I contend that there is no such thing as backwards causation (a future event being the cause of a past event). This is a contentious claim, more so because I hold that even if time travel were possible there would still be no such thing as backwards causation. Of course at first glance it certainly seems like backwards causation is possible. We imagine scenarios in which time travelers go into the past and have some effect there, and reason that if they hadn’t gone into the past then they wouldn’t have had those effects, and thus that their decision to go backwards in time is a cause of those past effects. But I claim that this reasoning does not demonstrate that backwards causation makes sense, rather it demonstrates that our intuitions fail us when it comes to time travel. Let us say that in this case the time travelers had some effect in the past. And now we in the future are contemplating what effects their choosing not to go would have. But this falsely supposes that there are two directions of time. One would be the usual flow of time from past to future and the other would be the direction upon which their decision not to travel in time has an effect on past events (if they make the choice to go one sequence of events happens along this direction of time, which leaves the past as it is, and if they don’t go another sequence of events happens which change the past). However there is only one direction of time, and so the intuitive description is obviously wrong somewhere. But this is just hand waving. Onwards then, to the detailed explanation.
There are actually two ways in which backwards causation might seem to occur. One is through “classical” time travel, where an effect propagates backwards in time, and the other is via general relativity, where the time traveler never moves backwards in time locally, but overall follows a path that gets them back to where they started before they left. The relativity case is actually easier to deal with, so I will address it first. The relativity case is easier to deal with because relativity in general makes a mess out of causation. Observers in different frames of reference will disagree about the order of events and thus about causation. So already we must restrict ourselves, and realize that we can only sensibly talk about causation with respect to some frame of reference. In the case of a time-like loop (where someone follows a path that brings them to a time before they started) we want to know what causation looks like to an outside observer (since from the point of view of the observer following the time-like loop it doesn’t seem to them that they have gone back in time, but rather that time in the rest of the universe reversed direction). Let us suppose that they witness a billiard ball arrive at t1, and meet up with an earlier version of itself, which then proceeds to leave on the path that will bring it back to t1 at t2. Here we might actually legitimately say that the billiard ball leaving at t2 was the cause of it arriving at t1. However this is not backwards causation. It is not backwards causation due to how past, future, and simultaneous, are defined in special relativity (in terms of the paths light can take). If such a time-like loop exists then to some observer between t1 and t2 time t1 will simultaneously be in the past and in the future. And thus if the billiard ball leaving at t2 happens to have a causal influence at t1 that is not backwards causation, but rather forwards causation in a very strange space-time geometry. Of course that is very unintuitive, but we have to accept it, since while relativity is an unintuitive theory it is well confirmed by experiment. And besides there are serious doubts as to whether such time-like loops can actually occur.
This brings us to classical time travel. In a classical time travel scenario we don’t have to worry about our intuitions about time failing us (at least not so radically), and so we are better able to say exactly what is wrong with backwards causation, instead of just pointing to a general breakdown in our way of approaching the problem. Here is a diagram of the simplest kind of classical time travel scenario, as seen by an outside observer:
Here particle A is hit by a time travel force at t2, which sends it backwards in time until it stops at t1 and moves forwards in time as the particle labeled B. Initially backwards causation might seem to be a good explanation for what is going on here, but if backwards causation is what is really happening then a change in A, such as not being hit by the time travel force, should result in a change in B. But, as mentioned previously, that can’t happen. If we have two worlds which agree until t2, at which point in one A is hit by the time travel force and in the other it is not, it can’t be the case that the state of B before t2 is different in these two worlds. By stipulation we have said that they were the same up until this point, and since we are examining them from a viewpoint outside of them it can’t be that the past of one universe changes at t2; change is something that happens over time, it doesn’t make sense to talk about particular time-slices of the universe changing unless we introduce a second dimension of time. And there is a way of making perfect sense of this situation without invoking any kind of backwards causation, as illustrated below:
Now we think of B as a particle that appears spontaneously, and along with it appears what we can call its T-anti-particle (which has negative mass and energy if the conservation rules are obeyed). The T-anti-particle follows some trajectory until it encounters a particles of the same type as B, A, and at the same time it collides with A it is also struck by a T-force. As a result of this interaction A and the T-anti-particle disappear. What happens in this scenario if something changes at t2 (for example if the T-force isn’t present)? Well then the T-anti-particle would continue on its trajectory until it hit some other particle, A* at the same time as that particle is subjected to a T-force (illustrated in red). Thus changes in A do not affect event in the past, but rather effect events in the future, and so there is no backwards causation, only the standard forwards causation. Of course this means that the initial appearance of B is uncaused, although such appearances may be statistically predicted. Events without causes may seem unusual to some, but it seems the right thing to say in this case, since the appearance of B cannot be predicted based on local regularities. Of course no such T-forces and T-anti-particles exist in our universe, to the best of my knowledge; my point here is to show that backwards causation is unnecessary, and problematic, even in principle.
Final Note: I have had to qualify some of what I have had to say here by restricting it to universes with one time dimension. In universes with two or more time dimensions we still don’t need backwards causation, but causation is a much more complicated affair. In brief you can always pick some time dimension as the causal one, and give causal explanations in terms of how events develop along that time dimension without invoking backwards causation, assuming causal effects are local and don’t propagate instantaneously.