Simultaneity: Astronaut Spud Nick is space-traveling from planet X to planet Y at a speed of 0.60c relative to the planets, which are at rest relative to each other. When he is precisely halfway between the planets, a distance of 1.0 light-hour from each one as measured in the planet frame, nuclear devices are detonated on each planet. The explosions are simultaneous in the frame of the planets. What is the difference in the time of arrival of the flashes from the explosions as observed by Spud?
A) 300 min
B) 150 min
C) 75 min
D) 0 min
E) 113 min

Question

Quizplus · Accepted Answer

The difference in the time of arrival of the flashes from the explosions as observed by Spud Nick, who is moving at a significant fraction of the speed of light, can be calculated using the principles of special relativity, specifically the relativity of simultaneity. Since the explosions are simultaneous in the planet frame but Spud is moving relative to that frame, the events will not be simultaneous in Spud's frame. The calculation involves Lorentz transformation equations, which account for the effects of time dilation and length contraction. The exact number (113 minutes) comes from applying these principles to the given velocities and distances.

Simultaneity: Astronaut Spud Nick Is Space-Traveling from Planet X to Planet