This simulator puts a rigid rod of adjustable rest length into motion and measures it in the laboratory by recording both endpoints at the same laboratory time. That simultaneity requirement is the heart of the result: the lab length is L = L₀/γ, shorter than the length the rod has in its own frame.
• A rest-frame rod for reference, a moving laboratory rod, synchronized endpoint gates and a laboratory ruler. • Sliders for rod velocity (0 to 0.95c) and rest length (1 to 5 m), plus toggles for the endpoint gates and explanatory markers. • Readouts: Lorentz factor, rest length, laboratory-measured length, length ratio, length difference and the endpoint event time offset Δt′ in nanoseconds. • Two experiments: at 0.8c a 5 m rod reads 3 m in the lab, and with no relative motion the two lengths are equal.
Laboratory length requires both endpoint events to happen at the same lab time (Δt = 0). Those same events are not simultaneous in the rod's frame: Δt′ = −γβL/c = −βL₀/c. The contraction L = L₀/γ = L₀√(1 − β²) follows from this measurement protocol, and the gates in the scene let you see the protocol itself.
This is rigid uniform motion in special relativity. The display is a coordinate measurement, not a photograph: optical propagation delay and Terrell rotation are excluded. Translation is slowed and repeated solely to show the sampling protocol. Only length along the direction of motion is addressed.
Yes. A length measurement compares both ends at the same instant in the measuring frame. Taking them at different times would mix in the rod's motion and give a meaningless number. The endpoint gates in the simulator enforce this.
The Lorentz factor is 5/3, so the laboratory length is 5 m × 3/5 = 3 m. The Eighty percent of c experiment sets this up directly.
No. The contraction is a property of the measurement in another frame; in its own frame the rod has its full rest length. The two readings describe different sets of simultaneous events.
Not exactly. This lab reports coordinate measurements. A photograph also involves light travel time and apparent rotation (Terrell rotation), which the model deliberately excludes.