The star Delta goes supernova. One year later and 2.0 ly away, as measured by astronomers in the galaxy, star Epsilon explodes. Let the explosion of Delta be at x_D = 0 and t_D = 0. The explosions are observed by three spaceships cruising through the galaxy in the direction from Delta to Epsilon at velocities v₁ = 0.30c, v₂ = 0.50c, and v₃ = 0.70c. All three spaceships, each at the origin of its reference frame, happen to pass Delta as it explodes.
a. What are the times of the two explosions as measured by scientists on each of the three spaceships?
b. Does one spaceship find that the explosions are simultaneous? If so, which one?
c. Does one spaceship find that Epsilon explodes before Delta? If so, which one?
d. Do your answers to parts b and c violate the idea of causality? Explain.