I am trying to retrieve the lenght-contration formula from the Lorentz transformations (and am failing miserably). I'd appreciate if someonew could tell me where I'm mistaken. Thanks.(adsbygoogle = window.adsbygoogle || []).push({});

Actually I just don't know how to represent a proper lenght in terms of events, but here's my latest "attempt"...

The Lorentz transformation tell us how space-time points transform from an inertial coordinate to another. So suppose for exemple, that S is the coordinate system at rest with respect to earth and some space station, and suppose S' is the system moving with speed +v (purely in the x direction) relative to S (a spaceship for instance). Suppose also that at t = 0, t' = 0 also and that at that time the origins O and O' coincide. Next, we need two events. Event 1, (say, a flash of light), will happen at t = t' = 0 and will happen at x = x' = 0. Event 2 happens simultaneously but at the space station, located, say, a distance x from the origin O. The LT tell us what is the space coordinate of that flash in the primes coordinate:

[tex]x' = \gamma(x -v0) = \gamma x[/tex]

So it's basically telling me that the distance Earth-Space Station is greater as seen from an observer in the spaceship. Evidently, this is not what I wanted to show. I would have liked to get the opposite, namely

[tex]x = \gamma x' [/tex]

How do we do this ?!?

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# How to retrieve the lenght-contraction from the LT?

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