Question

Consider a rocket traveling with along the x-axis with constant velocity 0.8c. At some time t′0=0s ,the rockets starts a clock and emits a photon. At t′1=0.6s he stops the clock. What is the separation between the rocket and the photon for the rockets reference frames, and for a reference frame at rest?

Answer 1

In the rocket's reference frame, the separation between the rocket and the photon remains zero after emission. From a rest frame's perspective, the separation is calculated using their respective speeds and the time elapsed, which would be the difference in distances covered by the photon and the rocket in 0.6s.

Step-by-step explanation:

The student's question deals with concepts from special relativity, focusing on the relative motion of photons and a rocket. When a rocket travels with a constant velocity of 0.8c along the x-axis and emits a photon, we can discuss the separation in different reference frames. In the rocket's reference frame, since it emits the photon, they remain at the same position; hence, the separation remains zero.

However, from the reference frame at rest, the photon moves at speed c (the speed of light), and the rocket moves at 0.8c. If the rocket clocks 0.6s of time, then in the rest frame, the photon will have traveled c × 0.6s distance, while the rocket travels 0.8c × 0.6s. The separation is the difference between these distances, which is (c-0.8c) × 0.6s.