Learning journey · stage 1

What does “at the same time” really mean?

Three stations on special relativity. At each one you commit to an answer first, then check it yourself in the experiment. Committing first makes the answer stick – especially when your guess was wrong.

Station 1 of 3

Two lightning strikes and a train

One of Einstein’s most famous thought experiments, from his 1917 book: a train runs along an embankment, and lightning strikes at its front and back.

Train and lightning

Train speed: 50 % c

Time: 0 ns

–

Gap between the two strikes, measured in this frame

–

What M′ in the middle of the train sees first (time in this frame)

Distance A–B on the embankment: 300 m. Time zero: the moment M′ passes M.

Station 2 of 3

The twin journey

If “now” is not the same for everyone, then time does not pass equally fast for everyone either.

Your own twin journey

Your age today (years)

Destination

Cruising speed: 99 % c

–

– yr

pass on board

– yr

pass on Earth

–

Lorentz factor γ

Simplified: constant speed out and back, with an instant turnaround; speeding up and braking are left out.

Station 3 of 3

GPS: relativity in everyday life

Sounds like science fiction? Your phone relies on it every day.

GPS without the relativity correction

Days without correction: 1

Speed (special relativity): −7.2 µs per day Weaker gravity (general relativity): +45.8 µs per day

– µs

Satellite clocks ahead (+) or behind (−) ground clocks

– km

Light travel distance c · Δt – the error in every range measurement to a satellite

The map is a sketch: grid and rings show the scale only.

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