Relativity · 2 min read · HSC Physics

Proper time t₀ is on the clock that's at both events.

One question that sorts out every time dilation and length contraction problem.

1. Step 1 · Events

   Name the two eventsEvery time interval runs between two events. Say what they are first: a muon is made, the muon reaches the ground.

2. Step 2 · Whose clock?

   Whose clock is at both events?The observer present at both events measures proper time, t₀. Here that’s the muon. Every other observer measures a longer time.

3. Step 3 · Light clock

   Moving clocks run slowIn a moving light clock the light travels a longer, diagonal path at the same speed c, so each tick takes longer. t is always bigger than t₀.

4. Step 4 · Two frames

   Same muon, two storiesEarth’s frame: the muon’s clock runs slow. Muon’s frame: the atmosphere is contracted. Name the frame you’re explaining from.

5. Step 5 · The limit

   Nothing with mass reaches cMomentum and energy grow without limit as v → c, so reaching c would take infinite energy.

Quick checklist

• Name the two events
• At both events → t₀
• Moving clocks run slow
• Name your frame
• Mass never reaches c

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