Page:Eddington A. Space Time and Gravitation. 1920.djvu/41

I] 224 minutes after lighting the cigar. His watch like everything else about him (including his cigar) is going at half-speed; so it records only 112 minutes elapsed when our signal arrives. The aviator knows, of course, that this is not the true time when our cigar was finished, and that he must correct for the time of transmission of the light-signal. He sets himself this problem—that man has travelled away from me at 161,000 miles a second for an unknown time $$x$$ minutes; he has then sent a signal which travels the same distance back at 186,000 miles a second; the total time is 112 minutes; problem, find $$x$$. Answer, $$x = 60$$ minutes. He therefore judges that our cigar lasted 60 minutes, or twice as long as his own. His cigar lasted 30 minutes by his watch (because the same retardation affects both watch and cigar); and that was in our opinion twice as long as ours, because his watch was going at half-speed.

Here is the full time-table.

This is analysed from our point of view, not the aviator's; because it makes out that he was wrong in his inference and we were right. But no one can tell which was really right.

The argument will repay a careful examination, and it will be recognised that the chief cause of the paradox is that we assume that we are at rest in the aether, whereas the aviator assumes that he is at rest. Consequently whereas in our opinion the light-signal is overtaking him at merely the difference between 186,000 and 161,000 miles a second, he considers that it is coming to him through the relatively stationary aether at the normal speed of light. It must be remembered that each observer is furnished with complete experimental evidence in support of his own assumption. If we suggest to the aviator