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I have a question. Are there any methods for detecting CTC? Is there a possibility of designing modern physics experiment in order to confirm / refute the possibility of CTC at any given time in a given space? (Only in a specific space).

I found the publication of 'Detection of closed timelike curves' (W. B. Bonnor) but free there are only two pages.

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    $\begingroup$ It's been done, already. Hawking invited future physicists to his party and nobody showed up. I think that's plenty of proof that CTCs don't exist. :-) $\endgroup$ – CuriousOne Mar 22 '16 at 20:51
  • $\begingroup$ I know that it is very problematic for the general case (if there are in the Universe?). But when we say a very limited space (eg. in the laboratory), we can prove that there is no CTC in this limited space? $\endgroup$ – Aurelio Mar 22 '16 at 20:58
  • $\begingroup$ You could keep measuring the weight of a closed container. If CTCs exist, a mouse should appear it in spontaneously because the mouse could have gone back to the past and become its own parents. :-) $\endgroup$ – CuriousOne Mar 22 '16 at 21:05
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Classically, (and with classically distinguishable particles) there is no method. Just like there is no method to prove that the universe is bounded spatially.

If you travel and things look the same, you can't prove they are the same, the universe could just be repetitive spatially and/or temporally.

I know that it is very problematic for the general case (if there are in the Universe?). But when we say a very limited space (eg. in the laboratory), we can prove that there is no CTC in this limited space?

Every experiment and observation has some finite precision. So classically, according to GR, you could have a very tiny spinning black hole that that is so small that the odds of it getting close enough to your detectors to be detected is super small and yet inside it could be a region with time travel. But the time travel region is inside an event horizon, so you wouldn't notice.

The precision issue is like trying to prove the mass of a photon is zero. With a good experiment you can prove that it must be tiny, and with better experiments could prove it must be even more tiny. But you can't prove it is zero.

You can exclude tiny black holes. But there could always be even more tiny ones that weren't ruled out. So whatever precision you have there could be a small enough black holes that aren't ruled out. So no experiment can rule out time travel. So relax, and don't worry about it. If there is time travel but it doesn't affect you, then it's no big deal.

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  • $\begingroup$ Why can't I tell that I am my own grandfather? The geneticists will disagree with you. And why can't I, as a physicist, detect energy conservation violation even classically? $\endgroup$ – CuriousOne Mar 22 '16 at 21:41
  • $\begingroup$ Thanks, I understand. But you write: "You can exclude tiny black holes. But there could always be even more tiny ones That weren't ruled out.". But can I exclude the CTC a specific size (in specific space)? $\endgroup$ – Aurelio Mar 23 '16 at 10:27
  • $\begingroup$ @MarekWolny There could be huge spaces inside those tiny event horizons. Inside could be wormholes to whole other infinite sized universes. In general relativity you can't look at a sphere is surface area $4\pi R^2$ and conclude that there is a volume of $4\pi R^3/3$ inside. So when I said tiny, I meant a tiny surface area which distorts the spacetime outside it in such a tiny fashion that your detectors wih their distance away and precision, don't notice it. I didn't mean they have tiny insides. Plus, the curve could be long and then go through. $\endgroup$ – Timaeus Mar 23 '16 at 15:40
  • $\begingroup$ @MarekWolny And there are many curves through the same point. So it could be that every single point in your region has a closed timelike curve that goes through that point. Oh, and the paper you cite is only three pages long, including the references $\endgroup$ – Timaeus Mar 23 '16 at 15:42
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Most effects on matter that are associated with closed timelike curves are also the kind of effects that usually are supposed to prevent them. But here's a few experimental ways some people have proposed to detect CTCs and various physical consequences :

  • The most obvious consequence is that, in a non-causal spacetime, curves are not required to cross every boundaryless spacelike hypersurface. In other words, curves (such as the curves of particles) may appear or disappear, with no possibility of prediction of those particles.
  • Closed timelike curves generally speaking break the unitarity of quantum fields, at least in a naive analysis (trying to construct a rigorous quantum field theory in a non-globally hyperbolic spacetime is not a trivial task). This is due to the fact that unitarity in QFT relies in part on time ordering which becomes meaningless if CTCs are present. Violating unitarity would have a number of consequences, such as violating the optical theorem, the Froissard bound and other such theorems relying on unitarity.
  • Closed timelike curves may violate various no-go theorems in quantum mechanics, such as the no-clone theorem.
  • Closed timelike curves usually cause an "accumulation" of fields unless conditions are perfect, due to the field propagating an unlimited amount of times around the curve, usually causing some divergence. Things are even more dire when quantum effects are considered.
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There is evidence that CTCs are possible at least in theory, however this would violate SW Hawkings Chronology Protection Conjecture as well as Novikov's self consistency principle.

The above would only apply in some conditions, I have done some preliminary calculations suggesting that a quantum computer with a large number of qubits could be modeled as a CTC in some observational circumstances, as the answer time travels back to a short interval after inputing the problem. It is possible that the wafer itself could in fact be only able to do one calculation as futher calculations would disrupt the CTC and stop the original answer from being read back: this would also happen if the wafer was allowed to heat up above its operating temperature at some point in the future corresponding to the actual time interval needed to do the quantum calculation.

If so then this provides a fascinating insight into the workings of the Universe, and actually puts a finite bound on computability as well as helping to unify quantum mechanics with general relativity!

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