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Memory Beta, non-canon Star Trek Wiki
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The time barrier was the name referring to an upper limitation of starship speed. This barrier was broken by the Federation sometime between the years 2236 and 2254. (TOS episodes: "The Cage", "The Menagerie")

The TOS novel: Final Frontier implies that the time barrier was a limitation to account for the navigation computer being unable to get timely sensor information while the ship was at warp speeds, due to time relativity. The creation of duotronics made possible the timed relation between the ship's forward warp drive velocity and the forward sensors—older ships were limited in travel duration as they had to repeatedly slow to verify course heading and obstacles.

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