fractals and holography may provide new insights into quantum gravity .

  Logical Summary: Unifying Quantum Mechanics (QM) with General Relativity (GR) We developed a mathematical and computational framework that connects quantum mechanics (QM) and general relativity (GR) by leveraging tensor networks, quantum entanglement, and machine learning . Here’s the step-by-step logical progression: 1️⃣ Reformulating Newton’s and Einstein’s Equations into a Unified Framework 🔹 Starting Point: Classical Mechanics Reformulation We modified Newton’s equation F = m a F = ma into a quadratic form : v 2 + g 2 = F v^2 + g^2 = F This combined kinetic (velocity-dependent) and gravitational (acceleration-dependent) energy , hinting at an underlying unification. 🔹 Extending to Relativity We reformulated relativistic energy as: E 2 = v 2 c 2 + c 4 E^2 = v^2 c^2 + c^4 Noted that when velocity is small, v 2 c 2 v^2c^2 vanishes , leaving only rest energy c 4 c^4 , drawing a link between rest mass and gravitational mass . 2️⃣ Linking Gravity and Electro...

  Visualization of a complex atomic orbital : 3D visualization of a complex atomic orbital : Visualization of the real and imaginary components of a quantum wavefunction over time What This Animation Represents: The left panel (Blue) : Shows how the real part of the orbital oscillates. The right panel (Red) : Shows how the imaginary part oscillates. The wavefunction rotates in complex space , meaning its real and imaginary components continuously transform into each other —just like how electric and magnetic fields oscillate in an EM wave Key Takeaways: This is analogous to how electromagnetic waves oscillate in phase : The real part can be seen as the "electric field" . The imaginary part behaves like the "magnetic field" . This behavior is fundamental in quantum mechanics : Describes electron orbitals in atoms and molecules. Crucial for molecular bonding and spectroscopy . Underlies quantum superposition and entanglement .

  A 3D plot displays the 1s orbital of a hydrogen atom, illustrating the probability density distribution in a spherical shape. The graph features labeled axes, depicting the spatial dimensions of the orbital.                                                                                                                                         Hydrogen Atom: 3d Orbital (n=3, l=2, m=2)                                                   ...