The Doctor strolled a few feet out of the TARDIS and stopped sharply.
"Do you recognise this?" he said, turning back to the two sisters who had remained standing in the door-frame.
"Yes" Elsa said slowly, as she gingerly stepped out. "I… built this. This is where Anna came to see me and…"
"And you definitely did not reject her and strike her, unlike the king told us."
"Actually… I did reject her and… strike her, but, it was an accident! And I never… I never…"
Elsa passed her hand on her face.
"Are you all right?" the Doctor asked with unexpected concern.
"Yes, sorry" she mumbled, "just feeling dizzy… what was I talking about? Oh yes, I built this. This is where Anna came to see me and..."
"Elsa, are you sure you're OK?" Anna asked, stepping out of the TARDIS.
"Yes, of course I am. Just… feeling… dizzy. Must be the ride… As I said, this is where you came to see me and… and… and… some… things… happened… Stuff." Elsa smiled wanly. "What were we talking about again?"
"Elsa? Is something wrong?" Anna asked, taking her sister's hand.
"Of course not! As I said, you came to see me there, and some stuff happened. Forgot what, will come back to me in a second. You came to see me there and..."
"In the TARDIS, now!"
The Doctor grabbed the young woman and forcefully marched her inside the box. Anna quickly followed back.
"I assure you, Doctor" Elsa said, "I'm quite fine…"
"No you are not" the Doctor cut. "You are too close to the divergence. This is impacting your memories."
"I did not feel anything", Anna said.
The Doctor looked at her, then back at Elsa.
"Then your memories probably changed before the divergence, but not your sister's. But the events so far have been almost identical, this is why the TARDIS is here."
"Elsa, are you all right now?" Anna asked with concern.
"Yes, I'm quite fine now. We can…"
"No, you can't" the Doctor said with authority. "You will both remain in the TARDIS, while I go outside to see what is happening. You will not leave it until I return. Is that understood?"
"But you said I had no problems with the divergence memory thing" Anna protested. "Why can't I come?"
"Because we are only here for observing. We must not interfere if we want to understand what is going on with these contradictory timelines. Now… you wait here, don't touch anything, and don't follow me."
The Doctor slammed the door behind him, leaving both sisters alone in the cavernous space.
"Is he always like this, Madame TARDIS?" Anna asked, looking at the column rising in the centre of the room.
"It won't answer you, Anna" Elsa scolded her sister. "I'm sure he means well. If we really are in the past, we probably should not interfere."
"Why not?"
Elsa racked her brain. Some old thought experiments of hers came back to her mind. At least her memory functioned correctly again, even though there was now an unsettling spot of doubt about some details from when Anna visited her in her palace.
"Imagine that you break something. And you can go back in time to prevent you from breaking it..."
"Oh that's right!" Anna exclaimed. "If the Doctor can travel in time, we could go back to fix everything I broke in the castle when I was young! There was this painting whose frame I broke when I…"
"No, wait", Elsa interrupted quickly, "listen, if you go back and stop yourself to break something… what will you remember?"
"What?"
"You will see yourself as a younger you, and stop her from breaking whatever you broke. But how will it feel? Right now, you don't remember encountering an older you coming to stop you. If you talk to yourself, will you remember it as you say it? Would your memories suddenly change…" Elsa's voice trailed off as the words evoked a very sad remembrance from her childhood, one that she was not sure had been fully fixed. In any case, she realised she was very uncomfortable talking with Anna about memories changing. She tried to switch to another track of her thought experiments. "Oh, and if you do stop yourself from breaking the frame, what will have happened? Will you still remember that you would have broken it? And would you still have decided to go back to tell you not to do it?"
Anna frowned.
"This looks complicated." She looked up, smiling mischievously. "Maybe I could go ask the Doctor if it really works like that and if we could prevent myself from breaking this frame?"
"Anna, stop!" Elsa shouted as her sister walked to the door. "The Doctor told us not to leave the TARDIS!"
"But I'm all right outside, you are the one with the convergence memory thing. I'm just going to ask him and come back!"
"But you can ask him when he's back!" Elsa shouted desperately, as her sister opened the door. Anna turned back.
"I'm just going to see how it's outside! I'm not touching anything! Just looking!" She stopped halfway through the door. "You can visit the dressing room in the meantime. It is huge!"
Elsa sighed as the door closed. Maybe she should have tried another way to reason her sister, but she knew that the fight was hopeless anyway. You could barely keep Anna in place in the castle, which she knew like the back of her hand, what force could have possibly prevented her to explore something that may be her past? Elsa herself had trouble refraining herself, even with the threat to her memories, and even knowing that the date happening outside may be the day her darkest fear had come true.
Anna trudged quickly to the snow toward the ice castle. The TARDIS had landed on the opposite side of the big stairwell that led to it, on the slope that rose behind the castle, which meant that she actually had to go down to reach it.
She had been to the castle a few times with Elsa or Kristoff and had had a lot of fun exploring it. Her sister had given her some skating lessons there while Kristoff was marvelling at the structure of ice, under the watchful eye of Marshmallow. She had even managed to get Elsa to play a game of hide and seek, which she was pretty sure that her sister had won only through cheating by rearranging the structure of the castle.
But the feature she remembered now was a window that Elsa had probably created for symmetry, but which happened to be almost on level with the downward slope. With a little run-up, it was possible to enter the castle through it and already be at the highest level.
She noticed the window below her and began running to gain momentum. Just as she was bracing herself for the jump, a cold voice echoed below her.
"I told you to stay inside!"
Anna nearly lost her balance as she jumped, but managed to grab the balcony, where she remained hanging. Below her, the Doctor scrambled back up.
"Why does nobody listen to me when I tell them to stay inside? Is your sister also walking around?"
"No, I think she stayed" Anna panted, trying to haul herself up to the balcony.
"Well at least one of you does as she's told. You should take her as an example."
"Hum… bit of help, here?"
"Where do you think you are going?"
"Inside the castle! That was where you wanted to go, right? Only there is no door on this side, and you said we should not touch anything."
The Doctor sighed theatrically, then reached up and pushed hard on Anna's soles. This gave her enough thrust to scramble onto the balustrade and collapse on the balcony. As she was recovering her breath, the Doctor collided with the balustrade and hauled himself up.
"Now, listen to me, Freckles" he hissed, crouching near her. "We are in your past, and possibly in a diverging timeline. You must not interfere with anything you see, no matter how much you want to. It could create a paradox of the worst kind. Do you understand?"
"Yes, I understand. You told me already! Hey, are there people talking?"
Anna had inched toward the window and tried to tug at it. She heard a whistling behind her and the large ice door slowly opened.
"Sonic screwdriver" the Doctor explained, showing her the glowing stick. "Also works for ice latches."
They cautiously entered. Anna recognised the large room, with the intertwined arches. She also recognised a voice echoing through the ice walls.
"And you're alive?"
"That's Elsa!" Anna whispered loudly.
"Do you know when is that?"
"He's just like the one we built as kids!"
"Wait, was that me? I sound… strange."
"That is your normal voice. Do you know what is supposed to happen now?"
"It's that day… the day Elsa froze the kingdom. She also froze my heart" Anna added matter of factly, "but she did not mean it! She did not mean any of this!"
"We can't! Goodbye, Anna"
"They… we… Elsa and… I, are going to come on this floor, Doctor!" Anna whispered as the voices echoed below.
The Doctor led her behind one of the thickest ice walls that was surrounding the central room.
"Do you remember if you came here?"
"No. Great hiding place, though. Until Elsa made the wall become transparent, that cheat!"
"Be ready."
"For what?"
"Telling me whenever something changes from what you remember."
"Even if it means that someone comes behind this wall?"
"Try to tell me quickly then!"
Both became silent, leaving Anna's pleading voice fill the castle, the strange echoes against the ice giving it an almost singing-like quality.
"Is that how I always sound?" Anna said eventually.
"Yes. What part of 'hiding silently' you don't understand?"
"But my voice sounds so high-pitched! And with all those strange inflexions…"
"Wait until you discover recorders." The Doctor quickly glanced at her. "You may live long enough to see one, provided you don't end up in the wrong timeline. Now hush!"
Footsteps echoed in the room. Crouching behind the almost opaque wall, Anna thought she saw a blue clad figure slowly enter the room.
"This is Elsa!" she whispered, inching cautiously to the side of the wall to get a better view. For once the Doctor did not try to restrain her and joined her instead.
"You don't have to live in fear any more!" Anna's voice echoed, growing closer. "I'll be right here now! For the first time since…"
"WILL YOU STOP!"
Anna gasped. The Doctor looked at her intently. She slowly shook her head, then looked back at the room. The blue clad Elsa had whirled round, looking at the person standing in the doorway, which was hidden from their view.
"Can't you please leave me alone when I want it, Anna!? Go back have fun to the castle! Why are you always chasing me?"
"She never shouted…" Anna whispered, dumbfounded.
"I don't want you to be alone…"
"Yes, I'm alone, but I'm alone and free! Can't you understand that at last?"
Elsa strolled to the large window and slammed the door open. Anna gasped as a magenta-caped figure entered her field of view, following Elsa to the balcony.
"I'm free here! Free to do whatever I want! I don't need to hide all the time, I don't have to be afraid of hurting people! Why do you always have to follow me around?" Elsa's voice came from the balcony.
"Actually we have this tiny little problem in Arendelle that…"
"Arendelle?" Elsa laughed. Hidden behind her wall, Anna shivered. It did not sound like any laugh she had ever heard from her sister. "Look how small Arendelle looks now! So insignificant! I don't care about Arendelle! You can rule it if you want! Maybe that's what you wanted all along!"
Anna opened her mouth to protest, but the Doctor squeezed her shoulder hard.
"She's not talking to you" he hissed. "You are not here."
Elsa strolled back into the large room. The figure in the magenta cape turned round and followed her from the balcony. Anna could not suppress another little gasp upon seeing her own face, bewildered and pained from the other side of the room.
"Elsa, I never wanted… I only want you to be happy…"
"Then why did you never leave me alone?! Why were you always chasing me around, never leaving me in peace!?"
"I… I wanted to be with you… I never knew you would be so…" The strawberry blonde girl seemed to be on the verge of tears. Anna, who could not tear her eyes from the impossibly familiar face, felt a lump in her throat as well.
"I sacrificed my whole life for you! Do you have any idea how hard that was?! Always remain hidden, always conceal, never feel? All of this to avoid hurting you?"
"Yes, I understand now, but there was no need for that, I know you would never had…"
"And you had to come every single day to pester me with your happy singing voice, asking me to play, as if there was no other concern in your life than what the next game would be… And I had to say no, and no, and NO, AND NO AGAIN! Because Papa said so and he was so damn afraid that I would hurt you! Papa and Mama's little girl!"
A blizzard was beginning to blow in the room. Anna shivered behind her wall.
"Elsa never swears…" she uttered, bewildered. "She never said all of this… she simply was afraid for me and I did not understand…"
Her past self was making no attempt to wipe the tears that were now running on her cheeks.
"Please Elsa… I never knew… I'm sorry… I only wanted you to be happy…"
The wind howled as snow was blown around the room.
"Then WHY DON'T YOU LEAVE ME ALONE NOW? I'm happy now! Simply leave me alone! ALONE!"
"Elsa, you are not well… Please, calm down, we can work this…"
The wind stopped as Elsa whirled furiously to face her sister.
"SHUT UP!"
Shards of ice radiated from the blue-clad queen. Behind the ice wall, Anna winced in sympathy as she saw one of the shards hit her twin squarely in the chest.
"This… this happened" she quavered. "But she was not looking at me…"
Her twin staggered back, clutching at her chest, before kneeling down.
"I… struck you?" Elsa asked, her voice a mixture of curiosity and horror.
"I'm… okay. I'm fine..." the other Anna panted.
"You're fine? I struck you and you're fine?"
"It did hurt a bit, but I'm…"
"You're fine? You're fine? I struck you and you're fine? That's it? So what, were you playing possum all those years ago? Making fun of good old Elsa? Or wanting to get Mama and Papa's attention?"
"Anna!"
Kristoff entered the room at running speed, ending his course on his knees at Anna's level. Olaf followed him closely.
"I'm fine!" Anna's twin said, looking at Elsa as he helped her back on her feet.
"Who's this? Are you drafting all the men of Arendelle to look after you now? Do you also want to marry this one?"
The ice castle was creaking around them. Anna nearly shrieked when the wall behind which she was hiding almost moved as it changed colour, taking a darker tint.
"Elsa, please, I don't know what you are talking about. Please, come back with us, we can fix this together, you are not…"
"I feared to hurt you all my life and you never were in any danger?" Elsa raised her hands, her face contorted into a feral expression that made her look like a different person altogether. Anna saw the sparkles around her sister's fingertips. She now knew perfectly well what that meant, but her younger self apparently failed to make the connection.
"Of course I'm not in danger with you, Elsa! Please, calm down, you're upset, we..."
"You're not in danger? Then if you're not in danger you will not feel THIS?"
Elsa raised her hand. Anna saw the blue flash in her sister's palm.
Kristoff grabbed her younger self by the shoulders and began pulling her behind him.
The Doctor moved to get a hold of Anna's arm.
He was one fraction of second too late.
Anna jumped from behind the wall, half running, half skidding toward the little group.
She balled herself up, her arms extended in front of her. Her feet positioned themselves on her own accord in the skating position Elsa had spent many lessons teaching her. Well, maybe not this Elsa…
Anna collided into Kristoff as he was stepping in front of Elsa's blast. The shock sent him and her twin skidding to the other side of the room, scattering Olaf's body parts in the process, as Anna, her momentum neatly killed, fell hard on the frozen floor. The silvery cold spray passed above her with a hissing sound, ending in the far wall with a crash of broken ice. Kristoff and the other Anna ended their course in a heap against the far wall.
Silence fell back, soon broken by embarrassed apologies from the other side of the room as Anna and Kristoff tried to disentangle themselves, and by Olaf excitedly shouting at his legs to come back to him.
Anna slowly rose from the floor, massaging her chin. She turned to the sound of heels approaching her, loudly clattering on the floor.
"What… are… you?" her sister asked, towering menacingly above her.
"Leaving!"
The Doctor had appeared at Anna's side, grabbing her arm and pulling her upright.
Elsa looked at the grey-haired man as he unceremoniously pushed Anna behind him, then glanced on the other side of the room at Anna and the ice harvester helping Olaf to put himself together.
"Who are you supposed to be? What is… this?" Elsa asked, pointing at her second sister.
Anna looked at the Doctor, who was now standing firmly between her and her other self. For the first time since she had met him, at least with this face, he looked as if he was at a loss for words.
"Why are you so angry at… her?" she could not stop herself asking.
This got a reaction from the Doctor.
"We are leaving. Now!"
"But, Doctor," Anna protested as he began marching her back toward the window, "Elsa is not right! We must…"
"Doctor?!"
Elsa's shout echoed in the castle as rays of ice once again radiated from her. Anna turned to see one of the shards flying straight at them, before the Doctor violently pushed her aside. Struggling to keep her balance, she reflexively glanced at the other side of the room in time to see the shards mercifully missing her other self and Kristoff, who she saw cringing as they flew over them. She heard the Doctor gasp and looked up to see him holding his chest.
"Get out! Everyone get out! Leave me alone!" Elsa was shouting.
She gestured as if throwing something on the floor. A cloud of ice rose from it and coalesced into a form. Anna found herself peering anxiously at it, and was relieved to see it take the familiar shape of Marshmallow instead of something scarier. The hulking snowman formed facing Kristoff and her past self, and went for them, picking them up like rag dolls.
"You too! Get out! Get out!" Elsa shrieked, pointing at Anna and the Doctor.
Marshmallow turned ponderously, still holding the struggling Kristoff and the other Anna. But the Doctor reacted first. Straightening up, he seized Anna's wrist and headed toward the window from which they had entered.
"Run!"
The Time Lord and the princess erupted on the balcony. Anna could not repress a little yelp as the Doctor kept running toward the balustrade.
"Jump!" he shouted, giving her a push.
Anna half-jumped, half rolled over the balustrade and fell face-first into the snow. The Doctor landed a second later a few feet from her.
"Are you OK?" he asked, pulling her out of the snow.
Spitting snow, Anna was about to answer when he cut her.
"Do you know what happens next? Was that an Ice Beast she invoked?"
"No" Anna protested, "that was Marshmallow… he's a bit rough, but he actually did not mean to harm us…"
The Doctor grabbed her wrist and began marching up the slope toward the TARDIS, pulling her behind him.
"So your past self is not in immediate danger right now? If your sister leaves ice-cream brain's big brother do the dirty work?"
"I… think… I hope so…" Anna panted, trying to keep up with the Time Lord.
As if answering her, her own voice echoed from the mountain behind them.
"It's not nice to throw people!"
"Yeah", Anna said cheerfully. "That's me and my strange-sounding voice after he threw Kristoff and me out. I will make him mad right after that. That did happen."
The Doctor did not answer, still trudging purposefully forward. Marshmallow's roar echoed behind them, now more distant.
"Oh, and now I made him mad. I threw a snowball at him. Everything is back to how it was! I fixed it!"
"You did not fix anything!" the Doctor said finally with ferocity. They were now a dozen meters away from the TARDIS, which stood reassuringly on the slope above them.
"Yes I did! Elsa was not doing anything like I remembered, and she wanted to fire some ice at Kristoff and I, then she created Marshmallow like I remember and…"
"I told you not to do anything! Do you remember me saying that? I said it because I wanted you not to do anything."
The Doctor pulled his key from a pocket as they approached the blue box.
"Now that you have interfered, we are part of these events. We can't leave this timeline!"
"What? But… it's become the correct one, now, right?"
"You tell me" the Doctor said, unlocking the door and swinging it open to let her enter. "Do you think the correct timeline is the one where your sister becomes mad at you, knowingly freezes your heart, and attempts to shoot an ice shard at you?" he asked loudly, entering the TARDIS.
The lone occupant of the TARDIS, who had been huddled near the console, stood up and gasped.
"Does it seem like something you could have done" the Doctor asked, striding toward her, "holding your sister responsible from your isolation, and trying to strike her with some kind of ice missile when you realised that a shard of ice going through her chest had left her standing?"
"Doctor!" Anna hissed indignantly.
"Hush, miss 'I fixed everything'! Go on, Platinum, tell me, was it something you considered that day?"
"No!" Elsa said, looking horrified. "I never held Anna responsible! I did not realise I had struck her, I would have sent her to the Trolls if I had known, I would never…"
"Please refrain from freezing the TARDIS again. Trolls? Do you mean, actual Trolls or simply those people who like to… Never mind, we'll come back to that later. Now, please answer me truthfully. Do you really mean what you said? Or are you saying that because it would make you look bad, or because it really felt like a bad idea in retrospect and you are glad you did not do it? I need you to be honest, it's very important."
"No" Elsa said, more forcefully this time. "I was never angry with Anna. Well… maybe a few times I did snap at her when she was knocking on my door, sometimes without her hearing me but… no, Doctor, I never wanted to hurt her. I always loved her! You have to believe me, Doctor! Whatever you saw me doing out there, it was not me!" Elsa said, trying to keep her voice from faltering.
The Doctor kept looking at her intently for a few seconds. Anna wordlessly walked up to her sister's side and clasped her hand tightly.
"Now it is" he whispered eventually.
"Wait, what? Doctor, Elsa told you she would never have done…"
"Doctor, I swear to you that I never wanted to hurt Anna! It was my worst nightmare!"
"I believe you." The Doctor took a deep breath. "But it does not matter now. It would have been simpler if you had, although that would not have explained why the timeline switch happened so suddenly. But now we don't have a choice."
The Time Lord looked at the two pairs of uncomprehending blue eyes.
"Time is not fixed. It's fluid. It is always being rewritten. You can take another decision, even if you already took it." He sighed at the sisters' blank expression. "Do you sometimes wonder whether you had tea or coffee for breakfast the day or the week before? Or whether you went for a stroll in the park or stayed at home a particular day some months ago?"
"Chocolate" Anna chirped. "I always drink hot chocolate for breakfast."
The Doctor glared at her.
"But sometimes, I do fail to remember if I did something or other" she added after a few seconds. "For instance, Kristoff and I can never agree what we had for picnic when we went to see the Northern Lights in the mountain last month. I'm sure there were sandwiches, but he insists he had me try the speciality from his adoptive mother with moss in it, but I'm pretty sure that was the day where we…"
"I don't care" the Doctor cut sharply. "The important point is that both of you could be right. Maybe at one point you did, and then you did not. Time is constantly rewritten. When you hesitated between two choices, and took one, and forget which one you took, you are simply oscillating between two states. Two timelines, two very minor timelines, only separated from one another by your petty choices at a given moment in time, and otherwise identical for everybody else. Do you understand that?"
"So, what you are saying, Doctor" Elsa said slowly after a few seconds of silence, "is that we could take another decision… in the past? For instance, I could have… not frozen the kingdom last year?" She bit her lip. "Last year for us, anyway."
"No you could not. Because you perfectly remember that day, and it had consequences for everyone around you. You, as you are standing now, could not switch to a timeline where you did not freeze the kingdom. In a few decades, when you are old and senile and don't remember the past well, while everyone who was around at that time is equally forgetful or dead? You could. Memories are the key."
Elsa pondered his words for a few seconds, desperately trying not to think of the elderly Anna she had met mere hours ago.
"So… when you asked me if I could have wanted to… hurt my sister…"
"I wanted to know if this was a possible timeline. Of course, even if it had been you should not have been able to switch while your memory of it was so fresh, but that would have been a simple time oscillation problem, and I know how to fix that. But if this was not a choice you would have made… then your mind was affected by something external to your timeline".
The Doctor looked at Anna and Elsa's perplexed expression and sighed.
"Freckles!" he asked, pointing at Anna. "What did you say earlier?"
"That I drink chocolate…"
"Before that! About the dreams!"
"Err… that I dreamt about Olaf wanting to get a tan and…"
"No, no, no, the nightmares! You said something about what gives you nightmares!"
"Oh yes. There is always something when I have a nightmare. Either I ate too much chocolate, or had a row with the people from the paintings… That was, when I was younger, I talked with the people in the paintings" she added with an embarrassed laugh.
"This is what I mean. Not the paintings. The painting thing is stupid. Having a row with imaginary people is stupid while you could have tea with them instead. But if you see timelines as dreams, then something outside of the dream can give you nightmares. If Platinum changed so much, it is because something or someone influenced her. And not by time rewriting itself as I just explained to you."
"Oh, so this bad Elsa was influenced by something to be angry with me?" Anna said, finally seeing a connection to the subject at hand.
"Or this not bad Elsa here was influenced not to be angry" the Doctor cut sharply, pointing at Elsa. "AND" he added, raising his word above Anna's indignant protests, "she would remember always not being angry if the influence went back far enough."
Anna smiled broadly.
"Oh, I think I understand! We can go back in time to when she was influenced, and then…"
"No. We can't" the Doctor said flatly.
"What? But Doctor, we just…"
"Now that you have interfered, we are part of these events. We can't go back to alter them. That would create a paradox. We already have one with both of you around while the events outside don't seem to lead to you becoming yourself."
"But… we were in the future and we came back to now…"
The Doctor smiled a humourless smile.
"Yes. We were. And I already took a lot of risks by coming back in that time after interfering with the future. But now you changed the events that would have led to it, and, more importantly, you nearly crossed your own timeline. That is two very big no-no's when travelling in time."
"But I… What did I change?"
"You prevented your sister to blast you a second time. As I understand it, this should have led to the mountain guy being blasted in your stead. We… learned that in the future. Now you have prevented it, but at the cost of weakening the fabric of time with all these paradoxes."
Elsa wrapped her arm around the suddenly trembling shoulders of her sister and hugged her tightly, looking severely at the Doctor, who did not seem to notice.
"What does all of this mean, Doctor?"
"It means we are trapped in this timeline. If we leave now without fixing all those time alterations, we may not be able to come back to this time period."
Elsa squinted.
"You mean… we would not be able to come back to Arendelle? To where… when we left?"
"No. Time has become too tangled. Of course, that is only part of the problem. The other part is that, currently, the correct timeline is the one outside, where you threw up a tantrum and tried to blast your sister."
Both sisters shivered.
"But that did not really happen! I don't remember it happening!"
"Yet you felt your memories changing when you left the TARDIS. That was time reasserting itself, trying to make you become the local version of yourself."
"That means I would become… the Elsa who tried to…" Elsa left the words hanging, too horrified to complete the sentence. She hugged Anna even more tightly, but even that did not prevent the temperature around her to drop a few degrees.
"Of course, that would only be the beginning" the Doctor said in a reassuring tone. "It's very unlikely that the version of yourself from this timeline boarded the TARDIS, and that probably goes for your sister as well. You should probably not be here with me at all in this timeline."
"But is there nothing we can do?" Elsa asked desperately.
"Yes there is. We can try to find out what influenced you, and in which direction. And if you are lucky and it happens that the timeline you remember is the one that was rewritten… then we have to make sure it is restored."
"What happens if we don't?" Anna asked timidly.
The Doctor looked at them. "The TARDIS will protect you for a while, but she can't sustain such a paradox for long. You will both cease to exist" he answered matter of factly.
Author's Notes: Anna's comments on her voice are not intended as a jab at Kristen Bell's lovely voice, but simply a reference to how one's own voice sounds strange when you hear it, and that she's supposed to be singing in that scene in the film.
What the Doctor explains about the past being constantly rewritten, with the proof being uncertain memories, is something I took from the "Good Night" mini-episode and expanded upon a bit with my own headcanon.
I'm playing a bit with the laws of time travel to prevent the Doctor from going further back in time to fix this, but these laws have always been rather fluid anyway (you probably need to be a Time Lord to understand them). Let us consider it is the same kind of laws that prevented him to rescue Amy and Rory from the past.