Strings and Things

  How the FeMo Cofactor of Nitrogenase Breaks the Triple Bond in N₂ Breaking the triple bond in dinitrogen (N≡N) is one of the toughest chemical reactions in nature, requiring large activation energy due to its strength (~945 kJ/mol). Yet, nitrogenase , powered by its FeMo-cofactor ( FeMoco ) , performs this feat under ambient conditions . 🔬 Overview of FeMo Cofactor (FeMoco) The FeMoco is the active site of molybdenum-dependent nitrogenase, and it consists of: [Mo-7Fe-9S-C-homocitrate] cluster One central interstitial atom (carbon) suspected to play a stabilizing electronic role It acts as the redox center where electrons accumulate and transfer to N₂ , step by step, ultimately breaking its triple bond. 🧩 Mechanism: How FeMoC Breaks N≡N 1. Substrate Binding N₂ binds at or near the Mo or Fe6 site on the FeMoco cluster. Hydrogen bonding and conformational changes help stabilize the binding. 2. Electron Accumulation The nitrogenase complex sequential...

  📖 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...

  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 .

  🚀 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...

  📖 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...

  🚀 Developing a Unified Framework: From Pendulum Energy Coupling to Quantum Gravity To fully develop a Quantum Tensor Cosmology Model that connects Quantum Mechanics (QM) and General Relativity (GR) , we must start from a simple mechanical system —the pendulum . 🔷 Why the Pendulum? The pendulum embodies fundamental energy coupling between kinetic and potential energy. It represents a classical analog to quantum oscillations in field theories. It allows us to derive mathematical structures that can be extended to relativity and quantum gravity. 📖 Step 1: Understanding Energy Coupling in a Classical Pendulum The total energy of a simple pendulum with mass m m , length l l , and angle θ \theta from vertical is: E = K + U E = K + U where: Kinetic Energy K = 1 2 m v 2 = 1 2 m ( l θ ˙ ) 2 K = \frac{1}{2} m v^2 = \frac{1}{2} m (l \dot{\theta})^2 Potential Energy U = m g h = m g l ( 1 − cos ⁡ θ ) U = mgh = mg l (1 - \cos\theta) This system exhibits periodic energ...