One Lorentz factor / six views

γ Lab Mass-Energy & Time Dilation Simulator

The same γ that multiplies energy is the factor that slows clocks.

Drag one slider from a parked car to a hair under light speed. Every panel below reads the same β and the same γ at the same instant — the energy bars, the two clocks, the muons falling through the atmosphere, and the wall at c that no amount of energy gets you through.

Pinned: “Relativistic mass” is optional language. What grows with speed is energy and inertia, not the rest mass m₀. Put the ship on a scale at rest and m₀ is exactly what it was.

Speed

β = v/c

Sets the speed. Linear up to 0.9c, then one decade of “nines” per notch — that is the only way to steer near c. Arrow keys nudge it.

The object

Rest mass m₀ ?

Scales every energy on the page. It never changes γ.

Proper interval Δτ ?

One tick of the moving clock. The lab sees it take γ times as long.

Units & physics

Changes the display only — the physics is the same numbers either way.

Classic pins γ to 1: kinetic energy is ½m₀v² and every clock agrees. Good below 0.1c, wrong above it.

Time

Pauses the animation and the clocks together. Nothing keeps counting behind your back.

Presets

Each one loads every control at once and opens the panel it makes the point on.

The ship's position on the track is β. The dashed line is c. Star streaks are stage dressing for speed, not a Doppler calculation.

Special relativity only: flat spacetime, constant velocity, no gravity. The GPS and ISS story has a general-relativity term this app deliberately leaves out, and the twin trip skips the acceleration at both ends. c = 299,792,458 m/s exactly. Source and physics notes are in the repository README.

γ = 1/√(1−β²) = 1 E = γm₀c² = — Δt = γΔτ = — relativity