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Bob and Alice are both 21. I'm imagining a scenario where Alice starts on a journey at 0.8c towards a distant planet.

Bob (stays still) says this planet is 16 light years away and that it takes Alice 16/0.8 = 20 years to get there (so Bob is 41 years old when Alice gets there). So Bob says journey time t = 20 years

Alice, travelling at 0.8c. So according to her time, t0 = t x √(1-0.8^2) = 12 years

(So Bob's registered time is dilated compared to hers).

Now (I think this is right!!), as Alice is travelling at 0.8c clearly can't travel 16 light years in 12 years (from her clock) so that she thinks she has only travelled L0 = L x √(1-0.8^2 = 9.6 light years, so she says "of course it only took me 12 years because I only had to travel 9.6 light years."

I drew this out on paper below and it feels right to me ..(please assist if I'm already confused)

This would be confirmed (would it not) if Alice fired a laser pulse at time zero that she records takes 9.6 years to traverse the 9.6 light years (from her perspective) but Bob who also sees the laser pulse records that it takes 16 years to traverse the 16 light years distance?

All OK with my thinking?

Kind regards,

Glenn.

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# B Time dilation and length contraction question

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