Strings and Things

  📖 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...