# What determines which stable time loops occur?

Let's say I can time travel, and right now I am duking it out with the big bad. Suddenly, future me appears and gives me a huge hammer, which I use to hit the big bad. Then I travel back in time and give past me the hammer. Past me smashes past big bad, and then goes back in time. It is now just me and past big bad, ready to finish the battle.

The above narrative is a stable time loop, according to Novikov self-consistency. The problem is, what determined that is was a hammer, as opposed to a laser gun, or a good-clone of the big bad? What mechanism can be used to determine which time loops form, and which do not.

In a comedic situation (like the above could be), the writers freely choosing stable time loops is all fine and good, but for serious works, the audience expects some mechanism to determine what happens in the plot.

• Are you interested in simple loops, like the one you describe, or strange loops like Heinlein's character in All You Zombies? – Cort Ammon Jun 27 '15 at 6:08
• I think all time frames can be overlapped with one another in a universe but would split into multiple parallel universes to spawn different timelines, in other words the moment you meddle with the past you created another timeline and all timelines existed over each other and cannot be influenced simultaneously unless you are a fifth dimensional intelligence being. – user6760 Jun 27 '15 at 6:34
• In short grandpa's paradox is a myth. – user6760 Jun 27 '15 at 6:36

Unlike many other readers, I think I know exactly what you're getting at.

Suppose you set up two wormhole ends close to each other with a short offset in time, and then throw a bowling ball into the "future" end. Assuming the wormhole mouths are not imposing special rules (let's suppose it is not turned on yet), nothing prevents you from arranging objects in space, as is normally the case.

Well, "the universe" chose this particular history. That includes natural phenomena and extends to "free will" too since ultimately the metabolism is your brain is physics and natural. One could ask how the universe chose this history over a different possibility. One answer is that it's locally random in every quantum random event with no special rule for larger scales.

This includes entanglement with space-like separated correlated observations, double-slit experiments, etc.

The Novikov self-consistency principle simply applies the exact same thing to spacetime with different topology. The wormhole allows two paths for the quantum wave function, exactly like a double slit, or more precicely, something like a gravitational lensing where paths are different lengths and different enough to be noticable. That's very interesting in itself, in that an interference pattern will show up if you use a narrow enough band-pass filter so the uncertainty in time covers the difference! Point is, what is collapsed and what isn't is not so simple, and context dependent. Delayed choice is also a mind-bending illustration of this.

So, given the arrangement of wormhole and bowling ball, which self-consistent solution (involving time loop) occurs is random with the same rules as anything else: each quantum event is random, but macroscopic events that require a longer chain of quantum events will be rarer because it is a slice of the total probably for the shorter chain.

Consider events A, B, C. For some specific C, you then have a choice of D's. So a specific D is rarer than other C's that end there. Complicated things are rarer than simple things.

Meanwhile, there are rules for random "collapse" (actually, decoherence) which is not, in general, a uniform distribution. Look at a non-local quantum correlation and Bell's Inequalities shows you that some outcomes are more probable. A photon going though a double slit has a higher probability of landing in the bright area of the interference patteren (which is why it's bright after a bunch of photons pass that way).

Now there is another deep principle driving things, known as action. Why does a ball follow Newton's laws? In general why are specific paths strongly preferred, for any phenomena? The interference cancels out most paths except near a maximum, minimum, or saddle point.

So, the richer topology of the wormhole region provides another interference pattern for any particle in the region, and this will impose solutions. This has never been discussed before to my knowledge, but it makes me wonder if there could occur what seems like a force on moving objects, due to this interference.

This should provide food for thought, and fodder for some plausible rules in the story. The people could "tune the interference pattern", "provide a larger pre-existing context for consistency", etc.

Now another thought: the self-interacting bowling ball appears globally as a violation of matter/energy concervation. Perhaps an action principle will invoke itself here, e.g. choosing the solution that minimizes the amount of "extra" energy, momentum, etc. that take place. Maybe it's a kind of information entropy that's minimized, and solutions are preferred which don't change the looping object as much, or minimize observations from the universe at large. You can come up with rules (e.g. momentum) and then as a twist reveal the real rules (e.g. excess momentum which as effects that ultimately spread beyond the time-travel region) which are more subtle.

Maybe the time travelers will find that angular momemtum is prioritized over mass/energy, or momentum non-concervation is minimized but mass itself is not a big deal. They can tune the situation by providing details that involve these variables.

However, you have to ensure that the universe doesn't act on a larger context and minimize excess mass and momentum to zero by not putting the wormholes near each other in the first place. The heros need to work to ensure that the overall context is not strongly not-preferred by the universe. They have to carefully work in stages, "committing" each step by making sure decoherence spreads out over a larger patch of the universe than their subsequent steps will work in. You'll have to fight and outwit Fate to get to the point of doing the experiment! Basically, make it worse not to, and (hand waving) allow "free will" to master these events.

Remember the delayed choice experiment? What seems like a done deal might still be in superposition to some other observer, and he collapses the wave function to a different outcome, erasing your events. In seems that this leads to a multiple worlds model, meaning you can push Fate where you want, but create a parallel universe with your action in it. But, so does any other activity so that can probably be ignored. But playing with that in combination with a wormhole network of FTL travel could make for interesting effects to use in a plot.

My own favorite idea, at least for a story, is that any time you turn on a time machine, something comes out that is part of a loop.

• While the bowling ball example uses a macroscopic object it actually just messes up with the movement vectors. When you use actual macroscopic objects within atmosphere for interactions more complex than a single collision your minimization rule(s) will essentially mean minimizing the mass/energy transferred back in time. While this makes perfect sense and is probably even correct, we unfortunately already have to hand-wave it away to allow moving macroscopic objects back in time. So it is useless as a solution for the question. – Ville Niemi Jun 28 '15 at 13:30
• Seriously, there is nothing special about what goes back. Only requirement is that it must pre-exist and be accessible so you can send it back. And must both enter and exit the loop. I explained the constraints in my answer. Although your answer is superior in that you actually understood the question... – Ville Niemi Jun 28 '15 at 13:45

The real answer as to which time loop occurs is nothing special.

First off, Novikov self-consistency is a special case. It is a solution for general relativity which admits time loops in which the laws of physics within a loop are identical to those outside of a loop. Accordingly, the choice of a hammer vs a gun is literally in the same class as deep questions such as "Why did I fall in love with Susan, rather than Alice?" and shallow questions as "Do I want eggs or pancakes for breakfast?" It's also in the same class as the strangeness of serendipity, such as "How is it that I just happened to miss the bus the day Susan was sitting there?"

Note that Novikov self-consistency, being a GR model, is deterministic. It does not admit any special support for freewill, beyond that which the laws of physics allow. You will need to adapt it if you want characters to ponder the oddity of life within a time loop.

In general, my recommendation is to start with a timeloop which could theoretically have occurred by starting with a non looping surface of spacetime and adding loops. There is no obligation within Novikov's rules to do this, but it tends to make people more comfortable because they can sort of work their way through the logic. Otherwise you enter the world of strange loops, which is another beast entirely. Those loops, like the one in Heinlein's All You Zombies is a mental-breakdown-in-a-can.

As an example, there is a classic proof for time travel using wormholes and a billiard ball. You start with the wormhole in place, and try to send the billiard ball through the wormhole in such a way that it comes out to strike itself mid-path. It has been proven that, for any spacing of the wormholes, there is a solution which causes the ball to leave the wormhole at a slightly different angle, grazing its younger self at a slightly different angle than intended. The result is that the younger ball is on the perfect trajectory to enter the wormhole at the angle required to leave the wormhole at exactly the angle which it emerged the first time (consistency). The thesis that proved this also came with a conjecture that the same could be done with any object, not just simple spherical billiard balls.

• Could you expand on the starting with nonlooping surface and adding loops? – PyRulez Jun 27 '15 at 15:18
• In the billiard ball example, it is possible to have a loop with two pairs of wormholes, such that a billiard ball appears from one hole, followed by annother billiard ball appearing from the other, colliding in just the right way so that the balls eventually find their way to the "future" side of the wormholes to keep the loop going. Nothing in GR prohibits it. However, people's minds get bothered by the question "but how'd the ball get there in the first place," which is only paradoxical because they don't understand the spacetime Novikov was describing. – Cort Ammon Jun 27 '15 at 22:11
• Such a system is not paradoxical at all. It's actually completely self-consistent. There is no issue with it. However, for the sake of the reader, it is considerate to start with an external source (such as a hand throwing a billiard ball) in a way that appears paradoxical, and then give them an oppertunity to watch as spacetime twists things to prove it was never paradoxical in the first place. It lets readers think of time as an arrow first, and only then consider the curves of the wormhole, rather than forcing them to understand the wormholes first. – Cort Ammon Jun 27 '15 at 22:13
• Oh, so you are saying that it is a type of branching time line time-travel theory, but that it always stabilizes eventually. I was thinking that too. – PyRulez Jun 27 '15 at 22:40
• Yeah. The branch does not have to even occur if you don't want it to, but it makes it easier on readers if they are allowed to visualize as though it does exist. – Cort Ammon Jun 27 '15 at 22:48

The thing is this could never work. Take the example of the gun. The gun holds six bullets in it. You shoot Big Bad once and go back in time, giving the gun with five bullets in it to your past self. He or She shoots Big Bad leaving the gun with four bullets, and then travels back in time. As you can see, this object constantly continues to age while trapped in this loop. After billions of years, even a very high quality hammer will be reduced to dust because it's being constantly used for infinity. Nothing useful could possibly survive this and that means this situation couldn't ever happen.

• That raises a good point for my specific examples. Could this generalize to other examples (like, say, an immortal attack dog? Or time loops not involving objects, but say, information (I go back in time to reveal the big bad's weakness), or other time loop scenarios?) – PyRulez Jun 27 '15 at 4:49
• This can't happen if Novikov self-consistency holds. There will be only one iteration of the loop and nothing can go back more than once. – Ville Niemi Jun 27 '15 at 4:55
• With this example, the object's entropy is constantly increasing throughout its journey. This is why it can't handle it. I haven't heard of any law stating that "information's" entropy must increase, so it might be possible. The standard example is giving Beethoven one of his symphonies before he writes it. As long as you can guarantee that none of the notes will "ever" change it is fine. And I think if the information were being constantly renewed such as in the Big Bad weakness example, it should be fine. – Stephen Jun 27 '15 at 4:55
• Or to be more exact, while you can loop the object more than once, every loop is a separate loop and should be considered separately. But it is probably better not to since that gets kind of complex... – Ville Niemi Jun 27 '15 at 4:58
• You do not need to fill the gun with the bullets that went through the time traveling portal. You can purchase them from off the shelf. All you have to do is be comfortable with the strange nature of a bullet that exists at two places at the same time (one "young," one "old"). The Korean show "The Great Doctor" played with this, where a time traveling surgeon had her surgical tools with her, and had to compare them against rusted antiquated tools that she had later left in her time travels. – Cort Ammon Jun 27 '15 at 6:10

Not sure if I understand what you are asking, but I think the basic idea is that since the time travel creates a closed time-like loop, it also creates a closed loop in causality. So it is useless to think this in the form of linear sequence of events, you get the hammer from future self and go back in time to give the hammer to your past self within the same time loop. There is no meaningful way to claim one event precedes or follows the other.

I think you want to know what prevents you from receiving a hammer and then giving a gun? The fact the the "then" in that sentence does not really exist. You can totally choose to give anything you wish, you have free will, but then that will be what you received "earlier" from your "future" self. The "then" referring to time after the time loop. Essentially everything inside the time loop is in indeterminate state until the time loop closes and an observation of what happened within the time loop can be made. And according to Novikov this cannot happen unless the loop is self consistent.

The important point to note this is that what enters and what exits the loop must match. The hammer must be there before the loop begins. When the future self brings back the hammer, there will be two hammers and two selves, and the hammer and self that go back must be the ones that didn't come from future. Only the ones that travelled back in time will exit the loop. The hammer doesn't necessarily need to be that close, but it must pre-exist.

This duplication does not violate conservation of energy because the exact same things that go forward in time doubled also go backwards in time in the loop.

Note that the loop must be created before the point you receive help from future and that it is consistent for you to receive a copy of the big bad that comes back to help himself defeat you. These should help you limit the power of the time travel.

• I mean, in the example above, is why did my story talk about a hammer instead of a gun. – PyRulez Jun 27 '15 at 3:18
• @PyRulez Because you wanted to use a hammer? The loop would be just as stable regardless of what you choose. – Ville Niemi Jun 27 '15 at 3:20
• The thing is is that gives the writer too much power. How can I explain why it was a hammer instead of a gun. If both are just as stable, what ultimately decides what happens? – PyRulez Jun 27 '15 at 3:21
• @PyRulez Yes, but other than the extra constraints of time travel, it does not change the plotting of the story in any way. It seems to me that you are trying to borrow trouble you do not actually need. Time travel stories are not really fundamentally different from other stories. – Ville Niemi Jun 27 '15 at 4:16
• "in the example above, is why did my story talk about a hammer instead of a gun." The answer to that is because it's easier to ignore the logical problems of that particular loop by using a hammer. Let's say your future self hands you a Colt M1911 with 7 rounds in the magazine. You fire and miss. Then you go back in time and hand yourself the gun with 6 shorts in the magazine. Then 5. Then 4. etc. What happens when you hand yourself an empty gun? – WhatRoughBeast Jun 27 '15 at 4:41

# 1. Causality, 2. Freewill, 3. Time Travel

(or 4. Parallel Universes)

You get to pick 2 of the bolded OR you must have #4 if you wish to remain consistent with physics as we now know it.

## One Universe explanation

If you want your Time Travel to occur in the same time line, then you must give up either causality or freewill. The problem is that physics as we understand it right now assumes both of them to be true. If I had to pick one, I'd pick causality and state that what we think of as freewill is simply our conscious rationalizing after we act that our actions were made by our choice and not predetermined.

Time loops in this setting are set in stone. If you travel back in time, you perform the same actions that you performed in the previous loop. Whether by choice or seemingly "random" chance, the Universe or you will always choose to take the same action, even if you promise yourself to not do it in future loops.

Putting it another way, if you used a hammer on "Big Bad" the first time through, something will always convince you to bring back a hammer in all future loops - because it has already happened.

## Parallel Universe explanation

Alternatively, if your story must have the first three, then to remain consistent with physics as we know it, the parallel universe interpretation of Quantum Mechanics must be invoked. Each decision we make is unique and causes a calving of Universes (think of Stephen Baxter & Neil Gaiman's Long Earth).

Traveling back in the timeline and changing a decision (or causing someone else to change theirs) leads to that timeline tracing out a new path into the future than the one originally taken.

This sort of time travel paradigm leads to a chaotic future. Each loop alters the Universe in unpredictable ways.

Putting this another way, in your first loop you bring back a hammer and defeat "Big Bad" but something happens that makes you wish you had sent back the laser instead. The next time through you send back the laser - but that flips you onto a different & divergent Parallel Universe. This will ultimately disrupt your time travel plans altogether.

## Another thought

Time lines which develop time travel and possess freewill will ultimately loop into extinction.

Consider the following: TT (time travel) inventor, goes back in time to alter the past and make it easier to invent time travel. His actions cause unforeseen side-effects. Each time he invents time travel he goes back to "fix" those side-effects. This happens in each future as long as time travel exists. Changes to the time line stop being made (which "sets" the time line making it permanent) only when one of those side effects is failing to create TT.

In all cases eventually, TT + freewill leads to no TT.

• Could you allow freewill most of the time, but mysterious accidents occur if you take actions that cannot be consistent (I can go back to see dinosaurs if I don't touch anything, but if I try to go back and kill my grand pa, "time" will predict this and the machine will explode?) – PyRulez Jun 27 '15 at 23:11
• I've seen it treated in all sorts of different ways. From a "mysterious force prevents you", to new information changes the characters mind to the original choice, to the grandpa you killed turns out to have been an adoptive/imposter grandparent, to grandma had a fling on the side which is where the character came from but kept those facts hidden from the family due to embarrassment. – Jim2B Jun 28 '15 at 0:02
• Physics does not assume "free will" is true. It has no concept of that. In fact, physics implies a "block universe" and we're left to figure out what "free will" means in light of relativistic time. – JDługosz Jun 28 '15 at 4:13
• It's not mysterious. Without time loops, plans don't work out and roulette wheels land where they may. Why does the presence of an observer from the future make it mysterious all of a sudden? When you read a book is it mysterious that it still contains the same text? You get the same mind-bending what is the present issues with the "galaxy far far away" example. (A better link ) – JDługosz Jun 28 '15 at 18:19
• Here is a direct description of the example I mean. Does the alien general suffer from mysterious forces because people on Earth are walking in opposite directions? His decision is in Alice's recent past, but Bob's future. The general is mysteriously forced to make the same choice for Bob's time as for Alice's. – JDługosz Jun 28 '15 at 18:30