Light clock and time dilation
Why does a moving clock run slow?
In a light clock, a pulse of light bounces back and forth between two mirrors, and each round trip counts as one tick. To an observer moving with the clock, the light simply travels up and down; seen from the ground, the clock is moving forward, so the light follows a longer diagonal path. The speed of light is the same for all observers, so from the ground the light takes longer to complete one tick: the moving clock runs slow. Conversely, the people on the spaceship find that the clock on the ground runs slow, and both statements are equally valid.
Lorentz factor vs. speed
At low speeds γ ≈ 1, barely noticeable; near the speed of light it rises sharply.
Think about it
Muons produced by cosmic rays at the top of the atmosphere have a proper lifetime of only about 2.2 μs and travel at 0.998c. Why do most of them reach the ground?
At v = 0.998c, γ ≈ 16. Seen from the ground, the muon's "clock" runs 16 times slower, so its mean lifetime is about 35 μs and it can travel about 10 km; without time dilation it could travel only about 660 m. Try setting v/c to 0.95 and see how many ticks your own clock makes for each tick of the moving clock.
Model assumptionsLight clock placed perpendicular to the motion, height unchanged · proper time τ₀ = 1 s (on-screen time) · the speed of light is scaled down on screen; the moving clock re-enters from the other side after crossing the edge
Data log
Set the parameters and click “Record data”. Record several rows with different parameters to plot their relationship and fit a straight line; pause and record at different times to study how a reading changes with time.