[KenoFischer]

I'll have a go at defining it, term-by-term,

> smooth

Meaning no abrupt kinks (for a notion of abrupt which is probably not physically achievable, so don't worry to much about it) or jumps/discontinuities in the path of a particle, applying to both space and time

> timelike

roughly speaking, traveling slower than the speed of light

> future-directed

meaning going into the direction of causality

> with intersections

meeting itself again.

In other words, it's a path through space/time on which you experience your own local time as always running forward, but yet somehow you end up in the past.

Perhaps an analogy is in order. Suppose we were in 1+1 dimensions, with the time dimension being compact (closing in on itself). Visualize this as an infinite cylinder (the infinite axis being space). Now, let's impose a finite speed of light (for simplicity 1cm/s) and define the direction of causality, say counter-clockwise. Then, this spacetime has CTC, because we can find a path that, is smooth, future-directed (going around counter-clockwise) and timelike (going at angles < 45 degrees compared to the spacial axis). The simplest such would be a simple circle around the cylinder, but any curve that matches the above rules and intersects itself would be considered a CTC.

Now, as a final note " a crude way of bringing out the fact that the application of familiar local laws of relativistic physics to a spacetime background which contains CTCs typically requires that consistency constraints on initial data must be met in order for a local solution of the laws to be extendable to a global solution." means the following. When we usually do physics, we know what happens locally (e.g. ball get shot at wall, bounces back), so we simply have to figure out (or decide if we're doing a thought experiment) where everything is in the universe at some particular time, apply our rules everywhere and we essentially know what's happening everywhere, anywhere. This doesn't work any more in the presence of CTC. "Consistency conditions" basically just means that you have to chose your placement of objects in such a way that they don't cause any paradoxes (there's a more technical notion here, but that's essentially what's meant).

[studentrob]

If time travel is possible, why is consistency a concern? If one thing changes at one time, couldn't another change at the same time? Could time travel exist without our being aware of it by constantly changing our understanding of events such that there appears to have been no change?

Does consistency mean that some change must cause many other changes in order to make everything end up in perfect alignment?

[simonh]

Larry Niven speculated that if time machines were possible, time travellers continually going into the past would change the circumstances that lead to them inventing their time machines and using them, resulting in an unstable timeline. The only steady state for this timeline would be one in which no time machine was ever invented.

So we may well live in a universe in which time travel is possible, and time travellers from alternate future timelines may even have arrived in it in the past (or may arrive in it in the future from more distant futures), but the 'final value' of the timeline would exclude the events that lead to their actual invention.

[KenoFischer]

Consistency here is a mathematical statement. Think about the cylinder example, and suppose you want to assign a number of each location. Then, naturally, going once around the cylinder puts you back at the same spot on the cylinder, so it needs to have the same number. At this point it is useful to remember that the numbers on the cylinder are fixed. We're already representing time as the compact dimension of the cylinder, so there's no extra time dimension.

Now, with this setup, let's imagine living in this 1D world, just sitting still, reading off numbers. Our life would be cyclic with period cm/((2pi r)s).

[KenoFischer]

Let me try to phrase this a different way. Suppose the universe is a database, where (t,x,y,z) are the unique keys. For every key there is some value of "physical reality" at that point in spacetime. All the original statement is saying that if you want to generate such a database by starting with only some of the entries and applying the laws of physics, then in the presence of CTC, there are some very strict conditions on what those initial rows can be if you don't want to run into a situation where you'd want to assign two different values to the same key (e.g. by getting to the same point forwards in time and backwards in time).

[logfromblammo]

Perhaps the database administrator chose the unique keys (observer_id, subjective_observer_time).

Then, the (t,x,y,z) coordinates could all be parametric functions of observer_id and subjective_observer_time. If you follow a CTC and meet your younger self, then convince your younger self to not follow the CTC, you may simply be reassigning your younger self to a new observer_id, rather than creating a paradox that destroys the database integrity.

As long as all observers obey the rules of causality locally, your elder time-twin will never remember meeting their own elder time-twin, and your younger time-twin will never remember not meeting their own elder time-twin. The CTC has no way of knowing whether anyone ever followed it or not, because it isn't an observer. So if you ever meet yourself, you're no longer meeting yourself, because the person you meet is from that moment no longer you. If you do anything at all within the past half of your own light cone that interrupts causality, you are just creating a new observer.

So the photograph doesn't change itself, like in Back to the Future. Marty can't erase himself, but he could erase all references to himself from the historical record, except for whatever he carried through the CTC. He could then take a DNA test that proves him without a doubt to be the child of two people who cannot recall ever even touching one another. Even if he mostly restores causality, upon reversing through another CTC to a time before he entered the first CTC, there will be a different third child of his parents living with them when he gets back--someone who might not ever traverse a CTC.

If that's how it works, time travelers could do no worse than completely erase themselves from all historical records and the memories of every living person. They would be considered people who never previously existed, who spontaneously appeared, complete with memories of future events that might never come to pass. In that case, almost anything even remotely plausible could come out of either end of a CTC.

[studentrob]

That makes more sense. I don't fully have it but that's on me. Thanks!

[TheOtherHobbes]

But this is not the same as a time machine. The article doesn't explain the difference between a machine you can use to travel back in time, and a contrived spacetime in which events run in a loop.

While it's dismissive of "paradox mongers" it doesn't deal with any of the very real issues created by very obvious potential paradoxes - not least of which is that physics fundamentals like conservations of energy stop working.

(If you can move anything or anyone back in time you have a universe with two of something instead of one of something - which means you can get something for nothing, over and over. If you can't do this because the CTC forms a time loop, you don't have a paradox, but you don't have much else of interest either.)

A contrived spacetime with a CTC is fundamentally useless as a practical time machine. And the whole point of a Thornian wormhole is that it offers practical engineering benefits - such as being able to travel in a way that effectively bypasses the speed of light limit.

In any case - relativistic speculations are metaphysical, because it's a fair bet that spacetime isn't a smooth continuous manifold at all. It just looks like one from a distance under normal conditions - normal meaning anything outside a singularity or black hole.

No one has much of a clue what spacetime is made of, and that makes it hard to say much about its properties under stress. For all anyone knows CTCs may be impossible because if you stress spacetime enough it may not act like a manifold any more, and a clean description of what happens at that point needs new completely physics.

[studentrob]

Okay, thanks for your reply. For me this is not plain English =)

[dvt]

Awesome explanation, +1.