Is time travel only possible if the world is deterministic?

Let's say that true free will (and not only the impression of free will) is only possible if the world is not deterministic (meaning that the future of universe in not determined by its state at an initial time t0). Let's say that "F" means "Free will exist" and "D" means "the world is deterministic".

I start therefore from: F <=> nonD.

Now, if time travel is possible, free will can be problematic, as I could go back in time and kill my father or even myself, making my time travel from the future impossible. This is a well-known paradox of time travel. Let's say that "T" means "Time travel is possible".

Then, in my view, F => non T.

Which means that : T => D.

As a conclusion, if time travel was ever found possible, it would then prove that the world is deterministic, and that free will is an illusion.

(additional comments based on Michael's answer: 1°. I should rather write that nonD => nonT and therefore T => D, in order to include other possibilities of nonD (other than F only). 2°. I am only talking about time travel in which a human being from the future can interact with other people in the past.)

• Just if we assume that time is only one and is a scalar magnitude. But what about to think about time as a tensor with different components? each of one valid or defining only one universe on its side? – Mario Enrique Nov 21 '13 at 22:28
• Bu why does the grandfather paradox imply no free will? Libertarian free will doesn't mean being able to do anything at all that you want (such as jumping over a 30 story building); it means being able to whatever you want that is physically possible for you to do. Killing one's ancestor back in time and cutting one's lineage isn't physically possible--whether we have free will or not. – Chelonian May 26 at 11:50

If you are only looking for a sketch of how you might travel in time without determinism, and you equate free will with determinism, then one can easily sketch a world which admits both free-will and time travel, and in which physical systems and events have apparent causes.

Allow me to sketch a bifurcating time-line admitting time travel. If we suppose that by and large matter/energy is conserved in the usual way, except when engaging in the mechanisms of time travel, then just because you have travelled back in time to kill your grandparent does not mean that you will stop existing. If you absolutely require chains of causality to be traceable over long stretches of time and beyond the process of time-travel itself, then it simply suffices for there to be one continuity (a) in which you are born, and another continuity (b) in which you arrive from the future:

Time t=-51. Your grandparent meets their future spouse for the first time.

Time t=-50(a). Your grandparents start a serious relationship. Nobody particularly interesting appears from the past.

Time t=-49(a). Your grandparents get married.

Time t=0(a) You are born to your mother.

Time t=30(a) You have invented a time machine, and travel back to time t=-50.

Time t=31(a) Your disappearance remains an unsolved case by the police, and you are presumed dead.

Time t=-50(b) Your grandparents start a serious relationship. You appear from the past.

Time t=-49(b) You kill one of your grandparents, preventing your mother from being born. Being a physical system which has a past which can be traced back some amount of time, and whose appearance in the past can in any case be explained by the mechanism of time-travel to a continuity in time in which this assassination did not occur, you continue to exist, because physics is not in the habit of simply allowing macroscopic physical systems to vanish.

Time t=-25(b) You are freed from prison for your crime of murder, on parole, due to good behaviour.

Time t=0(b) You privately and wryly commemorate your own zeroeth birthday.

Time t=25(b) You celebrate your 75th in-continuity birthday.

Time t=30(b) You die in a car accident.

To an observer experiencing the world without a time-machine, they would with some probability observe time-line (a), and with some probability observe time-line (b). There would be a copy of that observer for each time-line, observing each; this does not require duplication of matter (or entire universes) in principle, and can be achieved in configuration space by a similar mechanism as the so-called parallel worlds of the Many Worlds Hypothesis of quantum mechanics.

You might complain that I don't give you any way to determine the probability with which a subjective observer would see you appear from the past, or that merely with some probability appearing in the past isn't good enough. I actually suppose that your time-travel mechanism is 100% successful, conditioned on you engaging it; but this doesn't mean that a past observer actually sees you emerge with probability 100%. You could more fairly complain that it's not clear how to interpret probability without ensembles or repeated trials, which would be a very good criticism in fact; but we don't have to suppose that there's any actual numerical probability attached. There is just a nondeterministic event in which a past observer either sees you emerge from the future or doesn't, and potentially either lives to see you born, or to see you kill your grandparent; and as a subjective participant you are assured of finding yourself emerging in the past.

Does this represent the freedom of event-space required for what you want to call "free will"? So long as you are identifying F ≡ ¬D, it doesn't matter — in this hypothetical physical ontology, nature is not deterministic, which (by your assumption) means that "free will" is true by definition.

Of course, this answer is entirely speculative; you have not actually learned anything about time-travel from this, except that it is possible to imagine a way that it is compatible with a non-deterministic universe.

• Great answer. Just one remark though. I fear that the multiple world explanation leads to the following problem: there is a non-zero probability that I follow a time-line in which someone sends a hat through time right on my desk, right now. I would see it appear with no reason. But nobody ever observes such apparitions. In my view, it again means that if there are multiple worlds, time travel is not possible. So, again, if time travel is possible, the world is deterministic. In other words, if time travel is possible, the "multiple future worlds" theory send back irregularity to our present. – Julien Nov 20 '13 at 8:18
• @Julien: you arguments are not for determinism, but against time-travel regardless of determinism. Similar arguments about things you might expect to happen if time travel were possible, but which are not observed have been made before. And why could a hat not deterministically appear from nowhere before you? Just because you don't know the cause doesn't mean it has none, and cannot happen. Determinism adds no information to the question in this case. – Niel de Beaudrap Nov 20 '13 at 10:42
• @Julien: also, note that the fact that time travel might send back "irregularity" to our present under my theory just means that time travel is one possible source of subjective non-determinacy. But this is nothing more than to restate that the world is non-deterministic in this framework. So even by your own argument, it is not necessarily the case that if time-travel is possible then the world is deterministic, unless you specify how time-travel must work and appear to work with enough detail to rule out my proposal as a possibility. (Then you should ask what is motivating the restrictions.) – Niel de Beaudrap Nov 20 '13 at 11:06
• Well, sorry, I didn't make my point clear: I meant that irregularities would be really numerous if we had to see the effects of ALL the possible world that could follow the present time. Indeed, I agree that I could also see a hat appear on my desk in a deterministic world with time travel. What I meant is that I should see an infinity of objects appearing constantly on my desk from ALL the possible worlds sending me back an object from the future. Tu sum it up: I think that the multiple worlds with time travel would also make the present multiple. – Julien Nov 20 '13 at 11:17
• @Julien: You wouldn't see all of the possible objects, of course. As a subjective perciever, you would simply experience one possible world. I'd be more concerned about the fact that you never see any objects appearing from the future, which seems to bode ill for time-travel: it is either impossible or difficult, but in any case apparently rare, at least for objects to appear in our corner of the universe. – Niel de Beaudrap Nov 20 '13 at 11:37

There are some holes in your reasoning. In particular, this equivalence is wrong:

F <=> nonD

Although one can argue F => nonD, it's not true that nonD => F. For example, non-determinism can be caused by physical randomness, which has nothing to do with free will.

Here is another example of non-determinism. Consider a pot of warm water mixed from cold and hot one. It's not possible to determine the temperature of hot and cold water before mixing (due to information loss by growing entropy), so if you mentally reverse the arrow of time there would be no backward determinism in the mixing process. However, the loss of determinism didn't enable your backward-directed free will. You cannot look at warm water and will its components to have particular temperatures in the past.

Another hole has to do with somewhat unclear definition of time travel. I would recommend you to take a very close look at the resolution of EPR paradox, especially at state-observable distinction. This is important because what you would call "time travel" in fact exists for the states, but its nature is such that it doesn't affect the expectations of observables. Because all our experiences seem to depend only on the observables the above "time travel" among states does not contradict anything, as long as expectations of observables are unaffected.

• 1°. OK, I should then say that nothing else but determinism can prevent a paradox from happening in case of time travel. I only though of free will, but physical randomness could also cause a paradox. Now I have to change my reasoning: nonD => nonT so T => D . 2°. I agree that I should restrict my conception of time travel to "time travel of a human being able to interact with other people in the past". I will add a last comment in my question. – Julien Nov 19 '13 at 21:30

Here's a different take on it, with a different take on determinism.

If we assume time is an abstraction for change, then time travel is tantamount to undoing all the changes in the universe. Yes, this is a can of worms as multiple states can lead to the same next state, but let's just assume for the sake of argument that this is possible.

Now the determinism that becomes an issue is quantum indeterminism. That is, in order to roll back to the previous state (ignoring the objection above) we'd need a deterministic relationship from one state to the other, and QM shatters that dream.

Just thought another angle was worth mentioning.

If time travel is possible then free will is not. You people have discussed backward time travel. Let go forward. I send you forward 1000 years. The second you step out and observe that future the previous 1000 years become "history" and fixed to the observed outcome. Even if that previous 1000 years is in our future. Every action forward has the reaction of creating more history backward. And every time history is created in this manner, free will throughout the entire universe is destroyed until the experiment ceases. Either Time Travel is true or free will is true. I cant see a away around both. Or better yet, follow your example. Lets prevent your birth. I send you not to the day your grandparents met, but the year before. There meeting is now in your local "future". Since it is the "future" it is changeable right? You see the problem is this. George Washington might not have been the first POTUS. That decision is still up in the air. Look not to the year of his election to see if this is true, but the year before....

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• Traveling forward to 'a' future does not mean there is 'the' future. – jobermark Dec 9 '16 at 21:23
• What is your question? That your reasoning is correct? – wolf-revo-cats Dec 22 '16 at 17:53

The only way to travel into the future would be if there is no free will. On a person's path through time, each decision splits your future into at least two paths. Each hour you make at least a dozen decisions, creating a myriad of paths for a person to choose in any hour of time. The fact that you could arrive at specific point in the future means that all of your decisions are already mapped out for you and would therefore negate the possibility of free will. Further, travel into the past is predicated by the decisions that you have made, all leading to the point in time, where you are at the exact place in time inside a "Time Machine" or at a place where time travel becomes possible. Then, you travel back in time. The meer fact that you arrive in the past changes other peoples decisions which cascade into more peoples changed decisions, ad infinitum. Which would change the future almost immediately to where you, in the future, weren't in the precise point and place in time where you needed to be in order to travel back in time. So, you'd vanish, unless free will is an illusion and our decisions are preordained, then time travel will work!

• If you have any references to others who take a similar view this would give the reader a place to go for more information. Welcome! – Frank Hubeny May 26 at 1:58

It's a matter of nuance. Let's consider determinism first, Laplace's demon for example. If you know the initial conditions of a system (like the universe) with infinite precision, and the exact laws governing the system, then the past and future will be revealed to you. That's the problem, infinite precision. We do not have the capability of infinite information processing, we are finite systems/beings (in space and time) with finite capabilities. This is the phenomenon of chaos, sensitivity to initial conditions. So complete determinism might be meaningful to God, but not to us. Our best models related to how the universe works have a stochastic character (like quantum mechanics, as an example).

So your starting premise F <==> nonD might be meaningful to God, but not to us, simply because complete determinism is an illusion.

The best we can talk about (and that's even in principle) are our models of the universe, which in general have a stochastic character. Do not be misled in your thinking by simple deterministic classical system (that you learned about in school), we are talking about the universe here.

As a consequence, from God's perspective it's true, free will is not compatible with determinism. From our perspective though, I would be cautious.

There is an old analogy between time flow and the flow of water within a river bed (I know it's an old analogy, outdated and far from accurate, today the relational model is popular, but I will not get into that). And yet (following this outdated analogy), you see eddy currents forming every now and then. Hard to predict, impossible to control, but they are there.

As a consequence, going back to your question, we have to wait until a deeper understanding of free will and determinism are available , before we draw any conclusions about the relation between them (and the relation between time travel and determinism), at least from our perspective of finite beings, with finite information processing capabilities.

I will not discuss the grandfather paradox, or the information paradox related to time travel, they are duscussed in many places. I just wanted to discuss the definitions , the basics.

I noticed that all the answers have been talking about going backwards in time. My theory is that if time travel is possible, you would not need to build some sort of machine. It would merely take your mind and your spirit or consciousness if you will. And that going forward in time would be more probable because the past has already been determined. The future however has not, and the most ideal scenario would be to see your future actions and how they affect your life. Also note that you would ultimately have to return to the present and the trip would not take more than a few minutes. Like data being uploaded to a computer. So anyway my answer is that time travel is possible in a world that is free will based. But you yourself by your character and who you are have already determined what choices you will make with your free will. And it would take a very strong will and possibly devine intervention to change it.

• The past has already been determined, but it's not necessarily possible to know the (whole) past. Therefore, traveling back in time is still an interesting point of discussion. But besides that: you claim that time travel is possible in a world that is free will based. How's that exactly? If others have free will as well, then how would time travel be possible without knowing what everyone will choose? – Keelan Jan 26 '15 at 17:58