- #1
kapitan90
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Homework Statement
I am trying to derive the time dilation formula using Pythagorean theorem:
L = ct (in clocks rest frame)
D = ct'(in observer's frame, the clock moving with velocity u)
The Attempt at a Solution
So [tex]D^2 = L^2 +v^2t^2[/tex]
[tex]c^2{t'}^2=c^2t^2+u^2t^2[/tex]
So[tex]t'=t*\sqrt{1+v^2/c^2}[/tex]
but it should be
[tex]t'=t/\sqrt{1-v^2/c^2}[/tex]
Homework Equations
This would work if D=ct, not ct' and L=ct', but I guess it isn't right with my choice of frames of reference?
Sources: http://www.drphysics.com/syllabus/time/time.html