Strings and Things

  VQE Variational Quantum Eigensolver (VQE)-style model to optimize the energy landscape of the FeMo cofactor system. ⚛️ What We'll Do We'll simulate the FeMoco cluster as a quantum Hamiltonian and use a variational quantum circuit to minimize the ground state energy , similar to how: VQE finds the lowest-energy electron configuration of a molecule.  Simplified Model of FeMoC for VQE While the full FeMoco has a complex multielectron Hamiltonian, we’ll simulate a toy model capturing: 3 sites (qubits) representing key iron or molybdenum redox centers , A Hamiltonian H with coupling terms: H = Z 0 Z 1 + Z 1 Z 2 + X 0 + X 1 + X 2​ This models: Redox coupling between centers ( Z Z terms), Electron tunneling/exchange ( X terms). 🛠️ Steps to Build the VQE Model                Define the Hamiltonian (using Pauli operators). Build a parameterized quantum circuit (ansatz) . Use a classical optimizer to va...

                                                                              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...

  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...

  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)                                                   ...

  🚀 Exploring the Effects of Quantum Tensor Gravity Inside Black Holes Now, we investigate how Quantum Tensor Gravity (QTG) modifies the internal structure of black holes , aiming to: Replace Classical Singularities with Quantum Tensor Oscillations. Explore How Energy Transfer Inside the Event Horizon Prevents Information Loss. Modify the Penrose Diagram to Incorporate Quantum Gravity Effects. Predict Observable Consequences, Including Quantum Gravitational Wave Signatures. Simulate the Evolution of the Tensor Field T μ ν \mathcal{T}^{\mu\nu} Inside a Black Hole. 📖 Step 1: Why General Relativity Breaks Down in Black Holes 1.1 Classical Singularities in General Relativity In General Relativity (GR), black holes contain a singularity at r = 0 r = 0 , where: The curvature tensor R μ ν λ σ R_{\mu\nu\lambda\sigma} diverges . All physical quantities (density, energy) become infinite . Information loss paradox emerges , violating quantum mechanics. ➡ Key Question: C...