Physics

Special Relativity

Space and time are one fabric. Boost to a moving frame and its grid skews: clocks tick slow, rulers shrink, and simultaneity comes apart. Yet every arrow in spacetime keeps one length that all observers agree on.

ct′ axis (moving clock)x′ axis (moving now)event / four-vectorinvariant hyperbola

Drag the event (or the arrowhead in Displacement). Run sweeps the observer's speed back and forth.

Lorentz factor γ—

—

View

Observer boost β = v/c 0.00

Particle speed β_u 0.60

Energy E 2.00

Rest mass m 1.20

masslessheavy

Numbers

Lorentz factor γ—

Lab components (ct, x)—

Boosted components (ct′, x′)—

Invariant s²—

What to observe

Boost the observer. The indigo mesh and both primed axes scissor toward the light cone, but the dashed 45° cone never moves: light has one speed for everyone.
Put the event on the lab x axis and boost. The lab calls it simultaneous with the origin, but the indigo line through it (the mover's "now") tilts away: simultaneity is relative.
The first tick of the moving clock sits at lab height γ (time dilation), while the amber rod, 2 long in its own frame, covers only 2/γ of the lab x axis (length contraction).
In Displacement the arrow never moves while its components change, and (ct)² − x² stays fixed: the minus sign makes the change in one square cancel the change in the other. Every reading lands on the same hyperbola.

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