Light Flashes

Suppose that a spaceship travels at constant velocity between two planets, A and B. The spaceship sends out a light flash in all directions every 10 minutes by its own clock reading. Traveling toward B, its light flashes are seen at 5-minute intervals on planet B. What is the flash interval time as seen on planet A? One of these possibilities is correct: 5-minute intervals; 10-minute intervals; 15-minute intervals; 20-minute intervals.

Answer

The observer on planet A sees the flashes 20 minutes apart. From the STR postulate, we know that no observations of the light flashes only can discern which inertial frame is at rest. If the flashes sent out by the spaceship at 10-minute intervals are seen at planet B separated by 5 minutes, then flashes sent out from B at 10-minute intervals will be seen on the spaceship at 5-minute intervals.

One also realizes that if there were a light flash every 5 minutes from planet A, the observer on planet B would see them at 5-minute intervals. What is the interval for these flashes from A as seen by the spaceship observer? The answer is every 10 minutes, by invoking the STR postulate above. So the spaceship sees planet A’s flashes to be spaced twice as much apart as the interval at the source on A; likewise, the 10-minute flash intervals from the spaceship must be twice the interval at planet A, or 20 minutes apart.