Opinions on the Grandfather Paradox

Question

According to the grandfather paradox, the notion of changing events that have occurred in the past is logistically impossible due to the fact that the events have already occurred. This has lead many physicists to believe that backwards time travel is logistically impossible.

What is the opinion of other physicists here in regards to what would happen if we assume that backwards time travel is possible and a person were to modify something in the past. What effect would killing Hitler have if one were to return to the present and would the spacetime we once occupied still exist? If not, what happened to it?

Answer 1

By far the most popular approach to time travel is the Novikov Self-Consistency principle. In fact, I think it may qualify as the only "main stream science" concept of time travel because it fits into the known laws of physics.

In Novikov Self-consistency, it is impossible to create a paradox because the only path you can take is one which is self-consistent. In a paper, Novikov and his co-authors put together an example. They created a universe consisting only of a single billiard ball and a wormhole which could take one back in time. You hit the billiard ball towards the wormhole, and try to line it up so that when it pops out on the other side, it's on a trajectory to intersect itself. This appears to be a paradox, for if the ball collides with itself, surely it cannot go through the wormhole, so can't collide!

What Novikov et. al. showed was that there's another option. They showed that the ball might come out of the wormhole at a slightly different angle than you thought it should. Indeed, when you hit the billiard ball forward, and the "future" billiard ball comes out of the wormhole, it comes out at just the right angle to graze the "present" billiard ball, changing it's path slightly. In fact, it changes it to exactly the correct path such that it enters the "present" wormhole at just the right angle to come out of the "past" wormhole at exactly the angle it needed to graze the ball in the first place.

The authors showed that for any arbitrary topology of wormhole positions ball positions, initial velocities, and time-travel periods, there was always a self-consistent solution which avoided any paradox. The collisions varied in angle and energy, but always worked with the laws of conservation of energy and momentum.The authors then conjectured that this might also be true for scenarios with more wormholes or entities more complex than billiard balls.

Answer 2

The Novikov consistency condition I think can be extended further. A quantum state $|\psi\rangle$ that enters a closed timelike curve means that at the point the path loops there is the duplication of the state $|\psi>~\rightarrow~|\psi\rangle|\psi\rangle$. This is known to be not unitary. The reason is that if the state $|\psi\rangle~=~a|\alpha\rangle~+~b|\beta\rangle$ is duplicated we have $$ |\psi>~\rightarrow~|\psi\rangle|\psi\rangle~=~a^2|\alpha\rangle|\alpha\rangle~+~2ab|\alpha\rangle|\beta\rangle~+~b^2|\beta\rangle|\beta\rangle. $$ However this process is basis specific because we could just duplicate $|\alpha\rangle~\rightarrow$ $|\alpha\rangle|\alpha\rangle$ and $|\beta\rangle~\rightarrow$ $|\beta\rangle|\beta\rangle$. And the state $|\psi\rangle$ transforms into $$ |\psi>~\rightarrow~~a^2|\alpha\rangle|\alpha\rangle~+~b^2|\beta\rangle|\beta\rangle. $$ This means potentially a number of things, such as the two states, even given the existence of closed timelike curves, can't interfer in any way. This means the time traveling curve can't self intersect.

This argument can also be made for the destruction of quantum states. The reverse of duplicating states is also a nonunitary process. It is not hard for the reader to see this. It is also one reason that conservation of qubits is a pretty central idea of theoretical physics today.

If there are curves that loop through time they can't be closed, and quantum mechanically they probably have zero overlap. This would tend to mean that if one traveled back in time to kill their grandfather that the process would prevent that. In effect the probability path for not killing the grandfather is unity. This would then prevent the demolition of the time traveler by timelooping and killing his father or grandfather. In fact it means ultimately there can't be even a butterfly effect that changes the outcome of the time traveler being born. The quantum overlap of states of the traveler and the quantum states of systems back in time must then likely be zero or extremely small.

The most reasonable way to insure there is no such interference or overlap of time looped states is to say that such time travel is not physically possible. This is the most reasonable way to foreclose any possible self-looping path integral of paths = states that are effectively duplicated or in the grandfather case destroyed, is to say that this is not possible.