What determines which stable time loops occur?

Question

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.

Answer 1

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.

Answer 2

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.

Answer 3

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.

Answer 4

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.

Answer 5

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.