The Time Lords knew which points in time were "fixed", which the Ninth Doctor said was a maddening experience to have to go through. (TV: The Parting of the Ways) This was called "the burden of the Time Lords" by the Tenth Doctor, who was trying to explain to Donna why he couldn't prevent Mount Vesuvius from erupting or save the people of Pompeii. (TV: The Fires of Pompeii) The Time Lords could also create fixed points with their direct intervention, their abilities freezing probability into certainty. (PROSE: The Gallifrey Chronicles)
If one learned about their future beforehand (such as death), that would become a fixed point. (TV: The Angels Take Manhattan) Not even the Daleks, a race which slaughtered and conquered and changed bits of history with impunity, dared to tamper with fixed points, showing the danger of doing so. (TV: The Waters of Mars) When River Song interfered with a fixed point it caused time and space to collapse. (TV: The Wedding of River Song, COMIC: The Doctor and the Nurse)
Fixed points were events and/or individuals who had such long-standing impacts on the timeline that no one, not even Time Lords, dared interfere with their natural progression. The Doctor, free to interfere in alien invasions and save planets in most cases, could neither interfere nor interact with these fixed points, out of fear of damaging reality. Fixed points could be flexible and did not have to happen exactly the way they had in the original timeline but meddling with one could potentially result in reality falling apart. Were a fixed point to be interfered with, time would often find a way to make the timeline continue with minimal changes.
For example. when the Tenth Doctor saved Adelaide Brooke and two of her crew, Brooke (to whom the Doctor had confided the nature of fixed points, and more specifically, why her death was one) committed suicide to preserve the timeline with minimal changes. Because of the survival of the other two crew members, the events that occurred on Bowie Base One were revealed to the public. Adelaide was hailed as a hero for stopping the viral menace, which did not happen in the original timeline, but this and her death ensured that she would be an inspiration to her descendants. On this occasion, the Doctor had been able to bend a fixed point. However, he risked the safety of the whole of reality in the process even though he had not truly broken it because of Adelaide's sacrifice. Adelaide was confronted by a Dalek as a child, but it recognised her as a fixed point in time and left instead of killing her, inspiring her to pursue it into space and become that fixed point. (TV: The Waters of Mars)
The Eleventh Doctor was fated to die at Lake Silencio, meaning he had to die there, or more precisely, that the universe needed to believe that he had died there. That didn't stop others from attempting to kill him, however, as when Gantok prepared to kill him in revenge for being beaten at live chess, the Doctor was saved from being shot by his non-destined killer by a trap hole that fed Gantok to the ravenous skulls of the Headless Monks.
However if one actually broke a fixed point in time, as when River Song refused to kill the Doctor, time would freeze and collapse; reality would "die". If this happened whoever had broken the fixed point had to make physical contact with the person who was also a main part of it. In other words, when River shot the Doctor at Lake Silencio, the fixed point in time was focused entirely on just the two of them and time was still in flux all around them, explaining why the Doctor couldn't get time started again by touching either Amy Pond or Rory Williams, who had also been at Lake Silencio. If the Doctor and River touched each other - or kissed as they did at their wedding - time would start moving again. River is the only known person to change a fixed point to such a degree that the whole of reality was put in danger.
With a "still point in time" such as Lake Silencio, it was easier to create a fixed point in time. The only known way to actually create a fixed point in time was by writing events down after they had occurred. If someone read about events that were going to happen to them in the future then the events had to happen the way they had been written (or at least happen in a manner that would eventually lead to someone writing about them as they had been read) because a fixed point would be created. Time was still in flux as long as the reader had not read about his or her own future. At the same time, once someone became aware of their future history by reading about it, such a future was guaranteed to happen while the subjects did nothing to actively avoid that future; when the Fifth Doctor learned that he and Turlough were destined to meet the British Imperial Spacefleet on the Moon in 1878 after reading a diary about the expedition written after the fact, he noted that so long as he and Turlough walked towards the expedition's ships once they reached the park they could basically leave it up to chance when they met the expedition as such an encounter was predicted (PROSE: Imperial Moon).
Although such events had to play out as they were read, the original author's interpretations of such events were not always true. The Doctor had seen records of his "death" at Lake Silencio, but as it turned out, the Silence simply assumed that the fixed point at Lake Silencio meant that the Doctor would die, never realising that he could actually fake his death instead. The Doctor did turn up for his "death", just as he was destined to do, but he had "dressed for the occasion" and was safely inside the Teselecta at the time. This allowed him to survive his encounter with River at Lake Silencio, thus outwitting the Silence, and fooling almost the whole universe into thinking he was dead. (TV: The Wedding of River Song, The Angels Take Manhattan) Fixed points in time only became such when they were fully recorded; as a result, when the Eighth Doctor learned of the destruction of a hospital ship named after the home planet of its head, he was concerned that the destroyed ship had been the Traken, belonging to his old companion Nyssa, but because he hadn't definitively learned that the lost ship was the Traken, the Doctor was able to go back in time by a few months and go undercover on the Traken as Nyssa's assistant, Doctor Foster, preventing a Time Lord agent from destroying the Traken while able to affirm that he hadn't changed anything he knew for a fact (AUDIO: A Heart on Both Sides).
The Time Lords had records of all- or at least a good number- of fixed points in time and space. They were even aware of the fixed point at Lake Silencio as far back as the time of the Eighth Doctor, despite this event taking place only after Gallifrey's destruction, which allowed River Song to infiltrate a conspiracy led by Padrac that was intending to destroy the universe to ensure Gallifrey's survival, as their records included River's apparent assassination of a future Doctor (AUDIO: Songs of Love).
Jack Harkness was a unique fixed point in time and space who was made immortal by the Bad Wolf. The Ninth Doctor sensed that Jack was a fixed point immediately after his first resurrection and fled before Jack could catch up to them. The Tenth Doctor described Jack as "wrong" and, as such, even the TARDIS reacted to his presence; when Jack clung onto the outside of it, it tried to shake him off by travelling to the end of the universe. (TV: Utopia)
It should be noted that the Doctor, during his first incarnation, held to a much stricter definition of fixed points, once telling his companion Barbara Wright that "not one line" of history could ever be tampered with (TV: The Aztecs), although he was being hypocritical as he had recently had extensive interaction with historical figures such as Marco Polo. (TV: Marco Polo) When he was later given a chance to alter a timeline where human society was virtually falling apart in 2006 due to the actions of the Machine in 1966, the Doctor admitted to Barbara that they actually changed history every time they left the TARDIS, helping Barbara understand that he preferred to avoid bigger changes to history due to the risk of making things too complicated and inspiring the Doctor to change key events now and defeat the Machine later in his own lifetime. (TV: The War Machines, PROSE: The Time Travellers)
Notable fixed points
For reasons unknown to Time Lords, a mammoth that fell on and killed a Cro-Magnon became a fixed point. Videos of the event were played for young Time Lords "as a sort of learning experience." (PROSE: Keeping up with the Joneses)
As claimed by a projection of the Second Doctor within the T'keyn Nexus, (COMIC: Dead Man's Hand) the Great Fire of Rome, which the First Doctor was partially responsible for, was a fixed point in time. (TV: The Romans)
The destruction of Pompeii by the Vesuvius volcano was a fixed point in time. Initially the Tenth Doctor refused to interfere because Pompeii's destruction was fixed in time, explaining to Donna Noble that fixed points must always happen and can't be changed even if they are caused by aliens such as the Pyroviles as the two had believed. To his horror, the Doctor eventually realised that he created the fixed point by causing Vesuvius to erupt to destroy the Pyroviles. With a terrible choice before him, Pompeii or the world, the Doctor hesitated despite knowing it was fixed as he'd kill 20,000 people, but Donna took part of the burden upon herself by helping him push the lever that created the event. The Doctor refused to interfere further, believing that with history back on track they had done "enough". However, Donna convinced him to save "someone" and he saved the family that had aided them in discovering the alien plot. (TV: The Fires of Pompeii) This would later inspire the Twelfth Doctor to always look for a way to bypass time, as well as discovering why he took the form of Caecilius. (TV: The Girl Who Died)
In Nicaea in 325, the Fifth Doctor alluded to a fixed point when he warned Erimem against interfering in Arius' clash with the Council of Nicaea which would decide the future of the Catholic Church, stating:
History is tough and most changes we can make are swallowed up in the vastness of the whole but there are certain moments, certain events that shape history to such an extent that if they're changed everything that follows must change. This is one of those moments.
The Tenth Doctor also interfered with a fixed point in time shortly before or after the previous event, by saving the life of Emily Winter, a film actress in 1920s-era Hollywood. He was put on trial by the Shadow Proclamation for this. (COMIC: Fugitive)
While the Doctor was not against assisting friendly forces in a limited capacity, or dealing with isolated incidents, (TV: The Empty Child / The Doctor Dances, et al) the overall events of the Second World War were considered fixed points to the extent that the Doctor could not support Winston Churchill's use of Daleks to accelerate Allied victory (TV: Victory of the Daleks) or Mels' attempt to go back to a point prior to the war and kill Adolf Hitler (although a brief encounter with the dictator was unavoidable). (TV: Let's Kill Hitler) When Ace attempted to kill Hitler during an encounter in 1923, the Seventh Doctor interrupted her efforts, explaining that Hitler's removal could create a power vacuum where a more competent commander took control of the Nazis, preferring the known element of Hitler to the risk that some more dangerous leader could take over in his absence (PROSE: Timewyrm: Exodus).
While fixed points could not be altered, some details could be 'tweaked' if handled carefully. An example of this was Doctor Sean Calvin, who was destined to be discredited and essentially exiled for his failed plan to create an army of androids and a mind-control system to take over his home colony. Even after the Seventh Doctor convinced Calvin not to go through with the plan to take over the world, Calvin was eventually forced to use his equipment to save his planet from an alien invasion, resulting in a journalist learning about his original scheme and forcing Calvin to go into unofficial exile. However, the Doctor mused that his real goal was to ensure that Calvin's daughter, Odessa, was left with a positive example to follow, the Doctor departing with faith that Calvin's final words to his daughter would help her strive to be better and inspire others to do the same, her father's example helping her to recognise that people could not be defined by their mistakes no matter how great those mistakes were (AUDIO: Forever Fallen).
Implied by the Ninth Doctor to be a fixed point was the death of Pete Tyler on 7 November 1987. Rose Tyler saved his life and the paradox allowed the invasion of Reapers. The timeline returned to normal with the Reapers gone when Pete realised what had happened and ran out in front of the car that should have killed him. The only thing changed in the new timeline was where he died, that the driver of the car which struck him stopped and someone (Rose) was with him when he died. (TV: Father's Day)
When Mark Whitaker was manipulated by the Weeping Angels into attempting to save his wife, Rebecca Whitaker, from the accident that killed her, the Doctor stated that her death had to remain, although he referred to it as a complex event in time and space rather than a fixed one. This was because Mark and Rebecca's relationship had been facilitated by Mark going back in time in the first place: teenage Mark wouldn't have even met Rebecca had he not [literally] bumped into the Doctor, who was taking an older Mark back to his true time, for example. By preventing Rebecca's death, Mark would risk erasing their whole relationship, as erasing her death would eliminate his need to go back in time and thus create a complex tangle of space-time. (PROSE: Touched by an Angel)
The Doctor's apparent death in his eleventh incarnation was a fixed point in time arranged by the Silence. The Kovarian Chapter arranged for the event to occur in Utah, at Lake Silencio, on 22 April 2011 at 5:02 pm, a still point in time. When River Song tried to prevent this, an alternate timeline was created where all of time occurred at the same time and it was always 22 April 2011, at 5:02 pm. The Doctor set things right by kissing River, shorting out the time differential between them and making events revert to the moment when she was supposed to kill him. It was later shown that the fixed point was actually not his death and the Doctor who had "died" was actually the Teselecta - with the Doctor himself safely inside. (TV: The Impossible Astronaut, The Wedding of River Song)
The Doctor warned Amy Pond about creating fixed time by reading a book which chronicled their adventures; they attempted to get around this by using the chapter titles when needing to use the book to obtain Rory Williams' whereabouts, only for the Doctor to read the last chapter title, "Amelia's Last Farewell", resulting in Amy's departure becoming a fixed point. The Doctor immediately became fixated in changing history to prevent this from happening, such as demanding that River Song get her hand free from a Weeping Angel's grip without breaking her wrist, but was ultimately unsuccessful. As Amy prepared to allow a Weeping Angel to send her back in time to be with her husband, he warned her that in doing so she'd be creating a fixed point in time and he could never see her again. Wanting to be with Rory more than the Doctor, Amy didn't listen and let the Angel send her back. (TV: The Angels Take Manhattan)
Amy once encountered an agent of the Sentinels of History who caused the London Beer Flood, since it was part of destiny and a fixed point that was meant to happen. When Amy saved a woman who had originally drowned in the flood, she realised that the flood itself was fixed, but not the resulting deaths, since time and space did not begin collapsing. (COMIC: The Doctor and the Nurse)
According to the General, the death of Clara Oswald was an established historical event and could not be altered. Due to this, despite being extracted from her time stream the moment before her death, Clara had to eventually return to Gallifrey and die. (TV: Hell Bent)
The death of explorer Adelaide Brooke was one of the few times the Doctor, then in his tenth incarnation, intentionally interfered with a fixed point. His rationale was that, as the last surviving Time Lord, the Laws of Time were his to command. In the end, Brooke committed suicide, allowing the timeline to unfold with only minor changes. (TV: The Waters of Mars)
The destruction of Ockora in 2204 by use of the G-bomb was a fixed point. When the Second Doctor became involved in these events, he delayed the destruction of Ockara by several hours to try and rescue his companion Zoe Heriot from a Selachian prison and convince Commander Wayne Redfearn of the Triumph to negotiate for peace, hoping that convincing the Selachian Supreme Leader to withdraw in the hope that the Selachians choosing to remain isolated from the rest of the universe after 2204 would result in the same consequences for the rest of the universe as would have unfolded if Ockora had been destroyed. However, after the Selachians learned of the G-bomb, it was launched when the Supreme Leader and forty Selachian soldiers tried to take the ship. This platoon escaped the planet's destruction and boarded the Triumph, killing everyone on the ship with the goal of taking it back to Earth, before the other G-bomb was set off by the sacrifice of Professor Laura Mulholland, leading to the formation of another black hole. The Doctor considered the formation of another black hole an acceptably small change. (PROSE: The Final Sanction)
Jack Harkness became a fixed point in time after his resurrection by Rose Tyler, which caused him to become immortal. (TV: Utopia) Jack temporarily lost his immortality due to Miracle Day, but regained it alongside Rex Matheson when mortality was restored to the rest of the world. (TV: The New World, The Blood Line)
The death of Danny Pink by being hit by a car became a fixed point in time. His girlfriend Clara Oswald tried to blackmail the Twelfth Doctor into going back and saving Danny, but the Doctor warned that doing so would create a paradox. (TV: Dark Water)
When the Tenth Doctor first met River Song, in order to save everyone in the Library the Tenth Doctor was initially going to sacrifice himself, only for River to knock him out and restrain him so she could sacrifice herself in his place, telling him that if he died there all of their other meetings would never have happened. When he claimed time can be rewritten, she told him that that couldn't be; though no mention of fixed points is made, it's implied that because of River's interaction with his future selves that his survival during this encounter was a fixed point. (TV: Forest of the Dead)
Time in flux
The opposite of fixed points was time in flux. At these points time could change completely.
The Time Lord Marnal explained that, despite the Time Lords' web of time giving the universe structure, most events were in constant flux with other possibilities. It was for this reason the Time Lords established their non-interference policy, merely projecting their observations of reality on the universe instead of creating fixed-points by interacting with the different probabilities. (PROSE: The Gallifrey Chronicles)
Flux points were relatively insignificant (on a universal scale) events that could be altered with relatively little to no consequence. The Doctor often meddled at these moments. (TV: The Christmas Invasion, PROSE: I Am a Dalek) When the Tenth Doctor first met Martha Jones, he told her that "Crossing into established events is strictly forbidden ... except for cheap tricks." (TV: Smith and Jones)
Only the broad strokes have been laid down. Its in the moments between the ticks of the clock where life truly thrives, where we can make a difference.
The Fifth Doctor noted that bifurcation points, where history could continue on its original course or an alternate timeline could be created, could result in new timelines or erase the old ones if handled improperly, with Time Lords and similar races having the ability to influence whether a new worldline should come into being or history simply continue as it was. When faced with the prospect of creating a new timeline where the British Empire expanded into space in 1878, however, the Doctor chose to preserve the status quo with the aid of Kamelion, feeling that Victorian Britain wasn't socially ready for space travel (PROSE: Imperial Moon).
1966 was in flux, as discovered by the First Doctor when it was revealed that WOTAN was supposed to conquer Earth (PROSE: The Time Travellers) instead of being defeated by the Doctor. (TV: The War Machines)
The Third Doctor noted that some locations in space and time were temporal probability nexuses, where multiple strands of causality are exposed and weak, with the result that the smallest alteration to events in these locations can produce aberrant loops of existence or even new alternate timelines, where time would normally be able to resist and absorb minor changes. Events on the island of Salutua occurred on such a nexus point, made weaker by the Doctor's time bridge, resulting in an alternate timeline being created where Nancy Norton worked with Brokk to conquer the world, until the Doctor and UNIT were able to travel back and undo her rise to power (PROSE: The Eye of the Giant).
The destruction of Sir Reginald Styles's house as he was preparing for a vital peace conference in 1972 created a new timeline where the Daleks conquered Earth ahead of their previous invasion. However, realising that this timeline was a temporal paradox caused by the resistance from the Daleks' future travelling into the past and setting off a bomb to try and prevent the conference taking place without realising that it was already happening, the Doctor and Jo Grant were able to go back in time and prevent it going off. (TV: Day of the Daleks).
Sarah Jane Smith was shown an alternative timeline where the Earth of 1980 was a barren wasteland by the Fourth Doctor, who explained 1911 was in flux because of the threat of Sutekh, noting that history could be altered on that kind of scale when dealing with a being of Sutekh's immense power. (TV: Pyramids of Mars)
"From start to finish", the year 1961 was noted by the War Doctor to be in flux. This was partly the reason the Time Lords installed a quantum shield to protect Earth against potential Dalek incursions during the Last Great Time War. Nevertheless, the Dalek Time Strategist enacted a plot to break through the shield using a human agent whom was sent to East Berlin with a Shadow Vortex, proceeding to exterminate all life in a bid to disrupt and ultimately wipe out the Doctor's existence through the elimination of his Earth allies. The resulting invasion was averted by the War Doctor, who shifted its events to an alternate timeline where Lara was banished. (AUDIO: The Shadow Vortex)
The Ninth Doctor explained to Rose Tyler when she said that he couldn't give dead human corpses to the Gelth, as she knew for a fact that dead bodies weren't walking around in 1869: time was in flux, changing every second and her "cosy little world can be rewritten like that". (TV: The Unquiet Dead)
The year 200,000 was supposed to be the Fourth Great and Bountiful Human Empire, but due to first the Jagrafess and then Daleks that had fallen through time from the Last Great Time War, it was stunted and then fell apart. Instead of it being a great empire with great advances, technology was backwards due to the Jagrafess. The Doctor believed he had fixed it by getting rid of the Jagrafess, but the Daleks took over from behind the scenes, causing civilisation to get even worse while they rebuilt. Eventually, when the Doctor returned in the year 200,100, the Daleks attacked, devastating the Earth before they were destroyed by Rose Tyler as the Bad Wolf. (TV: The Long Game, Bad Wolf, The Parting of the Ways)
Although the Ninth Doctor told Rose that Harriet Jones would serve three successive terms as British Prime Minister, (TV: World War Three) he himself would, in his next incarnation, cause her political downfall after she took extreme measures against alien threats, (TV: The Christmas Invasion) leading to her losing the title of Prime Minister to Harold Saxon. (TV: The Sound of Drums) She would die the following year at the hands of the Daleks during their invasion of Earth. (TV: The Stolen Earth)
When Edward VII, along with Balmoral Castle, vanished into thin air, the Tenth Doctor explained that with him gone, the whole future of the royal family was threatened and there would be no George V, George VI, Elizabeth II, Charles III and Camilla, William V and so on. (PROSE: Revenge of the Judoon)
When the Tenth Doctor and Donna Noble were chasing Reverend Golightly to save Agatha Christie, the Doctor explained that Agatha could die and any books past her sixth would disappear. The Doctor specifically told Donna that "time is in flux; for all we know, this is the night Agatha Christie loses her life and history gets changed." (TV: The Unicorn and the Wasp)
After they saw Frank Openshaw exterminated by a Dalek, Rose Tyler and the Tenth Doctor meddled in history for him so that he met his wife Sandra years earlier than in the original timeline. (PROSE: I Am a Dalek)
In 2020, when a drilling operation in Cwmtaff disturbed a Silurian civilisation, the Eleventh Doctor told Amy Pond, Nasreen Chaudhry and Eldane that this encounter could lead to either a peaceful relationship or a devastating war. The Doctor called the event an opportunity. (TV: Cold Blood)
At one point, the Korven altered the history of Earth (which they had previously invaded in 2480), causing part of it to be controlled by the corrupt, totalitarian Department. (TV: The Eclipse of the Korven)
The Eleventh Doctor was forced to visit his own tomb on the planet Trenzalore by the Great Intelligence where he died in battle among millions. His tomb was his own TARDIS amidst a massive battlefield graveyard. (TV: The Name of the Doctor) Later, the Doctor travelled to a Trenzalore of a more recent era where the planet was a human world with a farming community which he defended during the centuries-long Siege of Trenzalore from many enemies. The Doctor was unable to change his future at first, but thanks to the Time Lords he was able to change the future he saw by regenerating into the Twelfth Doctor rather than dying after the Time Lords gifted him with a new regeneration cycle. (TV: The Time of the Doctor)
When robotic Knights crashed in 1190, Sherwood Forest, they accidentally began altering the course of history. The Knights allied with and modified the Sheriff into a cyborg, promising him the use of their numbers and skyship to take over England. Clara warned Robin Hood against going to an archery contest being held by the Sheriff, but was ignored: however, the Doctor didn't warn her against this as he didn't believe what was occurring to be real. (TV: Robot of Sherwood)
When it was discovered that Earth's moon was actually a giant alien egg about to hatch, it was left to humanity to decide whether to let the unborn creature live or detonate explosives to destroy it. Having confirmed that he was dealing with a moment in time that was in flux where anything could happen, the Twelfth Doctor took a more aggressive measure than his predecessor; in making humans choose, he left Clara behind until she made the decision. Had the explosives gone off, the replacement moon that the creature laid after hatching would not have existed in the future. (TV: Kill the Moon)
When the Earth of Clara Oswald's present day seemingly faced destruction at the hands of a solar flare, Clara noted to the Doctor that they had visited various future time periods of Earth and humanity. The Doctor explained that those futures would be erased if the Earth was destroyed at that point. (TV: In the Forest of the Night)
Behind the scenes
In the Star Trek: Voyager spin-off novels, which are non-canon in the Star Trek franchise, after Admiral Kathryn Janeway is assimilated by the Borg and destroyed in battle with the Enterprise-E, it is revealed that the date of her death is a fixed point in time across all realities where she exists; it is now a fact that all versions of Kathryn Janeway must die on that specific stardate, with the only two Janeways known to have lived beyond this time- the original Janeway and a Janeway extracted from a point before Voyager entered the Delta Quadrant who was trapped in the main timeline- only surviving with the aid of the god-like Q (the 'original' Janeway actually died before being brought back to life by Q's son and Kes, and the alternate Janeway was saved by Q in the guise of a local doctor).