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Spacetime diagram (special relativity)

An interactive Minkowski (1+1-dimensional) spacetime diagram. Build a scene from events, inertial worldlines, light rays, lines of simultaneity, observers (piecewise-inertial paths) and hyperbolae (curves of constant interval), and view it at once in two independently Lorentz-boostable frames. Objects carry a rest colour, mass and other attributes; the app shows their frame-dependent statistics — energy, momentum, relativistic Doppler colour shifts and proper time. Units are natural — c = 1 by default (Settings › Show c re-displays the powers of c in the readouts) — so light runs at 45° and causal character survives any boost.

Quick start. For a quick taste of the app, try the subjective-experience demo on the twin-paradox scene it opens with: in the left sidebar click the triangle-shaped ▶ Subjective experience tool (at the bottom), then click the bent red-violet Traveller worldline, then press ▶ Play on the timeline panel below. You’ll ride the traveller’s proper time while the other panel becomes their co-moving frame and a live panel shows what they see in their past light cone.

How to use
  • Sidebar tools (hover for the keyboard shortcut): the arrow selects — click an object to edit its numbers, or drag its points/lines. The other tools create objects by clicking or dragging on a panel; the hand pans and the crossed axes boost a frame by dragging.
  • Two frames. Each panel has its own controls (boost, re-centre, zoom, or jump to an object's rest frame) and can be swapped/aligned in the middle. The edit pane reads coordinates in the focused (blue-bordered) panel — click a panel to focus it. The hidden “lab” frame is never shown: velocities are always relative to the other panel.
  • Experience (▶): pick a worldline to ride its proper time — scrub or play, while the other panel becomes its co-moving frame and a live panel lists what it sees in its past light cone.
  • Scene menu: load an example, or export / import a scene as JSON. Settings toggles Doppler colour shifting and powers-of-c in the readouts.

An original tao-web applet (not a Java port), an aid for students of special relativity.

Left — co-movingfocusedsubjective
zoom
Right — co-movingfocusedsubjective
zoom
event (dot) timelike — worldline / observer (solid) light ray (dashed, 45°) line of simultaneity (dotted)

Coordinates are read in the focused panel. Boost the two panels differently to see that Δt, Δx are frame-dependent while s² = Δt² − Δx² is not.