Question

A space ship leaves the Earth and travels to Alpha Centauri at a speed close to the speed of light. Passengers on the ship, and scientists on Earth, measure the distance from the Earth to Alpha Centauri. Assuming that Alpha Centauri is not moving with respect to Earth during the trip, which observers measure the distance traveled as the proper length, and which observers measure the travel time as the proper time? Explain.

(A) Both the passengers and the scientists measure both proper length and time.
(B) The passengers measure both proper length and proper time.
(C) The passengers measure proper length and the scientists measure proper time.
(D) The scientists measure proper length and the passengers measure proper time.
(E) The scientists measure both proper length and proper time.
(F) The passengers measure proper time and neither set measures proper length.
(G) The scientists measure proper length and neither set measures proper time.
(H) The scientists measure proper time and neither set measures proper length.
(I) The passengers measure proper length and neither set measures proper time.
(J) None of the distances or times measured is proper.

Answer 1

Earth-bound scientists measure the proper length as they are at rest relative to the distance to Alpha Centauri, while the passengers on the ship experience length contraction and thus measure proper time, with (D) being the correct option.

Step-by-step explanation:

When a spaceship travels from Earth to Alpha Centauri at a speed close to the speed of light, the concept of proper length and proper time becomes critical. Proper length is the length measured by an observer who is at rest relative to the object being measured, and proper time is the duration measured by an observer who is at rest relative to the event being timed.

In our scenario, Earth-bound scientists are at rest relative to the distance from Earth to Alpha Centauri, and hence, they measure the proper length. Passengers on the ship are moving at a speed close to the speed of light, which results in length contraction; therefore, they do not measure the proper length. Rather, because the passengers are moving with the spaceship, their elapsed time or duration of the journey is the proper time. For scientists on Earth, the time will appear dilated due to the effects of special relativity.

The correct option for this question is (D) The scientists measure proper length and the passengers measure proper time.