“People assume that time is a strict progression of cause to effect, but actually, from a non-linear, non-subjective viewpoint, it’s more like a big ball of wibbly-wobbly… timey-wimey… stuff.” – The Doctor, “Blink”
There’s two ways of writing time travel fiction. The first is to rigorously uphold exact laws.
The second approach to time travel is, well, timey-wimey. Play fast and loose with the concept of rules but use the technology primarily to create plot rather than solve it.
Doctor Who falls solidly in the second category. Time travel is primarily a story creator, carrying the Doctor and companions to a new time and place every story, but rarely is it used mid-story as a solution to events.
What you can’t do is play fast and loose while using time travel to bypass challenges. That’s just lazy writing which quickly creates a world where the heroes are nigh unstoppable, using their time machine as a deus ex machina, get out of jail free card.
The Rules of Time Travel
Over the last 50 years, Doctor Who time travel has primarily been governed by the Blinovitch Limitation Effect along with a healthy dose of common sense. The Blinovitch Limitation Effect states one cannot go back in time to undo his own actions. First put forward in the third Doctor’s “Day of the Daleks,” the Effect fills in an obvious plot hole for time travel stories. There’s no redos in time travel.
The Effect also brings about dire consequences when a person meets an older version of himself, such as the nervous breakdown suffered by the Brigadier of 1978 when he met his 1983 self in “Mardwyn Undead.” It also explains why earlier versions of Time Lords forget encounters with future selves.
There’s also the concept of fixed points in time. Certain events simply have to exist in the time-space continuum. In addition, personal knowledge of an event makes it harder to change, and knowledge of one’s own future makes that future unchangeable.
One can, however, change the nature of that event. When Clara recently reported seeing the Doctor’s ghost in “Before the Flood,” that fact became set in stone. However, it didn’t stop the Doctor from avoiding death and then creating a hologram which Clara believed was a ghost. It’s a bootstrap paradox: Clara told the Doctor about seeing the hologram, and the Doctor created the hologram because Clara reported it.
The Good and the Bad of Time Travel Stories
“Blink” is quite arguably the best time travel episode in existence. Clever writing kept track of multiple timelines which effectively intersected one another to create a story driven by multiple individuals and messages moving backward and forward in time. The excellence of the episode made the featured Weeping Angels a monster favorite. However, subsequent Angel episodes prove that without that extremely clever writing, they’re just one more faceless villain for the Doctor to beat.
If “Blink” makes the best use of time travel, “The Big Bang” makes the worst. Here, the Doctor hops around time repeatedly to get people and items where he wants them in the present, roughly descending to a Bill and Ted’s Excellent Adventure level of writing. If time worked in such a fashion, it would make time travelers nearly invincible. Bill and Ted gets away with it because it’s a comedy. It didn’t need to make sense.
More of a Suggestion
Although the Doctor has warned his companions of the perils and impossibilities of interfering with time, the laws of time travel really seem to be more like the pirate code: they seem to be more like guidelines than actual rules. Surely, for example, the birth of the Daleks is a fixed point in time. The history of countless worlds has been shaped by their existence. Yet the Time Lords send the Doctor to destroy them before their genesis in “Genesis of the Daleks”.
Doctor Who is not a show that should be bound up in a bunch of rules. However, writers also need to impose common sense, and that starts translating into at least loose rules. But there’s also the fact that Doctor Who doesn’t actually depend on time travel for its stories beyond getting the characters from point A to point B. The stories ultimately are about the people, not the technology. The Doctor is a genius from a highly advanced race; he can have pretty much whatever tech he wants. But that’s not the point. The point of Doctor Who is the characters. The tech is always secondary.