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.
> 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...
This paper (among some others that are referenced in this Wikipedia article) are also cited here and referenced.
>which by the way only exists because you traveled back in time in the first place
No, you keep going forward all the time, but on a dimension closed on itself.
That's the whole point.
If time is closed on itself, then by definition there can be no change from one "round" to another, you have to return to the exact world state you started in. Otherwise it wouldn't be closed. Just like a coil is not a closed shape even if its projection (a circle) is.
> "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.
See https://news.ycombinator.com/item?id=42660606 (yesterday). Writing is not a reversible computation, therefore it requires an increase in entropy.
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?
As a layman on this topic, I understand that research does not need to work towards a predefined goal.
But for the sake of my understanding and edification, I would have loved to see some mention in the Abstract explaining the usefulness of the article. Is it "merely" a mental experiment to confirm that we know how to apply our equations in a synthetic environment? Do the conclusions influence or open venues for verifiable (experimental) research?
What about entropy? e.g. you send an egg around a CTC, the egg breaks (or like it’s a quantum particle whose wave packet disperses over time, or a bacteria powered by cellular respiration), the system cannot reconstruct without adding energy. So, no life on CTCs and likely not even quantum particles which are unstable and decay? No probability processes at all, not even the quantum vacuum fluctuations and zero point energy
> What about entropy?
Look at 3.1. "spontaneous recombination of an unstable particle" for how this works.
Thanks, and LOL:
we will model the spaceship as an idealized box with perfectly reflecting walls. This is necessary, because the second law of thermodynamics applies only to thermally isolated systems, to which we can assign a Hamiltonian [5, section 11] [Landau L and Lifshitz E 1980 Statistical Physics vol 5, 3 edn (Pergamon)].
Chasing down that source: https://ia802908.us.archive.org/31/items/ost-physics-landaul...
§11. Adiabatic processes
Among the various kinds of external interactions to which a body is subject, those which consist in a change in the external conditions form a special group. By "external conditions" we mean in a wide sense various external fields. In practice the external conditions are most often determined by the fact that the body must have a prescribed volume. In one sense this case may also be regarded as a particular type of external field, since the walls which limit the volume are equivalent in effect to a potential barrier which prevents the molecules in the body from escaping.
If the body is subject to no interactions other than changes in external conditions, it is said to be thermally isolated. It must be emphasized that, although a thermally isolated body does not interact directly with any other bodies, it is not in general a closed system, and its energy may vary with time.
In a purely mechanical way, a thermally isolated body differs from a closed system only in that its Hamiltonian (the energy) depends explicitly on the time: E = E(p, q, t), because of the variable external field. If the body also interacted directly with other bodies, it would have no Hamiltonian of its own, since the interaction would depend not only on the co-ordinates of the molecules of the body in question but also on those of the molecules in the other bodies.
This leads to the result that the law of increase of entropy is valid not only for closed systems but also for a thermally isolated body, since here we regard the external field as a completely specified function of co-ordinates and time, and in particular neglect the reaction of the body on the field. That is, the field is a purely mechanical and not a statistical object, whose entropy can in this sense be taken as zero. This proves the foregoing statement.
Let us suppose that a body is thermally isolated, and is subject to external conditions which vary sufficiently slowly. Such a process is said to be adiabatic. We shall show that, in an adiabatic process, the entropy of the body remains unchanged, i.e. the process is reversible.
I am unable to make these statements coherent
> 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
Fun!
This kind of seems analogous to: https://en.m.wikipedia.org/wiki/One-electron_universe
Both notice the duality between a loop and two paths that branch and meet.
Do Greg Egan books have a DOI?
Some of them should. Permutation City and the 3-Adacia series of short stories are worth a spot in anybody's reference library.
Am I interpreting this correctly to say that if you travel through the universe (at relativistic speeds?) and you arive at your destination, then you are reset to be the same person as when you started the journey?
> Am I interpreting this correctly to say that if you travel through the universe (at relativistic speeds?) and you arive at your destination, then you are reset to be the same person as when you started the journey?
If you manage to arrive at the same place and time that you started from (i.e. because you time-travelled, e.g. by going through a wormhole), then you are necessarily the same person when you arrive as you were when you departed.
It's kind of a cool result. The laws of physics conspire to keep the universe consistent even in the presence of time travel.
> It's kind of a cool result. The laws of physics conspire to keep the universe consistent even in the presence of time travel.
Indeed. I find this very cool and this paper gives some interesting examples of how this might unfold including Einstein clocks and the grandfather paradoxon.
Well in the model of General Relativity. Laws of physics are human descriptions of how we think nature operates based on current observations. It's not like we have a wormhole available to test time travel, assuming wormholes actually exist in nature. We don't really know if nature "conspires" to keep things consistent like that. Physicists do have a desire to come up with consistent theories though.
A closed timelike curve is the name in General Relativity for a time machine: you go forward in time and wind up in your past, and you go around and around the loop forever.
The point is that when you get to the same point in the loop your state must be what it was the last time you were at that point in the loop.
If you have a relativistic trajectory that doesn't form a loop in time there's no reset effect.
Ex falso quodlibet - "from falsehood, anything follows". If you start with a false assumption, you can logically derive any statement from it, even if that statement is absurd.
"A" universe, but not "the" (i.e. our) universe.
Specifically: https://en.wikipedia.org/wiki/Gödel_metric
It's specifically a universe where time travel definitely happens.
From the paper:
> Finally, we stress again that our main results are valid in an arbitrary background spacetime (including charged Kerr black holes [51, section 12.3]), provided that the CTC of interest is the orbit of a periodic one-parameter family of symmetries of the metric. This happens in all axisymmetric models whose rotation Killing field becomes timelike somewhere.
I think it's more like: "Quantum mechanics is consistent with what we expect to happen with matter that exists in a closed timelike curve: everything is reset upon return to the starting spacetime point."
It might make more sense of you think of spacetime as literally one thing, with one constant value. That value being c (or some meta value that boils down to the same thing).
Energy in all its forms (including velocity), mass, etc. or the lack thereof being ‘space’, and time being what you have ‘left over’ when you subtract ‘space’.
The more mass, or velocity, etc. you have, the less ‘time’ you get left over. That is time dilation, both in the presence of masses and when you’ve got a lot of velocity (because having a lot of velocity means you have a lot of energy).
That is an alternative formulation of e=mc^2. [https://en.m.wikipedia.org/wiki/Mass%E2%80%93energy_equivale...].
At the point your velocity hits c (somehow), you have no ‘time’ left over from your perspective, so wherever you go, you go there instantly from your perspective. No time has passed for you. Same if you are ‘inside’ a singularity like a black hole.
Space time curvature (aka gravity) may arise from that effect not just being a point one, but a subtle cumulative area effect.
In that model, time travel, FTL, and any other lack of causality (aka effect after cause) make no sense, because there is no ‘lever’ for such a thing to ever happen.
Maybe if someone could invent negative mass/energy (we currently have no evidence/idea such a thing could exist!), or a way to manipulate the fundamental factors that make spacetime spacetime. We have no concrete idea how to even conceive of trying such a thing idea right now though.
That result is terrifyingly boring in its implications though, which is why we try to avoid it.
Seems like a typo in the first sentence of the abstract: "...close timelike curve..." vs "...closed timelike curve..."