Faster than light
- Round
- Theory
- Points
- 10
- Level
- Bronze
- Taught in
- Section 13.6
Adapted from IOAA 2018 (Beijing), theory problem 1. We have restated it in our own words and kept the original data. The solution was last checked on 21 October 2026.
Say whether each statement is true or false.
(a) For some galaxies the apparent recession speed is greater than the speed of light. [2 points]
(b) The relation between speed and distance given by Hubble does not allow recession speeds greater than the speed of light. [2 points]
(c) The Hubble–Lemaître law does not break special relativity. [2 points]
(d) If some galaxies had apparent recession speeds greater than the speed of light, their photons could never reach us. [2 points]
(e) Because the expansion is speeding up, photons sent out now by galaxies whose apparent recession speed equals the speed of light will never reach us. [2 points]
- (a) is true. Galaxies beyond the Hubble distance,
- (b) is false.
- (c) is true. Special relativity limits motion through space, and the recession is the growth of space.
- (d) is false. Light from galaxies that now recede faster than light reaches us, since we see galaxies at redshifts above 1.5.
- (e) is false. Light sent out now can still reach us from somewhat beyond the Hubble distance, out to a limit called the event horizon, about 4900 Mpc away in our model against 4283 Mpc for the Hubble distance.
AnswerTrue, false, true, false, false.
This problem also appears among the olympiad problems of Section 13.6, Distances in an expanding universe, which teaches the ideas it uses. Equation and figure numbers refer to the course.