I have issues with how many time travel stories hand wave away a lot of science. My first objection was about how momentum was dealt with (or rather, not dealt with) in these stories. Now I'd like to focus on what Quantum Mechanics says about changes to the universe when time travel is present.
Often in time travel stories the author will try to get around the possibility of a paradox by claiming that the characters are only allowed to remain in the past so long as they don't change anything. Stories where the timestream would just spit out anyone that made a change in human history are an example in a seemingly never ending line of examples of humanity's hubris. Why on earth would the universe care whether humans noticed a change? The only things that the universe can be said to care about are the fundamental laws that it follows. And one of these laws appears to demand that if time travel is possible, the universe must be changed by it every time.
Just to be clear here, I am talking about fictional universes that allow time travel. My complaint is that time travel stories often don't support enough science to be called science fiction. Determining how the actual universe would work with time travel is left as an exercise for the reader.
Objection 2: Heisenberg Uncertainty Principle
Einstein is famous for having made a statement that is paraphrased as, "God does not play dice with the universe." I am disappointed that the reputed reply of Niels Bohr is not as famous, because I think it is just as good. "Einstein, stop telling God what to do."
So far, a vast amount of experimental data has shown that God does in fact play dice with the universe, by which I mean that the underlying mechanism of the universe for determining things like particle position and momentum is probabilistic in nature. A particle can be thought of as smeared out across many positions until it is measured, at which point it jumps randomly (based on probability) to one of the positions it was smeared across.
At the risk of Bohr's shade telling me to also stop telling God what to do, I will make my own claim. "God does not let us cheat at the dice of the universe." In the presence of time travel, the randomness that is at the heart of quantum mechanics cannot disappear.
Suppose you watch a physicist collapse the probability wave on a particle to measure the exact position of that particle. Now go back in time and watch the exact same experiment performed again. Does the physicist get exactly the same result? If so, then you have just cheated God at dice because you knew the outcome before it happened.
You have also created a situation where you can violate the Heisenberg Uncertainty Principle. It says that certain pairs of properties can never be known simultaneously with precision. The most commonly cited properties are the position and momentum of a particle. The more precisely you know one quantity, the less precisely you can know the other.
But suppose the physicist in our previous example sets up the experiment to measure either the exact position or the exact momentum. They don't actually know which one they will measure, they let you determine it. You set a switch to measure the exact position, then time travel back and set the switch to measure the exact momentum. Suddenly, both position and momentum are known beyond the boundaries of the uncertainty principle, and we have just cheated the universe out of obeying its own principles.
The only way I can think of to get around these issues is to assume that each and every time that time travel occurs, the outcome of the wave function collapse becomes completely unknown. The physicist measuring the position of the particle has to get different answers on each time travel trip. Just because the time traveller knew what the position was before, the act of time travelling has invalidated that result and they have no more idea than they did the first time around as to what its position might be this time.
So at the quantum level, time travel must automatically change the universe no matter what the time traveller does, or at least that portion of the universe within the light cone originating at the point the time traveller travelled back to.
What does that mean for human history? Would we see changes to history every time someone travels back in time? Not necessarily. Chaos theory is helpful to consider here. Strange attractors could allow for the overall shape of history to snap toward particular ranges of outcomes, keeping things fairly constant. Unfortunately, the butterfly effect suggests that relatively small changes (like differences in outcome from wave function collapse perhaps?) could cause history to jump to other attractors. So good luck to time travellers hoping not to substantially alter history. The outcome seems to be completely out of your hands no matter what you do.
Then there is the tendency for quantum effects at a macroscopic scale to disappear. Even if all the air molecules in a room suddenly went in different directions, would anyone notice or care? Still, recent experiments have shown that quantum effects can persist at the macro level. Plants extraction of energy from sunlight seems like a good example.
The resetting of probability waves by time travel does not suggest that the Many Worlds Interpretation of quantum mechanics must be correct in a time travelling universe, by the way. There could still be just one universe realized at any time out of many potential ones, just as in a world without time travel.
You can think about the set of states the universe can reach as a tree where travelling up the tree is moving forward in time. Each branching of the tree describes the states a particle could assume after a wave collapse. The Many Worlds Interpretation would say that each branch tip represents a universe that exists, but you could instead think of it as a universe that could potentially exist. Perhaps at any time there is a single actualized universe. Picture a caterpillar climbing up the tree. At each branching, it can choose any of the branches to follow based on the probability for that branch to be actualized (perhaps represented by the thickness of the branch). At any one time, the caterpillar is only on one path, representing the state of the current universe. If the caterpillar falls back down the tree (travelling backward in time) and has to start climbing again it may take a different route up the tree, but the universe would still have a single state, albeit not the one it reached before.
For those who think that causation would not allow that (since the cause of the new probability wave collapse would be the time traveller from the old collapse who would no longer exist), tune in next time for my essay on Time Travel and Causation.