import numpy as np import pandas as pd import json import os # Constants c = 299792458 # Speed of light in m/s E_mc2 = c**2 # Mass-energy equivalence in J/kg TSR = E_mc2 / (1.38e-23) # Temperature to Speed Ratio in K/m/s alpha = 1.0 # Proportional constant for TSR Q = 2 ** (1 / 12) # Fractal structure parameter dark_energy_density = 5.96e-27 # Density of dark energy in kg/m^3 dark_matter_density = 2.25e-27 # Density of dark matter in kg/m^3 collision_distance = 1e-10 # Distance for collision detection Hubble_constant = 70.0 # km/s/Mpc (approximation) Hubble_constant_SI = Hubble_constant * 1000 / 3.086e22 # Convert to SI units (s^-1) # Initial conditions temperature_initial = 1.0 # Planck temperature in K particle_density_initial = 5.16e96 # Planck density in kg/m^3 particle_speed_initial = TSR * temperature_initial # Initial speed based on TSR # Simulation time t_planck = 5.39e-44 # Planck time in s t_simulation = t_planck * 1e5 # Shorter timescale for simulation # Particle masses (in GeV) particle_masses = { "up": 2.3e-3, "down": 4.8e-3, "charm": 1.28, "strange": 0.095, "top": 173.0, "bottom": 4.18, "electron": 5.11e-4, "muon": 1.05e-1, "tau": 1.78, "photon": 0, "electron_neutrino": 0, # Neutrinos have very small masses "muon_neutrino": 0, "tau_neutrino": 0, "W_boson": 80.379, "Z_boson": 91.1876, "Higgs_boson": 125.1, "gluon": 0, # Massless "proton": 0.938, "neutron": 0.939, "pion_plus": 0.140, "pion_zero": 0.135, "kaon_plus": 0.494, "kaon_zero": 0.498 } # Conversion factor from GeV to J GeV_to_J = 1.60217662e-10 # Simulation setup num_steps = int(t_simulation / t_planck) # Tunneling probabilities to investigate tunneling_probabilities = np.arange(0.001, 1.5, 0.001) # Exclude 1.0 # Create a directory to store the data data_dir = "big_bang_simulation_data" os.makedirs(data_dir, exist_ok=True) # Functions to incorporate relativistic effects and collisions def relativistic_energy(particle_speed, particle_mass): epsilon = 1e-15 # A small value to avoid division by zero return particle_mass * c**2 / np.sqrt(max(1e-15, 1 - (particle_speed / c) ** 2 + epsilon)) def relativistic_momentum(particle_speed, particle_mass): epsilon = 1e-15 # A small value to avoid division by zero return particle_mass * particle_speed / np.sqrt(max(1e-15, 1 - (particle_speed / c) ** 2 + epsilon)) def update_speed(current_speed, current_temperature, particle_mass): """Update the speed of a particle based on temperature and mass.""" return TSR * current_temperature # Update speed using TSR def check_collision(particle_speeds, collision_distance, current_step): for j in range(len(particle_speeds)): for k in range(j+1, len(particle_speeds)): if np.abs(particle_speeds[j][current_step] - particle_speeds[k][current_step]) < collision_distance: return True, j, k return False, -1, -1 def handle_collision(particle_speeds, particle_masses, idx1, idx2, current_step): """Handle a collision between two particles.""" p1 = relativistic_momentum(particle_speeds[idx1][current_step], particle_masses[idx1]) p2 = relativistic_momentum(particle_speeds[idx2][current_step], particle_masses[idx2]) # Calculate velocities after collision using conservation of momentum total_momentum = p1 + p2 total_mass = particle_masses[idx1] + particle_masses[idx2] v1_new = (total_momentum / total_mass) * (particle_masses[idx1] / total_mass) v2_new = (total_momentum / total_mass) * (particle_masses[idx2] / total_mass) particle_speeds[idx1][current_step] = v1_new particle_speeds[idx2][current_step] = v2_new # Simulate the Big Bang with Dark Energy, Dark Matter, Tunneling, and Relativistic Effects for tunneling_probability in tunneling_probabilities: print(f"Simulating for tunneling probability: {tunneling_probability}") # Initialize arrays for simulation num_particles = len(particle_masses) particle_speeds = [[particle_speed_initial] * num_steps for _ in range(num_particles)] particle_temperatures = [[temperature_initial] * num_steps for _ in range(num_particles)] particle_masses_evolution = [[mass * GeV_to_J] * num_steps for mass in particle_masses.values()] tunneling_steps = [[False] * num_steps for _ in range(num_particles)] particle_masses_array = np.array([mass * GeV_to_J for mass in particle_masses.values()]) for current_step in range(1, num_steps): for j in range(num_particles): # Update temperature based on expansion of the universe particle_temperatures[j][current_step] = particle_temperatures[j][current_step-1] * (1 - Hubble_constant_SI * t_planck) # Update speed using TSR particle_speeds[j][current_step] = update_speed(particle_speeds[j][current_step-1], particle_temperatures[j][current_step], particle_masses_array[j]) # Apply tunneling effect if np.random.rand() < tunneling_probability: particle_speeds[j][current_step] = particle_speeds[j][0] tunneling_steps[j][current_step] = True # Check for collisions collision_detected, idx1, idx2 = check_collision(particle_speeds, collision_distance, current_step) if collision_detected: handle_collision(particle_speeds, particle_masses_array, idx1, idx2, current_step) # Calculate entropy using von Neumann entropy formula for j in range(num_particles): if particle_masses_array[j] == 0: entropy = 0 else: entropy = -particle_masses_array[j] * np.log1p(particle_masses_array[j]) # Update mass based on entropy particle_masses_evolution[j][current_step] = particle_masses_evolution[j][current_step-1] + entropy / c**2 # Print calculated masses at the end of the simulation print(f"Calculated masses at the end of the simulation using the von Neumann entropy (Tunneling Probability: {tunneling_probability}):") for j, particle in enumerate(particle_masses.keys()): print(f"{particle}: {particle_masses_evolution[j][-1] / GeV_to_J:.4e} GeV") # Save data to JSON file data_filename = os.path.join(data_dir, f"big_bang_simulation_data_{tunneling_probability:.2f}.json") data = { "tunneling_probability": tunneling_probability, "particle_masses_evolution": particle_masses_evolution, # No need for tolist() "particle_speeds": particle_speeds, "particle_temperatures": particle_temperatures, "tunneling_steps": tunneling_steps } with open(data_filename, "w") as f: json.dump(data, f)