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"To get anywhere, or even live a long time, a man has to guess, and guess right, over and over again, without enough data for a logical answer."
- Robert Heinlein

Inertialess Drive  
  Faster-than-light travel achieved!  

As far as I know, this is the first reference to the idea of faster-than-light travel in science fiction.

After weeks of ceaseless work, during which was lavished upon her every resource of mind and material afforded by three planets, the Boise was ready for her maiden flight. As nearly ready, that is, as the thought and labor of man could make her. Rodebush and Cleveland had finished their last rigid inspection of the craft and, standing beside the center door of the main airlock, were talking with their chief.

"You say that you think that it's safe, and yet you won't take a crew," Samms argued. "In that case it isn't safe enough for you men, either. We need you too badly to permit you to take such chances."

"You've got to let us go; because we are the only ones who are thoroughly familiar with her theory," Rodebush insisted. "I said, and still say, that I think it is safe. I can't prove it, however, except mathematically; because she's altogether too full of too many new and untried mechanisms, too many extrapolations beyond all existing or possible data. Theoretically, she is sound, but you know that theory can go only so far, and that mathematically negligible factors may become operative at those velocities. We do not need a crew for a short trip. We can take care of any minor mishaps, and if our fundamental theories are wrong, all the crews between here and Jupiter wouldn't do any good. Therefore we two are going--alone."

"Well, be very careful, anyway. Start out slow and take it easy."

"Start out slow? We can't! We can't neutralize half of gravity, nor half of the inertia of matter--it's got to be everything or nothing, as soon as the neutralizers go on. We could start out on the projectors, of course, instead of on the neutralizers, but that wouldn't prove anything and would only prolong the agony."

"Well, then, be as careful as you can."

"We'll do that, Chief," Cleveland put in. "We think a lot of us, and we aren't committing suicide just yet if we can help it. And remember about everybody staying inside when we take off--it's barely possible that we'll take up a lot of room. Good-bye to all of you."

"Good-bye, fellows!"

The massive insulating doors were shut, the metal side of the mountain opened, and huge, squat caterpillar tractors came roaring and clanking into the room. Chains and cables were made fast and, mighty steel rails groaning under the load, the space-ship upon her rolling ways was dragged out of the Hill and far out upon the level floor of the surface before the tractors cast off and returned to the fortress.

"Everybody is under cover." Samms informed Rodebush. The chief was staring intently into his plate, upon which was revealed the control room of the untried super-ship. He heard Rodebush speak to Cleveland; heard the observer's brief reply; saw the navigator throw his switches--then the communicator plate went blank. Not the ordinary blankness of a cut-off, but a peculiarly disquieting fading out into darkness. And where the great space-ship had rested there was for an instant nothing. Exactly nothing--a vacuum. Vessel, falsework, rollers, trucks, the enormous steel I-beams of the tracks, even the deep-set concrete piers and foundations and a vast hemisphere of the solid ground; all had disappeared utterly and instantaneously. But almost as suddenly as it had been formed the vacuum was filled by a cyclonic rush of air. There was a detonation as of a hundred vicious thunderclaps made one, and, through the howling, shrieking blasts of wind, there rained down upon the valley, plain and metaled mountain a veritable avalanche of debris: bent, twisted, and broken rails and beams, splintered timbers, masses of concrete, and thousands of cubic yards of soil and rock. For inertia and gravitation had not been neutralized at precisely the same instant, and for a moment everything within the radius of action of the iron-driven gravity nullifiers of the Boise had continued its absolute motion with inertia unimpaired. Then, left behind immediately by the almost infinite velocity of the cruiser, all this material had again become subject to all of Nature's everyday laws and had crashed back to the ground.

"Could you hold your beam, Randolph?" Samm's voice cut sharply through the daze of stupefaction which held spellbound most of the denizens of the Hill. But all were not so held--no conceivable emergency could take the attention of the chief ultra-wave operator from his instruments.

"No, sir," Radio Center shot back. "It faded out and I couldn't recover it. I put everything I've got behind a tracer on that beam, but haven't been able to lift a single needle off the pin."

"And no wreckage of the vessel itself," Samms went on, half audibly. "Either they have succeeded far beyond their wildest hopes or else ... more probably...." He fell silent and switched off the plate. Were his two friends, those intrepid scientists, alive and triumphant, or had they gone to lengthen the list of victims of that man-killing space-ship? Reason told him that they were gone. They must be gone, or else his ultra-beams--energies of such unthinkable velocity of propagation that man's most sensitive instruments had never been able even to estimate it--would have held the ship's transmitter in spite of any velocity attainable by any matter under any conceivable conditions. The ship must have been disintegrated as soon as Rodebush released his forces. And yet, had not the physicist dimly foreseen the possibility of such an actual velocity--or had he?

From Triplanetary, by E.E. 'Doc' Smith.
Published by Not known in 1934
Additional resources -

In this quote, it's clear that they've traveled the distance:

"We're not falling anywhere." Rodebush, foreboding in his eyes, walked over to the main observation plate and scanned the heavens. "However, it's not as bad as I was afraid it might be. I can still recognize a few of the constellations, even though they are all pretty badly distorted. That means that we can't be more than a couple of light-years or so away from the Solar System. Of course, since we had so little thrust on, practically all of our time and energy was spent in getting out of the atmosphere; but, even at that, it's a good thing that space isn't an absolutely perfect vacuum or we would have been clear out of the Universe by this time."

"Huh? Impossible--where are we anyway? Then we must be making mil ... Oh, I see!" Cleveland exclaimed in disjointed sentences as he also stared into the plate.

"Right. We aren't traveling at all now." Rodebush replied. "We are perfectly stationary relative to Tellus, since we made the hop without inertia. We must have attained one hundred percent neutralization, which we didn't quite expect, and therefore we must have stopped instantaneously when our inertia was restored. But it isn't where we are that is worrying me the most--we can fix our place in space accurately enough by a few observations--it's when."

"That's right, too. Say we're two light-years away. You think maybe we're two years older than we were ten minutes ago, then? That's possible, of course, maybe probable: there's been a lot of discussion on that theory. Now's a good time to prove or to disprove it. Let's snap back to Tellus and find out."

Robert Heinlein used the same idea for the Libby drive in Methuselah's Children (1942).

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Additional resources:
  More Ideas and Technology from Triplanetary
  More Ideas and Technology by E.E. 'Doc' Smith
  Tech news articles related to Triplanetary
  Tech news articles related to works by E.E. 'Doc' Smith

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