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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

2 Answers 2

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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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You have started your thinking by assuming that the popular idea of time travel to the past is possible, and from that you are led to various conundrums that can only be resolved by introducing other assumptions and conceptual sticking plasters, such as the Novikov principle, the idea that the rusty old watch will unrust on its journey back in time, and so on. (As an aside, you might want to consider the question of how you remain intact during the journey back if you assume the watch you are carrying must revert to its former state.)

Rather than inventing other measures to deal with the conundrums, you might instead prefer to conclude that your starting assumption is simply false- that the popular idea of time travel to the past is impossible, which sweeps away all of the conundrums.

Some philosophers of time advocate a view known as presentism, in which the past no longer exists, and from which they mount the 'no destination' argument against travel to the past (if the past doesn't exist, you can't travel there). There are various arguments against presentism, at least some of which are based on an incorrect and naive assumption that the present means a flat slice through spacetime. My own view is that mainstream presentism and the competing theories are arguments at cross purposes, and the differences can be resolved straightforwardly- however, that would be straying outside the scope of your question.

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  • As far as I understand it, the idea isnt that the watch unrusts or whatever, its that you couldn't possibly bring the same watch back unless it somehow un-rusted itself. But that's not the same as saying the person travelling back needs to revert to their original state. It would be like having an older you come give the present you a watch. Then you get older, and travel through time to give the younger you a watch. So it's always an older you travelling to the past, no need to change.
    – JMac
    Oct 25 at 12:42
  • And if you bought a new copy of that watch you gave yourself before you travel back, then giving that watch to the past you could be self-consistent. Obviously this all assumes time travel is possible, but that's a premise of the self-consistency principle, so it has to be assumed for the argument, even if its ultimately impossible.
    – JMac
    Oct 25 at 12:43
  • @jmac, but why would the watch unrust itself but the person carrying it not go through a similar process? Either both do or both don't. So if you make the unrusting assumption you have to make the unageing assumption too.
    – Marco Ocram
    Oct 25 at 12:58
  • Let's say you're 15 years old, and a 25 year old you comes from a time machine and gives you a 10 year old watch. In 10 years, if you go through the time machine to meet your 15 year old self again, you will be 25 (that is self-consistent), but that same watch will be 20 years old (not self-consistent), so the watch cant be the same one, while you can be the same person who met yourself as still have it self-consistent.
    – JMac
    Oct 25 at 13:20
  • @JMac I agree about the new copy of the watch, but that wasn't the scenario described in the question.
    – Marco Ocram
    Oct 25 at 13:27

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