What if the speed of light was 5 km/h? Inside the Relativity Park simulator

An interactive simulator published this month turns special relativity into a walk in the park — literally. In “Relativity Park”, built by developer Dmitry Brant, the speed of light is reduced to 5 km/h, roughly walking pace, so the effects of relativity become visible on human scales instead of hiding behind the numbers of particle physics.

A park where light crawls

The page runs in a browser and presents a small park: a corridor, lamp posts, a Ferris wheel, a carousel and a shuttle. A head-up display tracks your velocity, the ratio β = v/c, the Lorentz factor γ, how far ahead the world appears stretched, and two clocks — “your watch” and the world clock.

You accelerate with the arrow keys or WASD and look around with the mouse; the space bar stops you. The keys L, G, C and B toggle individual effects — light-travel delay, aberration and contraction, Doppler colour, and relativistic beaming — while R returns you to the start and Tab opens the settings.

What you see while walking

Pressing the up arrow condenses your field of view in the direction of travel and shifts it towards blue; turning to look behind shows a reddened, stretched-out view. The two timers show time dilation directly. The lamp posts flash once per second of world time: approach one and the flashing speeds up and turns blue, move away and it slows and reddens, combining time dilation with the relativistic Doppler shift.

The Ferris wheel and the carousel cars travel at 75% of the speed of light. Each car is contracted by its own motion, and because light from different parts of the ride arrives at different moments, the whole assembly appears as it looked at different times — the effect known as Terrell rotation. The shuttle at the end of the corridor behaves the same way.

More than a toy

The project’s documentation explains that the rendering is physically motivated rather than decorative. For every visible point, the renderer walks back down the past light cone to find when the light left; for moving objects that means solving g(a) = a − |p(t−a) − eye| / c = 0, where the derivative g’(a) = 1 + (v·n̂)/c can fall to 0.14 at the corners of a carousel car travelling at 0.857c — enough for a naive Newton iteration to jump a whole revolution and tear triangles across the scene.

Each point is then Lorentz-transformed into the observer’s instantaneous rest frame. Aberration, Lorentz contraction and Terrell rotation all follow from that single step — Terrell rotation, the notes add, is not really a rotation but what light delay does to an already-contracted object. Backface culling is switched off because the effect shows surfaces facing away from the viewer, and logarithmic depth is used since the apparent scene spans centimetres to tens of kilometres once the world ahead is stretched by γ(1+β).

The Ferris wheel deliberately mixes frames: each gondola is specified in its own rest frame, while the rim — a rigidly rotating ring with no global rest frame, Ehrenfest’s paradox — has its worldlines given directly in the world frame, subluminal and self-consistent.