Time Travel & Causality in General Relativity

[TheQuestionGuy14]

According to General Relativity, everything must be causal, something from the future cannot effect the past, and spacetime geometry is this way. By this logic, does this mean that if we were to ever time travel, via any means, arriving in the past is a violation of causality, as you are technically arrivinv before you left in the first place. Also, having memories of future events yet to unfold, which could unfold differently, would also be a violation of causality, wouldn't it? Thanks.

 

[Ibix]

Relativity permits things called "closed timelike curves", which are bits of spacetime that you could loop around and meet yourself in the past. But the implication of this is more the "you were always part of history" type of story, rather than "you can change history". You can't do anything different from what you remember because your past already includes a chunk of your future.

It's more than possible that the spacetimes that permit this kind of looping are purely mathematical curiosities and don't describe any spacetime that actually exists.

 

[TheQuestionGuy14]

Relativity permits things called "closed timelike curves", which are bits of spacetime that you could loop around and meet yourself in the past. But the implication of this is more the "you were always part of history" type of story, rather than "you can change history". You can't do anything different from what you remember because your past already includes a chunk of your future.

It's more than possible that the spacetimes that permit this kind of looping are purely mathematical curiosities and don't describe any spacetime that actually exists.

So in essence, going back in time would remove any future memories.

So we could have time traveled through a CTC without knowing. (Not really though).

 

[Ibix]

So in essence, going back in time would remove any future memories.

That isn't what I said. I have no idea how you got that from what I wrote.

The point is that that, if closed timelike curves are possible, you are described by a worldline. It doesn't change just because it happens to go round in a loop. You can decide "I'll behave differently when I'm future me", but when it comes to it you cannot actually behave differently because you behaved how you behaved.

At least, that is my understanding. It's completely incompatible with the notion of free will in an "if I could rewind time I could have chosen to do something different" sense.

 

[TheQuestionGuy14]

That isn't what I said. I have no idea how you got that from what I wrote.

The point is that that, if closed timelike curves are possible, you are described by a worldline. It doesn't change just because it happens to go round in a loop. You can decide "I'll behave differently when I'm future me", but when it comes to it you cannot actually behave differently because you behaved how you behaved.

At least, that is my understanding. It's completely incompatible with the notion of free will in an "if I could rewind time I could have chosen to do something different" sense.

I understand, but my question was slightly different. I was referring to a different scenario:

Let's say hypothetically, you go back in time exactly one week, and you don't meet yourself, let's say it's like the whole universe is going back a week but not you, as you are the time traveller. Let's not say how you went back, you just did. My question was, if you go back a week and kept your memories of the week ahead (so you now know the future), isn't this violating causality.

As the effect (the preserved memory) is occurring before the cause (the actual event that caused the memory, the week ahead), thus causality is broken.

 

[Ibix]

Let's not say how you went back, you just did.

Then you're not talking science, you're talking magic. You won't get a scientific answer unless you propose a detailed mechanism consistent with known physics. Which (so far as I am aware) means closed timelike curves or nothing.

 

[Sorcerer]

I understand, but my question was slightly different. I was referring to a different scenario:

Let's say hypothetically, you go back in time exactly one week, and you don't meet yourself, let's say it's like the whole universe is going back a week but not you, as you are the time traveller. Let's not say how you went back, you just did. My question was, if you go back a week and kept your memories of the week ahead (so you now know the future), isn't this violating causality.

As the effect (the preserved memory) is occurring before the cause (the actual event that caused the memory, the week ahead), thus causality is broken.

If I undersrand the basic premise of a closed timelike curve, whatever you did or will do is set in stone. If you have memories of the future , you will NOT be able to behave or even THINK in any way differently than you did the first time. Everything you think at that point in spacetime would always be the same. Every time you go through the loop.

At least that is my understanding of it.

 

[Mister T]

If I undersrand the basic premise of a closed timelike curve, whatever you did or will do is set in stone. If you have memories of the future , you will NOT be able to behave or even THINK in any way differently than you did the first time.

You were unable to remember the future the first time, so if you are able to remember the future the second time that is something different from the first time!

 

[Sorcerer]

You were unable to remember the future the first time, so if you are able to remember the future the second time that is something different from the first time!

But the spacetime point where the future returns is the same spacetime point where you first get the memories. The world line never has a point at the intersection where the future memories are not present.

Or is this incorrect? When I look at the world line, there is only one point where the future you returns, and it is the same point where you first get there. So why wouldn’t the future memories always have to be there at that spacetime point?

 

[PeterDonis]

Or is this incorrect?

It's correct. If your worldline is a closed timelike curve, then at any point on your worldline, the entire worldline (the entire closed timelike curve) is in your past light cone, and therefore you can in principle remember it.

In practice, it's possible that your memories would gradually decay as you go around the curve, so when you got back to the same point again, your memories of being there before would have gone. For example, suppose it took you 1000 years to go once around the closed timelike curve; when you got to the starting point again your memory would have to be accurate enough over a 1000 year span for you to remember being there before.

 

[Ibix]

If you have memories of the future ,

I think you are correct, but this phrasing is confusing. The problem with closed time-like curves (CTC) is that there isn't a way to define "the past" or "the future". Any given event may define a future light-cone, as always, but this may include itself, and some elements of its past light-cone as well. So if you interact with yourself after looping round a CTC then you don't remember "the future" per se, but you do remember events further along your worldline. You remember your personal future.

It's correct. If your worldline is a closed timelike curve, then at any point on your worldline, the entire worldline (the entire closed timelike curve) is in your past light cone, and therefore you can in principle remember it.

I must say I find the whole thing problematic. Say I fit a red light and a blue light to the front of my rocket. Then I fit a sensor (somewhere it can't see my own lights) that detects blue or red light and sends a current spike through the bulb whose colour it detects and blows the bulb. Then I enter a CTC and meet my future self, who illuminates my rocket with light from whichever bulb didn't blow - which (paradoxically) blows the bulb that didn't blow and leaves the bulb that did blow not blown. (Edit: this is just the shoot-your-own-grandfather paradox with a more technological and less homicidal spin)

I can't immediately see why I couldn't do that if I could find a CTC.

 

[PeterDonis]

Then I enter a CTC and meet my future self,

No, you don't. You are your future self. The scenario we are talking about is that your worldline is a CTC; if that's the case, there is only one of you at any point in spacetime. It's just that all those points are linked by a closed curve.

The scenario where you meet your future self is different: there are multiple "yous" in some local region of spacetime, which means your worldline is not a CTC, it's a more complicated "looping" curve that comes close to itself. These scenarios are even more difficult to imagine consistently than the simple CTC one; but a good example of how such a scenario might work is Robert Heinlein's classic story, "By His Bootstraps".

I can't immediately see why I couldn't do that if I could find a CTC.

You're assuming you have the freedom to set up the lights however you want. If your worldline is a CTC, you don't. The lights can only be set up in a way that is consistent when the fact that they are traveling around a CTC is taken into account. Otherwise you don't have a consistent scenario.

Similar remarks apply in the more complicated scenario when you meet your future self; but as I said above, it's harder to imagine such scenarios consistently.

 

[Khashishi]

Of course, your worldline isn't a CTC. The point is you can move close to the CTC and see an older or younger version of yourself. I think that Novikov's self-consistency principle holds here.
https://en.wikipedia.org/wiki/Novikov_self-consistency_principle

 

[Ibix]

No, you don't. You are your future self. The scenario we are talking about is that your worldline is a CTC; if that's the case, there is only one of you at any point in spacetime. It's just that all those points are linked by a closed curve.

You're right - I'm misusing the terminology. I was thinking of the closed timelike curve as the region of spacetime in which it is possible to have a closed worldline, or pass near your own worldline at an earlier (proper) time. But the "timelike curve" is a worldline and "closed" means exactly that.

You seem to have divined my meaning anyway. I was just thinking that I can imagine a timelike geodesic that enters a region of spacetime containing CTCs in such a way that it lies "near" a closed timelike curve, then ends up crossing itself. What happens to a test particle following that geodesic? Presumably your point is that its future self deflects it onto another nearby path that "just so happens" to put it onto exactly the path it needs to follow to deflect itself onto that path (hopefully there's a unique solution to that particular conundrum!).

I just can't see immediately how that would operate for a more complex system like my rocket and lights. (Edit: although it's all just particle trajectories, I suppose. On that view, I'm falling into the same trap as someone adding more and more bells and whistles to a "simultaneity detector" to try to invalidate Einstein's train.)

 

[PeterDonis]

Presumably your point is that its future self deflects it onto another nearby path that "just so happens" to put it onto exactly the path it needs to follow to deflect itself onto that path (hopefully there's a unique solution to that particular conundrum!).

This has actually been studied in the context of wormholes (which are one way of having a spacetime with CTCs), and the answer, interestingly enough, is that there are solutions, but not a unique solution! This is described in a late chapter of Kip Thorne's Black Holes and Time Warps. Unfortunately I don't have a handy online reference at the moment, but the gist is, suppose for example that we have a billiard ball headed for one mouth of a wormhole, and the wormhole is hooked up such that the billiard ball emerges from the other mouth at an earlier time (in the asymptotically flat frame in which the wormhole mouths are at rest) than it went in the first mouth. Then the billiard ball can end up hitting itself. The original "paradox" was, what if the ball hits itself in such a way that it gets deflected and never goes into the wormhole mouth in the first place? But the real question is, are there consistent solutions, with a given set of initial conditions (billiard ball headed towards the first wormhole mouth at such and such a speed), such that the ball goes through the wormhole? It turns out that there are, but there is not one unique solution for a given set of initial conditions. Which is counterintuitive, but not inconsistent.

 

[Imager]

I got confused about going back a thousand years, in that case there wouldn't be a me yet...

 

[Sorcerer]

This has actually been studied in the context of wormholes (which are one way of having a spacetime with CTCs), and the answer, interestingly enough, is that there are solutions, but not a unique solution! This is described in a late chapter of Kip Thorne's Black Holes and Time Warps. Unfortunately I don't have a handy online reference at the moment, but the gist is, suppose for example that we have a billiard ball headed for one mouth of a wormhole, and the wormhole is hooked up such that the billiard ball emerges from the other mouth at an earlier time (in the asymptotically flat frame in which the wormhole mouths are at rest) than it went in the first mouth. Then the billiard ball can end up hitting itself. The original "paradox" was, what if the ball hits itself in such a way that it gets deflected and never goes into the wormhole mouth in the first place? But the real question is, are there consistent solutions, with a given set of initial conditions (billiard ball headed towards the first wormhole mouth at such and such a speed), such that the ball goes through the wormhole? It turns out that there are, but there is not one unique solution for a given set of initial conditions. Which is counterintuitive, but not inconsistent.

Wouldn't having multiple solutions cause other problems for objects in the system other than the ball?

Or, given that we're limiting the system to just the ball, is that irrelevant in this case?Follow up question: is there an inverse proportionality relation between number of solutions and number of objects in the system? I.e., the more things in the system, the fewer number of solutions there can be? The reason being that there would be more interactions, which would mean more events have to consistently happen, limiting the possible outcomes that could occur.

 

[PeterDonis]

given that we're limiting the system to just the ball, is that irrelevant in this case?

Yes.

is there an inverse proportionality relation between number of solutions and number of objects in the system?

I don't know. I don't know how many objects have been considered in seeking solutions for these kinds of cases.

 

[Stavros Kiri]

but when it comes to it you cannot actually behave differently because you behaved how you behaved.

... and you are who you are (at that point in time).

At least, that is my understanding. It's completely incompatible with the notion of free will in an "if I could rewind time I could have chosen to do something different" sense.

I agree. + the latter case would have causality issues and paradoxes.

If I undersrand the basic premise of a closed timelike curve, whatever you did or will do is set in stone. If you have memories of the future , you will NOT be able to behave or even THINK in any way differently than you did the first time. Everything you think at that point in spacetime would always be the same. Every time you go through the loop.

At least that is my understanding of it.

Because you will be the same too. It's just that time repeats itself.

No, you don't. You are your future self. The scenario we are talking about is that your worldline is a CTC; if that's the case, there is only one of you at any point in spacetime. It's just that all those points are linked by a closed curve.

Exactly! + uniformity of time in the CTC will not give you a way of knowing where you are [relative past/present/future etc.] everytime in the loop. You just "are" ! ... [And that time line just happens to repeat itself, that's all.]

 

[PeterDonis]

that time line just happens to repeat itself

"Repeat itself" is not a good characterization of the timeline itself. The timeline is just a closed curve. There is only one of it.

"Repeat itself" might describe a sort of intuitive guess at what it would be like to have such a closed curve as your own worldline; but even that misstates it, because it implies that "you" go around the loop "multiple times" and can somehow distinguish one time from another. As you note, you can't. There is only one "you" and only one timeline, and the state of "you" at any given point on the timeline is just one state; it is what it is.

 

[Stavros Kiri]

A)

"Repeat itself" is not a good characterization of the timeline itself. The timeline is just a closed curve. There is only one of it.

"Repeat itself" might describe a sort of intuitive guess at what it would be like to have such a closed curve as your own worldline; but even that misstates it, because it implies that "you" go around the loop "multiple times" and can somehow distinguish one time from another. As you note, you can't. There is only one "you" and only one timeline, and the state of "you" at any given point on the timeline is just one state; it is what it is.

You're right. I agree. Could we say "time (or the events) repeats(/repeat) [itself(/themselves)?] in that timeline (i.e. in the CTC loop)" instead? Or just the "Closed Timelike Curve" term is enough and adequate to describe it all? (may be that's what you're trying to say ...)
And I know we're not just playing with words here. It's just that I didn't make those fine distinctions by sloppily saying ~"the time line repeats itself" ...

B) Also, and then (considering the above) what about memories? Are they possible? Do they even make sense?

E.g. What time scale loop trip are we talking about that can be possible? Because human life spans etc. may be way less, making that question meaningless. [e.g. if we're talking about the whole universe etc. ...]
But even in the case/(And even if) the time scale is appropriately chosen or fixed, then perhaps

In practice, it's possible that your memories would gradually decay as you go around the curve, so when you got back to the same point again, your memories of being there before would have gone. For example, suppose it took you 1000 years to go once around the closed timelike curve; when you got to the starting point again your memory would have to be accurate enough over a 1000 year span for you to remember being there before.

etc.

Or it (in any case) will seem totally normal (and uniform? [experience]) ... +/or may be just a [minor(?)] "Des a vu", [...] perhaps ...

Or is it that the memories are just the fresh events ... again ... , everytime! ?
[I tend to think this very latter is the one ...]

 

[PeterDonis]

Could we say "time (or the events) repeats(/repeat) [itself(/themselves)?] in that timeline (i.e. in the CTC loop)" instead?

No. There is only one copy of each event, and only one closed curve that the events are on.

Or just the "Closed Timelike Curve" term is enough and adequate to describe it all? (may be that's what you're trying to say ...)

Yes.

What time scale loop trip are we talking about that can be possible?

Theoretically, a CTC spacetime could allow CTCs on any scale; the scale is a free parameter in the mathematical solution so it can be adjusted to whatever you want. You could have, for example, a Godel spacetime whose scale factor was such that CTCs looped around with a "period" (length around the loop) of 1 nanosecond. The math doesn't really place any limits on this, and physically, most people think CTC solutions are not reasonable to begin with, so asking what scales are reasonable is kind of moot.

what about memories? Are they possible? Do they even make sense?

It's certainly possible for the state at one point on the closed curve to contain information about the state at another point or points on the closed curve. So "memory" in that sense is certainly possible. Whether it satisfies our intuitive notion of "memory" is not really a question of physics but of personal opinion.

 

[TheQuestionGuy14]

No. There is only one copy of each event, and only one closed curve that the events are on.
Yes.
Theoretically, a CTC spacetime could allow CTCs on any scale; the scale is a free parameter in the mathematical solution so it can be adjusted to whatever you want. You could have, for example, a Godel spacetime whose scale factor was such that CTCs looped around with a "period" (length around the loop) of 1 nanosecond. The math doesn't really place any limits on this, and physically, most people think CTC solutions are not reasonable to begin with, so asking what scales are reasonable is kind of moot.
It's certainly possible for the state at one point on the closed curve to contain information about the state at another point or points on the closed curve. So "memory" in that sense is certainly possible. Whether it satisfies our intuitive notion of "memory" is not really a question of physics but of personal opinion.

Overall, are we able to remember previous iterations of events? Like, are the events still in our future light cone, thus we can't remember it, or in our past, and we remember it all?

 

[Stavros Kiri]

Overall, are we able to remember previous iterations of events? Like, are the events still in our future light cone, thus we can't remember it, or in our past, and we remember it all?

I tend more towards

Or it (in any case) will seem totally normal (and uniform? [experience]) ... +/or may be just a [minor(?)] "Des a vu", [...] perhaps ...

Or is it that the memories are just the fresh events ... again ... , everytime! ?
[I tend to think this very latter is the one ...]

I'm also waiting for @PeterDonis 's opinion

 

[jbriggs444]

Overall, are we able to remember previous iterations of events? Like, are the events still in our future light cone, thus we can't remember it, or in our past, and we remember it all?

You could, I think, have the equivalent of a [finite] shift register. Where at the crossing of, let's say, three events on the CTC, the bits are all shifted down by one.
Event 1: 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0
Event 2: 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0
Event 3: 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1

In this 15 bit example, one might view it as a "memory" of the "previous five passes" through the CTC. Or, as @PeterDonis suggests, it might be viewed otherwise.

Of course, there is only one CTC. The "five passes" are constrained to be identical and there are only three configurations that the shift register ever takes on.

 

[Ibix]

Overall, are we able to remember previous iterations of events? Like, are the events still in our future light cone, thus we can't remember it, or in our past, and we remember it all?

I think the point is that, if you are on a CTC, there is no previous iteration. There's no clear distinction between your future and your past. Say it takes a year to traverse the loop - the you a year from now is the you now; the you a year ago is the you now. There is only one of you. What you remember now is what you remember now. So anything that is capable of going round a CTC must naturally reset itself to some previous state somehow.

However, in spacetimes which permit CTCs there may be trajectories "near" CTCs that let you loop round and pass near your own worldline. In these, you simply meet your future self, who could (in principle) remember meeting your past self. Peter seems to think this can be done in a consistent way (or at least, that no-one's proved you can't and there are some simple cases where solutions have been found). And a consistent way means that when you are "future you" you will behave as you did when "past you" met you because that's the only way you can get a consistent description of what's going on.

 

[PeterDonis]

are the events still in our future light cone, thus we can't remember it, or in our past, and we remember it all?

If your worldline is a CTC, there is no distinction between your "past" and your "future". Your entire worldline is in its own past and future light cone.

 

[PeterDonis]

I'm also waiting for @PeterDonis 's opinion

I've already given it.

 

[Stavros Kiri]

I've already given it.

Ok yes, you're right:

It's certainly possible for the state at one point on the closed curve to contain information about the state at another point or points on the closed curve. So "memory" in that sense is certainly possible. Whether it satisfies our intuitive notion of "memory" is not really a question of physics but of personal opinion.

And I think it's a good answer, perhaps the only strictly valid one.

 

[TheQuestionGuy14]

If your worldline is a CTC, there is no distinction between your "past" and your "future". Your entire worldline is in its own past and future light cone.

So, would it be a very weird experience if this occurred? Would our memories mess up or something?

 

[PeterDonis]

would it be a very weird experience if this occurred?

I would expect so, yes.

Would our memories mess up or something?

I've already addressed this in previous posts. At any point on your worldline, your state is what it is, and it can contain information about the state at other points on your worldline. Whether this fits our intuitive notion of "memory" is not a question of physics but of terminology.