Relativistic Addition of Velocities
Relativistic Addition of Velocities
This Demonstration considers the composition of velocities in accordance with the special theory of relativity. Consider a system moving with velocity represented by the red arrow, with magnitude and direction , with respect to a stationary frame of reference. The red disk recapitulates this magnitude, which has an upper limit extending to the red circle, corresponding to the speed of light . The blue arrow represents a second velocity, which has a magnitude and direction , with respect to the moving frame of reference. The velocity with respect to the original stationary frame is then represented by . A compact formulation gives the components of parallel and perpendicular to : =and=The gray arrow represents the vector .
u
α
c
v
β
w=u⊕v
w
u
w
u+
v
1+u·v/
2
c
w
⊥
v
⊥
1+u·v/
2
c
1-
.2
u
2
c
w