Is the "Doctor Who" spacetime affected by Hawking's chronology protection mechanism?

Question

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.}

Answer 1

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.

Answer 2

Is this really possible?

No.

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

No.

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:

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.