Special Relativity: Time Dilation & Length Contraction Lab
Push a spaceship toward the speed of light and watch its onboard clock run slow and its length shrink, exactly as γ predicts.
Slide the spaceship's speed toward the speed of light and watch its onboard clock run slow and its length shrink, both exactly as predicted by special relativity.
About the Special Relativity: Time Dilation & Length Contraction Lab
Free special relativity: time dilation & length contraction lab. Push a spaceship toward the speed of light and watch its onboard clock run slow and its length shrink, exactly as γ predicts. Drag, change the sliders and see the result live. No sign-up, works on phone and computer. Built for physics, the special relativity: time dilation & length contraction lab runs instantly in your browser: change a setting or drag an object and the result updates at once, so you learn by trying things out rather than only reading about them.
Push a spaceship toward the speed of light and watch its onboard clock run slow and its length shrink, exactly as γ predicts. Use it to explore physics ideas at your own pace, then check what you found against the key ideas further down this page.
How to use the Special Relativity: Time Dilation & Length Contraction Lab
- Use the controls to change Ship speed, Proper time interval Δt₀ (measured on the ship), Proper length L₀ (measured on the ship). The simulation reacts instantly.
- Press "Fire light-clock tick", "Reset to defaults", "Lab Report" to start, reset or change what is happening.
- Where you see a glowing handle, object, weight or atom, drag it with your mouse or finger. Everything responds in real time.
- Watch the readouts and graphs update as you experiment, and compare what you see with the key ideas below.
Things to try
- Push the speed slider past 0.9c and watch the ship clock nearly freeze compared to the ground clock.
- Set the speed to 0.6c and check γ against the formula by hand.
- Try the muon-decay-distance challenge.
- Find the exact speed that contracts a meter stick to 60 cm.
Key ideas you can learn
- Time dilation: a clock moving relative to an observer ticks slower by the Lorentz factor γ = 1/√(1-v²/c²).
- Length contraction: an object moving relative to an observer is measured shorter along its direction of motion by the same factor γ.
- These effects are symmetric - each observer sees the other's clock run slow and rod shrink - and only become noticeable at a sizeable fraction of the speed of light.
- Real-world proof: fast-moving muons created high in the atmosphere reach the ground far more often than their short rest-frame lifetime would allow, because time dilation stretches their lifetime in our frame.
Show my work
Challenges
Challenge 1 - muon decay distance
A muon is created with a proper (rest-frame) lifetime of 2.2 µs and travels at the speed set by the slider above. In the lab frame, how far (in meters) does it travel, on average, before decaying? Use d = v × γ × Δt₀ with Δt₀ = 2.2 × 10⁻⁶ s and c = 3.00 × 10⁸ m/s.
Challenge 2 - contract a meter stick to 60 cm
Set the speed slider so that a 1.000 m proper-length rod appears contracted to exactly 0.60 m to the ground observer. Use L = L₀/γ, so v/c = √(1 − (L/L₀)²). Enter the speed (as a fraction of c) you found.
Where this is used in the real world
GPS satellites must correct for real time dilation from their orbital speed, and particle accelerators routinely see unstable particles 'live longer' exactly as relativity predicts.
Who is this simulation for?
Physics students in middle school, high school and first-year university, teachers who want a quick demonstration for the projector, and anyone revising for exams. It works well for flipped classrooms because students can explore before the lesson.
For teachers: project it on the board, let students predict what will happen, then run it together. For students: change one thing at a time and write down what changes.
Frequently asked questions
Why don't we notice time dilation in everyday life?
Because γ is extremely close to 1 unless v is a large fraction of the speed of light - at highway speeds the effect is many orders of magnitude too small to detect.
Is length contraction just an optical illusion?
No - it is a real effect of how space and time mix between reference frames, confirmed by particle-accelerator experiments, even though nothing physically 'squeezes' the object in its own rest frame.
Is the Special Relativity: Time Dilation & Length Contraction Lab free to use?
Yes. It is completely free, with no signup, no download and no ads inside the simulation. It runs in your web browser.
Does the Special Relativity: Time Dilation & Length Contraction Lab work on a phone or tablet?
Yes. It uses touch as well as the mouse, so you can drag objects with your finger. A larger screen makes the controls easier to see.