On Gallifrey, the Doctor's home planet, a Time Lord traitor is at work, stealing the bio-data code of another Time Lord and killing a technician who stumbles across the crime. The traitor provides the bio-data to a creature known as the Renegade, which is composed of anti-matter and uses the bio-data to invade the TARDIS and then the Doctor's metabolism. His companion, Nyssa, helps him recover. The Renegade is shielded in this attempt by the Arc of Infinity, a curious curve between the dimensions containing quad radiation, which can shield anti-matter. The Doctor decides to head to Gallifrey to track down the supplier of his bio-data, conscious that unless the creature trying to cross universes is stopped, its incursion could cause a chain reaction fatal to our universe.
The High Council of the Time Lords is also taking the matter seriously and has decreed that the Doctor’s TARDIS should be recalled for the same reason. The Chancellery Guard under the over-zealous Commander Maxil seizes the Doctor and Nyssa. He stuns the Doctor to ensure his delivery to the High Council.
When the Doctor is brought before the High Council, the new Lord President, Borusa, is inscrutable, while Chancellor Thalia and Cardinal Zorac are openly hostile; only his old friend Councillor Hedin seems pleased to see him. The President stresses the gravity of the situation since the Renegade poses such a threat to the Universe, and the High Council has had no alternative but to issue a Warrant of Termination on the Doctor to ensure the Renegade can no longer bond with him. The Doctor is taken away protesting, sure his bio-data has been compromised and stolen from within the High Council. Fortunately an old friend, Damon, another technician in the records section, provides him with the proof he needs that a member of the High Council did indeed steal his bio-data extract. The Doctor is soon taken for execution, despite Nyssa’s attempts to save him, and placed in a dispersal chamber. Sentence is carried out.
The supposed death of the Doctor, however, has not solved the situation. Unbeknownst to the High Council, his mind has been taken into the Time Lord living repository of knowledge, the Matrix, while his body is hidden behind a force shield in the termination cubicle. The Renegade, who demands an opportunity to return to the Universe it once inhabited, contacts him. The truth of the aborted execution is discovered by the wily Castellan, who tells first Nyssa and Damon that the Doctor is alive; and then the High Council.
Meanwhile, in Amsterdam, the Doctor’s former companion Tegan Jovanka arrives looking for her cousin Colin Frazer. She is greeted by his friend Robin Stuart, who explains that Colin has disappeared while they were crashing in the crypt of the Frankendael mansion. When neither of them can persuade the police to take an interest, they decide to investigate the crypt themselves. They find a hypnotised Colin working for a curious birdlike creature, which is armed with a deadly weapon. They are rendered unconscious and their minds scanned, revealing to the Renegade, who has established its base in a TARDIS hidden at the Frankendael, that Tegan knows the Doctor. The Renegade uses Tegan as bait to force the Doctor to obey him, also releasing Colin from his slavery as a reward. The Doctor is returned to normal space on Gallifrey where he makes for the High Council Chamber. Lord President Borusa has fallen under suspicion of being a traitor because the Castellan reveals it was his codes that were used to transmit the bio-data. The truth, however, is that Councillor Hedin is the Time Lord in league with the Renegade. He is in awe of his master, the mighty Omega, first of the Time Lords and pioneer of time travel (see The Three Doctors). Hedin wishes to release Omega from his exile in a universe of anti-matter, not realising the great Time Lord has been driven mad by his years of solitary confinement. The Castellan kills Hedin, but this does not prevent Omega using the Arc of Infinity to seize total control of the Matrix and, therefore, the organisation of Gallifrey.
Fortunately the Doctor and Nyssa manage to slip away and return to the TARDIS. They use scant knowledge provided by Tegan to determine that Omega has established his base in Amsterdam on Earth, and head there immediately, desperately trying to find the Frankendael crypt she described. After a lengthy hunt they find the lair defended by the birdlike creature, the Ergon, and Nyssa disposes of it with its own matter-converter gun. They reach Omega’s TARDIS at the point at which both the ship is destroyed and Omega makes full transference to Earth using the Arc of Infinity. When he peels his decayed mask away, he reveals the features of the Doctor, whom he now perfectly resembles.
Omega heads off into Amsterdam with the Doctor and Nyssa in hot pursuit. Within a short time, the Doctor’s prediction of an unstable transfer begins to come true: Omega’s flesh decays and it is clear his new body is not permanent. When the Doctor and Nyssa catch up with him, it is a painful task for the Doctor to use the Ergon’s anti-matter converter on Omega, expelling him back to his own universe of anti-matter. The Time Lord High Council on Gallifrey detects the end of the threat. Once Tegan has checked on her cousin’s progress in hospital, she decides to rejoin the TARDIS crew, this time as a willing traveller.
Every story during Season 20 featured an adversary from the past. For this serial, it was Omega, who had faced the first three incarnations of the Doctor in the 10th anniversary story The Three Doctors (1973).
Tegan is the first companion to have rejoined the TARDIS crew after having departed in an earlier story.
This story's Castellan, played by Paul Jerrico, would return in The Five Doctors. It is stated that the Doctor's execution in this story is only the second time in Time Lord history that the race has sentenced one of its own to death, the first being Morbius from The Brain of Morbius. The Doctor's failure to return Romana to Gallifrey (as seen in Warriors' Gate) and Leela's decision to remain on Gallifrey (at the end of The Invasion of Time) are mentioned briefly. The Doctor isn't quite finished with Omega, as heard in the audio Omega, which takes place shortly after this TV story.
The working titles for this story were The Time of Neman and The Time of Omega. For Parts One and Two, the character of Omega was credited as "The Renegade" on the end credits. Colin Baker stated on Doctor Who: The Colin Baker Years video that John Nathan-Turner believed his performance was a little arch, and therefore gave him the nickname of Archie.
Substantial portions of the story were filmed on location in Amsterdam. This was only the second time the show had filmed outside of Britain. John Nathan-Turner hoped to repeat the success of the first story filmed overseas, City of Death. Amsterdam was chosen both because the BBC had recently developed contacts there and because it was cheap to arrange travel and hotel accommodations. Story writer Johnny Bryne had some trouble at first because the producers wanted a plot that made the Amsterdam setting a key factor in the course of events, rather than him just happening to be there.
Part One was broadcast on a Monday in contrast to the rest of this season's episodes, which were all transmitted on consecutive Tuesday and Wednesday evenings.
Footage of the Fifth Doctor is used in the 2013 episode "The Name of the Doctor".
The story features a guest appearance by Michael Gough (who had previously played the Celestial Toymaker in the story of the same name). Leonard Sachs previously played Admiral Gaspard de Coligny in The Massacre of St Bartholomew's Eve. Ian Collier previously played Stuart Hyde in The Time Monster.
Colin Baker (who would later portray the Sixth Doctor) appeared in the serial as Commander Maxil. It was his performance in this role (which, according to Baker, producer John Nathan-Turner repeatedly told him to "tone down") that first brought him to the attention of the production office. Shortly after the production, the Assistant Floor Manager on the serial, Lynn Richards, invited Colin Baker to her wedding reception. Amongst the other guests were Ron Jones, Peter Davison, Sarah Sutton, Eric Saward, John Nathan-Turner and Gary Downie. Baker has said in a number of interviews that his entertaining form at the party directly led to his being cast as the Sixth Doctor the following year. Baker reprised the role of Maxil as an uncredited cameo in the 2006 Big Finish Productions audio play Gallifrey: Appropriation.
Elspet Gray, who played Thalia, later played Hera in the audio play Immortal Beloved. Her character's name is shared with the Greek Muse of comedy. At the Fifth Element convention in London in February 2010, Alastair Cumming (who played Colin Frazer) explained that he is not related to Fiona Cumming (director of the Fifth Doctor serials Castrovalva, Snakedance, Enlightenment and Planet of Fire), despite frequent reports that she is his mother.
A novelisation of this serial, written by Terrance Dicks, was published by Target Books in July 1983.
Arc of Infinity was released on VHS in March 1994. A double-pack DVD featuring both Time-Flight and Arc of Infinity was released on 6 August 2007. This serial was also released as part of the Doctor Who DVD Files in Issue 108 on 20 February 2013.