Interactive Modern Physics Simulations — from the Schrödinger equation to spacetime curvature
GPU-accelerated · Exact Geodesics · OpenGL / GLSL · Python
Schwarzschild gravitational lensing — 800 RK4 steps per pixel, accretion disk with relativistic Doppler and Novikov–Thorne profile
Physics Lab is a collection of computational experiments that simulate phenomena from quantum mechanics, special relativity, and general relativity. Each experiment implements real physics — no shortcuts, no crude approximations — and renders results in real time via OpenGL/ModernGL or generates high-quality videos via ffmpeg.
The project was built around three principles: physical fidelity (exact equations, validated numerical methods), performance (GPU shaders, Split-Step FFT, CuPy when available), and pedagogical clarity (HUDs with real-time parameters, interactive controls to explore the parameter space).
Interactive simulation of a Schwarzschild black hole with exact geodesic ray tracing. Each screen pixel fires a photon whose trajectory is integrated using the orbit equation in the Schwarzschild metric.
Implemented physics:
- Photon orbit equation:
d²u/dφ² + u = 3Mu²(u = 1/r, geometric units G = c = 1) - 4th-order Runge-Kutta integration (800 steps per ray)
- Event horizon at r = 2M, photon sphere at r = 3M, ISCO at r = 6M
- Impact parameter:
b = r₀ sin(α) / √(1 − rₛ/r₀) - Accretion disk with Novikov–Thorne temperature profile:
T(r) ∝ [f(r)/r³]^(1/4) - Gravitational redshift:
g_grav = √(1 − 3M/r) - Relativistic Doppler:
g = g_grav / (1 − Lz·Ω)withΩ = √(M/r³) - Observed intensity:
I_obs ∝ g⁴ · B(g·T)(relativistic invariance) - Blackbody → sRGB conversion (Mitchell Charity approximation)
- Procedural star field with gravitational lensing
Controls: Mouse (orbit), Scroll (zoom), Arrows (disk/temperature), D (disk on/off), B (bloom), R (reset)
Near-polar view (88.8°) — the Einstein ring appears as a secondary image inside the black hole shadow
Gaussian wave packet incident on a rectangular potential barrier. Solves the 1D time-dependent Schrödinger equation via Split-Step Fourier (2nd-order symmetric):
ψ → exp(−iV dt/2) · ψ half-step in position space
ψ → FFT → exp(−ik²/2 dt) · ψ̃ full step in momentum space
ψ → IFFT → exp(−iV dt/2) · ψ half-step in position space
2048-point grid, natural units (ℏ = 1, m = 1). The wave packet has kinetic energy E = 12.5, the barrier has height V₀ = 15 — a classically forbidden but quantum-mechanically allowed tunneling regime.
t = 4.80 — wave packet hitting the barrier, with part already transmitted by quantum tunneling
t = 8.80 — after interaction: reflected (left) and transmitted (right) packets, demonstrating tunneling through a classically forbidden barrier
2D Schrödinger on a 1024×1024 grid (1M cells), GPU-accelerated via CuPy. Simulates a wave packet passing through a double slit and forming the interference pattern. Includes wave function collapse simulation with positional detection.
t = 15.0 — |ψ(x,y)|² after passing through the double slit, showing the quantum interference pattern
N = 1,005,000 detections — the collapse histogram reproduces the |ψ|² interference pattern
Pair of particles in an entangled state flying in opposite directions. 2D wave function: ψ(x₁,x₂) ∝ exp(−(x₁−x₂)²/4σᵣ²) · exp(−(x₁+x₂)²/4σᵣ²) · exp(ik₀(x₁−x₂)). 1024×1024 grid with GPU. Generates three videos: |ψ|² evolution, 2 million detections revealing correlations, and instantaneous collapse upon measuring one particle.
|ψ(x₁,x₂)|² at t = 14.0 — the joint distribution in (x₁, x₂) space shows correlation along the diagonal, while the marginal distributions (projections) are broad
N = 1,755,000 detections — the scatter plot (x₁, x₂) reveals the entanglement correlation: measuring x₁ determines x₂
Measurement of x₁ = +0.2 instantaneously collapses x₂ to −43.9 — the red line marks the measurement slice in configuration space
Full Bell test simulation with the |Φ+⟩ = (|00⟩ + |11⟩)/√2 state. OpenGL rendering with 4 synchronized panels (1920×1080) showing the violation of Bell's inequality via the CHSH protocol:
S = E(a₁,b₁) − E(a₁,b₂) + E(a₂,b₁) + E(a₂,b₂) = 2√2 ≈ 2.83 > 2
The value S = 2√2 (Tsirelson's bound) violates the classical limit S ≤ 2, ruling out local hidden variable theories.
Phase 2: angular sweep θ — the 4 panels show EPR source, Bloch spheres (Alice and Bob), detection scatter (a×b), and correlation E(θ) vs classical and quantum predictions
Final result: S = 2.87 > 2 — Bell inequality violation confirmed, consistent with the quantum limit of 2√2 ≈ 2.83
Two procedural analog clocks rendered via fragment shader. The stationary clock marks coordinate time t, while the moving clock marks proper time τ = t/γ. The Lorentz factor γ = 1/√(1 − v²/c²) visually delays the moving clock's hand in real time.
Stationary clock (cyan) vs moving clock (amber) — the γ factor delays proper time τ relative to coordinate time t
A cube and a sphere side by side, with ghost wireframes showing the rest length L₀ and solid shapes showing the contracted length L = L₀/γ. The contraction happens entirely in the GPU vertex shader — each vertex is compressed along the axis of motion by the factor 1/γ = √(1 − v²/c²).
Ghost wireframes show rest length L₀, solid shapes show contracted length L = L₀/γ
Fully procedural Minkowski diagram (fragment shader). Two overlaid reference frames: S (blue, orthogonal) and S' (amber, tilted). Three interactive scenarios: relativity of simultaneity, light cone and causality, temporal order reversal.
Minkowski diagram — reference frames S (blue) and S' (amber) with events transformed by the Lorentz equations
Twin A stays on Earth; Twin B travels to a distant star at velocity v and returns. When they reunite, B is younger: τ_B = T/γ < T = τ_A. The simulation shows the asymmetry that comes from the change of reference frame at the turnaround (acceleration), resolving the "paradox".
Traveling twin (green) ages less than the stationary one (cyan) — the asymmetry comes from the acceleration at turnaround
physics-lab/
├── relatividade geral/
│ └── 01-lente-gravitacional/ # Geodesic ray tracing (GLSL)
│ ├── main.py # Interactive app (Pygame + ModernGL)
│ └── shaders/
│ └── blackhole.frag # RK4 in fragment shader
├── relatividade restrita/
│ ├── common/ # Shared engine
│ │ ├── engine.py # BaseApp, bloom, orbital camera, HUD
│ │ └── shaders/ # Bloom, grid, starfield, compositing
│ ├── 01-dilatacao-temporal/
│ ├── 02-contracao-lorentz/
│ ├── 03-transformadas-lorentz/
│ └── 04-paradoxo-gemeos/
├── mecanica quantica/
│ ├── 01-schrodinger-1d/ # Split-Step Fourier 1D
│ ├── 02-dupla-fenda-colapso/ # Split-Step Fourier 2D (CuPy/GPU)
│ ├── 03-emaranhamento/ # EPR with 2M detections
│ └── 04-bell-test/ # CHSH with OpenGL renderer
└── requirements.txt
The shared engine (common/engine.py) provides: OpenGL 3.3 Core context via Pygame, HDR bloom pipeline (extract → multi-pass Gaussian blur → composite), orbital mouse camera, HUD system with procedural fonts, and full-screen quad framework for ray tracing shaders.
git clone https://github.com/JoaoHenriqueBarbosa/physics-lab.git
cd physics-lab
pip install -r requirements.txtDependencies: NumPy, Matplotlib, Pygame, ModernGL. For GPU acceleration in 2D quantum mechanics experiments, also install CuPy (optional — works with pure NumPy, but slower).
System requirements: OpenGL 3.3+ (any dedicated or integrated GPU from the last ~10 years).
# General Relativity — interactive black hole
python "relatividade geral/01-lente-gravitacional/main.py"
# Special Relativity — time dilation
python "relatividade restrita/01-dilatacao-temporal/main.py"
# Quantum Mechanics — tunneling (interactive)
python "mecanica quantica/01-schrodinger-1d/main.py"
# Quantum Mechanics — double slit (generates video)
python "mecanica quantica/02-dupla-fenda-colapso/main.py" --save- Schwarzschild, K. (1916) — Schwarzschild Metric
- Luminet, J.-P. (1979) — Image of a Spherical Black Hole with Thin Accretion Disk, Astron. Astrophys. 75, 228–235
- Novikov, I. D. & Thorne, K. S. (1973) — Black Holes (Les Houches)
- James, O. et al. (2015) — Gravitational Lensing by Spinning Black Holes in Astrophysics, and in the Movie Interstellar, Class. Quant. Grav. 32, 065001
- Bruneton, E. (2020) — arXiv:2010.08735
- Clauser, J. F. et al. (1969) — CHSH Inequality
Made with real physics, coffee, and one productive night.