Transformation of velocities Section 5 Transformation of velocities

How does x-component of velocity of material particle transform when changing to a new inertial reference system? V vx’ vx K’ K In the limit c ®¥, we must get the classical result: vx = vx’ + V

V and vx enter symmetrically since vx || V In the limit c ®¥, we do get the classical result: vx = vx’ + V

Do vy and vz also change? Yes No Sometimes 1 2 3

vy and vz do also change! V vy’ vy K’ K

The change in vy and vz does not happen classically v’ and V enter unsymmetrically when they are not parallel. This is due to the non-commutativity of the Lorentz transform. In the limit c ®¥, we get the classical result:

Special case Then Usual undergraduate formula V and v’ enter symmetrically in this case

Here are some homework problems The sum of two velocities never exceeds c Approximate velocity transformation formulas for V<<c.

Does the apparent direction of motion for material particles depend on the reference frame? Classically? Relativistic particles? V K q q’ K’

Transformation of the direction of motion (homework) V K q q’ K’

Light has the same speed in all frames of reference. Does it have the same direction?

Aberration of light Light always travels at speed c in every inertial reference system, but not in the same direction. In equation for material particles, put

Approximate aberration formula for V << c. (HW) q < q’ if q’ is positive Aberration angle