Time dilation was a natural process, caused by gravity.
As described by the Twelfth Doctor, the closer a person or object was to the source of gravity, the slower time would move for them.
Because of the black hole into which the Mondasian colony ship was being drawn, time was moving faster at the bottom end of the ship than the top end. Indeed, whilst it was Day 2, 10 hours and 45 minutes exactly on Floor 0000, it was Day 365,433, 10 hours, 2 minutes and 21 seconds on Floor 1056. (TV: World Enough and Time)
Teri Billington funded unofficial research into particle acceleration at the University of Cambridge with the goal of time dilation. She was very nearly successful, but her particle accelerator was disassembled by Liz Shaw. (AUDIO: The Sentinels of the New Dawn)