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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).

Awesome explanation, +1.

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?

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).

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

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).

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

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.

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.

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.

There is a fair overlap between the analytic-philosophy community and physicists and mathematicians. So the analytic community generally doesn't talk out of its arse about these things.

I'm from the other side of philosophy, the continental-philosophy area, which mostly talks about ethics and art and identity, so for me to talk about CTCs I would be talking out my arse.

Philosophy is, generally, very hard to read. So much so that reading Descartes' Meditations (considered an alright starting text) in my first philosophy course took me about 30 mins per page.

But, it seems to me that this is one of those areas where analytic philosophy seems to be breaching an area where actual experiments can be proposed and tested in a physical sense, and it leads me to think, what's the point? The logical (philosophical) consistency of light being a particle and a wave doesn't come in to the reality of it. Was it worth ancient Greeks wondering whether all matter was made of water?

I think similar questions can be asked about continental philosophy. I certainly read a lot of it as a lot of wank that could be answered by real-world surveys (what makes people happy? I dunno, how about we ask them). But I think questions like, how do we determine whether happiness is the thing we should optimize for in life, are still relevant, and philosophical, and more basic! I think the underlying basic question of CTCs might be, does something being a logical paradox actually prevent it from happening?

And, if CTCs are a physical phenomena that we can't observe (maybe, yet), what's the point of a philosopher wondering about them? Shouldn't that be a theoretical physicists job?

>But, it seems to me that this is one of those areas where analytic philosophy seems to be breaching an area where actual experiments can be proposed and tested in a physical sense, and it leads me to think, what's the point?

I think it would be fair to flip that around: if your philosophy doesn't result in testable predictions, then what's the point?

What I was talking about in that quote is that CTCs are definitely being seriously talked about and explored in relation to tested elements of our understanding of the universe by theoretical physicists, the experts in physics, and so I think its time for philosophers to give up that ground.

Similarly I feel like there are philosophy-of-politics discussions that can (through political change) become the realm of actual politicians, sociologists, etc.

I apologize, but I'd like to flip your question about again. I think philosophy is the realm of the untestable, so in my mind you're asking "what's the point of philosophy". I think philosophy is the place to explore the full ramifications and implications of untestable ideas. I'd also ask what's the point of your question? If its not testable, I think its a philosophical question, QED. If it does result in a testable prediction, what's the test?

Hi, I'm just some dude, but wouldn't it be best for everyone to work on the problem until the problem is solved? Also, what about philosophers who are also physicists? I had a physics professor in college who had a degree in philosophy, and she didn't seem to mind talking with non-physics philosophers about physics-related topics.

Well, yeah, in my initial comment I said that there are a lot of analytical philosophers that have an understanding of physics. But, I think that CTCs are better suited as an undergraduate physics topic than an undergraduate philosophy one. We did talk at length on them in one of my undergrad philosophy classes.

I think its a fair question if everyone should work on the problem, but I'm wondering if that same question could be applied to every problem?

I don't think many would agree that a mathematics degree should be made entirely of pottery electives. I'm not saying we shouldn't encourage mathematicians to dabble in pottery, I'm just saying pottery is not mathematics, like CTCs don't seem to me to be philosophy.

Oh, it's definitely not cool to force people to do things. I didn't know it was like that. Someone probably thought that it's a really important problem, though. Like, if it were up to me, I'd be okay with forcing students to take a course on global warming, since I think global warming is a really important problem. But that's just me though. Anyway, I'm sorry you had to spend time doing stuff you weren't all that interested in.

I wasn't forced and I found CTCs to be interesting. The time travel discussions were all interesting, but to me they don't feel like philosophy.

If it's not testable, what's the point? If it is not testable you are literally saying it has no effect on the world.

Note that something can be political or sociological and still be testable. You can have a utilitarian moral philosophy where you assign utilities and sum them up, then do surveys or focus groups to to measure agreement with the results.

But if a theory literally has no testable predictions? That is the definition of useless.

>>If it is not testable you are literally saying it has no effect on the world.

It's provable that things that are true are not demonstrable(see Gödel's incompleteness theorem). It follows that things that are not testable are true, and for some d definition of truth, it means they have an effect in the word. So we absolutely can, in a meaningful way, wonder about the posible consequences of something that while not testable may be true. Just because something it solely potentially meaningful does not mean it it's entirely meaningless.

That's a very uninteresting and unscientific definition of truth. But even less interesting is arguing over definitions.

As a scientific person, I'm only concerned with truth that derives directly from observation. "True but not demonstrable" is an oxymoron.

Can you observe the truth of the statement:

"Truth from observation is the only truth that matters."

Where can I also observe this?

>>You can have a utilitarian moral philosophy

Let me stop you right there. You can have a utilitarian moral philosophy, sure. But the question of if you ought to have such a philosophy is a philosophical one. To get to the point of having tests of optimized utility there is an underlying question that has no tests, which is are tests for utility really the best tests to run?

Its either turtles all the way down: tests testing the effectiveness of tests, or, you get into philosophy.

Which is arbitrary and meaningless.

Have fun with your waste of a mind.

Interesting. What test do you propose to determine whether it is arbitrary and meaningless?

> I think it would be fair to flip that around: if your philosophy doesn't result in testable predictions, then what's the point?

"Untestable philosophies are pointless" is an untestable philosophy, and therefore pointless by its own standards. This is a well-known problem with logical positivism, which is roughly the position you are advocating.

No brag, but I read meditations in a few lunch breaks when working a manual job power washing ride on lawn mowers at uni.

It's a simple read.

If you'd have said Kant, I might have agreed with you.

Most of the time complicated philosophy (or science) are hard to read because either they're talking crap (Hegel) or they can't write for shit (Kant). Descartes was pretty good in my book (although obviously the 2nd half complete failed).

I found Kant to be easier than Descartes and Heidegger to be by far the hardest to read of all. Hegel has for me been somewhere between Descartes and Heidegger, but I think its no surprise that Zizek was a Hegelian and also read a bunch of Lacan :D

I think Heidegger is actually deliberately obscure!

@KenoFischer already did a great job explaining the paragraph, but the audience is professional philosophers, philosophy graduate students, and some philosophy undergrads. I parsed this SEP entry for one of my undergraduate courses (Philosophy of Space & Time).

If you're interested in the topic, I suggest reading Time and Space by Barry Dainton[1]. It was suggested reading for our class and primed me for anything from time time travel to general relativity.

[1] http://www.amazon.com/Time-Space-Barry-Francis-Dainton/dp/07...

There's always Wikipedia:

In mathematical physics, a closed timelike curve (CTC) is a world line of a material particle in spacetime that is "closed", returning to its starting point.

So it's essentially like in the movie Groundhog Day I guess.

In Groundhog Day, there is no material particle that returns to its starting point, only information (Phil's memory in particular.)

Although, intuitively it seems that a time machine for information should be easier to build than one for matter, because information is so much easier to teleport.

If you had a tiny wormhole and put one end of it into a high-speed centrifuge for a while, until there was a meaningful time differential between the two ends, you might not be able to send even an entire photon through it, but you might be able to do something like bounce a laser off each end such that if you modulate the input polarization at one end, the polarization of light reflected from the other end changes at the appropriate time. No mass or energy travels through the hole itself, but information is transmitted.

An even better (although quite contrived) example is given in the movie "Predestination":

http://www.imdb.com/title/tt2397535/

Alternatively, read the short story "All you Zombies" by Robert A. Heinlein, on which most of the movie is based:

http://emilkirkegaard.dk/en/wp-content/uploads/Robert-A.-Hei...

Suppose electrons would naturally time travel occasionally. But, we could gain no knowledge about the future from those electrons. It's not interesting.

CTC means time-travel with structure. If you can send say a book back in time then our ideas of paradox ect have meaning.

Next suppose you could time travel, but only far from your own past that light can't reach you. Further you block other time travelers so you can't send messages back to your self. Again not interesting, you need to be able to influence your past (self intersect) to be fun otherwise it's just like moving quickly.

If electrons sometimes time traveled on a human time scale we could exploit that, eg. by building a huge assembly of electron guns, phosphors and photomultipliers. We could gain knowledge of the future signal sent to the electron guns by watching when the phosphors lit up while the electron guns were switched off.

Depends on scale. Suppose they are rare and show up in random locations with random velocity's random amounts of time in the past etc. As in 1 electron in the observable universe per day.

If all their properties are randomized then I don't see how they can be said to "travel". That would be indistinguishable from electrons spontaneously appearing and unrelated electrons spontaneously disappearing.

This is one of the major reasons I said time travel without information transfer is not interesting. Even if it actually happens, it's not distinguishable from something else.

PS: Quantum entanglement is also less interesting than you might think for similar reasons.

In the case of entanglement though it is actually distinguishable from other, less "interesting" phenomena though, right? That's what the loophole-free Bell tests are about.

I didn't understand anything. :-(