Recent content by spaceofwaste

The usual representation I see of an element of SO(2) is: \left( \begin{array}{ c c } cos(\theta) & sin(\theta) \\ -sin(\theta) & cos(\theta) \end{array} \right) and it is easy to show that if you make a passive rotation of a cartesian frame by \theta then this matrix will take the...

I come out with this monster finally anyway: \theta_r-\theta_i=-2tan(\gamma)+arctan(\frac{u_(y')(i)+vu_(x')(i)u_(y')(i)}{\gamma(u_(x')(i)+v+v[u_(x')(i)]^2+v^2u_(x')(i)})+arctan(\frac{u_(x')(i)+vu_(x')(i)u_(y')(i)}{\gamma(u_(y')(i)+v+v[u_(y')(i)]^2+v^2u_(y')(i)}) where the u_(y')(i) etc...

Hi, I'm working through an exercise in Sean Carrol's spacetime and geometry book. The question asks you to consider an inertial frame S with coordinates x^\mu=(t,x,y,z) and a frame S' with primed coordinates. Which is related to S by a boost v in the y direction. Imagine a wall( or mirror)...