- #1
James Chase Geary
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Homework Statement
S and S' are in standard configuration with v=αc (0<α<1). If a rod at rest in S' makes an angle of 45o with Ox in S and 30o with O'x in S', then find α.
Homework Equations
We are in the world of Lorentz transformations so we have
t'=(t-vx/c2)/(1-v2/c2)1/2
x'=(x-vt)/(1-v2/c2)1/2
Angles are involved. For a rotation of frames through angle θ we have
x'=xcosθ + Tsinθ
T'=-xsinθ+Tcosθ
where T=ict and T'=ict'
The Attempt at a Solution
I am unclear how to apply the angles here. It is definitely not 45-30=15 is the angle to be used as the rotation angle. Going that route I always seem to get something like α=.268i.
Working through the formulas, I get to
α=√(1-(1/cos2θ))
θ=15 gives the answer above; the back of the book gives √(2/3) as the answer. Either I'm getting a wrong relation for α or else the angle I'm using is wrong.
Note this is from D'Inverno, Introducing Einstein's Relativity, Exercise 3.1