Disclaimer:Characters and situations owned by the BBC.
Spoiler: for Doctor Who's The End of Time and all three seasons of The Sarah Jane Adventures.
Cause and Effect
If you have survived Slitheen, Sontarans, paintings come to life and alternate realities, the awareness that you could have died because you crossed the road without paying attention is somewhere between bewildering and embarassing. Especially if your mother's time-travelling alien friend whom you very much want to impress and who has already praised you for your world-saving skills has to save you from this fate.
Luke takes refuge to mathematics, which is a tried and true coping method. Calculations are something he's really, really good at, and they make sense in a way random road accidents do not. So he calculates the odds of the Doctor appearing just at the right moment to save him. The results are somewhat disconcerting. They also lead him to the conclusion the Doctor must have known what would happen, and when exactly. The most likely way he would have known is if Luke has, in fact, died in a future the Doctor is familiar with.
This conclusion is anything but comforting. Luke remembers the horrible world that resulted out of his mother's attempt to change the timeline and save her parents from a car accident. The devastated earth, and the few surviving humans in slavery. He also remembers what Maria has told him about the first time the Trickster crossed their paths, that time Mum's best childhood friend lived instead of died, and Mum herself was dead, which also meant Luke had been, in that reality. And then there was Peter, whom his mother had meant to marry only a few months ago, Peter whose life again had been an alteration of the time line, nearly resulting in catastrophe and definitely resulting in breaking his mother's heart.
So far, the world doesn't show any signs of changing into a devastated wasteland as the result of Luke's continued existence, but then, some apocalypses are longer in coming. He asks Mr. Smith to keep a watch on any discrepancies between population records before and after Luke's almost road accident. Just in case people suddenly got blotted out of existence. Mr. Smith assures him all changes on record appear to be the result of normal birth and death rates. Still, Mr. Smith himself could have been altered. Or lying. Two years have passed since the time Mr. Smith attempted to use Luke to destroy the world, and the supercomputer hasn't shown any signs of rejecting his new, benevolent program since, but Luke won't ever completely trust Mr. Smith again.
"Clyde," he asks his best friend, "did you ever wonder whether you're supposed to exist?"
Clyde gives him a suspicious look. "Did that Wormwood woman come back from the dead to mess with you again?" he asks immediately, something that Luke can truthfully deny, though his sense of accuracy leads him to point out they can't know for sure Mrs. Wormwood is dead. He doesn't like to think of her, though; it's a topic that makes him nearly as uncomfortable as the idea his life could doom the universe. So he says:
"I was just thinking about Peter."
Clyde makes a sympathetic face. "He was pretty decent. A bit thick, though. I mean, if you fall down the stairs and should be dead, and some creepy alien shows up and saves you, it's clear something is up, right?"
"Err," says Luke.
"He should have told Sarah Jane the score from the start," Clyde continues relentlessly, and Luke changes the subject again. Next, he tries Rani, and also tries a more subtle approach.
"Remember that time where the Trickster tricked Mum into saving her parents and your mother ended up as a slave in hell?"
"Don't tell me he's back again," Rani says alarmed.
"I don't think so," Luke replies, after a slight pause, and Rani uses her evil powers of mind reading which he's half convinced she has on him.
"You didn't happen to meet someone who does something wonderful for you just recently, did you?" she asks.
"Nobody I haven't met before," Luke equivocates. "You were there, though. When they decided they had to die to save the timeline – Mum's parents, I mean."
"They were heroes," Rani says. "It was rotten for Sarah Jane, though."
"Do you think you could have done it?" Luke bursts out. "Get yourself killed on the road because otherwise the world ends?"
Rani hesitates and looks increasingly troubled. "I hope so," she says. "I mean, I think I would, but you can't know for sure, can you? It's not like risking your life. We do that all the time, but I always think we'll end up alive, you know? They knew they would die, and be gone forever." She grimaces. "I really don't know, Luke. " Then she zones in on just what he had hoped she'd ignore. "So whom did you meet, and what did they do for you?"
The main reason why Luke hadn't told her or Clyde so far was that if his existence should doom the world, he doesn't want them to know. Because if he needs to die, it should be in a way that doesn't make them feel guilty beforehand, or sad for him, or trying to stop him. Except that a part of him wants to be stopped, because the thought of dying for the conservation of the time line makes him feel mostly empty and more alone than anything since Maria found him and gave him friends, and a mother. He opens his mouth, not sure whether he'll admit to the Doctor's visit, but then Rani continues: "Mrs. Wormwood isn't back, right? Don't tell me Mrs. Wormwood is back!"
"Why does everyone think Mrs. Wormwood is after me?" Luke asks, honestly annoyed.
"Because she is," Rani declares matter of factly. "And you know evil masterminds always come back from the dead. Especially if they're someone's parents."
"She's not my mother," Luke says, and is saved from further argument when Rani's mother Gita bustles in and tells them dinner is ready.
When he returns to his home, Mr. Smith still hasn't noticed any post-Christmas reality distortions, but he has proved his continuing untrustworthiness by snitching on Luke to his mother. He has prepared for this eventuality, though, and launches into a really good explanation of why he asked Mr. Smith to monitor the situation. Given all the nightmares before Christmas and what happened on Christmas Day, complete with a planet appearing and disappearing in the sky, one shouldn't trust all danger has passed, right?
But his mother just looks at him, and his brilliant distraction evaporates before her sad, knowing gaze.
"You're wondering whether the Doctor did the right thing in saving you, aren't you?"
Luke nods, miserably. Of all the people, he hadn't wanted his mother to figure this out. She has lost her parents as a small child, and then again only last year; she has lost Peter just a few months ago. He doesn't dare to imagine what it would be like for her to lose him, and for the same reason Peter and her parents died.
But then he imagines what it would be like for her if the world ended and all her other friends died with it. He imagines finding out that Maria never existed, or seeing Rani and Clyde worked to death.
"He did," Sarah Jane declares firmly.
"How can you be so sure?" Luke asks, and with a very low voice tells her about his calculations of the odds.
"Remember what he said to us when he showed you the TARDIS?" his mother replies. Luke assumes she doesn't mean the part where the Doctor might have taken them along if she hadn't declared them too young for these kind of travels. Well, the Doctor didn't offer directly, but close to. Nearly. It would have been brilliant. Not that life on Earth isn't.
"He told us we'd save the world again," he says cautiously, and she nods.
"Exactly. You, Clyde and Rani. You are all going to do great things, and he knew that because he must have visited you in the future."
"But he also knew about the car, and doesn't that mean…"
"It means there was always someone there to save you from getting hit," his mother says, and puts her arm around his shoulders. "He just had to make sure of that. So he did it himself. Time works like that for him, Luke."
A causality loop, cause and effect; it's entirely possible. Just as much as Luke's original assumption. Instead of the Doctor being familiar with his death-by-car-date, it could simply be that he met Luke in Luke's future, but his own past, and that Luke will tell him when exactly to be at Bannerman Road.
"I should have thought of that," Luke says striken, still digesting the idea that he overlooked a logical explanation where his mother did not, and that instead of being the cause of doom and destruction and in need to die, he'll continue to save the universe with his mother and his friends.
"Well, I have a bit more practice," his mother says and ruffles his hair. They exchange relieved smiles. But the sadness hasn't entirely vanished from her eyes, and when Luke asks: "So you think we'll see him again? The Doctor, in the future?", it deepens even as it mingles with that mixture of wistfulness and exasperation she always shows when talking about her old friend.
"Definitely. When you least expect it. That's when he'll be there."
Of course, there is yet the chance she's wrong, and Luke's original fear was the right one. Still, until the first signs of apocalyptic consequences to Luke's continued existence show up, he decides to go with his mother's assumption. After all, it could just as well be that she'll need him to save the world next week, and he did promise Clyde to go to a football match together next week. Maria and he got interrupted mid-online chat about everyone turning into some alien with bleached blond hair and how she has a photo of that guy in her dress. And he really should tell Rani he has seen the Doctor, not Mrs. Wormwood, because otherwise she'll give him books about parent issues again.
That night, Luke writes a note to himself, both on paper and in his own computer, describing the exact moment the Doctor whisked him away from the car that was about to hit him as best he can, so he can give the Doctor the information in the future. Then he decides to be extra cautious, makes a copy of this and tells Mr. Smith to text it to the phone number they used for the Doctor back when the Daleks were there, along with a note.
Dear Doctor, Luke wrote, thanks for having saved me or saving me in your future. I'm really looking forward to seeing you again. P.S. Do you think you could maybe just come to dinner as well? I think Mum is worried about you.
Mr. Smith informs him this is too long for a text message, as the Doctor appears to be using a standard human cell phone. So Luke redrafts his message, keeps it to the bare essentials of when and where he needs to be rescued, and adds just four words, making the message complete.
Dear Doctor: Thank you.