“You get back to your numbers, O’Toole; you have no soul These laddies want to measure how fast you do it. They don’t care how fast-they’ve already recovered from the blow that you do it faster than light-but they want to know exactly how fast. They can’t accept the idea that you do it ‘instantaneously,’ for that would require them to go to a different church entirely. They want to assign a definite speed of propagation, such-and-such number of times faster than the speed of light. Then they can modify their old equations and go right on happily doing business at the old stand.”
“They will,” agreed O’Toole.
“Then there is a third school of thought, the right one…my own.”
O’Toole, without looking up, made a rude noise.
“Is that your asthma coming back?” Babcock said anxiously. “By the way, you got any results?”
“They’re still doing it in nothing flat. Measured time negative as often as positive and never greater than inherent observational error.”
“You see, son? That’s the correct school. Measure what happens and let the chips fly where they may.”
“Hear hear!”
“Quiet, you renegade Irishman. Besides that, you m-r’s give us our first real chance to check another matter. Are you familiar with the relativity transformations?”
“You mean the Einstein equations?
“Surely. You know the one for time?”
I thought hard Pat and I had taken first-year physics our freshman year; it had been quite a while. I picked up a piece of paper and wrote down what I thought it was:
“That’s it,” agreed Dr. Babcock. “At a relative velocity of ‘v’ time interval at first frame of reference equals time interval at second frame of reference multiplied by the square root of one minus the square of the relative velocity divided by the square of the speed of light. That’s just the special case, of course, for constant speeds; it is more complicated for acceleration. But there has been much disagreement as to what the time equations meant, or if they meant anything.”
I blurted out, “Huh? But I thought the Einstein theory had been proved?” It suddenly occurred to me that, if the relativity equations were wrong, we were going to be away a mighty long time-Tau Ceti, our first stop, was eleven light-years from the Sun… and that was just our first one; the others were a lot farther.
But everybody said that once we got up near the speed of light the months would breeze past like days. The equations said so.
“Attend me. How do you prove that there are eggs in a bird’s nest? Don’t strain your gray matter: go climb the tree and find out. There is no other way. Now we are climbing the tree.”
“Fine!” said O’Toole. “Go climb a tree.”
“Noisy in here. One school of thought maintained that the equations simply meant that a clock would read differently if you could read it from a passing star … which you can’t… but that there was no real stretching or shrinking of time-whatever ‘real’ means. Another school pointed to the companion equations for length and mass, maintaining that the famous Michelson-Morley experiment showed that the length transformation was ‘real’ and pointing out that the increase of mass was regularly computed and used for particle-accelerator ballistics and elsewhere in nuclear physics-for example, in the torch that pushes this ship. So, they reasoned, the change in time rates must be real, because the corollary equations worked in practice. But nobody knew. You have to climb the tree and look.”
“When will we know?” I was still worrying. Staying several years, Einstein time, in the ship I had counted on. Getting killed in the course of it, the way Uncle Steve said we probably would, I refused to worry about. But dying of old age in the Elsie was not what I had counted on. It was a grim thought, a life sentence shut up inside these steel walls.
“When? Why, we know right now.”
“You do? What’s the answer?”
“Don’t hurry me, son. We’ve been gone a couple of weeks, at a boost of 124% of one gee; we’re up to about 9,000 miles per second now. We still haven’t come far-call it seven and a half light-hours or about 5,450,000,000 miles. It will be the better part of a year before we are crowding the speed of light. Nevertheless we have reached a sizable percentage of that speed, about five per cent; that’s enough to show. Easy to measure, with the aid of you mind readers.”