# Special Relativity Diagram Problem

1. Feb 9, 2009

### Tedjn

1. The problem statement, all variables and given/known data

Frame S' has velocity v relative to frame S. At time t = 0, a light ray leaves the origin of S, traveling at a 45 degree angle with the x-axis.

(a) What angle does the light ray make with respect to the x' axis in frame S'?

(b) Repeat part (a), replacing the light ray with a particle of mass m and speed u.

(c) Repeat part (a), replacing the light ray with a rod that is stationary in frame S.

2. Relevant equations

Minkowski diagram

$$v'_x = \frac{v_x - v}{1-vv_x/c^2}$$
$$v'_y = \frac{v_y}{\gamma(1-vv_x/c^2)}$$
$$\theta = \tan^{-1}(v/c)$$

3. The attempt at a solution

(a) In frame S', the axes are both rotated inwards (if v is positive) by angle $\theta$. However, I am not sure if the angle wanted in part (a) is still 45 degrees in frame S' (even though it is clearly $45 - \theta$ looking from frame S).

(b) The particle has identical components of velocity $v_x = v_y$ so I should just be able to use the above equations to solve for $v'_x$ and $v'_y$. However, the same question from part (a) remains; is angle measured differently in the S' frame as opposed to the S frame? In other words, in the S' frame, is the angle between x' and ct' still considered 90 degrees?

(c) You can treat S' as the stationary frame and S as the moving frame, in which case the axes of S will rotate outwards assuming it is moving with negative velocity relative to S'. In that case, it is a simple matter of determining the angle from the above formula and calculating the apparent angle with the x' axis.

Thanks!