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Reading a question on sci-fi stack exchange I find the wikipedia article on Novikov self-consistency principle in which is described the Polchinski paradox and the solution proposed by Thorne and some of his students.

So I try to understand how it is possible to enter in a wormhole and what happens if I do it.

It seems to me that someone that is in a wormhole could see his future because if you stay, suppose stationary, in a time-loop your future is your past. This sounds strange to me, but maybe is only a matter of habits, could someone explain to me why there isn’t anything inconsistent in all of this?

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First of all, wormholes are not the same as closed timelike curves (time loops). Wormholes are a way to connect two spacetime regions that would otherwise be separated. Wormhole may link two different universes or two distant regions of the same universe at the approximately the same moment in time. Such structures would not necessarily cause any of the paradoxes associated with time travel.

Even if wormhole connects regions of the same universe at different times in a way that corresponds to time travel (when we can say that closed timelike curves are formed), formation of such curves does not mean that there would be any material object traveling along one. There may not be any object (or being) for which its future is its past, just that future has a potential to influence past, and that influence is exercised in accordance to ordinary laws of physics.

So if time-traveling wormholes are at all possible, then there should be nothing special in traveling through one (at least in comparison with travel through wormholes connecting distant regions of space).

There are many models of wormholes so the answer to what would be the experience of someone traveling through one depends on the model chosen. One model is Reissner-Nordström black hole. Observer who falls into such a black hole can emerge in another universe. For visualizations of such a journey I recommend Andrew Hamilton webpage. Note, that inner Reissner-Nordström geometry is unstable, or quoting A. Hamilton:

Warning: If you fall into a black hole, you will die. You will not go through a wormhole to another time and place.

Another class of wormhole models is by Matt Visser:

  • Visser, M. (1989). Traversable wormholes: Some simple examples. Physical Review D, 39(10), 3182, arXiv version.

This is most closely resembles sci-fi tech: traveling through one could be as simple as walking through the doorway without anything noticeable happening during the crossing.

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  • $\begingroup$ If there is a closed time-like curve you can argue that even an atom couldn’t go through, but you have to accept that some idealization like material point could go through, or a field (that it’s not an idealization I think) could propagate along it. Sure what Thorne & co. have found would be something like a function on a circle, perfectly coherent, but let me think that I stay in the loop (because it let me do it) I want to know what I see and what happens to me $\endgroup$
    – Annibale
    Apr 7 '18 at 17:15
  • $\begingroup$ Moreover my original question is not what happens if I am in a loop that fits my size, but if how and what happens when I enter in one of these $\endgroup$
    – Annibale
    Apr 7 '18 at 17:18
  • $\begingroup$ @Annibale to second comment: I updated the answer to include discussion of couple of WH models. $\endgroup$
    – A.V.S.
    Apr 7 '18 at 18:12
  • $\begingroup$ @Annibale to first comment: other than travel through the wh there would be nothing unusual in what you experience before or after, no new forces, no unusual changes to oneself. $\endgroup$
    – A.V.S.
    Apr 7 '18 at 18:31

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