Question

A person is watching a rocket with an astronaut inside move by at a speed near the speed of light.
Which of the following statement is true?

• A. The passage of time on the astronaut's watch is faster from the person's perspective than from the astronaut's
• B. The passage of time on the astronaut's watch is the same from the perspective of the person and the astronaut
• C. The passage of time on the astronaut's watch is faster from the perspective of the astronaut than from the perspective of the person
• D. The passage of time on the person's watch is faster, from his own perspective, as the rocket files by, than it was before the rocket flew by
• E. The passage of time on the astronaut's watch is faster, from his own perspective, as he flies by the person, than it was before he flew by the person

Answer 1

The correct option is A The passage of time on the astronaut's watch is faster from the person's perspective than from the astronaut's

Passage of time as measured by the person in rest frame $t=\frac{\tau }{\sqrt{1-v^2/c^2}}$ $⟹t>\tau$

where $\tau$ is the passage of time as measured by the astronaut in moving frame.

$⟹$ Watch in a moving frame runs at a slower rate than that in rest frame.

Thus passage of time on the astronaut's watch is faster from the person's perspective than from the astronaut's perspective.