ravel Simulator
(Exploring Near-Light-Speed Physics with Python Code)
Relativistic Space Travel Simulator
(Exploring Near-Light-Speed Physics with Python)
This simulation models time dilation, length contraction, and energy requirements for near-light-speed travel using Einstein's Special Relativity.
---
🚀 Key Physics Equations
Lorentz Factor (γ)
\[
\gamma = \frac{1}{\sqrt{1 - \frac{v^2}{c^2}}
\]
2. Time Dilation
\[
\Delta t' = \gamma \Delta t
\]
3. Length Contraction
\[
L' = \frac{L}{\gamma}
\]
4. Relativistic Kinetic Energy
\[
E_k = (\gamma - 1)mc^2
\]
---
💻 Python Simulation Code
```python
import numpy as np
import matplotlib.pyplot as plt
from matplotlib.widgets import Slider
# Constants
c = 299792458 # Speed of light (m/s)
year_sec = 31536000 # Seconds in a year
def lorentz_factor(v):
"""Calculate the Lorentz factor γ for velocity v."""
return 1 / np.sqrt(1 - (v**2 / c**2))
def simulate_relativity(v_fraction):
"""
Simulate relativistic effects at a given fraction of light speed.
Args:
v_fraction (float): Fraction of light speed (0 < v < 1).
Returns:
dict: Time dilation, length contraction, and energy ratios.
"""
v = v_fraction * c
gamma = lorentz_factor(v)
# Time dilation (1 year onboard)
t_earth = gamma * 1 # Earth time (years)
# Length contraction (1 light-year distance)
L_contract = 1 / gamma # Contracted distance (light-years)
# Energy (for 1000kg spacecraft)
m = 1000 # kg
E_k = (gamma - 1) * m * (c**2) # Kinetic energy (Joules)
E_k_equivalent = E_k / (1e19) # Equivalent in "Jupiter masses" (simplified)
return {
"velocity": v,
"gamma": gamma,
"time_dilation": t_earth,
"length_contraction": L_contract,
"energy_joules": E_k,
"energy_jupiter_masses": E_k_equivalent
}
# Interactive Plot
fig, ax = plt.subplots(3, 1, figsize=(10, 8))
plt.subplots_adjust(bottom=0.25)
# Slider for velocity
ax_slider = plt.axes([0.2, 0.1, 0.6, 0.03])
slider = Slider(ax_slider, 'Velocity (% of c)', 0.01, 0.99, valinit=0.5)
# Update function
def update(val):
v_fraction = slider.val
data = simulate_relativity(v_fraction)
# Clear previous plots
for a in ax:
a.clear()
# Plot 1: Time Dilation
ax[0].set_title(f"Time Dilation: 1 year onboard = {data['time_dilation']:.2f} years on Earth")
ax[0].bar(['Onboard', 'Earth'], [1, data['time_dilation']], color=['blue', 'red'])
# Plot 2: Length Contraction
ax[1].set_title(f"Length Contraction: 1 light-year becomes {data['length_contraction']:.4f} light-years")
ax[1].bar(['Original', 'Contracted'], [1, data['length_contraction']], color=['green', 'orange'])
# Plot 3: Energy Requirements
ax[2].set_title(f"Energy Required: {data['energy_joules']:.2e} J (≈{data['energy_jupiter_masses']:.2f}× Jupiter's mass energy)")
ax[2].text(0.5, 0.5, f"γ (Lorentz Factor) = {data['gamma']:.2f}", ha='center', va='center', fontsize=12)
plt.draw()
slider.on_changed(update)
update(0.5) # Initialize
plt.show()
```
---
📊 What This Simulates
1. Time Dilation
- At 90% light speed, 1 year for the traveler = 2.29 years on Earth.
- At 99% light speed, 1 year onboard ≈ 7 years on Earth.
2. Length Contraction
- A 1-light-year distance shrinks to 0.14 light-years** at 99% *c*.
3. Energy Requirements
- Accelerating 1 ton (1000kg) to 90% c requires ≈10²⁰ Joules (~1,000x global annual energy output).
---
🔮 Extending the Simulation
- Add acceleration effects (constant 1g thrust).
- Model relativistic Doppler shifts (how stars look at near-c).
- Simulate warp-drive metrics (Alcubierre solution).
Would you like these extensions? Let me know how deep you want to go! 🚀