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import numpy as np
import matplotlib.pyplot as plt
# Constants
c = 299792458 # Speed of light in m/s
hbar = 1.0545718e-34 # Reduced Planck constant in J·s
alpha = 1.0 # Fine-structure constant
# Define string properties
string_length = 1e-35 # Length of the string in meters
string_tension = 1e30 # Tension of the string in N
# Define initial conditions
initial_position = 0.0 # Initial position of the string
initial_velocity = 1e6 # Initial velocity of the string
# Simulation parameters
time_step = 5.39e-44 * 1e3 # Time step for the simulation
total_time = 1e-40 # Extended total simulation time
# Initialize arrays to store position and velocity data
num_steps = int(total_time / time_step) + 1
position = np.zeros(num_steps)
velocity = np.zeros(num_steps)
# Set initial conditions
position[0] = initial_position
velocity[0] = initial_velocity
# Main simulation loop
for i in range(1, num_steps):
# Calculate acceleration using string equation of motion
acceleration = -(string_tension / hbar) * position[i - 1]
# Update velocity and position
velocity[i] = velocity[i - 1] + acceleration * time_step
position[i] = position[i - 1] + velocity[i] * time_step
# Plot the results
plt.figure(figsize=(10, 6))
plt.plot(np.arange(num_steps) * time_step, position, label="String Position")
plt.xlabel("Time (s)")
plt.ylabel("Position (m)")
plt.title("String Evolution in Time")
plt.grid(True)
plt.legend()
plt.show()
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