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 ) # Hubble constant in SI units (s^-1) # Initial conditions temperature_initial = 1.42e32 # Planck temperature in K particle_density_initial = 5.16e96 # Planck density in kg/m^3 particle_speed_initial = c # Initially at the speed of light # Simulation time t_planck = 5.39e-44 # Planck time in s t_simulation = t_planck * 1e5 # Shorter timescale for simulation # Quark masses (in GeV) - used for initial mass values and comparison quark_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, } # 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(0.1, 1.1, 0.1) # 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 def relativistic_energy(particle_speed, particle_mass): if particle_speed >= c: return np.inf return particle_mass * c**2 / np.sqrt(max(1e-10, 1 - (particle_speed / c) ** 2)) def relativistic_momentum(particle_speed, particle_mass): if particle_speed >= c: return np.inf return ( particle_mass * particle_speed / np.sqrt(max(1e-10, 1 - (particle_speed / c) ** 2)) ) def update_speed(current_speed, current_temperature, particle_mass): rel_momentum = relativistic_momentum(current_speed, particle_mass) return c * np.sqrt( max(1e-10, 1 - (rel_momentum / (rel_momentum + dark_energy_density)) ** 2) ) # 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 particle_speeds = np.zeros((len(quark_masses), num_steps)) # 2D array for speeds particle_temperatures = np.zeros( (len(quark_masses), num_steps) ) # 2D array for temperatures particle_masses_evolution = np.zeros( (len(quark_masses), num_steps) ) # 2D array for mass evolution tunneling_steps = np.zeros( (len(quark_masses), num_steps), dtype=bool ) # 2D array for tunneling steps # Create an array of masses for each quark particle_masses = np.array([mass * GeV_to_J for mass in quark_masses.values()]) for j, (quark, mass) in enumerate(quark_masses.items()): particle_masses_evolution[j, 0] = particle_masses[j] # Initialize mass for i in range(1, num_steps): particle_speeds[j, i] = update_speed( particle_speeds[j, i - 1], particle_temperatures[j, i - 1], particle_masses[j], ) value = ( 1 - (particle_speeds[j, i] / (TSR * temperature_initial)) + dark_matter_density ) if np.random.rand() < tunneling_probability: particle_speeds[j, i] = particle_speeds[j, 0] # Tunneling effect tunneling_steps[j, i] = True # Mark tunneling step if value < 0: value = 0 particle_temperatures[j, i] = ( alpha * particle_speeds[j, i] ** 2 ) # Apply TSR equation # Update mass based on energy conversion speed_squared_diff = ( particle_speeds[j, i] ** 2 - particle_speeds[j, i - 1] ** 2 ) # Avoid division by zero (if speed doesn't change, mass doesn't change) if speed_squared_diff == 0: particle_masses_evolution[j, i] = particle_masses_evolution[j, i - 1] else: # Calculate the change in relativistic energy energy_diff = relativistic_energy( particle_speeds[j, i], particle_masses[j] ) - relativistic_energy(particle_speeds[j, i - 1], particle_masses[j]) # Avoid NaN by checking if energy_diff is practically zero if abs(energy_diff) < 1e-15: # Adjust the tolerance as needed particle_masses_evolution[j, i] = particle_masses_evolution[ j, i - 1 ] else: # Update mass based on energy difference new_mass = ( particle_masses_evolution[j, i - 1] + energy_diff / c**2 ) if np.isfinite(new_mass): # Check if the new mass is finite particle_masses_evolution[j, i] = new_mass else: particle_masses_evolution[j, i] = particle_masses_evolution[ j, i - 1 ] # Apply expansion of the universe (redshift) particle_speeds[j, i] *= 1 - Hubble_constant_SI * t_planck # Apply expansion of the universe (cooling) particle_temperatures[j, i] *= 1 - Hubble_constant_SI * t_planck # Print calculated masses at the end of the simulation print( f"Calculated masses at the end of the simulation (Tunneling Probability: {tunneling_probability}):" ) for j, quark in enumerate(quark_masses.keys()): print( f"{quark}: {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:.1f}.json" ) data = { "tunneling_probability": tunneling_probability, "particle_masses_evolution": particle_masses_evolution.tolist(), } with open(data_filename, "w") as f: json.dump(data, f)