Remember Godel was trying to prove Relativity/Einstein wrong that was the whole point of his work
What he showed was that Einsteins equation allowed CTC's .. we agree even today.
That the presence of CTC's basically renders relativity unworkable ... we agree even today.
Godel noted his model wasn't a model of our universe ... we agree even today
What you are forgetting is we have more than relativity, we have QM ... and CTC's are completely incompatible with QM.
Ok I am going to have work up a complete proof for you this one isn't easily covered in layman media.
Wikipedia bluntly sucks and is out of date:
https://en.wikipedia.org/wiki/Closed_timelike_curveThey sort of agree CTC's and QM don't mix but not forcefully.
The most recent semi-believable paper I know of on the subject is
http://phys.org/news/2013-02-spacetime-violate-heisenberg-uncertainty-principle.htmlYou will note they discuss all the background on how CTC's are incompatible with QM and how they were playing with special versions called OTC's to reignite the debate.
Despite such paradoxes, CTCs in general are compatible with general relativity; however, they are not compatible with quantum mechanics.
Science media actually accurately got current status correct .. someone did there homework.
I ignored the paper because what they don't discuss is you would need to rewrite half of QM for all that to be true. In the article they describe it as extending QM
I mean it only violates HUP, the no cloning principle and then even better they have things called "dispersion-free states" in which all observables vanish but that state can't even be described in QM. Hey this is a really good theory so far I was just waiting for the pink unicorn's to dance on in.
