``` # Name: LorentzViolationSimulation.py # Purpose: Test Planck-scale Lorentz violation using the IO framework. # Status: Toy model with foundational progress. import numpy as np import micropip await micropip.install('numpy') await micropip.install('matplotlib') class PhotonNode: def __init__(self, energy): self.energy = energy # Photon energy (J) self.state = {'position': 0.0} # Initial position self.alpha = 1e-18 # Framework's predicted value self.E_planck = 1.22e28 # Planck energy (J) def compute_velocity(self): # IO's prediction: v(E) = c(1 - α E/E_planck) c = 3e8 # Speed of light (m/s) return c * (1 - self.alpha * self.energy / self.E_planck) class CausalLattice: def __init__(self, num_nodes): self.nodes = [PhotonNode(0.0) for _ in range(num_nodes)] self.distance = 1e24 # Mock distance to GRB source (meters) def emit_photon(self, energy): photon = self.nodes[0] photon.energy = energy return photon def simulate_arrival_time(self, photon): v = photon.compute_velocity() return self.distance / v # Setup: Simulate three gamma-ray photons lattice = CausalLattice(5) energies = np.array([1e-13, 1e-12, 1e-11]) # In joules (1 GeV = 1.6e-10 J) times = [lattice.simulate_arrival_time(lattice.emit_photon(E)) for E in energies] # Plot prediction vs. classical physics plt.plot(energies, times, 'ro-', label='IO Prediction') plt.axhline(y=lattice.distance/3e8, color='blue', linestyle='--', label='Classical Physics (α=0)') plt.xlabel('Photon Energy (J)') plt.ylabel('Arrival Time (s)') plt.title('Lorentz Violation Test') plt.legend() plt.show() ```