In Season 3 of the the revived Doctor Who, the Doctor and Martha Jones go back in time to 1599 London, where they defeat the villainous Carrionites, who were most likely going to destroy, or at least take over, Earth. With all that not happening in the events of "Turn Left," why doesn't the world end?
It is true that, in the Turn Left universe, the Doctor died during the events of The Runaway Bride and so was not able to take part in any of the events shown in seasons 3 and 4. In Turn Left we see the consequences of the Doctor not intervening in the events of Smith and Jones, Voyage of the Damned, Partners in Crime and The Poison Sky.
I think it is wrong to assume that because the Doctor could not help to foil plan of the Carrionites (as described in the Season 3 episode The Shakespeare Code), that the plan must necessarily have succeeded. As the Doctor tells Donna at the end of Turn Left, the universe is capable of compensating when time is interfered with.
Just got lucky, this thing. It's one of the Trickster's Brigade. Changes a life in tiny little ways. Most times, the universe just compensates around it, but with you? Great big parallel world.
So if the Doctor wasn't able to intervene, we can assume that the universe compensated by having the Carrionites plan fail for some other reason. Perhaps Shakespeare figured it out on his own, or Captain Jack showed up instead of the Doctor. Or perhaps the Carrionites were distracted by a butterfly that Martha would have stepped on if she had been there with the Doctor.
MARTHA: It's like in the films. You step on a butterfly, you change the future of the human race.
DOCTOR: Tell you what then, don't step on any butterflies. What have butterflies ever done to you?
It's basically a grandfather paradox.
- The alternate timeline of Turn Left was created when (alternate) Donna chose to turn right instead of left.
- If the (alternate) world had ended in 1599, then (alternate) Donna would never have been born.
- So, she would not have been able to make the decision to turn left or right.
- So, the alternate timeline could not have been created.