The Relativity of Time — Question 5

Question 5

A round trip compares elapsed times at shared endpoints

A traveler goes from Earth to a stationary beacon 4.0 light-years away and returns, moving at $0.80c$ on both legs. Acceleration intervals are idealized as negligible. Earth and the beacon share an inertial frame.

1. Find the Earth-frame duration and traveler proper duration.

2. Find their age difference at reunion and identify why one global reciprocal inertial-frame comparison is unavailable.

Question 5 - Solution

A round trip compares elapsed times at shared endpoints

(a) Method and calculation

$$T=2D/v=2(4.0)/0.80=\boxed{10.0\,\mathrm{yr}}.$$$$\gamma=5/3,\qquad\tau=T/\gamma=\boxed{6.0\,\mathrm{yr}}.$$

(b) Interpretation and further calculation

$$\boxed{T-\tau=4.0\,\mathrm{yr}}.$$$$v_{\mathrm{traveler}}:\quad+0.80c\ \longrightarrow\ -0.80c.$$

Physical check

The traveling worldline changes inertial frames at turnaround. Both ages are read locally at the same reunion event.