Special relativity – time dilation, length contraction, muons and GPS
PhysicsKinematicsAges 17–18
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Sign in to playA light clock and a ruler on a rocket moving at speed v: change v to see the Lorentz factor γ = 1/√(1 − v²/c²), time dilation Δt = γΔt₀ and length contraction L = L₀/γ, viewed from the Earth frame or the rocket frame. The Muons screen releases muons at height h and compares how many reach the ground in the Earth frame, in the muon frame and without time dilation. The Spacetime screen draws a Minkowski diagram with two draggable events, the Lorentz transformation, the relativity of simultaneity and the invariant spacetime interval. The GPS screen works out how far a satellite clock drifts each day, and the twin paradox.
Lesson: Special relativity: Einstein's postulates, time dilation, length contraction, simultaneity and spacetime diagrams
What it shows
Einstein's special relativity rests on two postulates: the laws of physics are the same in every inertial frame, and light in a vacuum travels at the same speed c for every inertial observer. A photon bouncing in a moving light clock follows a longer zigzag path at the same speed, so the moving clock ticks more slowly: Δt = γΔt₀. Moving objects are also shorter along their motion, L = L₀/γ. Cosmic-ray muons reaching the ground, the drift of GPS satellite clocks and the relativity of simultaneity on a spacetime diagram all follow from these ideas.
How to use
On Light clock, drag Speed v or press a Presets button and switch Frame between Earth and Moving object; compare the tick counts and the rulers. On Muons, set Muon production height h and Muon speed v, then press Release muons. On Spacetime, drag events A and B or choose an Events button, and tick S′ grid. On GPS and twins, drag Orbit altitude and choose a star under Trip to.
Parameters you can change
- Screen Light clock and ruler, Muons in the atmosphere, Spacetime diagram, GPS and the twin paradox
- Speed v (as a fraction of c) 0–0.999 c
- Frame of reference shown Earth, Moving object (rocket, muon)
- Height at which muons are produced 1–20 km
- Muon speed (as a fraction of c) 0.9–0.9999 c
- Satellite orbit altitude 200–36000 km
Questions to explore
- In the Earth frame the rocket clock runs slow; why does an astronaut see the Earth clock running slow instead?
- Muons live only about 2.2 μs, so how do so many reach the ground from 10 km up, explained in both frames?
- Two lightning strikes hit the ends of a train at the same time for someone on the platform; which strike happens first for a passenger?
