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I was thinking over Novikov's principle, trying to explain it to some younger people interested in the topic when I had a realisation. This is probably easily explained, but its stuck in my head now and I'd love some rationalisation.

Let's say at t=1 I receive a watch from my future self, then at t=2 I go back in time to t=1 and give this watch to my past self to start the loop (then I return).

The state of the watch at t=1 must therefore be the same as the state of the watch in t=2. The problem is - the watch must necessarily degrade, therefore the watch at t=2 must be degraded from the state of the watch at t=1, causing a problem. If this is treated like a equation this results in t2 != t2, a logical contradiction.

Either I must be misunderstanding the principle, or Novikov's theorem must postulate some way around this problem, some highly unlikely event which keeps the watch from undergoing any sort of degradation. Or I casually disproved the theorem, and I very much doubt its the latter.

Thanks for hearing me out to this point, hoping some light can be shone on the concept!

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    You've rediscovered one of the paradoxes of self-existing objects (more starkly, they are nowhere created or destroyed, being trapped in a loop). But "the watch must necessarily degrade" appeals to the second law of thermodynamics, which is not a fundamental law but a statistical trend due to initial conditions of the observed universe. If closed timelike curves do exist it cannot hold along them, with or without Novikov's chronology protection, see e.g. Rovelli, Can we travel to the past?
    – Conifold
    Jun 21, 2022 at 3:36
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    Aah interesting! Thank you for the sources and information Conifold. So, given that Novikov's principle seems to be self consistent, we can imagine what would happen if we were to carry out this experiment, right? I'm just trying to imagine what it would look like in a universe with closed timelike curves and the principle, where a watch is taken back to my past self (or at least trying to imagine one possible method of resolution).
    – user59314
    Jun 21, 2022 at 3:37
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    The watch will unage when taken backwards to maintain consistency. The authors under the first link argue for including the second law under chronology protection, in which case Novikov's principle would rule out self-existing objects altogether just as it rules out grandfather killings.
    – Conifold
    Jun 21, 2022 at 3:42
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    But ruling out self-existing objects would rule out self-consistent time travel all together would it not? Or... actually thinking about I suppose, using my example, I could simply have never been delivered the watch at t=1. That's interesting, makes a lot of sense.
    – user59314
    Jun 21, 2022 at 3:48
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    Echeverria and Klinkhammer once wrote Novikov self-consistency (no new physics) principle intends beyond the simple tautology that history must be consistent, making the additional assumption that the universe obeys the same local laws of physics in situations involving time travel that it does in regions lack closed timelike curves (CTCs). Thus 2nd law of thermodynamics still holds during time-travel backwards and watch aging is not issue as you stated. Indeed you can regard someone gives you a watch right now as some future being travelled backward together with that watch to give you...
    – Double Knot
    Jun 21, 2022 at 5:39

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The Novikov self-consistency principle says that temporal paradoxes just do not actually happen; they have a probability of 0.

Your time loop scenario would result in a paradox. So the Novikov self-consistency principle says that it will not happen. Simple as that.

If you tried to set up a time loop in which you send the same watch back that you got from the time loop, you would fail. Maybe you'd trip and break your time machine, or there'd be a power failure preventing it from working, or you'd just change your mind, or something like that. That's what the Novikov self-consistency principle would say, anyway.

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  • the more likely explanation as to why the time loop doesn't happen: before the loop starts you have no watch - so you can't start it
    – somebody
    Jun 21, 2022 at 18:45
  • it can't possibly be that you already have it - if in loop n you have 1 watch, in loop (n+1) you have the watch you brought in, plus the one you were given, = contradiction
    – somebody
    Jun 21, 2022 at 18:48
  • The Novikov principle, as originally formulated, only applies to logical inconsistencies with fundamental laws of physics. Since the second law is not that, and is, in fact, violated in far less exotic situations the original Novikov's principle would not preclude its violation in the time loop scenario either. The watch returning to its primordial state when sent back may go against the common sense, but it is not a logical inconsistency with fundamental laws.
    – Conifold
    Jun 21, 2022 at 19:35
  • @Conifold You're not wrong, but the Novikov self-consistency principle doesn't say that violations of thermodynamics are any more likely in a time-loop than they are in everyday life. Theoretically it could happen, with incredibly small probability, that the watch returns exactly to an original state, in the same way an egg could spontaneously un-break, but the Novikov self-consistency principle says nothing to encourage this astounding event.
    – causative
    Jun 21, 2022 at 19:49

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