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galm_2727
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- TL;DR Summary
- I was trying to come up with a thought experiment for showing the length contraction, but I'm not getting the correct expression and I can't see where is the mistake.
Alice travels in a spaceship, which she measures to be L. The spaceship is moving with velocity v relatively to Bob. Alice makes a light beam traveling along the spaceship and measures the time interval it takes to go from one end to another, ΔtA.
So, equation (1): L = c × ΔtA
From Bob's point of view, the light beam will take a time ΔtB and the length of the spaceship will be:
L' = c × ΔtB - v × ΔtB = (1 - β) × c ΔtB
But ΔtB = ϒ ΔtA. Therefore:
L' = (1 - β) ϒ c ΔtA
Using (1), we have:
L' = (1 - β)1/2 / (1 + β)1/2 L
Could you help me spot my mistake/wrong assumption?
So, equation (1): L = c × ΔtA
From Bob's point of view, the light beam will take a time ΔtB and the length of the spaceship will be:
L' = c × ΔtB - v × ΔtB = (1 - β) × c ΔtB
But ΔtB = ϒ ΔtA. Therefore:
L' = (1 - β) ϒ c ΔtA
Using (1), we have:
L' = (1 - β)1/2 / (1 + β)1/2 L
Could you help me spot my mistake/wrong assumption?