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Life on a Closed Timelike Curve

91 points by the_mitsuhiko 6 days ago | 57 comments

neonate 3 days ago

https://web.archive.org/web/20241223001630/https://iopscienc...

cosmos0072 3 days ago

I have a degree in theoretical physics, and also did research on general relativity.

The result is cool, but it's not directly applicable to the traditional (sci-fi) scenario "I travel to the past and meet myself / my parents / my ancestors"

The reason is simple: the authors suppose a CLOSED timelike curve, i.e. something like a circle, where you travel back in time and BECOME your younger self - which by the way only exists because you traveled back in time in the first place.

A slightly different scenario would be much more interesting, but my guess is that it's much harder to analyze:

a NEARLY closed timelike curve, which arrives from the past, coils around itself one or more times - like a coil, indeed - allowing causal interaction between the different spires (i.e. one can interact with its future self/selves and with its past self/selves), and finally the last spire leaves toward the future.

codethief 3 days ago

> The reason is simple: the authors suppose a CLOSED timelike curve, i.e. something like a circle, where you travel back in time and BECOME your younger self

Exactly. This part of the paper is not really surprising or newsworthy. If you apply periodic boundary conditions, you get periodicity, duh. In the case of CTCs, this has been known for a long time[0].

> A slightly different scenario would be much more interesting, but my guess is that it's much harder to analyze: […]

Agreed. The only result I'm aware of in this context is a paper from the 90s by Echeverria, Klinkhammer, and Thorne about a thought experiment (Polchinski's Paradox) involving a billard ball entering a wormhole and colliding with its past self. Wikipedia[0] gives a good overview of the result.

[0]: https://en.m.wikipedia.org/wiki/Novikov_self-consistency_pri...

zozbot234 3 days ago

More generally, imposing "self-consistency" on a closed cycle of interactions is just a matter of picking a fixed point. Such a fixed point will always exist if the underlying system is continuous - and continuity may always be assumed if the system be non-deterministic. (For example, a billiard ball enters a wormhole sending it to the past with probability 50%, or else it is knocked away by a billiard ball sent from the future (and does not enter the wormhole) with probability 50%. This system is self-consistent, but this is achieved by a "mixture" of two outcomes.)

lupire 3 days ago

Can the ball roll into wormhole, emerge in the past, hit its past self and stop, while its past self it knocked to roll into the wormhole, emerge in the past, hit its past self ...

zozbot234 3 days ago

Sure, this is another self-consistent solution which is discussed at length in the papers referenced above. But the neat thing about non-determinism is that it adds continuity - thus, a guaranteed existence of some self-consistent solution - even when the underlying system is discrete (as in, the ball is only allowed to either enter the wormhole on its own or be knocked off altogether - which is what creates the purported paradox).

codethief 2 days ago

Could you elaborate on what you mean by fixed point? Fixed point of what? And what continuity and non-determinism are you referring to exactly?

zozbot234 2 days ago

A fixed point involving the dynamics of "complex interpersonal interactions" (to quote the above-linked Wikipedia article) that are typically involved in these purported time-travel paradoxes. Continuity of the underlying physics is enough to ensure that such a fixed point will definitely exist, and allowing for non-determinism is just a convenient way of recovering a sort of continuity even if the underlying physics is assumed to not be continuous.

(These concerns are somewhat comparable to those that involve issues of so-called "metastability" in electronic circuits and indeed other physical systems which are designed to only have a limited number of "discrete" states.)

the_mitsuhiko 3 days ago

This paper (among some others that are referenced in this Wikipedia article) are also cited here and referenced.

PaulHoule 3 days ago

Most 'time loops' in science fiction might better be described as time knots.

I think of https://en.wikipedia.org/wiki/Predestination_(film) which is much more complicated than the usual time travel scenario; presumably the protagonist leaves but doesn't really enter since the protagonist is their own mother and father (the matter that makes them up does enter since they eat and breathe the way everybody else does; thinking the story through I'd think if I was going to have such a miraculous and singular existence I'd rather be a fantastic creature of some kind [dragon?] as opposed to a relatively boring intersex person capable of both reproductive roles)

Also https://en.wikipedia.org/wiki/The_End_of_Eternity which tames the complexity of time travel by presupposing 'eternity' has a second time dimension, making large-scale engineering of history practical. 'Eternity' itself owes it's existence to a time loop which is ultimately broken by the protagonist.

pdonis 3 days ago

> a NEARLY closed timelike curve, which arrives from the past, coils around itself one or more times - like a coil, indeed - allowing causal interaction between the different spires (i.e. one can interact with its future self/selves and with its past self/selves), and finally the last spire leaves toward the future.

The classic sci-fi story describing this is Heinlein's By His Bootstraps. Note, though, that even in this version, the causal interactions are fixed: the same person experiences the events multiple times from different viewpoints, but the events have to be the same each time. They can't change. In Heinlein's story, the main character tries to do something different at one of these interactions and finds that he can't.

j1elo 3 days ago

also a good example is the movie Triangle

lupire 3 days ago

And the TV show Dark

cgh 3 days ago

Isn't the cool part of this the assertion that the arrow of time flips at points of minimum and maximum entropy? In other words, it's two parallel timelines, not a continuous loop of entropic time. The article dedicates itself to proving this assertion with a bunch of math of which I understood maybe 10%.

I am not a physicist, etc so if I sound daft then that's why.

A_D_E_P_T 3 days ago

> "In the introduction, we stated that, since a CTC is a compact set, there is an event x0 where the entropy of the spaceship is minimal. In the proximity of such event, our macroscopic notion of causation breaks down. This is evident in figures 2 and 3, where the existence of the low-entropy state at proper time T does not have any macroscopic cause in its near past or future. It just 'fluctuates into existence'. Indeed, any form of order that the event x0 carries (including objects and people) has no logical cause that can be expressed in purely macroscopic terms. For example, if there is a book, nobody wrote it. If a person has a memory, this memory is illusory, and its content is meaningless (by human standards). This is because our notions of 'writing' and 'forming a memory' implicitly rely on increasing entropy [1], and there is no event with lower entropy than x0."

I don't believe that "our notions of 'writing' and 'forming a memory' implicitly rely on increasing entropy." Entropy's relation to the arrow of time is complex but it's enough for entropy to be non-static, and for things to durably exist in the world, for there to be a notion of movement in time. If something was written at time T, entropy fluctuated into a minimum at T+100, and entropy increased again at T+200, at all points the original writing event would be traceable back to T.

Time appears to stop and things become causally disconnected from each other when entropy reaches minima or maxima and stays there. Even so, local fluctuations can lead to the emergence of an arrow of time -- e.g. if a glucose molecule coalesces out of the void, you can measure time by it, as it's not perfectly stable.

cryptonector 3 days ago

See https://news.ycombinator.com/item?id=42660606 (yesterday). Writing is not a reversible computation, therefore it requires an increase in entropy.

A_D_E_P_T 3 days ago

You write something at T, under normal background conditions of increasing entropy. Entropy at some T+n fluctuates to a minimum, and at T+n+1 begins to rise from that minimum. None of this appears to necessarily reverse what you've written at T?

cryptonector 3 days ago

If you've made some state change that amounts to irreversibly changing information, then you've increased entropy, full stop. I believe TFA is obviously correct that closed timelike loops involve forgetting, thus no time travel paradoxes.

andyjohnson0 3 days ago

> Using Wigner's theorem, we prove that the energy levels internal to the spaceship must undergo spontaneous discretization.

I am in no way qualified to understand this paper. But I have a question.

Is it normal for physicists to talk about a mathematical result being a "proof" of the predicted behaviour of a physical system? To what extent would claims of a proof in physics require experimental validation?

I appreciate that Wigner's theorem is well established, and that mathematics is the framework for describing physics. I also appreciate that experimental validation of the situation described in the paper is very likely beyond our abilities, even in the future. My question is about how physicists view the idea of proof