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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)
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