Libby got that completely baffled look which mathematical-physicists wear whenever laymen try to talk about physics in nonmathematical language. “You’re referring to the Lorentz-2 FitzGerald contraction. But, if you’ll pardon me, anything one says about it in words is necessarily nonsense.”
“Why?” she insisted.
“Because . . . well, because the language is inappropriate. The formulae used to describe the effect loosely called a contraction presuppose that the observer is part of the phenomenon. But verbal language contains the implicit assumption that we can stand outside the whole business and watch what goes on. The mathematical language denies the very possibility of any such outside viewpoint. Every observer has his own world line; he can’t get outside it for a detached viewpoint.”
“But suppose he did? Suppose we could see Earth right now?”
‘~There I go again,” Libby said miserably. “I tried to talk about it in words and all I did was to add to the confusion. There is no way to measure time in any absolute sense when two events are separated in a continuum. All you can measure is interval.”
“Well, what is interval? So much space and so much time.”
“No, no, no! It isn’t that at all. Interval is . . . well, it’s interval. I can write down formulae about it and show you how we use it, but it can’t be defined in words. Look, Nancy, can you write the score for a full orchestration of a symphony in words?” –
“No. Well, maybe you could but it wonld take thousands of times as long.”
“And musicians still could not play it until you put it back into musical notation. That’s what I meant,” Libby went on, “when I said that the language was inappropriate. I got into a difficulty like this once before in trying to describe the lightpressure drive. I was asked why, since the drive depends on loss of inertia, we people inside the ship had felt no loss of inertia. There was no answer, in words. Inertia isn’t a word; it is a mathematical concept used in mathematically certain aspects of a plenum. I was stuck.”
Nancy looked baffled but persisted doggedly. “My question still means something, even if I didn’t phrase it right. You can’t just tell me to run along and play. Suppose we turned around and went back the way we came, all the way to Earth, exactly the same trip but in reverse-just double the ship’s time it has been so far. All right, what year would it be on Earth when we got there?’
“It would be . . . let me see, now-” The almost automatic processes of Libby’s brain started running off the unbelievably huge and complex problem in accelerations, intervals, difform motion. He was approaching the answer in a warm glow of mathematical revery when the problem suddenly fell to pieces on him, became indeterminate. He abruptly realized that the problem had an unlimited number of equally valid answers.
But that was impossible. In the real world, not the fantasy world of mathematics, such a situation was absurd. Nancy’s question had to have just one answer, unique and real.
Could the whole beautiful structure of relativity be an absurdity? Or did it mean that it was physically impossible ever to backtrack an interstellar distance?
“I’ll have to give some thought to that one,” Libby said hastily and left before Nancy could object.
But solitude and contemplation gave him no clue to the problem. It was not a failure of his mathematical ability; he was capable, he knew, of devising a mathematical description of any group of facts, whatever they might be. His difficulty lay in having too few facts. Until some observer traversed interstellar distances at speeds approximating the speed of light and returned to the planet from which he had started there could be no answer. Mathematics alone has no content, gives no answers.
Libby found himself wondering if the hills of his native Ozarks were still green, if the smell of wood smoke still clung to the trees in the autumn, then he recalled that the question lacked any meaning by any rules he knew of. He surrendered to an attack of homesickness such as he had not experienced since he was a youth in the Cosmic Construction Corps, making his first deep-space jump.