Lorentz boost animation

lorentz-boost-anim.py

# Import necessary libraries
import numpy as np
import matplotlib.pyplot as plt
from matplotlib.animation import FuncAnimation

# Define the SplitComplex class
class SplitComplex:
    def __init__(self, real, j_component):
        self.real = real
        self.j_component = j_component

    def __mul__(self, other):
        real_part = self.real * other.real + self.j_component * other.j_component
        j_part = self.real * other.j_component + self.j_component * other.real
        return SplitComplex(real_part, j_part)

# Updated Lorentz boost function using the SplitComplex class and the boost
def lorentz_boost(t, x, boost):
    event = SplitComplex(t, x)
    transformed_event = boost * event
    return transformed_event.real, transformed_event.j_component

# Create a grid of events in spacetime
t, x = np.meshgrid(np.linspace(-2, 2, 10), np.linspace(-2, 2, 10))
t = t.flatten()
x = x.flatten()

# Define highlighted points and their paths
highlighted_points = [
    (1.5, 0.5),
    (0.5, 1.5),
    (-1.5, -0.5),
    (-0.5, -1.5)
]
paths = {point: {'x': [], 'y': []} for point in highlighted_points}

# Update function for the animation
def update(phi):
    ax.clear()  # Clear the entire axes
    
    # Reset basic settings for the ax after clearing
    ax.set_xlim(-3, 3)
    ax.set_ylim(-3, 3)
    ax.set_xlabel('x')
    ax.set_ylabel('ct')
    ax.axhline(0, color='black', linewidth=0.5)
    ax.axvline(0, color='black', linewidth=0.5)
    ax.axline((0, 0), slope=1, color='red', linestyle='--', linewidth=0.5)
    ax.axline((0, 0), slope=-1, color='red', linestyle='--', linewidth=0.5)
    
    # Use the boost for the transformation
    boost = SplitComplex(np.cosh(phi), np.sinh(phi))
    t_prime, x_prime = lorentz_boost(t, x, boost)
    ax.scatter(x_prime, t_prime, color='blue')
    
    for point in highlighted_points:
        t_point, x_point = point
        t_prime_point, x_prime_point = lorentz_boost(t_point, x_point, boost)
        ax.scatter(x_prime_point, t_prime_point, color='red', s=50, zorder=5)
        paths[point]['x'].append(t_prime_point)
        paths[point]['y'].append(x_prime_point)

    for point, path in paths.items():
        ax.plot(path['x'], path['y'], color='green', alpha=0.5)

    ax.set_title(f"multiplication by {boost.real:.2f} + {boost.j_component:.2f}j")

# Create the figure for the animation
fig, ax = plt.subplots(figsize=(6, 6))

# Create and save the updated animation
ani = FuncAnimation(fig, update, frames=np.linspace(-1, 1, 20), blit=False, repeat=True)
gif_path = "./lorentz_boost_animation_cleaned.gif"
ani.save(gif_path, writer='pillow', fps=10)