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A picosecond was a unit of time measurements. It was one of the smallest time units known.
While in the Worldsphere, the Seventh Doctor displaced the TARDIS one picosecond forward in time in order to prevent it and God from communicating. (PROSE: The Also People)
Lolita and her twin sister were born within a picosecond of each other. (PROSE: Toy Story)
In the 5th year of the War in Heaven, negotiations over the Venue Accords lasted less than a picosecond and concluded that peace was an impossibility. (PROSE: The Book of the War)
The planet Mordeela was shielded by a barrier which kept it one picosecond ahead of the rest of the universe, with one weak point to allow access for Kotturuh ships. (PROSE: The Knight, The Fool and The Dead)
Behind the scenes
Although not elaborated upon in the franchise, a picosecond is one trillionth of a second.