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Thoughts about Causality and Paradoxes

  1. Dec 8, 2009 #1
    I do not know the details, but I have read that some theories allow backwards time travel using wormholes. Backwards time travel seems so impossible because of things like Grandfather's paradox and such.
    I had an idea and was wondering if anyone who knew more than me about the subject could share their thoughts.

    Let's say that we were to open up a wormhole from the present time here on Earth to many years in the past on some planet very far away. Let us say that the spatial distance that the wormhole traverses is [tex]\Delta x[/tex] and the amount of time into the past it connects to is [tex]\Delta t[/tex]. Let us also say that the distance is far enough away such that we can say [tex] \Delta x \geq c \Delta t [/tex] where c is the speed of light.

    We let one of our friends jump through the wormhole to this other planet and he looks back through the portal at us. Being a brilliant genius, he looks up at the sky on the unknown world, calculates the direction of earth relative to his current location and shines an extremely powerful laser towards us (not through the portal, through normal space). A few seconds later, our sensors on earth pick up his signal coming through the atmosphere which has traveled many light years over the course of many years.

    My point: what if backwards time travel is possible, but only to locations in space far enough away such that any action you perform in the past can only affect the future of your original time (due to the speed of light limit) i.e. it is impossible for the laser to reach earth before he went through the portal. In this way, causality can never be violated, and we can still say we traveled back in time. He has two paths to communicate with us, through space and through the wormhole, and through neither medium will he violate causality.

    Some might ask: what if your friend opens another wormhole such that the spatial locations of this new wormhole are the same as the previous worm hole, but this time the time travel is reversed, and should he enter that new wormhole, he would wind up on earth in the distant past. Surely then he could violate causality.

    I thought I remembered reading something a while ago saying that (don't quote me on this) the ability for a worm hole to exist depends on the presence of a strong gravitational field, and that the "past" end must be in an area of higher gravitational field (or was it the other way around), then the "present" end of a wormhole. If that is the case, then you can never have two wormholes with different time directions leading to the same areas of space because the gravitational field of those areas will determine which way time will flow through the wormhole. Thus you still can't violate causality.

    I know that discussions like this are mostly just hand-waving since it is hard to prove anything like this and it is so complicated, but I think it is a fun thought exercise.
    Let me know what you think.
  2. jcsd
  3. Dec 9, 2009 #2


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    Killing your grandfather before your father was born paradoxical. But closed time-like curves are not paradoxical. You can go back in the past, hand yourself a manual to build a time travel machine, build the machine, travel back to the past.

    Time, Closed Timelike Curves and Causality
    Francisco Lobo, Paulo Crawford
  4. Dec 9, 2009 #3
    Thanks for the document, I'll start reading it. I don't know what closed time-like curves are.

    I don't know what you mean by handing yourself a manual. In my scenario, it would be impossible to interact with your past self because any action you performed in the past on planet X would only have an effect on Earth AFTER you went through the portal. In other words you can never change what you already know to have happened (like the history of Earth). But what about the history on the other side of the universe (as a figure of speech)? We don't know even know what is happening on the sun at this exact moment. We only know what happened 8 minutes ago (the minimum time it takes for light and hence information from the sun to reach us). What I am saying is that no causality would be violated if you traveled to the sun (or a similar, less hot place) between 0 and 8 minutes ago and erased it from existence, then came back. When you come back to Earth, it will be as if nothing changed for a few minutes, because the effects of your actions take 8 minutes to propagate from the sun to earth.
    With the speed of light constraint I mentioned above, it would never be possible for the effect of your action on the sun to reach earth before you jumped into the time machine on earth. It could effect Mercury a few minutes before you entered the time machine on Earth, but not Earth. However long it takes for light from Mercury to reach Earth would be the maximum amount of time into the past where your actions could effect Mercury.
    Google says average distance between earth and Mercury is 58 million km.
    Assuming that distance, 58 million km/c = 3.22445292 minutes
    Performing a time traveling action on Mercury at a time before 3.22 minutes in the past from Earth's perspective might violate causality, so let's forbid it with the constraint I mentioned above.
    So if it is 3:00 PM on Earth, you jump into your time machine and go to the sun 6 minutes prior at 2:54 PM, erase it from existence with whatever technology/magic powers (lol) you have available to you, and then return to the Earth pretty quickly at 3:01 PM. The sky will still be bright blue. At 3:02, however it will suddenly go black. Note that the surface of Mercury saw the sun go black at about 5 minutes past the point where the sun went out (approximating 8 min for sun to earth, 3 min for mercury to earth, 8-3 = 5 min for sun to mercury) at 2:59 PM. This is good because we estimated that any time-traveling changes you make should not effect Mercury before 3 minutes from when you traveled: at 2:57 PM. No causality is violated, even though you destroyed the sun 6 minutes before you entered the time machine and turned the surface of mercury black 1 minute before you entered the time machine.
    Ok, I'll read your document now.
    Last edited: Dec 9, 2009
  5. Dec 9, 2009 #4
    You're severely restricted in the choice of places where you can jump through the second wormhole without violating causality. Not only are you not allowed to jump back to Earth, but you can't even jump anywhere in the general direction of Earth, because the destination of the second jump can't be in the causal past of the origin of the first jump.
  6. Dec 9, 2009 #5


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    In "pure" general relativity there is no theoretical reason you couldn't move the wormhole mouths around so that you could exit one mouth in the causal past of the point where you entered the other mouth, which is why traversable wormholes lead to closed timelike curves in GR. However, some calculations in semiclassical gravity suggest that quantum effects could destroy the wormhole at exactly the point where the mouths are moved into positions that would enable causality violations--something to do with virtual particles being able to circulate in a feedback loop between the two mouths, with the energy possibly going to infinity at the point where causality violations would otherwise become possible. But without a full theory of quantum gravity no one knows for sure whether this kind of effect would actually be able to prevent causality violations and enforce the chronology protection conjecture.
  7. Dec 9, 2009 #6
    Well, if you opened up a wormhole from planet X to planet Y where planet Y is closer to Earth, then the wormhole could travel into the future (from X's perspective) given the configuration described above? The wormhole from X to Earth is a portal to the future from X's perspective, so why couldn't you do the same thing with an intermediate point Y?
    All this talk is starting to make the notion of future and past seem meaningless. You can't describe the future without saying with respect to a particular location.

    Earth <------------> Y <---------------> X

    But how then do the gravitational fields come into this?
    My understanding was that the relative strengths of the gravitational fields between Earth and X would determine the direction of time flow through the wormhole.
    I think I see a hole in my reasoning now.

    What if Earth has a weak gravitational field.
    X has a medium one.
    and Y has a very large one.

    Assuming travel to the past occurs towards the stronger field (I don't remember if it was stronger or weaker),
    then you could make a portal to the past (relative to Earth) from Earth to X.
    Since Y has a stronger field, you can make a portal to the past (relative to Earth and X) from X to Y. Using the light speed constraint alone does not seem like enough to ensure that causality is not violated. Was this what you were saying hamster143?
    Perhaps the dependence on the gravitational fields could explain this? i.e. the presence of Y's field would make it harder to travel further back in time on X, such that the situation described above couldn't ever get you any further into the past on Y than if you made a portal directly from earth to Y. But what are the repercussions of this? Why is Y a special point when determining how far you can travel into the past from earth to X? This means that you would need to consider the gravitational field everywhere else in the universe as well doesn't it?
    Last edited: Dec 9, 2009
  8. Dec 9, 2009 #7
    Thanks for that JesseM, I posted before I realized you responded.
    That's very interesting. Clearly I am oversimplifying this problem. Thanks for the explanation.
  9. Dec 9, 2009 #8
    Personally I'm in favor of either the multiverse scenario or the Novikov self-consistency principle.
  10. Dec 9, 2009 #9
    I wish I had more time to learn about this stuff, it is so fascinating.
    I went into Engineering, but sometimes I wish I had gone into Physics so I could understand these sorts of things better.
    I don't really know anything about these principles and theories you are talking about.

    I should probably get back to studying for finals though, lol.
    Thanks for your time people.
  11. Dec 9, 2009 #10
    They are quite simple.

    The multiverse theory tells you that you can go back in time, but the timeline you arrive at is no longer the same timeline as the one you left. So, you're free to kill your grandfather, it'll prevent the copy of you in the new timeline from being born, but you yourself are still there, and there's no contradiction.

    The Novikov principle is that you can loop back into your own past, but you can't change your own past, because your chronology must be self-consistent.
  12. Dec 9, 2009 #11
    I cannot think of any physical way to verify the multiverse idea. It's not really time travel in that case, but traveling from one universe to another, isn't it? Why would this alternative universe be similar to ours? Does this theory say that new universes are formed whenever alternate possibilities can be realized (say for example: the result of a random quantum mechanical process)? I would think that in most of these other universes your grandfather wouldn't exist, (what about a universe where Earth was never formed?).
    Can you really call it time travel if you go back a billion years and the Earth is gone? And by what basis could a wormhole possibly select one of these infinite possibilities?

    I could be interpreting this wrong. Are you saying that a new universe (identical to yours until the time you traveled to) would be created once you opened a "time" portal?
    If the multiverse idea can validate these questions or if there is a way to potentially physically test it, then it would satisfy me. Otherwise, it seems like a claim with no basis.

    The Novikov principle: Does it explain why you can't change your own past? What prevents you? Can you get as close as you want to changing your past, but be prevented by some unexplainable phenomena right before you are able to do it?
    It seems like it is just a statement that causality can never be violated without explaining what will prevent that if time travel is possible.

    Either way, it seems like most accepted theories agree that the past (of our own universe) cannot be changed. If that is the case, then traveling back in time isn't really different from traveling to a new place in space, since you can't do anything fundamentally new or exciting ( i.e. change history).

    It's still fun to think about though.
  13. Dec 9, 2009 #12
    The idea is that the universe would branch at the point of the arrival of the wormhole, creating two branches, one where the opening of the wormhole is present and the other is where it's not. Any changes you make as you come out of the wormhole stay in that one branch. Since "you", the real you, were born in the other branch, nothing you do can affect that fact.

    In particular, you don't get any "closed timelike curves".

    The Novikov principle does not explain why you can't change the past. It just says that nothing that didn't happen, can't happen, and everything that did happen, must have happened. If you know for a fact that there wasn't a wormhole opening at the point X at the time Y, you can't travel there. If you don't know that, you might open a wormhole that leads there, but you'll be somehow constrained by what you can do once you're on the other side (who knows, maybe a brick will fall on your head as soon as you're through).
  14. Dec 9, 2009 #13


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    There is an interpretation of quantum mechanics called the "many-worlds interpretation" which does say the universe is constantly branching into diverging histories whenever the rules of QM allow for multiple possibilities, here's some info:


    Many physicists find it to be the most elegant way of understanding QM since it doesn't require the mysterious "wavefunction collapse" of the earlier Copenhagen interpretation, but it makes all the same predictions about actual testable experiments as any other interpretation so there isn't any experimental way to determine if it's true. I guess if time travel were possible and travel back in time took you to a different branch of history this would no longer be the case, but since the connection between general relativity and QM isn't fully understood, I don't think there's any reason to be confident that you'd end up in a different branch even if backwards time travel were possible and the many-worlds interpretation was true (it might be that travelers always stay within a branch consistent with their personal history so that the Novikov principle would apply to any given branch, for example).
    It helps to think in terms of the "timeless" perspective of relativity, where all of history exists as a fixed 4-dimensional structure, rather than imagining the universe is "making things up as it goes along". Years ago on this board I got into a big discussion about the self consistency idea and timelessness, you might want to check out that thread, especially my post #10.
    Last edited: Dec 9, 2009
  15. Dec 9, 2009 #14
    Thanks both of you for responding.
    I came to the same conclusion about determinism mentioned on that other thread.
    I have not taken a course in quantum mechanics so I don't know about this true randomness that it can introduce. If the universe were a supercomputer with unbounded memory and speed, you should be able to predict everything in the future based on initial conditions right (initial states (position, momentum, etc) of all things in the beginning)? That is what determinism means. That makes sense to me unless somethings cannot be predicted (like a truly random process). Since I have not taken any QM course, I find it hard to imagine that anything truly random could actually exist. Especially since the word "random" is constantly applied to deterministic processes that are not random, just really complicated and hard to measure or predict (like the motion of tiny particles). Is this QM randomness a true randomness in the sense that there is no physical way of determining the outcome until afterwards? Or could it be that the theory is insufficient in determining the outcome? It is quite a leap to construct a theory that cannot explain something entirely and to say that in nature itself the solution cannot be determined. I know that I am ignorant to QM which is why I ask.

    JesseM, your idea of brute forcing possibilities and leaving only ones that our self-consistent and that obey the laws of physics is a good one. I like it.

    It makes perfect sense to me that the future would be fixed by determinism, but this does not mean that I believe in destiny in the traditional sense. The future is fixed, but no one can know it because it is too complicated to calculate. If someone tells you you are destined to do something, you should not believe them because they are probably wrong. If you choose to do something using "free will" and you do it, then you already were going to do it since the start of the universe (i.e. it could have been predicted 100%/well maybe not with QM). If you choose not to do it, and don't do it, then you were already going to not do it. Since you cannot predict the fixed future, you should never think: no matter what I do in life I am destined to fail or succeed or anything like that. From the perspective of any human, your future could be either. It is determined by the universe. Your "choices" are the results of your motivations (wants, needs) which are ultimately a result of the environment, i.e. the universe.

    It seems like I am getting off topic, but what I am trying to say is that a purely deterministic universe would make sense I believe. In a purely deterministic universe, perhaps QM would not be truly random (again I acknowledge my ignorance on the subject). If that is the case then the multi-world idea wouldn't make sense because there would be no random event from which you could branch.

    The idea of returning to your own past through closed-time-like curves bothers me. I am not sure what I should ask to relieve my discomfort with the idea yet though.
  16. Dec 9, 2009 #15
    I dont think that wormholes exist. But closed time-like loops exist - at least inside the rotating black holes. If superextreme black holes exist, then closed time-like loops are also 'exposed' to the whole universe.

    Inside closed time-like loops, you can meet your own copy. I would give my right hand to understand HOW the inconsistent solutions are 'cancelled' in CTL. Say, I was to kill my 'past' copy. How nature would react?

    1. How soon it would try to stop me? 1 second before the event (like, the gun would fail) or 1 day (I would change my mind)?
    2. What would be the energy spent on the 'correction'? High (a car will hit me) or very low (small error in DNA molecule -> soemthing goes wrong -> sudden death)

    I understand that the 'reaction' and 'energy spent' is just an illusion, the only the self-consistent solutions of the omnium in the CTL exist.

    Of course, we dont have an answer now.
  17. Dec 9, 2009 #16
    I guess I can't really make a good question about CTC's unless I understand the mathematics and the assumptions that allow them to exist. That won't be anytime soon I'm afraid.
    I can abide with the answer nobody knows though.
    Thanks for the response.
  18. Dec 9, 2009 #17


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    Those rotating black hole solutions aren't necessarily realistic either, the CTCs only exist within a "Cauchy horizon" inside the black hole and incoming radiation (including gravitational radiation) is infinitely blueshifted on this horizon (see this paper for example), which would presumably have a disruptive effect, and in any case we need a theory of quantum gravity to deal with any situation where energy densities approach infinity according to GR. So just like with the possibility that virtual particles circulating through wormholes would build up to infinite energy at the exact moment the wormholes are put into a position that allows closed timelike curves, this might be another hint that the universe really does enforce chronology protection and that GR solutions which contain closed timelike curves are just artifacts of the fact that GR is really only an approximation to a true theory of quantum gravity.

    The most popular candidate for a theory of quantum gravity, string theory, also apparently has a number of results that seem to suggest the chronology protection conjecture is correct:

  19. Dec 9, 2009 #18
    A little bit of humor:
    http://home.comcast.net/~mmiguel1/string_theory.png [Broken]
    Last edited by a moderator: May 4, 2017
  20. Dec 9, 2009 #19
    JesseM, I see your point. But it is very hard for me to believe that you cant build a superextreme BH. Say, I am throwing objects at proper angles at almost extreme BH.I know that there are *some* simulations showing that such BH would repel things. Any thing thrown at any angles??? Hard to believe. But even if it is true, what it would do with massless particles with spin? polarized light? reflect back? :)

    Of course, it is possible that even when BH becomes superextreme quantum gravity prevent CTL formation, as you say, while naked singularity is possible.
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