-1: maths dors not equal physics. GR allows closed timelike loops but no physicist actually thinks they are possible ...

@MoziburUllah - That's obviously not true, Kip Thorne who discovered this solution obviously takes the possibility seriously in his book Black Holes and Time Warps mentioned in this answer. Or are you using "thinks they are possible" to refer to a strong claim about their physical possibility, as opposed to referring to the epistemological possibility that they will be allowed by the final theory of physics? (i.e. 'I am certain time travel will be physically possible in the final theory of physics' vs. 'it's possible time travel will be allowed by the final theory, but far from certain')

@Hypnosifil: Plenty of physicists explore formal consequences of a theory, especially theoretical ones, but the final arbiter in physics is not theory but experiment. No-one's discovered timelike loops. Physics is not about free speculation but something that in the end that has to be tested in the laborotory or discovered in nature.

No physicist would reject the possibility without having a good reason. They made that mistake once before. The maths said black holes were possible. All the sensible physicists said 'Ridiculous!' and rejected them out of hand. Then a younger and more open-minded generation came along and said 'Why not?' and studied the question seriously, and now we have pictures of black holes. With wormholes, we may be in the same state physicists in 1920 were with black holes. No physicist would say at this point they definitely can exist, but that doesn't mean they can't. 'Prove it', as they say.

@MoziburUllah Physics is about any predictions of physics models that could in principle be tested (with an obvious bias towards predictions of models that have many other successful predictions under their belts, like general relativity), it can involve theoretical analyses of things that might require levels of technology far beyond our own, or simply enormous time spans like the far future fate of the universe.

@Nullius Verba: No, just because the maths allows it foes not mean that it is possible. Newtonian mechanics is time indifferent, nevertheless Newton did not make the mistake of thinking that time can run backwards. And there's a difference between being open-minded and thinking, well, if QM is bizarre, then any old shtick goes. No, it doesn't. In QM, physicists were forced to those conclusions because of experiment and not because of free speculation.

@Hypnosifil: "with an obvious bias towards predictions of models that have many other successful predictions". Exactly - there is no more successful principle than the forward march of time, of causality, in a word ... no-one has discovered or demonstrated where causality does not work, physically speaking. No-one.

I didn't say it was possible. I said we don't know if it is possible or not. That's different. There is no experimental evidence to show that it is not possible. Saying it is not possible without evidence is just as bad. Experiment has led us to the maths of GR, and the maths allows it. Maybe there is some reason we don't yet know of why it can't happen, but until experiment reveals that to us, the question is still open. As it was with black holes.

@MoziburUllah "there is no more successful principle than the forward march of time, of causality" That's not a "physical model" that makes quantitative predictions, it just seems like a sort of intuition expressed in words. It's not clear what these words would mean even in philosophical rather than scientific terms--for example, does "forward march" mean rejecting McTaggart's B-theory of time in favor of the A-theory with an objective present moment that is always "moving forwards"? Does "causality" mean something beyond just laws that allow you to predict later events from earlier ones?

@Hypnosofil: Physics is merely intuition about nature strengthed by reflection on nature. You seem to be confused about what is meant by causality and physics, after all, you linked to Hawking's Chronology Protection Conjecture which isn't a conjecture but a formalisation of an intuitive physical principle that all physicists assented to and so didn't need formalising. So which is it? You accept Hawkings Chronology Protection Principle or you reject it? Or does it depend upon who you arguing with and how you might win that argument? Because then it isn't a principled argument but merely ...

@Hypnosifil: ... an attempt to win an argument by any means possible ...

Kip Thorne's book is excellent, I highly recommend it. Clearly written and geared for the non-specialist, with lots of easy-to-grasp examples.

@MoziburUllah - "Physics is merely intuition about nature strengthed by reflection on nature" 20th century physicists have learned to be very suspicious of grounding physics too much in "intuition" and generally just follow the hypothetico-deductive method where you have various abstract mathematical models that make predictions and then you go out and compare those with real experiments. The chronology protection conjecture is indeed a mere conjecture, based primarily on generalizing a theoretical analysis of how vacuum fluctuations would behave in the vicinity of a wormhole.

"You accept Hawkings Chronology Protection Principle or you reject it?" See my earlier comment about the distinction between epistemological possibility and physical possibility, which you didn't reply to. Epistemologically I think the conjecture may be correct, in which case time travel would be physically impossible, but since it's conjectural I think it's also epistemologically possible it's incorrect (and Hawking and other physicists would agree), in which case time travel would be physically possible. My personal hunch is that it's correct, but that's just a hunch.

@Hypnosifil: No, it's not a conjecture but a Principle on causality. Aristotle followed it. Newton followed it. Maxwell followed it. Einstein followed. Hawking followed it. But for you its a mere conjecture that somehow hasn't proven its worth. Completely wrong. Moreover, you haven't understood what is meant by "reflection" on "intuition".

@Hynosifil: Throwing around words like "epistemological possibility" makes no sense in physics. Physics is not about epistemology but about the basic ontological categories of physical nature. You're simply displaying a lack of understanding about basic philosophical notions.

@MoziburUllah - I didn't say physics was itself "about epistemological possibility", but physicists can and do talk about the degrees of confidence they have in theoretical hypotheses/conjectures that have not yet been well-tested empirically, and "degree of confidence" is an epistemological matter. They do not "accept" the chronology protection conjecture in the sense of having the same high degree of confidence about it that they do about other untested predictions that have many different lines of theoretical support, like Hawking radiation.

"it's not a conjecture but a Principle on causality." Why did they call it a "conjecture" then? And as Bertrand Russell & others have argued, old notions of "causality" include lots baggage that go beyond what's actually present in physics, which is just a bare notion of universal laws that make it possible to predict later physical states given sufficient knowledge of the physical state at an earlier time (note it is also possible to predict earlier given later, the 'arrow of time' is thought to be statistical rather than fundamental).

"Einstein followed. Hawking followed it." Neither accepted any "principle of causality" of the kind that would absolutely rule out time travel. In a public talk where he addressed Godel's GR solution of a rotating universe that involved closed timelike curves, Einstein responded saying that in this type of solution one could no longer speak of events happening "before" or "after" one another, and only said tentatively "It will be interesting to weigh whether these are not to be excluded on physical grounds."

Meanwhile, Hawking did not rule out closed timelike curves as a matter of fundamental philosophical principles, if you look at his original paper on chronology protection, he was basing the conjecture on suggestive theoretical results like the observation that CTCs could only develop in a finite region (as opposed to a global solution like Godel's) if the matter/energy fields violated the weak energy condition, as well as results on quantum back-reaction as they become close to forming (discussed in Thorne's book).

Also see Hawking's comments about CTCs in this public lecture, he certainly does not confidently dismiss them based on abstract principles of "causality", he says it is an "important subject for research", and furthermore he defines the chronology protection conjecture not in terms of time travel being absolutely excluded but just as the idea that "the probabilities are very small" for CTCs in "a macroscopic region", and says at the end time travel "can't be ruled out, according to our present understanding".