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As I understand it, Novikov's principle is either philosophical or scientific. I heard that it is a consequence of the stationary-action principle (principle of least action) in quantum mechanics. Does this mean that Novikov's principle is scientific?

I also heard the following: in quantum mechanics, instead of the stationary-action principle, there is a functional integral that diverges for closed timelike curves. Is this so, and what does this mean?

My question can be formulated differently - does modern physics allow time travel (if it does, then obviously Novikov's principle is a scientific hypothesis). I cannot understand the article by S. Lloyd “Closed Timelike Curves via Postselection: Theory and Experimental Test of Consistency”. In this article, the authors describe an experiment where they tried to cause a time paradox and a random factor counteracted this. It seems to me that if Novikov's principle worked in its original understanding, the universe would not have allowed Lloyd to conduct this experiment, in the same way as the universe does not allow a time traveler to kill his grandfather (as it is described in popular fiction).

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Ironically, it's best if I address these points out of order.

if Novikov's principle worked in its original understanding, the universe would not have allowed Lloyd to conduct this experiment

Since no time machine has ever been built, it's worth explaining how this experiment really works (see p. 3). Two qubits were stored in each photon, and these are metaphors for information about the future and past, and post-selection filtered for photons where the bits matched. Insofar as Novikov's principle says more than just every sci-fi writer's "you can't change the past" reasoning, it identifies certain quantum-mechanical probability amplitudes as $0$. Lloyd's experiment leverages the same mathematical reasoning to a post-selection experiment, as it applies to more than just time travel, whose behaviour we can't test yet for obvious reasons. (You'll find physicists often test aspect $B$ of some logic when aspect $A$ is beyond present technology, like Hawking radiation.)

it is a consequence of the stationary-action principle (principle of least action) in quantum mechanics. Does this mean that Novikov's principle is scientific?

If we can test it, it is. I suppose it comes down to whether you think the aforementioned acoustic black hole experiments make Hawking radiation scientific.

there is a functional integral that diverges for closed timelike curves. Is this so, and what does this mean?

That $S=\infty\implies e^{-S}=0$ for a Euclidean action, thereby making a relevant amplitude $0$.

does modern physics allow time travel

We're still working on that.

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  • $\begingroup$ Unfortunately, I did not understand your answer, as it is too complicated for me. Can you at least answer the following question: does the Lloyd's experiment confirm the Novikov's principle, or does it confirm the many-worlds interpretation, or maybe it refutes the Novikov's principle as I formulated it in the question? $\endgroup$
    – Linkey
    Commented Oct 14, 2021 at 11:18
  • $\begingroup$ @Linkey The experiment illustrates the principle's applicability to post-selection, but doesn't tell us what would happen if someone built a time machine. (For all you know, they'd find they can "change history", if only because they slipped into another Universe.) Nor does it dis/prove any interpretation. You might enjoy my discussion of interpretations here. $\endgroup$
    – J.G.
    Commented Oct 14, 2021 at 19:28
  • $\begingroup$ I argue with a person on another forum, and he writes that time travel is impossible, since for the principle of least action a functional integral diverges for closed timelike curves. When I showed him an excerpt from a Wikipedia article on Euclidean action, he wrote that this article should be read from the beginning, and besides that in the middle it says “the Wick-rotated Schrödinger equation does not have a direct physical meaning”. Can you argue that he is wrong? $\endgroup$
    – Linkey
    Commented Oct 15, 2021 at 6:43
  • $\begingroup$ @Linkey Which functional integral diverges for CTCs? (Divergences can sometimes be removed with e.g. BRST quantization, so I suspect you may need to ask a new question about the technicalities of this anyway.) $\endgroup$
    – J.G.
    Commented Oct 15, 2021 at 7:04

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