Relativity Simulation & Spacetime Visualisation

A Python project for simulating and visualising Special Relativity — Lorentz transformations, spacetime diagrams, causal structure, time dilation, length contraction, twin paradox, and uniformly accelerated (Rindler) worldlines.

Built as part of an independent study in General Relativity and Computational Physics.

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Features

Module	What it does
simulations/lorentz.py	Core Lorentz boosts, γ, time dilation, length contraction, velocity addition, spacetime interval
visualizations/spacetime_diagram.py	Minkowski diagrams with light cones, boosted axes, simultaneity lines, multiple observers
visualizations/relativistic_effects.py	γ vs β plots, twin paradox, relativistic velocity addition
visualizations/causal_structure.py	Causal classification (timelike / lightlike / spacelike) of event pairs
notebooks/exploration.ipynb	Interactive Jupyter notebook covering all topics

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Visualisations

Minkowski Spacetime Diagram

• Lab frame and boosted observer worldlines
• Future and past light cones from the origin
• Boosted ct′ and x′ axes
• Lines of simultaneity in the moving frame
• Optional Rindler (uniformly accelerated) worldline

Relativistic Effects

• Lorentz factor γ as a function of β
• Time dilation ratio t/τ vs β
• Length contraction ratio L/L₀ vs β

Twin Paradox

• Full spacetime diagram of the travelling and stay-at-home twins
• Annotated departure, turnaround, and reunion events
• Correct proper-time computation for each twin

Causal Structure

• Shaded timelike, lightlike, and spacelike regions
• Classification of arbitrary event pairs by their invariant interval s²

Velocity Addition

• Relativistic vs Galilean velocity addition
• Demonstrates the speed-of-light speed limit

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Physics Background

Lorentz transformation (boost along x-axis):

ct′ =  γ(ct − βx)
 x′ =  γ(x  − βct)

where β = v/c and γ = 1/√(1 − β²).

Spacetime interval (Lorentz invariant):

s² = −(Δct)² + (Δx)²

• s² < 0 → timelike (causally connected)
• s² = 0 → lightlike (on the light cone)
• s² > 0 → spacelike (no causal connection)

Uniformly accelerated worldline (Rindler, natural units c = 1):

ct(τ) = (1/α) sinh(ατ)
 x(τ) = (1/α) cosh(ατ)

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Project Structure

relativity-sim/
├── simulations/
│   ├── __init__.py
│   └── lorentz.py            # Core physics
├── visualizations/
│   ├── __init__.py
│   ├── spacetime_diagram.py  # Minkowski diagrams
│   ├── relativistic_effects.py
│   └── causal_structure.py
├── notebooks/
│   └── exploration.ipynb     # Interactive notebook
├── output/                   # Generated figures (git-ignored)
├── main.py                   # CLI entry point
├── requirements.txt
└── README.md

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Getting Started

1. Clone the repository

git clone https://github.com/<your-username>/relativity-sim.git
cd relativity-sim

2. Install dependencies

pip install -r requirements.txt

3. Run the full demo suite

python main.py

Figures are saved to output/.

4. Run a specific demo

python main.py --demo spacetime     # Minkowski diagram
python main.py --demo observers     # Multiple observers
python main.py --demo effects       # γ, dilation, contraction
python main.py --demo twins         # Twin paradox
python main.py --demo velocity      # Velocity addition
python main.py --demo causal        # Causal structure
python main.py --demo acceleration  # Rindler worldline
python main.py --demo intervals     # Interval table (text)

5. Interactive Jupyter notebook

jupyter notebook notebooks/exploration.ipynb

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Example Usage (Python API)

from simulations.lorentz import gamma, boost_event, time_dilation, spacetime_interval

# Lorentz factor
g = gamma(0.8)
print(f"γ = {g:.4f}")   # γ = 1.6667

# Boost a spacetime event
ct_p, x_p = boost_event(ct=5.0, x=3.0, beta=0.6)

# Time dilation: proper time τ=10 s in a ship at β=0.8
t = time_dilation(tau=10, beta=0.8)
print(f"Coordinate time: {t:.2f} s")

# Classify two events
s2 = spacetime_interval(0, 0, 3, 1)   # s² = −8  → timelike

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Dependencies

• Python ≥ 3.9
• NumPy ≥ 1.24
• Matplotlib ≥ 3.7
• SciPy ≥ 1.11
• Jupyter (for notebook)

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References

• Susskind, L. & Friedman, A. — Special Relativity and Classical Field Theory (Theoretical Minimum series)
• Carroll, S. — Spacetime and Geometry: An Introduction to General Relativity
• Tong, D. — Lectures on General Relativity
• Misner, Thorne & Wheeler — Gravitation

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Author

Adithyan S
Integrated M.Sc. Physics, Amrita Vishwa Vidyapeetham, Amritapuri
Research interests: General Relativity · Quantum Field Theory · Quantum Gravity · Computational Physics