# Is the “Doctor Who” spacetime affected by Hawking's chronology protection mechanism?

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