Relativistic Energy as a Compton Wave Function

This repository contains a unified mathematical and computational framework that bridges Einsteinian mass-energy equivalence with quantum wave mechanics. By re-interpreting rest mass ($m_0$) as a high-frequency internal oscillation—the Compton Clock—this project provides a granular visualization of relativistic dynamics at the quantum threshold.

🔬 Theoretical Core

The project is built on the premise that mass is not a static scalar, but a dynamic determinant of a particle's waveform.

• The Compton Frequency Axiom: We define the angular frequency ($\omega$) of a particle's "internal heartbeat" using the relation $\omega = \frac{m_0 c^2}{\hbar}$.
• The Hybrid Hamiltonian: We utilize a modified Schrödinger Hamiltonian that explicitly includes the rest-mass energy term: $\hat{H} = -\frac{\hbar^2}{2m}\nabla^2 + mc^2$.
• Relativistic Scaling: The system incorporates the Lorentz Factor ($\gamma$) to simulate time dilation and length contraction within the wave packet envelope.

🛠 Features

• Attosecond Resolution: High-granularity temporal scaling ($10^{-18}$ s) allows for the observation of "Zitterbewegung" (trembling motion) within the wave packet.
• Interactive "Follow Mode": A simulation environment where the observer frame stays locked to the particle, revealing how the internal "clock" blue-shifts as velocity approaches $c$.
• Dynamic Dispersion Control: Unlike standard non-relativistic packets, this model ensures group velocity ($v_g$) correctly approaches the speed of light without exceeding it.

📂 Project Structure

• /docs: The full whitepaper: Relativistic Energy as a Compton Wave Function.
• /src: Python scripts utilizing mpmath and numpy for high-precision relativistic wave simulations.
• /simulations: Pre-rendered visualizations of Lorentz contraction and phase shifts.

🚀 Getting Started

1. Dependencies: Ensure you have the core physics stack installed.

pip install mpmath numpy matplotlib scipy

2. Run the Simulation: Execute the main wave packet script to observe the "Compton Clock" in action.

python3 relativistic_wave_packet.py

🛰 Future Research: The Zeta-Mass Connection

This repository serves as the physical "hardware" for the A Physical Model for the Riemann Hypothesis project. Future iterations involve substituting the static rest mass ($m_0$) with a discrete spectrum derived from the imaginary parts of the non-trivial zeros of the Riemann Zeta function $\zeta(s)$.