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"Evolutionary success ... is going to absolutely require mobility on, at a minimum, an interplanetary scale. We either go or we die out."
- Richard Morgan

Jump Through Hyperspace  
  Device that makes faster-than-light travel possible.  

Where would sf be without faster-than-light (FTL) travel? Stuck in the solar system, that's where.

To Gaal, this trip was the undoubted climax of his young, scholarly life... To be sure, he had traveled previously only as far as Synnax's only satellite in order to get the data on the mechanics of meteor driftage which he needed for his dissertation, but space-travel was all one whether one travelled half a million miles, or as many light years.

He had steeled himself just a little for the Jump through hyper-space, a phenomenon one did not experience in simple interplanetary trips. The Jump remained, and would probably remain forever, the only practical method of travelling between the stars. Travel through ordinary space could proceed at no rate more rapid than that of ordinary light (a bit of scientific knowledge that belonged among the items known since the forgotten dawn of human history), and that would have meant years of travel between even the nearest of inhabited systems. Through hyper-space, that unimaginable region that was neither space nor time, matter nor energy, something nor nothing, one could traverse the length of the Galaxy in the interval between two neighboring instants of time.

Gaal had waited for the first of those Jumps with a little dread curled gently in his stomach, and it ended in nothing more than a trifling jar, a little internal kick which ceased an instant before he could be sure he had felt it. That was all.

And after that, there was only the ship, large and glistening; the cool production of 12,000 years of Imperial progress; and himself, with his doctorate in mathematics freshly obtained and an invitation from the great Hari Seldon to come to Trantor and join the vast and somewhat mysterious Seldon Project.

From Foundation, by Isaac Asimov.
Published by Doubleday in 1951
Additional resources -

Occurred first in the foundation stories; I don't know an earlier use. The novel Foundation is a compilation of five stories, four of which were published from 1942-1944 in Astounding. The jump through hyperspace is described in The Psychohistorians which was written as a prequel for the novel in 1951

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