Warp: Real-Time Special Relativity Simulator with Adjustable Velocity & Frames

Warp Special Relativity Simulator — Visualize Time Dilation and Length Contraction

What it is

An interactive simulator designed to demonstrate core effects of special relativity: time dilation and length contraction, with supplementary visualizations for relativity of simultaneity, Lorentz transforms, and relativistic Doppler shift.

Key features

Real-time adjustable velocity slider (0 → 0.99c) to see continuous changes.
Side-by-side frames: stationary observer vs. moving observer.
Animated clocks showing proper time vs. dilated time.
Scaled rulers demonstrating length contraction along the direction of motion.
Light-ray tracing to illustrate signal delays and simultaneity differences.
Numeric readouts for gamma (γ), contracted length, dilated time, and relativistic velocity addition.
Preset scenarios (twin paradox, fast-moving rod, passing trains) and custom scene builder.
Exportable screenshots and CSV of numeric data for classroom use.

How it visualizes the physics

Computes Lorentz factor γ = 1/sqrt(1−v^2/c^2) and applies it to time intervals and longitudinal lengths.
Shows transformed spacetime diagrams (x vs. ct) with worldlines; users can toggle between inertial frames using Lorentz boosts.
Renders light cones and simultaneous-event lines in each frame to make relativity of simultaneity explicit.
Uses color/opacity cues to indicate signal delay and Doppler-shifted emission frequencies.

Educational value

Makes abstract formulas tangible: manipulate v and immediately see quantitative and qualitative effects.
Supports stepwise lessons: introduce γ, then time dilation, then length contraction, then simultaneity, then combined scenarios.
Useful for high-school through undergraduate levels and outreach demonstrations.

Limitations & assumptions

Idealized inertial frames only (no general relativity or acceleration except simple instantaneous frame switches).
One-dimensional motion along a single axis for clear visualization.
Visual scaling and animation may exaggerate effects at moderate v to aid intuition.

Quick tutorial

Set velocity near 0.8c. Note γ and watch moving clocks run slower compared to stationary clocks.
Place a rod aligned with motion; observe its measured length shrink by factor 1/γ.
Toggle spacetime diagram to see worldlines tilt and simultaneous-event lines rotate between frames.
Run the twin-paradox preset to compare proper-time accumulation for the two paths.