The Cosmic Speed Limit Suppose you launch a pod at ½ c from a rocket traveling at ½ c relative to the Earth. How fast will it go?

The pod travels at ½ c relative to the rocket. Which line is the pod’s? A B C D t t’ x’ x

The pod must cover one unit of space in two units of time. B C D t t’ x’ x

How fast is it moving relative to the Earth? x’ x

How fast is it moving relative to the Earth? It travels at 4/5 c t t’ x’ x

The relativistic equation for velocity addition is v = (v’ + vrel)/(1 + v’ vrel) How fast is the pod moving relative to the Earth according to the equation? v = (½ + ½)/(1 + ½ *½) = 4/5

The relativistic equation for velocity addition is v = (v’ + vrel)/(1 + v’ vrel) How fast is the light of the rocket’s headlights moving relative to the Earth according to the equation? v = (1+ ½)/(1 + 1 *½) = 1

Reality Check #1: The cyclotron at Triumf can form pions moving at 0 Reality Check #1: The cyclotron at Triumf can form pions moving at 0.96 c which decay by emitting muons and neutrinos.

Many of these emitted particles go faster than 0 Many of these emitted particles go faster than 0.96 c, but none go faster than light.

Reality Check #2: At CERN, neutral pions were accelerated to 0.99975 c. When these pions decayed, they emited light.

All the light emitted by the pions traveled at c.