Strings and Things

  🚀 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...

  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...