Light Clock — Counting Ticks

Source

Collection: Wiki SR simulations (v1) — SuperSTEM Special-Relativity engine.
Concept: Because light travels at exactly c in every frame, a moving light clock's photon covers a longer slanted path per bounce, so a moving clock ticks slower — its tick counter falls behind the rest clock's by the fixed factor 1/γ.
Serves: A concrete, geometric route to time dilation: identical clocks, one moving, and their integer tick counters. The live ratio of counters homes in on the exact value 1/γ.
Inquiry: After many ticks, how does the moving counter compare with the rest counter? Where does the ratio settle, and why?
Misconception: That "a tick is a tick" (time is absolute), or that a fast-moving clock racks up more ticks. Both ignore that the invariant is c, not time.

Pedagogy principles applied

ID	Principle	How it shows up here
H1	Misconception is structural, not a text card	The "time is absolute" and "faster clock ticks more" errors are wrong prediction choices; the rebuttal appears only if the student picks one.
D6/D7	Guided inquiry reveals in stages	Five sidebar step-cards run fundamental → full (predict → observe → verify → introduce c & γ → resolve).
J	Invariant panels are scoped	The invariant here is the speed of light c, called out in the formal region — this is a dilation sim, so no spacetime-interval readout is forced into the sidebar.
A2	Fewest objects	Opens with two light clocks and three counters (rest, moving, ratio) — every one is read by a step.
C	Every number earns its place	Rest ticks, moving ticks, their ratio, γ and 1/γ are each predicted, read, or compared; the ratio plot is the payoff.

Light Clock

Speed

The two light clockseach up-and-down round trip is one tick

rest clock (v = 0) moving clock (v = β·c) photon (speed c)

Tick ratio over timemoving / rest → 1/γ

Guided Inquiry

1 · Predict the counters

The moving clock's photon must travel a longer, slanted path to bounce between its mirrors. After many ticks, how will the moving tick counter compare with the rest counter?

2 · Release the photons

Press ▶ in the top bar. Both photons launch at the same instant and both move at exactly the speed of light. Watch the yellow moving-clock photon trace a slanted (zig-zag) path across the lab while the blue rest photon just goes straight up and down.

3 · Read the counters

After a few ticks, compare the Rest ticks and Moving ticks readouts in the sidebar, and the live ratio. As time runs on, the ratio moving/rest …

4 · Why exactly 1/γ?

The one number that never changes is the speed of light c — both photons move at exactly c. Turn on ∑ Formal (top bar) to see γ and the tick relation. With the light path longer by a factor γ in the lab, the moving clock's tick rate is …

5 · Moving clocks tick slower

Because c is the same in every frame, a moving light clock's photon takes a longer path per bounce, so it ticks slower — by exactly 1/γ. That is time dilation, built from nothing but the constancy of the speed of light. Drag the β slider to see the ratio's target 1/γ move, then hit Finish to explore freely.

Controls

▾

moving clock speed v = 0.80c

00.99c

Readouts

▾

Rest ticks—

Moving ticks—

Ratio moving / rest—

The one number that never changes: the speed of light c. Both photons move at exactly c. That forced constancy is what makes the counters diverge.

Lorentz factor

Time dilation (lab path longer by γ)

Tick ratio

Live values

γ = —, Δt/Δτ = —, predicted ratio 1/γ = —