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GR and Time Travel Paradoxes

  1. Mar 28, 2005 #1
    Time travel can occur in general relativistic models in which one has closed time-like curves (CTC's). A time like curve is simply a space-time trajectory such that the speed of light is never equalled or exceeded along this trajectory. Time-like curves thus represent the possible trajectories of ordinary objects. If there were time-like curves which were closed (formed a loop), then travelling along such a curve one would never exceed the speed of light, and yet after a certain amount of (proper) time one would return to a point in space-time that one previously visited.

    There are a number of solutions to Einstein's field equations which permit the theoretical existence of such CTC's (eg Goedel's rotating universe).

    Does this mean that time travel is at least a theoretical possibility?

    If yes, how do we address the infamous paradoxes that arise (eg I could go back in time and, God forbid, kill my own mother before I was born)?

    Or does the emergence of CTC solutions within GR point to some basic problem with the internal consistency of GR that has remained hidden until now?

    see http://arxiv.org/PS_cache/gr-qc/pdf/0211/0211051.pdf

    Interested to hear your thoughts!

    MF :smile:
    Last edited: Mar 28, 2005
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  3. Mar 28, 2005 #2


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    I go with "basic problem with the internal consistency of GR that has remained hidden until now?"

  4. Mar 28, 2005 #3


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    For some serious academic discussion on the issue, do a search on Richard Gott. Here's an example.

    It's not my area at all, so I can't say much about it other than the fact that it is being seriously considered.
  5. Mar 28, 2005 #4


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    One possible way of addressing paradoxes that scientists have explored is simply to postulate that only self-consistent histories are allowed, meaning you don't really have the free will to do whatever you want when you reach the past. Human actions are hard to model, so instead they like to look at simpler models involving inanimate objects. For example, if you have two mouths of a wormhole that function as a time machine, so if you go in the right mouth, you will exit the left mouth before you entered the first, then you can imagine shooting a billiard ball into the right mouth, and trying to create a paradox by aiming it on a trajectory such that when it comes out of the left mouth, it will hit its earlier self and knock it away from the wormhole entirely. This is known as "Polchinski's paradox" for the physicist who thought it up. But what was found was that no matter what initial position and velocity you give the billiard ball, there will be at least some self-consistent solutions--in the case of Polchinski's paradox, what can happen is that the ball's future self will come out at an angle to give a glancing blow to its earlier self, which instead of completely knocking it away from the wormhole just alters its angle of approach slightly, and this altered angle is exactly the right one to insure that it will come out the other mouth at the right angle to give its earlier self the same glancing blow! There was still a problem, though--it was found there could actually be multiple self-consistent outcomes for the same set of initial conditions (an infinite number of possible outcomes, if you allow the ball to loop through the wormhole multiple times), yet this was supposed to be a purely deterministic classical model, so how would nature decide which outcome would happen in a given case? Later they were able to apply quantum mechanics to the problem and actually calculate the probability of different outcomes, though, so this seemed to be the solution. Of course this does not show that GR is correct in predicting CTCs, but it shows that such a prediction doesn't necessarily have to lead to paradoxes. All this is discussed in detail on pp. 508-515 of physicist Kip Thorne's book Black Holes and Time Warps.
  6. Mar 28, 2005 #5
    yep, and if you don't have the book then check out the following very readable link for a similar explanation :

    If you follow all this, then you should come to the conclusion that some kind of self-consistent histories mechanism could remove the paradoxes of time travel - but at what price?

    It's easy to model self-consistent histories for billiard balls and quantum objects, but what happens when humans are involved?

    The implication is that if CTC's and time travel is allowed, and only self-consistent histories are allowed, then it would be possible for me to go back in time and visit my mother, but somehow (becasue of the self-consistency constraint) it would be impossible for me to prevent my own birth, no matter what I do.......... is this feasible?
    What exactly would prevent me from putting a gun to my mother's head?
    If I would be so prevented, what implications does it have for our free will?

    MF :smile:
  7. Mar 28, 2005 #6


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    Sure, why not? Your brain is just a large collection of particles whose individual behavior is not so much more complicated than a billiard ball's. I'd think that the quantum principles that were used to calculate the probabilities of different billiard ball outcomes could in principle be used to calculate the probabilities of different outcomes for an arbitrarily complicated system of particles, including a whole planet and all the human brains on it.
    Maybe you would change your mind, or you'd get hit by a truck on your way to do so, or humans would never reach the point where they are able to build time machines in the first place.
    Doesn't every theory that treats the mind as the behavior of a physical brain, as opposed to some supernatural entity that manipulates the brain from the outside, pretty much negate the idea of "free will"? Any deterministic theory of the brain would seem to be incompatible with free will, and quantum randomness is just randomness, not "freedom" (if you feed the output from a random number generator into a deterministic A.I. computer program to give it unpredictability, that's not really the same as 'free will', is it?) Personally I don't think the concept of free will even makes sense as a philosophical idea, regardless of the how the laws of nature work, but that's another issue.
  8. Mar 29, 2005 #7


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    That whole concept is just wrong. You can spiral around in spacetime, but never break the time barrier. Even if you did [which you can't], you would be in imaginary space. That is an unphysical solution.
  9. Mar 29, 2005 #8


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    What does "break the time barrier" mean? In GR there are solutions where you can travel into the past while never locally exceeding the speed of light or moving backwards in time. I don't think there's any disagreement among physicists that GR does allow for closed timelike curves in certain situations, the open question is whether these would still be possible in a theory of quantum gravity (most physicists would probably bet the answer is no).
  10. Mar 29, 2005 #9
    OK, time for a Gedanken experiment.
    We have a time machine, I go back in time and put a loaded gun to my mother's head....... so far nothing wrong, I have not violated any self-consistency constraint. As long as I do not pull the trigger, the universe is OK, and this should all (in theory) be possible - do you agree?

    So there I am, standing with a loaded gun to my mother's head.

    Are you suggesting that it will be physically impossible for me to pull the trigger?

    If so, what exactly (in a physical sense) will stop me from pulling the trigger?

    I agree that's another issue, and whether free will exists or not depends very much on how you define free will. Humans have a "feeling" of free will, and in a certain sense they are free even in a deterministic universe - what we need to do is to encapsulate that "feeling" of free will in a definition of free will which is compatible with determinism.
    No matter what you think of free will, the fact is that I am free to take a loaded gun and put it to my mother's head and pull the trigger in the present day if I so choose..... what exactly would constrain me from choosing to do exactly the same thing in the past?

    MF :smile:
  11. Mar 29, 2005 #10


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    What will stop you? The fact that only self-consistent histories are allowed, and a history where you kill your mother before you are born would not be self-consistent. Perhaps the conceptual problem is that you are thinking of time flowing forward, with the universe deciding "what happens next" on the fly, based on past conditions. A better way to think about it is simply generating a whole bunch of random histories, and then throwing out all the ones that don't fit with the laws of physics.

    Here's an analogy. Imagine you want to write a computer program to generate a possible chess game. One way is to start with the pieces in their starting configuration, then have the program generate each successive configuration on the next turn from the configuration on the previous turn, using only legal chess moves. But here's another, more elaborate way to do it. have the computer generate an entire series of configurations at once, completely randomly, so it just picks randomly which pieces to put in which positions on which turn. It is very unlikely that the resulting series will look like a legal chess game--a piece might randomly be on a particular square on one turn, but then the next turn randomly be on some totally different square that it shouldn't be able to get to in one move by the rules of chess. But suppose you have access to an idealized computer with nearly infinite speed and memory, and you have it generate a gigantic number of random series this way--if your number is large enough, chances are at least some of the series would just happen to satisfy the rules of a legal chess game. So you could specify that the computer should throw out all series which violate the rules of chess, and be left only with series that represent legal chess games. But since you are dealing with an entire series at once, you could also place other constraints on them, like "throw out all series where white wins", or "show me only series where the black rook checkmates the king in 25 moves", whatever you want. For sufficiently detailed conditions, it might be very hard to generate a chess game that matched them in the traditional way of starting from the beginning and basing each new configuration of pieces on the configuration of the previous turn, but using this brute-force method of generating a near-infinite number of entire histories, and throwing out all but the ones that satisfy your constraints, it's easy to get a game that satisfies any conditions you like without even having to think about it or plan the details of the game.

    Similarly, suppose you were using this incredibly powerful computer to generate a simulation of an entire universe--instead of picking some initial conditions and then letting it evolve forward according to some set of laws of physics, you could again specify your "laws" in terms of constraints on entire histories, with the computer generating a huge number of random histories and then throwing out all the ones that don't satisfy the conditions. If the "laws of physics" you pick happen to allow time travel, then obviously any universe that respects the laws of physics locally at every point in spacetime must be globally self-consistent, and the computer will find some histories satisfying this condition. But the computer does not need to have any intelligence to do this, it's just randomly generating a huge number of possibilities until it finds one that satisfies the constraints. From the point of view of a time traveler in this universe, it might seem like the universe was cleverly finding ways to "outsmart" them and thwart their plans, but it would actually be the result of a fairly simple rule, just not a dynamic rule.
    Do you? If you think in terms of the block time view as opposed to the "moving present" view, then there is "already" a timeless truth about what you will do in the future...so if the spacetime we are living in does not include you shooting your mother, then in a sense you don't have the "free will" to do so. But perhaps what you mean is just that there are possible spacetimes consistent with the laws of physics where you do kill her, and other possible spacetimes where you don't, so in this sense you do have the "freedom" to do so even if in this particular spacetime it happens to be true that you will not.
  12. Mar 29, 2005 #11
    Wow, my head hurts! But thankyou for taking the time to explain. I understand the concept (I think), but I'm still having trouble translating that into what it would mean in reality.

    For example, I consider myself free and if I take it into my head to do so then I can jump about all over the place but no matter how hard I try, the laws of physics do not allow me to jump from here to the moon..... I accept that and I can rationalise it in terms of what I understand of the constraints of the laws of physics.

    But where I have trouble is translating this into the time-travel scenario. There would seem to be no constraint preventing me from going back in time and putting a gun to my mother's head, in fact no constraint that would prevent me from pulling the trigger (the gun might be loaded with blanks after all). But somehow, if the gun is loaded with real ammo, some "cosmic censor" manages to step in at the last moment and prevent me from pulling the trigger?

    Maybe I'm being very dense, or stupid, or both, but I just do not see how it can work, what physical process would suddenly step in at the critical moment to prevent an action or event which violates self-consistency?

    But... and here is the crux of it....if you tell me that I do not have the free will to shoot my mother in the present day, I can if I so choose prove you wrong by doing just that, without violating any laws of physics..... whereas what you are saying is that this does not apply in the time travel case, that somehow in that case there IS a law of physics which will prevent me from shooting my mother, regardless of whether you tell me in advance that I can shoot my mother or not, and regardless of whether I want to prove you wrong or not.

    The multiverse theory, is that what you mean here? - that if I kill my mother before I was born I am simply causing another version of reality, that there is a timeline existing, in a "parallel universe" where my mother is killed and I am not born? Personally I'm not comfortable with that (but that's my problem!)

    MF :smile:
  13. Mar 29, 2005 #12


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    Again, just think in terms of my thought-experiment earlier where some mega-computer generates entire histories at random (randomly curved spacetime manifolds with random lines drawn on representing worldlines of particles, perhaps) and then checks each one to see if it obeys the laws of physics at every point in spacetime, and throws out all the ones that don't, leaving only the tiny fraction that do to return as output to the user. If this computer program generated a particular history for you to examine, then just by knowing the rules the computer used to do so, you could know with 100% certainty that any time travel would be perfectly self-consistent, right? So suppose you examine it, and see that somewhere in spacetime intelligent life evolved, and one of the simulated beings was asking the same questions you're asking. Since the history is already complete you can't actually interact with this simulated being, but if you wanted to think up an appropriate response in your mind, what would it be?

    One problem with the way you're thinking about this is saying that the thing that would prevent you from killing your mother would only intervene at the last minute. But if you think in terms of generating entire histories and then throwing out all the ones that aren't consistent with the laws of physics at every point, then it's probably much more likely that inconsistencies would be avoided in a more "subtle" way that involved events long before the critical moment of the time traveler meeting his mother, like no time travelers would decide to try to kill their mothers in the first place, or no one would even invent time travel even though it's allowed by the laws of physics. As an analogy, suppose you program a computer to generate 10 random numbers from 1-100, and then throw out all the strings of numbers that don't contain three eighteens. It would be wrong to expect that the first seven numbers would simply obey the normal laws of probability, and then if (as would be more likely than not) none of those first seven was an 18, you would "miraculously" see three 18s in a row at the end. In fact, if you use this rule you are likely to see the three 18s distributed at random throughout the string of ten numbers--do you agree?
    But what do you mean "can if I so choose"? Again, it seems to me you're not thinking in terms of the "block time" view, where the future is just as set as the past. If you imagine a God's-eye-view of spacetime as a whole, like unrolling a movie film so you can see every frame at once, from this perspective you can timelessly see whether or not whether someone shoots their mother...if you can see that the answer is no, then is that person correct in saying he "can shoot her if he chooses to"?
    No, I didn't really mean that. I just meant that if there is a possible universe where you shoot your mother, in some sense maybe that means you "can" do it, even if in the real universe it is already set that you never will. Again, I'm trying to clarify what you mean by "can", from the block-universe perspective.
  14. Mar 29, 2005 #13
    Another thought :
    Causal loops are also possible with CTCs. Though not strictly a paradox, they do pose challenging questions to our intuitions. For example, with a time machine I could send the answer to "Fermat's last theorem" back to a mathematician in the past, he/she could publish it as his/her theorem, and it becomes part of the accepted literature, which (one day) I then copy and transmit back to a mathematician in the past.......

    This is entirely possible within GR, CTCs, Block Time and violates no self-consistency rules...... but the problem is : Where did the original solution come from?

    MF :smile:

    "There's the King's Messenger. He's in prison now, being punished: and the trial doesn't even begin till next Wednesday: and of course the crime comes last of all."
    "Suppose he never commits the crime?" said Alice.
    "That would be better, wouldn't it?"
  15. Mar 29, 2005 #14
    But that's exactly the problem, I don't know!
    Being : "Can I travel back in time to visit my mother before I was born?"
    Consistency-Cop : "Yes"
    Being : "Can I then put a loaded gun to her head?"
    Consistency-Cop : "Yes"
    Being : "Can I then pull the trigger and kill her?"
    Consistency-Cop : "No"
    Being : "What exactly prevents me from doing this final act?"
    Consistency-Cop : "The law of self-consistency"

    It's an "answer", yes... but I'm sorry it's not an answer that I can make any rational sense out of!

    Likely, maybe, but not essential. I see no reason why there should not be a self-consistent solution which includes me putting a loaded gun to my mother's head... but just not pulling the trigger. If that is a self-consistent solution then it is allowed. I hope you agree with this?

    If so, if I am standing there with the loaded gun at my Mother's head (God bless her!), I simply cannot see what it is that "forces" me not to pull the trigger?

    From the point of view of pure probability yes I agree, but the fact is there is an acceptable solution which contains 3 x 18's as the last three numbers in the sequence (in fact there are many such solutions). You are not saying that such a solution is forbidden, are you? We already know that we do not live in a very "likely" universe (just look at how low entropy is at our present time, compared to how high it could be).

    Yes, my statement is still correct - I can shoot my mother if I so choose. From God's perspective, He sees that the person never chooses to shoot his mother. But the universe could equally well be that the person does shoot their mother, in which case God will see that this person does choose to shoot their mother. There is no "law" either way, constraining me to either shoot or not shoot my mother. But in the time travel case, you are saying there IS a law, the self-consistent history law, which would prevent me from shooting my mother no matter what I choose to do. There is a subtle difference.

    I'm lost here. How can there be a universe (if we exclude the multiverse approach) where I shoot my mother before I was born, if this is ruled out by the self-consistent history law?

    MF :smile:

    Alice laughed, "There's no use trying," she said, "one can't believe impossible things."
    "I daresay you haven't had much practice," said the Queen. "When I was your age, I always did it for half-an-hour a day. Why, sometimes I've believed as many as six impossible things before breakfast."
  16. Mar 29, 2005 #15


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    But would you agree that in the computer simulation analogy, there's no "force" that prevents a simulated being from killing his mother? In this case, it's just that any of the randomly-generated histories that contained discontinuous points where the laws of physics don't hold (as would probably have to be the case in any spacetime which contained both the events of the being killing his mother before he was born and of the same being around to make the trip back in time years later) would have been thrown out by the computer program. The only ones remaining would be the ones that just happened to contain no inconsistencies.

    As another analogy, suppose someone goes through a huge amount of footage or convenience store robberies and throws out all the ones where someone is shot, leaving only the ones where no one is. He then gives you some of the footage he has selected. Knowing how the footage was selected, you know that the robbers will never shoot anyone, even if you see them holding a gun to the clerk's head and looking like they could shoot at any moment...is there some "force" that's preventing them from doing so?
    In the "block time" view, all your future actions are set anyway, so again, think of the analogy of watching footage of a robbery that's already happened, knowing in advance that the person who gave you the footage rejected all the clips where anyone actually got shot, only leaving the ones where no one did. As you watch a particular clip, would you ask "what is it that forces the robber not to pull the trigger?"
    OK, that's what I meant in the earlier posts when I was talking about the meaning of "can" in terms of there being a possible universe where you shoot your mother.
    On this particular tangent about possible worlds, we weren't talking about time travel, we were talking about the question of whether you "can" shoot your mother now, after you've already been born.
    Last edited: Mar 29, 2005
  17. Mar 29, 2005 #16
    Yes, I agree there is no force, but there is an "active selection of possible histories", and I think this points to the problem. In the present time, the only constraints on my free will to do as I choose seem to be physical laws which "force" me to do only those things which are physically possible, and I can rationalise this. But in the time travel scenario, there is no force involved..... that is why I cannot rationalise exactly what it is that would prevent me from killing my own mother (if I so choose). I believe you would agree that I can have the intent, the wish, to kill my own mother in both the present and the time-travel scenario? And in the present I could carry out that wish. But in the time-travel scenario I could not carry out that wish, even though I could go all the way up to putting a gun to her head and even pull the trigger.... its just that she cannot die!

    Yes, I can see this. But also, if there are enough videotapes, there will be some tapes which contain scenes where the robbers have the intent to kill, where they put the gun against the victim's head, and they pull the trigger..... but for some strange reason the victim never dies. I can see this is logically plausible, but it is still very hard to rationalise it.

    Yes, I would ask that. At least, I would ask : "there have been so many times in these clips that robbers have tried to shoot their victims, how come none of them ever succeeded?"

    It's almost like there is a cosmic censor, who eliminates all the non-consistent histories? I know you will say that there does not need to be a supreme being or controlling entity which carries out this censorship, that the "censor" is simply the laws of logic and self-consistency......hmmm.

    BTW - I'm interested to know what you think of causal loops (post #13 in this thread)?

    Thank you.

    MF :smile:

    "And what does it live on?"
    "Weak tea with cream in it."
    A new difficulty came into Alice's head, "Supposing it couldn't find any?" she suggested.
    "Then it would die, of course."
    "But that must happen very often," Alice remarked thoughtfully.
    "It always happens," said the Gnat.
  18. Mar 30, 2005 #17
    This is a great thread discussion, I never thought about how the nonexistence of free will solves the classic time travel paradoxes. I have nothing more to add to this simple but elegant idea, but I would like to make a point about free will.

    ha! You are assuming that you have free will. This is not very likely, because you are made of matter and matter moves according to deterministic laws. ( Please do not object using QM, because the probabilities are deterministic and so can hardly be called free).

    In this excerpt from an essay I wrote, I use the term "Metaphysical Freedom" to mean the genuine type of freedom . This as opposed to common usage where a gun to your back or a prison cell effects your freedom.

    Theorem: Metaphysical Freedom is a force.

    Proof: In order for a decision to be acted upon, an electrical current stimulates various parts of the nervous system. If there is to be a correspondence between the physical actions of the body and the decision of the mind, the decision must be related in a one to one way with this electrical current. This one to one relationship is precisely what we think of as cause and effect, and the cause of electrical current is a force. Therefore, by the definition of a force as the cause of a deviation in smooth motion, the decision is a force.

    Heuristic Argument: Clearly, Metaphysical Freedom cannot be a Newtonian Force, because it does not depend on the position or energy of any other particles in the universe. The MF force is a very peculiar force indeed. Actually, it is at least 6 billion different forces (depending on how you feel about animals) because my MF force cannot interact with the matter in your body, or anyone else’s. Adding to the strangeness is that our brains seem to be made of ordinary matter, with no additional properties (of the likes of charge or mass) to affect the interaction with our minds. Also, my MF force did not exist in the universe before 1985 and will not exist after my death, in the sense that it won’t be able to interact with any matter in the universe.

    Summary: It is easier for me to believe that Metaphysical Freedom is an illusion rather than believing in a hopelessly complex, highly non-universal, peculiar force. Occam’s Razor is very clear about this issue, simplicity itself should be used when deciding between two theories which cannot be distinguished.
    Last edited: Mar 30, 2005
  19. Mar 30, 2005 #18
    Thank you :biggrin:

    ha! You make the presumption that your definition of free will is the same as mine!

    MF :smile:
  20. Mar 30, 2005 #19
    I think we have a deep problem with epistemology here.

    From the discussion so far, it would seem that the self-consistent histories (SCH) hypothesis does provide at least a possible theoretical solution to the causal paradoxes associated with time travel in GR.

    The SCH hypothesis simply put : Only self-consistent histories are allowed, such that any possible history which included, for example, me going back in time and killing my own mother before I am born, would be eliminated by SCH.

    The SCH hypothesis seems to solve the problem?

    But let us examine this SCH hypothesis in greater detail.

    The SCH hypothesis does not prevent me from going back in time and meeting my mother before I was born, therefore the statement (A) :

    (A) "I go back in time to meet my mother before I was born, and I pass on the knowledge to her that I am her future son"

    is allowed to be true under SCH.

    On the surface, what the SCH hypothesis appears to be saying (and this is what we have been debating so far) is that, given (A), then the following statement (B) is also necessarily true :

    (B) "I cannot kill my mother before I am born"

    BUT the SCH hypothesis is actually much stronger than the above suggests. What the SCH hypothesis is actually telling is that, given (A), then the following more general statement (C) is necessarily true :

    (C) "my mother CANNOT DIE before I am born".

    (Why is (C) necessarily true? Because from the moment of our meeting due to (A), my mother knows that the universe is necessarily such that I will be born as her son, therefore she knows that she will not die before I am born)

    This is a very different proposition altogether.

    What this means is that NO MATTER WHAT MY MOTHER DOES from the moment of our meeting until my birth, she will not die.

    She can jump off a building, starve herself, drink poison, do absolutely anything, but the SCH hypothesis will not allow her to die....

    Is this credible?

    I don't think so. There is obviously still something very dubious about either the SCH hypothesis, or about time travel in GR, or both.

    MF :smile:

    "That's the effect of living backwards," the Queen said kindly: "it always makes one a little giddy at first-----"
  21. Mar 30, 2005 #20
    We can discuss the definition of free will if you wish (I would love that!), but in the meantime, if it helps, replace the words "free will" in the post you refer to by the word "ability".

    Therefore instead of the phrase :

    the only constraints on my free will to do as I choose

    my phrase becomes :

    the only constraints on my ability to do as I choose

    happy now?

    MF :smile:

    "When I use a word," Humpty Dumpty said in a rather scornful tone," it means just what I choose it to mean -- neither more nor less."
    "The question is," said Alice, "whether you can make words mean so many things."
    "The question is," said Humpty Dumpty, "which is to be master -- that's all."
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