that owing to his high velocity the relative speed of the wave overtaking him can only be 25,000 miles a second, he will reply "I have determined the velocity of the wave relatively to me by timing it as it passes two points in my conveyance; and it turns out to be 186,000 miles a second. So I know my correction for light-time is right."[1] His clocks and scales are all behaving in an extraordinary way from our point of view, so it is not surprising that he should arrive at a measure of the velocity of the overtaking wave which differs from ours; but there is no way of convincing him that our reckoning is preferable.
Although not a very practical problem, it is of interest to inquire what happens when the aviator's speed is still further increased and approximates to the velocity of light. Lengths in the direction of flight become smaller and smaller, until for the speed of light they shrink to zero. The aviator and the objects accompanying him shrink to two dimensions. We are saved the difficulty of imagining how the processes of life can go on in two dimensions, because nothing goes on. Time is arrested altogether. This is the description according to the terrestrial observer. The aviator himself detects nothing unusual; he does not perceive that he has stopped moving. He is merely waiting for the next instant to come before making the next movement; and the mere fact that time is arrested means that he does not perceive that the next instant is a long time coming.
It is a favourite device for bringing home the vast distances of the stars to imagine a voyage through space with the velocity of light. The youthful adventurer steps on to his magic carpet loaded with provisions for a century. He reaches his journey's end, say Arcturus, a decrepit centenarian. This is wrong. It is quite true that the journey would last something like a hundred years by terrestrial chronology; but the adventurer would arrive at his destination no more aged than when he started, and he would not have had time to think of eating. So long as he travels with the speed of light he has immortality and eternal youth.
- ↑ We need not stop to prove this directly. If the aviator could detect anything in his measurements inconsistent with the hypothesis that he was at rest in the aether (e.g. a difference of velocity of overtaking waves of light and waves meeting him) it would contradict the restricted principle of relativity.
