Velocity Transform

1
Velocity Transform
Differential position
Divide all elements by dt
2
Velocity Transform (continued)
Velocity is NOT a four-vector
3
Adding Velocities
Tom
Dick
v0bc.9c
L
Harry
v0bc.9c
Toms velocity to Harry
Dicks velocity to Tom
Dicks velocity to Harry
4
Pion Decay
Pion decays to two photons in its rest frame
g
p
g
Photons move at vc.
In frame where pion is moving with v.99c, what
are photons velocities?
Something moving at the speed of light, moves at
the speed of light in all frames.
5
Stellar Aberrations
In stationary system
In moving system
q
v
6
Stellar Aberrations (continued)
In stationary system
In moving system
q
v0
7
Proper Velocities
Try to make velocity a four-vector
Position in rest frame
Velocity in rest frame
Transform this into moving frame
Proper velocity is a four-vector
8
Proper Velocity (continued)

• Square of velocity is the same in all reference
  frames.
• For any frame except the rest frame, proper time
  is a computed quantity.
• Proper times are different for particles with
  different velocities.

Conclusion Proper velocity is not very
useful! (But we will use it anyway when we talk
about Lagrangians.)