Energy in different frames.

1. Apr 2, 2009

chewwy

something which seems so fundamental that i can't find anywhere that derives it is the following:

E' = gamma * (E - p.v)

where E is the energy in one frame, p the momentum, v the relative velocity of the other frame, and E' the energy in the other frame.

i.e. energy transforms like time. i can't quite see where this comes from though.. help?

2. Apr 2, 2009

Staff: Mentor

It comes from the fact that energy is the "zeroth" component of the momentum four-vector $(p_0, p_1, p_2, p_3) = (E/c, p_x, p_y, p_z)$, just like time is the "zeroth" component of the position four-vector $(x_0, x_1, x_2, x_3) = (ct, x, y, z)$.

3. Apr 2, 2009

tiny-tim

Welcome to PF!

Hi chewwy! Welcome to PF!

(have a gamma: γ )
Yes, it's because (E,p) is defined as the derivative of (t,x),

so E' = γE - γ(p.v),

just as t' = γt - γ(x.v)

4. Apr 2, 2009

chewwy

okie doke. thanks everyone!