Light clock

A tick is one complete out-and-back light trip between two ideal mirrors separated by transverse distance h. The stationary tick period is Δτ=2h/c. For an identical clock moving sideways at v=βc, the laboratory period is Δt=γΔτ, with γ=1/√(1−β²). Its light moves sideways at βc and vertically at ±c/γ: its total speed stays c. Both the outgoing and returning legs continue in the direction of motion.

Both drawings show simultaneous laboratory positions of two clocks, not two frames at the same proper phase and not an image received through a telescope. At laboratory time t the moving clock has elapsed proper time τ=t/γ. One tick has stationary path 2h and moving laboratory path 2hγ. At h=1 m, β=0.6: γ=1.25, Δτ≈6.671282 ns, Δt≈8.339102 ns and moving path 2.5 m.

Change h or β to update immediately. Negative β reverses motion. Use t/Δτ (0…10) or the time slider to compare both clocks at the same laboratory time. N counts completed round trips. At β=0.6, enter 1.25 to see one completed moving tick while the stationary clock is already in its next cycle. Each view follows its current cycle by subtracting completed-cycle translation; absolute motion continues. An exact positive cycle boundary shows the completed path. Each view fits separately with equal x/y spatial scale, so high speeds produce a shallow ray. Mirror/photon sizes are schematic.

Play advances 0.35 stationary ticks per screen second, deliberately slowed down. Pause stops at the current time; t=0 returns to the start. Play at the end restarts from zero. Options offers a quarter-tick step and path lengths. Reset restores h=1 m, β=0.6 and time 0. Playback stops at 10, when the tool/page is hidden or reduced motion is enabled. Manual time remains available with reduced motion. Changing physical parameters also pauses playback. Invalid time hides moving elements and clears time readings while retaining the complete path and periods; invalid physical parameters clear the comparison.

h ranges 0.01…1000 m and β−0.99…0.99. Exact raw h/β inputs, including unfinished or invalid text, survive navigation, reload and language changes. A new view starts at time 0, without playing. Animation time, computed results, paths and open menus are not saved. Typed time retains its precision across parameter changes and resizing. No acceleration, gravity, Doppler or optical arrival-time model.

OpenStax, University Physics 3, §5.3. c=299792458 m/s.