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Recently, there has been a paper1 (and an accompanying layman-ized white paper2) on "Traversable Achronal Retrograde Domains In Spacetime", TARDIS for short. It proposes a spacetime geometry that contains closed timelike curves.

Now, Hawking once proposed3 a mechanism that apparently causes all closed timelike curves to more or less destroy themselves. Basically, quantum fluctuations cycle through the curve and build upon themselves (in a sense, they overlay with their "past selves"), leading to a divergent expectation value for the energy-momentum tensor.

The media (which has dubbed it the "Doctor Who spacetime") seems to have caught on to this paper as the next time machine. Usually, the term "closed timelike curve" is associated with time machines because of the causality violations a CTC can cause.

Is this really possible? Or does Hawking's mechanism protect this system from a causality violation, destroying the CTCs in it?

1. arXiv:1310.7985 [gr-qc]; "Traversable Achronal Retrograde Domains In Spacetime", Benjamin K. Tippett, David Tsang

2. arXiv:1310.7983 [physics.pop-ph]

3. Hawking, S. W. (1992). Chronology protection conjecture. Physical Review D, 46(2), 603.

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Note the paper [1] itself is completely classical. Your question is mentioned towards the end under "Questions for Future Consideration," along with other serious pathologies which would possibly (probably) turn up. Also the paper is not in a journal and has no cites on INSPIRE yet, so these would still be open questions. But everytime someone invents a metric that violates the energy conditions like this bad things invariably happen to it. I'm 99% certain this geometry will turn out to be semiclassically unstable. – Michael Brown Nov 1 '13 at 10:39
@MichaelBrown Ah, I have only scanned through it (plan to read it tomorrow), so I didn't notice that it didn't do any nonclassical analysis. I understand that it's not yet published, though as the media caught on to it IMO it may be a good idea to have this question or similar on the site. Yeah, even if the Hawking thing doesn't work there will be some other instability, somewhere. – Manishearth Nov 1 '13 at 11:10
I'm not sure anything can be gained asking if quantum magic can save us, given that this is a nonexistent problem. There is more evidence that the universe contains unicorns than there is that it contains energy-condition-violating stress-energy. – Chris White Nov 1 '13 at 18:37
@Manishearth The problem is more fundamental than a divergent $T$, or any sort of time evolution (whatever time evolution means in a non-hyperbolic universe - if you accept time travel you give up hyperbolicity). The problem is of an unphysical $T$. Just because I write down the Lagrangian for a pink dragon doesn't mean Nature is obligated to either produce one or provide some law against its existence. – Chris White Nov 1 '13 at 18:54
@ChrisWhite Good point, however I'm not asking if we can disprove the physical-ness of the spacetime. I'm pretty sure that the spacetime isn't physical. I'm just wondering if it plays nice with Hawking's mechanism -- as far as I can tell, research in CTCs died down after Hawking proposed his mechanism. Not sure, though. – Manishearth Nov 2 '13 at 5:28

2 Answers 2

The Chronology Protection Conjecture is an entire bundle of rough theorems, counterexamples and conjectures. Hawking's original paper on the topic hinges on two main arguments :

  • That compactly generated closed timelike curves (aka "a time machine", roughly) will violate the energy conditions.
  • That a Cauchy horizon (the part of spacetime where the time travel starts being possible) will always collapse due to quantum effects

A few more arguments, more or less valid, exist that make time travel hard to solve (such as stability or non-uniqueness of the development of spacetime), but those are the two big ones. The first one is somewhat questionable, as the definition of "compactly generated" may not include all possible spacetimes (cf. Ori, Soen and Krasnikov on those topics), and the energy conditions lately have shown themselves to not necessarily be that important. If it holds up though, this spacetime would not violate that theorem, as it quite clearly states that the energy conditions are violated.

As for the second part, the conclusion lists it as an unsolved problem of this spacetime. As far as I know, quantum instability of the Cauchy horizon has not been applied to many spacetimes (roughly just Misner space and various wormhole spacetimes). It is hard to say if it would prevent this time machine, as there is no general theorem that you can readily apply.

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Here's the abstract of Hawking's paper. I'm afraid it's founded on misunderstanding. The reality that underlies curved spacetime is inhomogeneous space. See Einstein talking about it here, and There is no way to move through this space such that everything else not just moves back to where it was, but never moved at all. If you'd like to discuss this properly, do ask a question. – John Duffield Jul 29 at 9:03

Is this really possible?


Or does Hawking's mechanism protect this system from a causality violation, destroying the CTCs in it?


Hawking's chronology protection conjecture is redundant because time travel is science fiction, because there is no forward travel through time, and no backward travel through time, because there is no motion through spacetime. You move through space over time, and we depict this as your world line. But a world line isn't something you can point to in the clear night sky. It's an abstract thing. It doesn't actually exist. And you don't move up this world line, or along it. It's a line in a static "all times at once" depiction of space and things and their motion, and the map is not the territory. In similar vein you don't go round a closed timelike curve. See how the Wikipedia article says a CTC "is a world line in a Lorentzian manifold, of a material particle in spacetime that is 'closed', returning to its starting point. This possibility was first raised[citation needed] by Kurt Gödel in 1949". There's nothing much wrong with that. But check out A World Without Time: The Forgotten Legacy of Gödel and Einstein. See this page in it, where author Palle Yourgrau says Wheeler conflated a circle with a cycle:

enter image description here

IMHO he's correct. You don't move round that CTC. There is no way you can move such that everything else in this universe not only moved back to where it was, but never moved at all. Your 24-hour CTC doesn't describe some Groundhog day which you live over and over again. It describes some causeless Mayfly day, where your life is 24 hours long and you're born from your own egg. There is no opportunity for causality violation, and no need for any chronology protection conjecture.

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You directed me here. I think there exists a discrepancy between how we each express the realization of CTCs. The ones you explain in this answer are certainly Mayfly days. However, in Misner space, you can construct a chronology horizon where a worldline can traverse the space and use the chronology horizon to be returned to the same location but at an earlier time. Misner space explains why there are no travellers from the future walking around right now because it only allows such CTCs to connect a worldline to points after the "time machine" was created – Jim Apr 8 at 16:02
Jim: a worldline is an abstract line drawn in the mathematical space called spacetime. It isn't some line that traverses space that you can travel along. – John Duffield Apr 9 at 7:51
A worldline is traversable by defining a path element (normally proper time) and deriving the equations of motion according to that element. I know we both know what a worldline represents, but when one says it is traversed or it traverses, what they normally mean is you start from a point on the line and move in the direction of increasing path parameter (again, usually proper time). I am not confusing this by thinking that the worldline itself is moving or that it is physically traversable. I am only defining the path element of a line and integrating over it – Jim Apr 9 at 13:22
Try all that for a vertical worldline where you're just sitting in your chair. You aren't actually moving "in the direction of increasing proper time". Your proper time is nothing more than some cumulative display of some regular cyclical motion inside your clock. And again: there is no way you can move such that all other motion in this universe is not only undone, but never even happened. – John Duffield Apr 13 at 15:48
I am guessing that the question on CTCs will mean whether our reality actually allow Misner space or similar structures to exists as part of spacetime hence allowing CTC like structures. Or in John Duffield's view, whether the laws of physics actually allow motions to suddenly go undone even if the cyclic motion in the clocks continues to tick forward $$$$ I think the jury is still out for that one, but I am not sufficiently knowledgeable in that to comment more. It is true that we never observed motions suddenly go undone, but the possibility is not ruled out due to not being observed yet – Secret Aug 16 at 18:16

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