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"Always listen to experts. They'll tell you what can't be done and why. Then do it."
- Robert Heinlein

Superluminal  
  Faster than the speed of light.  

As far as I know, the first use in a science fiction story.

Slowly across the micro-universe they were weaving the copper webs which would define the positions of entry and termination of their superluminal jump through tachyon space.
Technovelgy from Patterns of Chaos, by Colin Kapp.
Published by Worlds of IF in 1972
Additional resources -

No less a science fiction luminary than Isaac Asimov used this word in a gritty 1969 article The Luxon Wall in Fantasy and Science Fiction:

It turns out, as you can see for yourself if you try a few random examples, that for any object traveling at superluminal velocities, the proper-mass is imaginary.

The earliest mention I can find is in Seeing Things. The Scientist and Spiritualism by Rupert Hall in Pearsonís Magazine (US) February 1909.

He finds that the manifestations of the mediums are not progressive, but devolutionary, infra- and not super-normal, sub- and never super-luminal.

Of interest (to me, anyway) is the fact that the word derives from "lumen" which is the unit of luminous flux, but can also be derived from a latin word meaning "opening" into a central cavity or interior space.

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Additional resources:
  More Ideas and Technology from Patterns of Chaos
  More Ideas and Technology by Colin Kapp
  Tech news articles related to Patterns of Chaos
  Tech news articles related to works by Colin Kapp

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