transmitted at a frequency of Hz, by her clock, and received by Bob at a frequency of Hz, by his clock. This implies a Doppler factor of . So Bondi's k-factor is another name for the Doppler factor (when source Alice and observer Bob are moving directly away from or towards each other). If Alice and Bob were to swap roles, and Bob sent flashes of light to Alice, the Principle of Relativity (Einstein's first postulate) implies that the k-factor from Bob to Alice would be the same value as the k-factor from Alice to Bob, as all inertial observers are equivalent. So the k-factor depends only on the relative speed between the observers and nothing else. The reciprocal k-factor Consider, now, a third inertial observer Dave who is a fixed distance from Alice, and such that Bob lies on the straight line between Alice and Dave. As Alice and Dave are mutually at rest, the delay from Alice to Dave is constant. This means that Dave receives Alice's blue flashes at a rate of once every seconds, by his clock, the same rate as Alice sends them. In other words, the k-factor from Alice to Dave is equal to one. Now suppose that whenever Bob receives a blue flash from Alice he immediately sends his own red flash towards Dave, once every seconds (by Bob's clock). Einstein's second postulate, that the speed of light is independent of the motion of its source, implies that Alice's blue flash and Bob's red flash both travel at the same speed, neither overtaking the other, and therefore arrive at Dave at the same time. So Dave receives a red flash from Bob every seconds, by Dave's clock, which were sent by Bob every seconds by Bob's clock. This implies that the k-factor from Bob to Dave is . This establishes that the k-factor for observers moving directly apart (red shift) is the reciprocal of the k-factor for observers moving directly towards each other at the same speed (blue shift). The twins paradox Consider, now, a fourth inertial observer Carol who travels from Dave to Alice at exactly the same speed as Bob travels from Alice to Dave. Carol's journey is timed such that she leaves Dave at exactly the same time as Bob arrives. Denote times recorded by Alice's, Bob's and Carol's clocks by . When Bob passes Alice, they both synchronise their