A laser beam moving at velocity c relative to us is turned on just as three (hypothetical) observers pass by us in the same direction as the beam. Observer 1 has velocity c/2, observer 2 has velocity 0.999c, and observer 3 has velocity c. If metersticks had different lengths in different frames, or clocks ticked at different rates in different frames, it is not impossible that the first and second observers could measure the beam to be moving at speed c relative to them, but the third observer could not find that the beam is moving at speed c relative to her. Prove this quantitavely.

A laser beam moving at velocity c relative to us is turned on just as three (hypothetical) observers pass by us in the same direction as the beam. Observer 1 has velocity c/2, observer 2 has velocity 0.999c, and observer 3 has velocity c. If metersticks had different lengths in different frames, or clocks ticked at different rates in different frames, it is not impossible that the first and second observers could measure the beam to be moving at speed c relative to them, but the third observer could not find that the beam is moving at speed c relative to her. Prove this quantitavely.