The length contraction means that an object is the longest in the frame in which

Question

The length contraction means that an object is the longest in the frame in which it is at rest.

Lets assume i have a meter stick with length ?x in my rest frame which is x,ct and i want to know how long my meter stick seems to an observer moving with a frame x?,ct?.

1st: I draw world lines of a meter stick in a rest frame and they are vertical (parallel to ct axis) as meter stick is stationary in this frame.

2nd: If an observer in a moving frame x?,ct? wants to measure my meter stick he measures its edges at the same moment in his time, so i draw a tilted line (parallel to x? axis).

3rd: If i mesure the length ?x? which is a length of a meter stick as observer in frame x?,ct? sees it, it seems to me that he sees a longer distance than me.

This is not correct. Could anyone tell me what am i missing here?

Explanation / Answer

What you've missed is that the distance along the x? axis is not the same as the distance along the x axis. The locus of events that are 1 unit of proper distance from the origin is a hyperbola. This can be used to calibrate the x? axis. See calibration hyperbola.

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