We're robbed of a sequence in this episode of The Doctor convincing and reprogramming a space ship's computer to turn into a TARDIS. Tom Baker's narration only briefly touches upon the perceived science required to perform this fantastic feat. It's the only bit of TARDIS-related bafflegab in this episode.
For equally confusing reasons, a chance pulling of a lever by Claire brings Professor Chronitis back to life (complete with a nightgown and cap on!), with a bit of verbal sleight-of-hand spewed forth by Douglas Adams to cover up what happened. It's a bit of a double bluff on the part of Adams. Is he making all of this up, but, because he seems to know what he's talking about, and speaks from a background of a great interest in science, do we believe him?
I suppose the supposed time science in this story is best explained by a line Chronitis says in this episode: "Think of me as a paradox within an anomaly and get on with your tea."