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The Novikov self-consistency principle states that all changes that occur due to time travel into the past were always part of history, and so the course of events is not changed. While this is useful in explaining away lots of the logical paradoxes that might occur during time travel, it allows for the possibility of causal loops, sometimes known as bootstrap paradoxes.

How would you keep causal loops from happening in a time travel story using the Novikov self-consistency principle? Characters shouldn't just be able to get everything they need from their future selves.

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    $\begingroup$ When you say "time travel story", are we assuming that the protagonist has substantially unfettered time travel ability? Or that there exists a traversable wormhole or whatever that part of the plot centers around? Different answers to this suggest different possible responses. $\endgroup$ – Malice Vidrine Dec 9 '16 at 1:49
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    $\begingroup$ Use some principle other than the Novikov self-consistency principle? I mean, the answer is in the question: The NSCP allows for the possibility of causal loops. $\endgroup$ – Random832 Dec 9 '16 at 5:45
  • $\begingroup$ Isn't the principle developed to prevent time loop event? Loosely put you will have no luck trying to murder your past self... $\endgroup$ – user6760 Dec 9 '16 at 6:19
  • $\begingroup$ Novikov self-consistency principle is an oxymoron $\endgroup$ – Brad Thomas Dec 9 '16 at 22:06
  • $\begingroup$ @BradThomas What do you mean by that? $\endgroup$ – klipty Dec 9 '16 at 22:34
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The problem with causal loops is that they only happen because they happen (the fact that the loop happened is all the justification it needs in order to happen). The solution to causal loops is that they only happen because they happen. In other words, all you need in order to justify that a loop does not happen is that it doesn't happen.

For example, say Bob wants to go back in time and tell himself the critical piece of information he needed in order to defeat the main villain - only problem is, when he was his past self, he never received that information. By the Novikov principle, Bob's attempt to go back and convey that information must somehow fail. Perhaps, for example, his time machine breaks down, or his message gets garbled along the way. Or, knowing that his attempt will fail - thanks to the evidence proving that it did - he doesn't even try.

The point is, you don't need a way to prevent causal loops. Causal loops prevent themselves by not having happened.

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    $\begingroup$ @Douglas That's a good point. One way to avoid allowing that would be to introduce an unreliability in the time machine; maybe it sometimes breaks down, or misses the target time by a little, or puts you in the wrong place. That way, there are a lot more "reasonable ways" to stop a determined time traveler. $\endgroup$ – Reese Dec 9 '16 at 10:07
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    $\begingroup$ Stated another way: causal loops happen only because the author lets them happen. :-) $\endgroup$ – SRM - Reinstate Monica Dec 9 '16 at 10:21
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    $\begingroup$ @xDaizu You don't seem to have understood my answer, then. I'm not saying anything about bootstraps being inconsistent with Novikov. I'm saying that they can be prevented without outside justification. In the scenario you describe, the whole loop could be prevented by you not encountering your future self in the first place. This would result in a perfectly consistent chain of events which does not involve a bootstrap paradox; thus the author doesn't need any better justification for omitting the loop than just "the loop didn't happen". $\endgroup$ – Reese Dec 9 '16 at 12:14
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    $\begingroup$ @xDaizu No, that's not what I'm saying at all. You're right that I'm not proposing a meta explanation, but I'm not saying that bootstrap paradoxes are inconsistent with Novikov. I'm saying that characters can't force a bootstrap to happen. If the "beginning" of the bootstrap didn't happen, then the loop can't be made to happen at all. To be clear, I'm talking about any particular loop, not loops in general - one loop might happen or not happen, at the universe's discretion, but the characters can't control it. $\endgroup$ – Reese Dec 9 '16 at 13:07
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    $\begingroup$ @xDaizu If it happens, it happens, as I said several times in my answer. OP's question was not about how causal loops can be completely excluded, only how we can prevent the ones that would give the characters everything they want. My point is that if the author wants to withhold something from the characters, the mere fact that it was withheld is sufficient in-universe reason. I am not attempting to say that bootstrap paradoxes don't happen or can't happen. I'm saying that they never have to happen, and that an author can avoid them while still staying true to the characters. $\endgroup$ – Reese Dec 9 '16 at 13:30
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The answer is simple you don't have to, the physics, as assumed by Novikov and other authors, takes care of it.

The Novikov consistency principle assumes certain conditions about what sort of time travel is possible. Specifically, it assumes either that there is only one timeline, or that any alternative timelines (such as those postulated by the many-worlds interpretation of quantum mechanics) are not accessible.

Given these assumptions, the constraint that time travel must not lead to inconsistent outcomes could be seen merely as a tautology, a self-evident truth that can not possibly be false. However, the Novikov self-consistency principle is intended to go beyond just the statement that history must be consistent, making the additional nontrivial assumption that the universe obeys the same local laws of physics in situations involving time travel that it does in regions of space-time that lack closed timelike curves. This is clarified in the above-mentioned "Cauchy problem in spacetimes with closed timelike curves",[3] where the authors write:

That the principle of self-consistency is not totally tautological becomes clear when one considers the following alternative: The laws of physics might permit CTC's; and when CTC's occur, they might trigger new kinds of local physics which we have not previously met. ... The principle of self-consistency is intended to rule out such behavior. It insists that local physics is governed by the same types of physical laws as we deal with in the absence of CTC's: the laws that entail self-consistent single valuedness for the fields. In essence, the principle of self-consistency is a principle of no new physics. If one is inclined from the outset to ignore or discount the possibility of new physics, then one will regard self-consistency as a trivial principle.

EDIT: This is in response to a request for clarification of paragraph three above. Firstly, this paragraph is itself a quotation from this paper:

Friedman, John; Michael Morris; Igor Novikov; Fernando Echeverria; Gunnar Klinkhammer; Kip Thorne; Ulvi Yurtsever (1990). "Cauchy problem in spacetimes with closed timelike curves". Physical Review D. 42 (6): 1915.

Their argument can be simplified as follows: if the normal or ordinary laws of physics permit closed timelike curves (CTCs) then this should lead to physical events of a fairly exotic kind, ones we do not see in nature, and that the affect of the self-consistency principle is to ensure this new, exotic physics doesn't occur, and that the physics we see in time travel situations is the same physics we see in non-time-travel situations. They call this a no new physics condition.

This is another one of those tautologies that plague time travel. Novikov self-consistency not only prevents the past from being changed, it also prevents the nature of physics itself being changed. End EDIT

What follows for time travellers are the following implications (OK, this is also a tautology, but time travel logic is full of them.):

Implications for time travelers

The assumptions of the self-consistency principle can be extended to hypothetical scenarios involving intelligent time travelers as well as unintelligent objects such as billiard balls. The authors of "Cauchy problem in spacetimes with closed timelike curves" commented on the issue in the paper's conclusion, writing:

If CTC's are allowed, and if the above vision of theoretical physics' accommodation with them turns out to be more or less correct, then what will this imply about the philosophical notion of free will for humans and other intelligent beings? It certainly will imply that intelligent beings cannot change the past. Such change is incompatible with the principle of self-consistency. Consequently, any being who went through a wormhole and tried to change the past would be prevented by physical law from making the change; i.e., the "free will" of the being would be constrained. Although this constraint has a more global character than constraints on free will that follow from the standard, local laws of physics, it is not obvious to us that this constraint is more severe than those imposed by standard physical law.[3]

Similarly, physicist and astronomer J. Craig Wheeler concludes that:

According to the consistency conjecture, any complex interpersonal interactions must work themselves out self-consistently so that there is no paradox. That is the resolution. This means, if taken literally, that if time machines exist, there can be no free will. You cannot will yourself to kill your younger self if you travel back in time. You can coexist, take yourself out for a beer, celebrate your birthday together, but somehow circumstances will dictate that you cannot behave in a way that leads to a paradox in time. Novikov supports this point of view with another argument: physics already restricts your free will every day. You may will yourself to fly or to walk through a concrete wall, but gravity and condensed-matter physics dictate that you cannot. Why, Novikov asks, is the consistency restriction placed on a time traveler any different?

While time travel with Novikov self-consistency apparently allows a seemingly vast array of counter-intuitive situations. Even your future selves cannot prevent what they know happened to themselves from happening. Any path accessing changes to the past will have a probability of zero. Effectively they don't exist and you cannot travel them.

Even if the bad guys blow up your lab, you at a later time who they were, when they planted the bomb, there is no way you can stop it from happening.

The sort of universe this implies is one where a time traveller can go to those points in time where they make them happen as they had or will happen. There is no going back to undo what you did in the past -- or in the future. If you have been to the future and done something, well, that becomes part of your past.

This suggests such zero-probability pathways effectively constitute what Stephen hawking suggested with his Chronology Protection Conjecture.

Source for the above quotations is the Wikipedia entry on the Novikov self-consistency principle

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  • $\begingroup$ So in summary these loops are impossible because time-travel physics restrict free will; you cannot make them in the first place? $\endgroup$ – Zxyrra Dec 9 '16 at 3:55
  • $\begingroup$ Could you clarify the article you quote? It isn't entirely concise. The third paragraph in the first blockquote says the Law's authors believe that normal physics explain CTC's, yet it also says after that if you assume there are normal physics, CTC's cannot happen? Could you clarify this in the answer so that other readers understand what meaning you're using? $\endgroup$ – Zxyrra Dec 9 '16 at 3:58
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    $\begingroup$ @Zxyrra Thanks for pointing that out. This wouldn't be the first time a web site or a Wiki entry contradicted itself. I was amused to see a site arguing a particular case, strangely enough also about time travel, where the citations flatly contradicted the article's conclusions. I'll see what I can do clarification-wise. $\endgroup$ – a4android Dec 9 '16 at 4:03
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    $\begingroup$ Nice explanation. Of course, on the other hand, if you only thought that the past happened a certain way (e.g. you had read the newspaper story confirming someone's execution but didn't actually see the dead body), then you can still make it turn out "differently." A well-known story with this approach is Harry Potter and the Prisoner of Azkaban; a lesser-known example (but actually an even better book) is The Door into Summer by Robert Heinlein. $\endgroup$ – Wildcard Dec 9 '16 at 8:08
  • $\begingroup$ @Wildcard There is a more complicated every event has an infinite number of self-consistency solutions. Basically there are an infinite number of ways of trying to change the past, but the past can't be changed. Historical inaccuracy doesn't come into the Novikov model in the narrow sense. A time traveller might to find she had, apparently, changed a past event into something else not recorded by history. But the event is now the way it always was. Our tastes differ. "The Door into Summer" is a dud. Heinlein has written better. $\endgroup$ – a4android Dec 9 '16 at 11:56
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Conservation of entropy law. Whether matter or information or energy, you cannot come out of a time travel trip with less entropy than when you went in. Kage Baker's books handle this extremely well, although the author never uses the conservation law by name (just refers to "history's shadow"). Anything you tell your past self will be completely forgotten by the time you find the time machine. Any object you take back and leave has no apparent effect on history as the time traveler knows it until after the traveler went into the past.

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    $\begingroup$ Entropy is NOT conserved: "Second law of thermodynamics: In a natural thermodynamic process, the sum of the entropies of the interacting thermodynamic systems increases." - wikipedia $\endgroup$ – DOS4004 Dec 9 '16 at 3:30
  • $\begingroup$ As I thought I explained, but let me try again in other words: you can't bleed off your entropy into your own backstory. However much entropy you build up, you're going to preserve that much regardless of your actions in the past. The conservativation of entropy law applies to time traveler, and is an additional law to normal thermodynamics. Does that make sense? $\endgroup$ – SRM - Reinstate Monica Dec 9 '16 at 10:20
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Some kind of loops will not happen because of entropy. Consider information: if you go back in time and give an answer to your younger self, where did the information come from?

The large decrease in entropy over the span of the loop will prevent that particular self-consistent solution from being chosen.

The normal examples given for Novikov concerns objects that come out smashed and destroyed. The entropy increases over the passage through the loop. (Or more generally, if you inspect the state later you’ll find no compelling evidence of a miracle; if you didn’t have the area under surveillance you’d determine that nothing happened in that zone that couldn’t occur in a mundane situation.)

It’s easier for the loop to not exist! If nobody came from the future to tell you how to go back in time, then you wouldn’t go back in time.


※ Forward, who you'll recall from the linked Wikipedia article helped Kip Thorne with the calculations, has a dramatic example of it in Timemaster:

With an attack impending, the defenders set up a time-delayed pair of wormhole mouths so the ship is resting between the mouths (which face each other).

Later, when the attacker approaches close, a derilect ship pops out of the from-the-future mouth and crashes into the would-be attacker, and then drifts harmlessly past the defenders. The attacking vessel, now disabked by the collision, is deflected by the collision such that it is thrown into the to-the-past mouth. The surviving attackers, unable to maneuver now, exit the wormhole and crash into their arriving ship.

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  • $\begingroup$ This is an interesting "answer" but, not being familiar with the "normal examples given for Novikov" you're referring to, it's mostly unintelligible. Upvoted anyway for being interesting. Perhaps you could edit to explicitly include whatever laws you are assuming as a starting point concerning entropy and time travel? $\endgroup$ – Wildcard Dec 9 '16 at 8:11
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It sounds like you want the usual situation to be the self consistent time loop, but under certain extraordinary circumstances you want the characters to be able to change events, perhaps (somehow) to different self consistent loop.

This is very similar to the concept of a strange attractor.

In the mathematical field of dynamical systems, an attractor is a set of numerical values toward which a system tends to evolve, for a wide variety of starting conditions of the system.[1] System values that get close enough to the attractor values remain close even if slightly disturbed.

I'm imagining a metaphor for the time loop as a ball rolling around in one of various circular valleys. Some are of the valleys are deeper than others. Some valleys are bigger than others. The interesting case would be the valleys that nearly touch another, and so at a key moment it might be possible to make just the right change to switch from one valley to another, and so from one time loop to another.

A planet that orbits around one star in a binary system, and whose orbit is close to the null point between the stars does something like this.

I would use the "sciency" phase "quantum bias" to describe a tendency for the effects of most small changes to not create butterfly effect ripples, but for the odds to usually stack themselves so that even with big choices and big changes, that events will tend to counterbalance and turn out in almost the same way.

The question would then become, "What sort of key point in the time loop is most likely to cause the loop to shift from one to another?". Most time travel stories will have something irrevocable (like a death preventing a birth) be the event that tips things to a different sequence. I think it would be fun if the event was deeply random, causing a Rube-Goldberg-eque cascade of events.

The most obvious solutions to how just the right event could be found (they should be rare) would be either a quantum artificial intelligence, or someone with a mysterious talent/sensitivity. Or more comically, you could have a "anti-Gilligan" who through dumb luck tends to stumble into the event that will shift the situation to the new loop.

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The most common solution I have seen to this problem is the "many worlds" approach. When you go back in time and change something, rather than change your own history, you create a new, independent timeline where your change was always part of history. So if you went back in history and killed Hitler, you would create a new alternative present where Hitler died, but your own present would remain unchanged.

Another approach that I have only seen occasionally is some sort of self-correcting force in the universe. Basically, a series of coincidences will occur that prevent any attempt at changing history from succeeding.

The first approach makes things very easy, you can do whatever you want, and you may be able to give some other version of yourself a better life, but your own present remains unchanged. The second approach may seem contrived, but if implemented well could make for an interesting story.

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    $\begingroup$ As pointed out by a quote in a4android's answer, the many-worlds hypothesis is essentially precluded by the Novikov self-consistency principle that the OP is is interested in. $\endgroup$ – Caleb Hines Dec 9 '16 at 5:10
  • $\begingroup$ How, exactly? The new timeline is fully self-consistent. $\endgroup$ – TheBlackCat Dec 9 '16 at 14:05
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    $\begingroup$ @TheBlackCat The Novikov self-consistency principle is an actual thing. There is the assumption that it's the same timeline. $\endgroup$ – wizzwizz4 Dec 9 '16 at 17:02
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There are three interesting articles (1, 2, 3) from Seth Lloyd, where he addresses time travelling (and also the grandfather and unproven-theory paradoxes) in quantum mechanics. In the third, he describes two ways how to send the unproven theory into to the past. He concludes that depending how we try to do it, it is either impossible (zero probability of success - something will fail), or the content of the theory is determined by the rest of the universe. In other words, the actor is not free to send to the past whatever he wants, because what can be successfully sent is already determined by the self-consistency requirement.

I think this supports the most upvoted answer from Reese. The fact that the character is determined to send himself the correct answer back in time does not guarantee he shall succeed. The selection of the self-consistent solutions already navigates around possible paradoxes and this can lead to "strange coincidences". If there is time traveler resolved to kill his grandfather, some strange coincidence must prevent him from doing it. We should not be surprised by that, as there are now causes in the future and requirements on self-consistency at play, so the probability and entropy probably does not work completely as we are used to. The time traveler resolved to send himself the hypothesis thus creating the bootstrapping time-loop can succeed, because it is not self-contradicting. But it should not be surprising if some unexpected random failure or unexpected event prevents him from doing so, because such things probably do happen when time machines are involved.

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A paradox is a temporal gearlock, wherein a system conflicts with itself and must therefore grind to a halt. A causality loop is a temporal perpetual motion machine, and must therefore decay into some lower-energy state at each repetition. The Novikov Self Consistency Principle only holds when the traveler is still moored within time. A method of time travel that unmoors the traveler temporarily, making a bubble of the traveler's subjective present, would circumvent that. Obviously this isn't a terribly hard scifi line of reasoning, but no good time travel story is.

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The Universe is already the sum total of all the time travels to ever happen.

This is an alternate, more intuitive way of stating that the probability of changing the past is zero. It is zero because the past has already been changed. Let's see how this plays out with a few apparent paradoxes. Of course, a chronophysicist will tell you that this is a gross oversimplification, the way the Bohr model is for an atomic physicist.

  • The inventor of the time machine goes back in time to give their past self the plans

At some point, in a hypothetical not-yet-time-travelled universe, someone invents time travel. The decide that spending decades to do so wasn't worth it, so they travel in the past to give the plans to their young past self who just started working on the problem, creating a hypothetical time-travelled-once universe. The new inventor builds a machine in a few months and decides to go back in time to give the plans to their much younger teenage self, to skip some more years, etc... Until at some point, they went back in time and gave the plans back at the exact time where they received it.

All those previous hypothetical universes don't really exist, only the "final" one does. They are theoretical constructs that help calculating the actual result, not unlike virtual particles in quantum mechanics.

And voilà, you end up with what appears to be a causal loop at first glance, but actually isn't.

  • Grandfather paradox redux: after receiving the plans in their youth, the inventor decides to not go back in time and give their past self the plans

This is impossible in the real universe, because it already happened. The inventor, or some very convincing fake, already went back in time to give the plans. So if the inventor didn't, then something else did, disguising itself as the inventor. How improbable this is depends on what is going on in the entire timeline from this point - as a rule of thumb, it's not going to happen without a good reason.

So in most cases, it won't be a "final" state. Then, how does the next hypothetical timeline iteration happens? The trick is, the new looping event doesn't have to be the same. Maybe someone else uses the time machine at some point to go back further in time, causing a new event cascade that ends up causing the inventor to not bother with time travel in the first place. Or someone made a genesis bomb, which went back to Big Bang times and scrambled what would become this part of the Universe, causing completely different galaxies to be born.

Side note: Time travel and the Fermi paradox: if the Universe allows technical civilisations to build time machines that don't require a receptor (think H.G. Wells' Time Machine, instead of wormholes), then it allows for said technical civilisations to reach back to deep time, potentially the beginnings of the Universe, and scramble the constituent parts of their future star systems or galaxies to non-existence - whether by accident or self-destructive action is unimportant. This may considerably limit the probability of existence of such civilisation. The good news is, if the NSFP applies, you already live in a universe where your civilisation don't retroactively wipe itself out of existence! Lucky you. Though it may mean your civilisation is probably not going to discover those time machines at all.

So hypothetical timelines will keep modifying until one is reached where its own time travels cause its own events - and this is what actually happens. What looks like a strap-on causal loop is actually the first consistent timeline that could have existed in the first place.

  • Causal oscillations: timeline A causes timeline B, timeline B causes timeline A

Alice and Bob play Heads or Tails. Alice says Heads, and Bob reveals that it was Tails. But Alice is cheating: she uses a time machine to tell her past self the result. So what actually happens is that she says Tails. Bub Bob is cheating: he changes the result depending on what Alice says. So what actually happens is that he reveals Heads. But then, it means Alice actually told her past self that it was Heads...

In reality, the oscillation are never perfectly stable. Hypothetical timeline 1 is not quite the same than hypothetical timeline 3, even if in both cases, Alice and Bob choose the same faces in both. Those variations will at some point break the loop and end up with a stable timeline.

What it means for time travellers:

It is not that time travellers cannot change the past, so much that they did already.

While there are what looks like strap-on causal loops, they are actually the natural result of time travels to happen during the existence of the Universe.

And while there may very occasionally be events that look causally inconsistent (that is, caused by the arrival of a time travel that doesn't seem to happen at its supposed departure spacetime), this is caused by a mistake on what is actually the cause of the event (the actual departure spacetime). Note that this can be weaponised: you can change the past (or future) as long as you are not certain what actually happened. This may imply deception of your past self, so an event you think actually happened (preventing you from changing it) did not in fact happen (so you can change what did happen).

Harder to identify but present nonetheless are events that should be more common than they are, like time travel WMD. Those are events that could later cause themselves to not happen, which by nature will proportionally decrease their actual probability.

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