In this post
, Michael Huemer presents a mistaken view of time travel. I think Huemer is a great philosopher, so I was surprised to find that each of the major points in his article contain clearly flawed reasoning (or don't prove the conclusion that time travel is metaphysically impossible).
In this article, I will go through Huemer's points, discussing why the reasoning presented in each is unsound.
1 - "The one thing you obviously can’t talk about moving in is time itself. Time cannot be related to time in the way that space or color or physical state could be."
Huemer's assertion is contradicted by both special and general relativity. Firstly, in special relativity, every moving massive object has a four-velocity (velocity with four components). The latter three components are the object's rate of positional change in the three spatial dimensions. Surprise, surprise, the first dimension is pretty much the object's velocity in time.
But what would the object be moving relative to in time? The answer is its proper time. The proper time is the time of an object as measured by a clock traveling along with the object. Notably, if you were to watch an object traveling close to the speed of light, its proper time clock would be moving very slowly. This means that for every unit of proper time passage for the object, time in the reference frame the object is traveling relative to passes by more than one unit! So different objects are traveling through time (relative to their proper time) at different rates (if their velocities vary)!
Huemer mentions that dt/dt would be nonsenical. In special relativity, the first component of the four-velocity is
Where tau is the proper time.
Now for general relativity. In general relativity, gravity is the bending of spacetime, not a force. So gravity affects objects by curving spacetime so as to make it that a straight path through spacetime will move towards massive objects.
Consider an object placed in a stationary position above a stationary star. Clearly the object isn't moving in space, as it is stationary. We all know that such an object would begin to apparently accelerate towards the star, so gravity must be affecting it. But for gravity to affect objects, they must be moving through spacetime (to have their path curved). Therefore, the object must be moving in spacetime. Since it isn't moving in space, it must be moving in time.
2 - "In the year 2100, Marty got into a time machine. Then, he got out of the time machine in the year 1900.
That’s contradictory. That story says that an event happened (getting into the time machine) and another event (getting out of the time machine) occurred both after and before the first event. (“Then” indicates something happening after, but the year 1900 is by definition before, not after, the year 2100.) So that’s obviously impossible."
This supposed contradiction is easily resolved by distinguishing Marty's future and past from the world's future and past, which Huemer mistakenly takes to be one and the same (he defends this assumption in 7, which I will respond to later). The resolution is that Marty's future is in the world's past. So Marty stepping out of the time machine happened in the world's past (and this doesn't "then happen" for the world). However, Marty stepping out of the time machine is in Marty's future (and so him stepping out does "then happen" for Marty).
3 - "Here’s a plausibly necessary metaphysical principle: A material object cannot be wholly present in two places at once. E.g., I could not be in Paris and Denver at the same time. (A part of me might be in Paris while another part was in Denver, but it couldn’t be that the whole me was in both places at once.)"
This point from Huemer is doubly wrong. Firstly, this metaphysical principle does not seem at all necessary. Secondly, time travel need not violate this principle!
Why isn't the principle necessary? Just imagine that there's a box present in two places. Whenever you poke a hole in the box, a hole appears in both of its locations. When you kick it, it moves in both locations, et cetera. One object, two locations. Perfectly conceivable, yet in contradiction with the principle, so such a principle is clearly not necessary.
Why doesn't time travel need to violate this principle? We can revise our understanding of objects. Typically, objects are taken to be 3 dimensional. However, they could be 4 dimensional instead, with extension in time. At each moment in time the object is present, it is really a particular part of the object that is present. In Huemer's cases, there would not actually be a single object at two different places at once. Rather, there would be two parts of one object, at the same moment in time but different places in space. Obviously, it is acceptable for different parts of an object to be in different places at the same time. Just consider my right and left hand. They are both parts of me, but are in different places at once.
4 - "If you send an object (with nonzero energy) “to another time”, what that actually means, physically, is that the energy of the universe goes down right after the object goes into the time machine; also, at some other time the energy goes up." - supposed violation of conservation of energy.
Wrong! As a first indication that Huemer is wrong, consider the following. General relativity is a theory known to obey conservation of energy, and wormholes, which allow traveling backwards in time, are allowed by the laws of general relativity. So somehow conservation of energy must be satisfied by the process of an object going through a wormhole to the past.
How is this possible? Huemer makes a simple mistake. He assumes the past moment that an object travels to is disconnected in space and time from the future moment. But with wormholes, spacetime is deformed in a continuous way to spatially connect a future moment in spacetime to a past moment in spacetime.
Conservation of energy is a local principle. It states that there should be no point in spacetime where energy is on net being generated or lost. Because wormholes connect the two moments in spacetime continuously, there is no such point as an object travels through the wormhole! In its path through the wormhole, as energy is being sunk into a point (from the object moving out of previous spacetime in its path), it is being sourced into another point (from the object moving into the next section of spacetime in its path). These points are exactly connected, obeying local conservation of energy.
This explanation is also given here: https://physics.stackexchange.com/questions/79291/does-the-concept-of-a-wormhole-violate-the-law-of-mass-energy-conservation
5 - Huemer’s argument here is that time travel allows backwards causation--it allows things to cause other things before they happened. He argues that this is impossible. As Huemer acknowledges, he has no argument for rejecting backwards causation. I disagree with him that backwards causation is impossible. Backwards time travel, as featured in consistent time travel stories, is perfectly conceivable to me (and most people), indicating that the impossibility of backwards causation is not obvious.
6 - I agree with Huemer that inconsistent time travel is metaphysically impossible. As Huemer notes, however, there exist consistent time travel stories (like 12 monkeys). Consequently, point 6 does not rule out backwards time travel altogether, just some forms of it (which I agree are impossible).
Although Huemer doesn't raise the following point, I imagine many readers will be thinking it: "If backwards time travel is possible, isn't contradictory time travel necessarily possible? Since I know I could go back and shoot my grandfather if I wanted to and had a time machine. So backwards time travel must not be possible at all." If we have libertarian free will, this argument is somewhat viable. However, for reasons I won't get into here, libertarian free will is incoherent.
In the case of compatibilist free will, the fact that a person "can't change the past even though they can go to the past" is no different fundamentally from "can't change the future even though they can go to the future". All of the same supposed paradoxes arise, but just more frequently for backwards time travel, because we tend to have more knowledge about the past than the future. Just as it's the case that you won't go into the past and shoot your grandfather (since your grandfather was not shot), it is also the case that you won't go into the future and not have a child (assume you do have a child in the future). It's just that you already know one of these facts and not the other.
Compatibilists accept that even when set of facts are fixed by features of the universe not chosen by a person, that person may be responsible for those facts. This can apply in both backwards and forwards time travel. The laws of the universe and the initial conditions entailed that I would write this article, but I still wrote it with free will (I promise no one forced me to do it via mind control). Likewise, the laws of the universe and initial conditions (assuming GR is true and wormholes are present) could entail that an individual travels back in time and makes a dent on the moon intentionally. They're still the one responsible for the dent, and did so with their own free will.
7 - Huemer responded to David Lewis who proposed that there are two times--exactly what I proposed in section 2. Huemer says there’s no reason to think that there are such two times. Huemer is blatantly wrong here. Firstly, there is already a straightforward sense of two times, as in special relativity! An object's proper time, vs. external time.
Secondly, if he is to avoid begging the question against backwards causation in point (7), an even more direct solution to this issue presents itself. Causation has a direction, so we can identify an objects "personal time" via the direction and path of its causal chain. When an object travels back in time, what is happening is that its causal chain points forward into the past (where the past is what is in the backwards direction of the environment's causal chain).
There you have it. Huemer's arguments against time travel debunked. All of the points I made in response have already been made by David Lewis, which makes it surprising that Huemer had no good reply to Lewis. Considering how compelling the responses are, it's quite ironic that Huemer describes Lewis' views on time travel as "no exception [to his craziness]".