- #1
alksjadf
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Homework Statement
How fast must a meter stick be moving if its length is observed to shrink to 0.5 m?
The Attempt at a Solution
A meter stick moving at speed V to a stationary observer is the same thing as a stationary meter stick and an observer moving at speed V.
Lproper = Lp = 1 meter
Lobserved = L' = .5 meter
y = 1/sqrt(1- v^2/c^2)
Time it takes for observer to cover the distance of 1 meter, /\t:
/\t = Lp/V
Length moving observer sees, L':
L' = V*/\t'
where /\t' is the time it takes for the meter stick to fly by in observer's reference frame
Choosing Proper Time:
If I choose proper time to be /\t then:
/\t*y = /\t'
Through substitution this leads to:
L' = Lp*y (WRONG)
If i choose proper time to be /\t' then:
/\t = /\t'*y
Through substitution this leads to:
L' = Lp/y (RIGHT)
Why can't I choose the wrong one? What makes the other one right?