Advanced physics unifies gravity, motion and time into one picture: mass curves the geometry of spacetime itself, and anything moving through that curved geometry — a planet, a light ray, an observer's own clock — follows the shape it creates. This simulation makes that abstraction visible and adjustable.
A wireframe grid stands in for spacetime; the central mass dents it exactly like a rubber sheet, y(r) = −k·M / √(r² + r₀²). A green observer orbits along that curve while a yellow light ray sweeping past is deflected more sharply the closer it passes to the mass — the same qualitative effect that bends starlight during a solar eclipse.
Raise Central mass to deepen the well and bend the light ray harder. Orbit speed (v/c) sets how fast the observer moves as a fraction of light speed, which drives its Lorentz factor γ and how far its proper time τ lags behind coordinate time t. Simulation speed scales playback; toggle the light ray on or off; Restart zeroes both clocks.
The proper-time lag you see between τ and t here is the same mechanism — time dilation, Δτ = Δt / γ — that keeps GPS satellite clocks in sync with ground clocks only after correcting for both their orbital speed and the weaker gravity they sit in.
General relativity replaces "gravity as a force" with "gravity as geometry": mass tells spacetime how to curve, and curved spacetime tells matter (and light) how to move. This scene visualises both halves of that statement at once — the curved grid, and the paths that follow it.
y(r) = −k·M / √(r² + r₀²) — depth of the spacetime well at distance r from a mass M.
γ = 1 / √(1 − v²/c²) — Lorentz factor from orbital speed v.
Δτ = Δt / γ — proper time elapsed for the moving observer versus coordinate time.
Every equation on this page — Schrödinger's iℏ∂ψ/∂t = Ĥψ, Einstein's E = mc², Maxwell's ∇×E = −∂B/∂t — describes a different slice of the same universe; this simulation focuses on the relativity slice because it is the one you can watch bend in front of you.