Special Relativity in 14 Easy (Hyper)steps

8. Constant speed of light  nonsimultaneity of events

The Sulaco is built on a General Products #2 hull, with a pair of periscopes located 150 feet fore and aft of its radio antenna (as measured in its rest frame).  The Nostromo, built on a General Products #3 hull, also has periscopes 150 feet fore and aft (in its rest frame) of its antenna.

The flash of light from the collision which destroyed the ships' antennas a few pages back is seen by observers stationed at a pair of periscopes on each ship.

In a ship's rest frame, light from the flash must travel 150 feet to reach the periscopes, so both periscopes on a ship record the flash 150 nsec after the antenna is destroyed.

Nostromo rest frame

The Nostromo observes the Sulaco traveling with speed 0.6c to the right, as shown in the following animated GIF.  Note the Lorentz-contracted length of Sulaco.  (Sulaco's clocks also tick slowly.)

Observers at Nostromo's fore and aft periscopes see the flash simultaneously. Let's assume the antenna was destroyed at ship's time 0, and that Nostromo's crew members stop their clocks when they see the flashes at ship's time 150 nsec.

Observers on Nostromo see the light from the flash arriving at Sulaco's aft periscope at Nostromo ship's time 75 nsec. They see light arriving at Sulaco's forward periscope later-- at Nostromo ship's time 300 nsec.

According to Nostromo: Nostromo's periscopes are illuminated simultaneously, Sulaco's are not.

Sulaco rest frame

The Sulaco observes the Nostromo traveling with speed 0.6c to the left, as shown in the following animated GIF.  Note the Lorentz-contracted length of Nostromo.  (Nostromo's clocks also tick slowly.)

Observers at Sulaco's fore and aft periscopes see the flash simultaneously. Let's assume the antenna was destroyed at ship's time 0, and that Sulaco's crew members stop their clocks when they see the flashes at ship's time 150 nsec.

Observers on Sulaco see the light from the flash arriving at Nostromo's aft periscope at Sulaco ship's time 75 nsec. They see light arriving at Nostromo's forward periscope later-- at Sulaco ship's time 300 nsec.

According to Sulaco: Sulaco's periscopes are illuminated simultaneously, Nostromo's are not.

The crews on Sulaco and Nostromo disagree about the simultaneity of the arrival of light flashes at the various ships' periscopes.