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.
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.)
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 ...
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).
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.)
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.
> 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.
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.
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.
Your younger self doesn’t have to be a future state of your present self, you just have to induce it, eg, being your own father or grandfather. Your younger self doesn’t have to be in your future if you allow some overlap (father) or short gap (grandfather) on the circle.
> "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.
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?
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.
> 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
Is this not inherently circular reasoning? "For X to happen, the laws of physics must allow X to happen". It seems totally obvious. Am I missing something? Of course entropy must be discrete and reversible in order to reverse entropy, it just doesn't work that way as far as we know in the real universe.
I consulted Wikipedia on "Closed Timelike Curve" and didn't understand the explanation either. I could distinctly hear a "woosh" sound as it all flew by above my head.
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?
So they assume four-dimensional space-time of a certain shape, similar to how a two-dimensional sheet could be curved taking various shape. Then they calculate how would physical objects behave in space-time of that shape.
Can such shapes exist anywhere in our universe, realistically or even just theoretically? For all we know, perhaps not.
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
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)].
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.
It's a poorly worded way of saying, if heat doesn't exist, and objects don't gain or lose energy, but only change configuration in a controlled way, physics is reversible. This is traditional time-symmetric Newtownian physics before thermodynamics. "What does down bounces back up."
Entropy is measure of information. If an object changes state according to some law or data that you don't know, then you can't predict the result, and you can't set up conditions to undo the changes. Thus you can't reverse it, because you don't know the original state. If you can explicitly model every particle, you can reverse it.
You can't uncrack an egg, because you don't know an egg works. But you can unopen a door, because you know how a door works. All you need is a perfectly elastic mirror, carefully placed to bounce the swinging door off of.
An expert egg mechanic can uncrack an egg with a precise arrangement of mirrors.
Thank you for this suggestion. Here’s what Mr. Gippity came up with: *Title: The Loops of Eternity*
In the heart of a Gödel-type universe, the Eternal Voyager drifted along its predestined closed timelike curve, a path that looped through space and time. Captain Alyssa Raines stared out at the swirling axially symmetric stars, her reflection caught in the reinforced glass. For as long as she could remember, she had lived this voyage, though memory itself was a fickle thing here.
Time aboard the Voyager was peculiar. Every cycle through the curve, entropy reset itself. Memories, once etched into her mind, dissolved at the journey's endpoint, leaving only fragments. She wrote notes obsessively in a battered journal, hoping to tether herself to some semblance of continuity. Yet, each "new" cycle, she found the same journal waiting, her handwriting foreign, the pages detailing lives she did not remember living.
The ship itself obeyed the laws of quantum mechanics in this bizarre space. Energy levels within the Voyager spontaneously discretized, ensuring that after each loop, all systems—including Alyssa herself—reset to their initial state. It was as if the universe conspired to erase the ship’s passage, preserving the self-consistency of history.
Yet Alyssa began to suspect something was different this time. She had found a sketch in her journal—an intricate design of a watch. It was labeled "the clock outside time." She didn't recall drawing it, but the annotations intrigued her: “To break free, entropy must not reverse.”
Determined, she poured herself into constructing the clock. Using the ship's limited resources, she crafted a device meant to measure time independent of the curve. If her hypothesis was correct, the clock would retain its state even after the loop's reset. It was a desperate hope to escape the recursive prison.
As the ship neared the curve's maximal entropy point—a moment she called "the entropy mirror"—the clock’s hands trembled. For the first time, Alyssa felt something unusual: a visceral sense of causality breaking apart. The clock ticked steadily as the Voyager looped. And when the curve closed, the clock did not reset.
Alyssa awoke in her cabin. The journal was still there, her memories still fragmented. But the clock was ticking. It was no longer bound by the curve.
She realized the truth: if she could detach herself from the curve's entropic cycle, she could chart a path out of this endless loop. But as she stared at the clock, another thought struck her—a chilling possibility. What if breaking free meant unraveling the ship, herself, and the delicate balance of this universe?
Would she risk the fabric of existence for freedom? Or was she merely another iteration of herself, destined to face the same question, time and time again?
---
Alyssa decided to test the clock further. She placed it next to the ship’s chronometers and watched their synchronization fail. The Voyager’s clocks dutifully reset as the loop neared its close, but her device ticked on, untouched by the curve’s bizarre physics.
“This isn’t just a clock,” she whispered, her voice trembling. “It’s an anchor.”
For weeks—or what she perceived as weeks—she studied the ship’s systems, using the clock to track the curve’s progress. The Voyager was designed to be self-sustaining, powered by the same quantum mechanics that bound it to the loop. But Alyssa discovered a flaw: a subtle energy fluctuation near the engine core. It was faint, like a whisper of resistance against the curve’s grip.
She theorized that if she amplified this anomaly, she could destabilize the ship’s entanglement with the curve. The ship might escape. But the consequences were unknowable. What happened to matter and entropy outside the loop’s boundaries? Would the ship be torn apart? Would she cease to exist, or would she find herself in a world where time flowed freely?
Her journal, with its fragmented entries and cryptic diagrams, offered no answers. But one entry stood out, written in bold, shaky letters:
"If you’re reading this, you’ve made it further than I ever did. Trust the clock. Trust yourself."”
Alyssa clutched the journal to her chest, her heartbeat echoing in the silent cabin. “I’ve tried this before,” she murmured. “But this time, it’s different. The clock proves it.”
She worked tirelessly, modifying the engine core to channel the energy fluctuation. She rerouted quantum stabilizers, recalibrated entropic dampeners, and rewired the naviga tion array. Each adjustment brought the ship closer to instability, the hum of the engines growing erratic.
As the loop approached its endpoint, the Voyager shuddered violently. Alyssa strapped herself into the captain’s chair, the clock clutched in her hand. “If this fails,” she said to no one, “I won’t remember. But if it works…” She couldn’t finish the thought.
The engines roared. The ship’s lights flickered. The clock ticked faster, its hands spinning wildly. A deafening crack reverberated through the Voyager as reality itself seemed to fracture.
And then…
Silence.
---
Alyssa opened her eyes to find herself floating in a void. The ship was gone, the stars replaced by an endless expanse of swirling light. The clock lay in her hand, its hands still, yet glowing faintly.
A voice echoed through the void, neither male nor female, yet familiar. “You have broken the loop.”
“Who are you?” Alyssa asked, her voice shaking.
“I am the possibility you created, the sum of all your choices. You have untethered yourself from the curve, but at great cost.”
“What happens now?” she whispered.
The light around her coalesced into a single point, growing brighter. “You may step into the unknown or return to the loop. Choose.”
Alyssa hesitated, the weight of countless lifetimes pressing down on her. She looked at the clock, its faint glow a reminder of her defiance. “I’ve spent eternity trapped in the same cycle,” she said. “I’ll take the unknown.”
The light enveloped her, and for the first time in as long as she could remember, Alyssa felt truly free. Where she emerged, she did not know. But she carried with her the knowledge that she had broken free of eternity’s loop—and that, for now, was enough.
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.
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.
> 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.
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).
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.
> That result is terrifyingly boring in its implications though, which is why we try to avoid it.
What result?
A result that the entire Universe is deterministic and already determined, like a movie already recorded to tape that we are somehow watching play from inside?
But I was referring to the possibility that it’s energetically impractical to ever get out of the solar system (or even travel within our solar system) in a way that any human is likely to ever want to do it. (Aka no FTL, or even near light speed)
And this likely applies to anything we’d call ‘life’ too.
And that time is actually one way, so no do overs, and no time travel. (Either because of the 2nd law of thermodynamics, or the 2nd law is an effect of this!)
If we accepted that, it would kill what - 95% of all Sci-fi ever?
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.
Wouldn't the fact that entropy must increase mean that you can never get to the exact same state as you were before?
Consider that Heisenberg's uncertainty theorem states that we cannot know precisely the position and velocity of a particle at the same time, not even in theory. Thus, they don't have precise values even in theory. Then how could you ever return back to the precisely same state which never had a precise value to begin with?
> Wouldn't the fact that entropy must increase mean that you can never get to the exact same state as you were before?
What you're running into is the observation that near closed timelike curves quantum mechanics inevitably becomes important.
> Consider that Heisenberg's uncertainty theorem states that we cannot know precisely the position and velocity of a particle at the same time, not even in theory. Thus, they don't have precise values even in theory.
This is a popular-level understanding of QM. The first sentence is true because it includes the all important 'at the same time'. The second is... trickier.
Position and momentum are observables, not state variables (unlike classical mechanics). They are incompatible so they suffer from Heisenberg uncertainty. But that doesn't mean a state can't have a definite position or momentum.
You can construct a wavefunction with a definite position. By Heinsenberg uncertainty, if you try to measure its momentum you can get any value. Likewise you can construct a wf with a definite momentum but if you measure its position you can get any value.
Nevertheless the system has a definite wf. For these two different wfs it is perfectly fair to say the first has a definite position and the second a definite momentum.
> Then how could you ever return back to the precisely same state which never had a precise value to begin with?
If the system goes around a CTC and returns to the same wavefunction it's the same. Quantum mechanical systems have definite states. But weirdly in QM position + momentum are not state variables.
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.
> 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."
https://web.archive.org/web/20241223001630/https://iopscienc...
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...
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.)
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 ...
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).
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?
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.)
This paper (among some others that are referenced in this Wikipedia article) are also cited here and referenced.
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.
> 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.
also a good example is the movie Triangle
And the TV show Dark
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.
>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.
Your younger self doesn’t have to be a future state of your present self, you just have to induce it, eg, being your own father or grandfather. Your younger self doesn’t have to be in your future if you allow some overlap (father) or short gap (grandfather) on the circle.
This reminds me of comic strips where someone interacts with an adjacent frame.
futurama solved that: fry travelled back and became his grandfather's younger self, rather than his own younger self
> "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?
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.
> 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.
Is this not inherently circular reasoning? "For X to happen, the laws of physics must allow X to happen". It seems totally obvious. Am I missing something? Of course entropy must be discrete and reversible in order to reverse entropy, it just doesn't work that way as far as we know in the real universe.
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.
You know, there are no photographs of the man. Are we certain that he's not from the future, hiding out in his past as a fugitive?
I consulted Wikipedia on "Closed Timelike Curve" and didn't understand the explanation either. I could distinctly hear a "woosh" sound as it all flew by above my head.
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?
So they assume four-dimensional space-time of a certain shape, similar to how a two-dimensional sheet could be curved taking various shape. Then they calculate how would physical objects behave in space-time of that shape.
Can such shapes exist anywhere in our universe, realistically or even just theoretically? For all we know, perhaps not.
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
It's a poorly worded way of saying, if heat doesn't exist, and objects don't gain or lose energy, but only change configuration in a controlled way, physics is reversible. This is traditional time-symmetric Newtownian physics before thermodynamics. "What does down bounces back up."
Entropy is measure of information. If an object changes state according to some law or data that you don't know, then you can't predict the result, and you can't set up conditions to undo the changes. Thus you can't reverse it, because you don't know the original state. If you can explicitly model every particle, you can reverse it.
You can't uncrack an egg, because you don't know an egg works. But you can unopen a door, because you know how a door works. All you need is a perfectly elastic mirror, carefully placed to bounce the swinging door off of.
An expert egg mechanic can uncrack an egg with a precise arrangement of mirrors.
Yes but mirror boxes are not real, except maybe the case of quark color confinement inside a proton?
For a bit of fun you can use this prompt:
Read this paper and write a time-travel story plot line based on its contents https://iopscience.iop.org/article/10.1088/1361-6382/ad98df#...
Thank you for this suggestion. Here’s what Mr. Gippity came up with: *Title: The Loops of Eternity*
In the heart of a Gödel-type universe, the Eternal Voyager drifted along its predestined closed timelike curve, a path that looped through space and time. Captain Alyssa Raines stared out at the swirling axially symmetric stars, her reflection caught in the reinforced glass. For as long as she could remember, she had lived this voyage, though memory itself was a fickle thing here.
Time aboard the Voyager was peculiar. Every cycle through the curve, entropy reset itself. Memories, once etched into her mind, dissolved at the journey's endpoint, leaving only fragments. She wrote notes obsessively in a battered journal, hoping to tether herself to some semblance of continuity. Yet, each "new" cycle, she found the same journal waiting, her handwriting foreign, the pages detailing lives she did not remember living.
The ship itself obeyed the laws of quantum mechanics in this bizarre space. Energy levels within the Voyager spontaneously discretized, ensuring that after each loop, all systems—including Alyssa herself—reset to their initial state. It was as if the universe conspired to erase the ship’s passage, preserving the self-consistency of history.
Yet Alyssa began to suspect something was different this time. She had found a sketch in her journal—an intricate design of a watch. It was labeled "the clock outside time." She didn't recall drawing it, but the annotations intrigued her: “To break free, entropy must not reverse.”
Determined, she poured herself into constructing the clock. Using the ship's limited resources, she crafted a device meant to measure time independent of the curve. If her hypothesis was correct, the clock would retain its state even after the loop's reset. It was a desperate hope to escape the recursive prison.
As the ship neared the curve's maximal entropy point—a moment she called "the entropy mirror"—the clock’s hands trembled. For the first time, Alyssa felt something unusual: a visceral sense of causality breaking apart. The clock ticked steadily as the Voyager looped. And when the curve closed, the clock did not reset.
Alyssa awoke in her cabin. The journal was still there, her memories still fragmented. But the clock was ticking. It was no longer bound by the curve.
She realized the truth: if she could detach herself from the curve's entropic cycle, she could chart a path out of this endless loop. But as she stared at the clock, another thought struck her—a chilling possibility. What if breaking free meant unraveling the ship, herself, and the delicate balance of this universe?
Would she risk the fabric of existence for freedom? Or was she merely another iteration of herself, destined to face the same question, time and time again?
---
Alyssa decided to test the clock further. She placed it next to the ship’s chronometers and watched their synchronization fail. The Voyager’s clocks dutifully reset as the loop neared its close, but her device ticked on, untouched by the curve’s bizarre physics.
“This isn’t just a clock,” she whispered, her voice trembling. “It’s an anchor.”
For weeks—or what she perceived as weeks—she studied the ship’s systems, using the clock to track the curve’s progress. The Voyager was designed to be self-sustaining, powered by the same quantum mechanics that bound it to the loop. But Alyssa discovered a flaw: a subtle energy fluctuation near the engine core. It was faint, like a whisper of resistance against the curve’s grip.
She theorized that if she amplified this anomaly, she could destabilize the ship’s entanglement with the curve. The ship might escape. But the consequences were unknowable. What happened to matter and entropy outside the loop’s boundaries? Would the ship be torn apart? Would she cease to exist, or would she find herself in a world where time flowed freely?
Her journal, with its fragmented entries and cryptic diagrams, offered no answers. But one entry stood out, written in bold, shaky letters:
"If you’re reading this, you’ve made it further than I ever did. Trust the clock. Trust yourself."”
Alyssa clutched the journal to her chest, her heartbeat echoing in the silent cabin. “I’ve tried this before,” she murmured. “But this time, it’s different. The clock proves it.”
She worked tirelessly, modifying the engine core to channel the energy fluctuation. She rerouted quantum stabilizers, recalibrated entropic dampeners, and rewired the naviga tion array. Each adjustment brought the ship closer to instability, the hum of the engines growing erratic.
As the loop approached its endpoint, the Voyager shuddered violently. Alyssa strapped herself into the captain’s chair, the clock clutched in her hand. “If this fails,” she said to no one, “I won’t remember. But if it works…” She couldn’t finish the thought.
The engines roared. The ship’s lights flickered. The clock ticked faster, its hands spinning wildly. A deafening crack reverberated through the Voyager as reality itself seemed to fracture.
And then…
Silence.
---
Alyssa opened her eyes to find herself floating in a void. The ship was gone, the stars replaced by an endless expanse of swirling light. The clock lay in her hand, its hands still, yet glowing faintly.
A voice echoed through the void, neither male nor female, yet familiar. “You have broken the loop.”
“Who are you?” Alyssa asked, her voice shaking.
“I am the possibility you created, the sum of all your choices. You have untethered yourself from the curve, but at great cost.”
“What happens now?” she whispered.
The light around her coalesced into a single point, growing brighter. “You may step into the unknown or return to the loop. Choose.”
Alyssa hesitated, the weight of countless lifetimes pressing down on her. She looked at the clock, its faint glow a reminder of her defiance. “I’ve spent eternity trapped in the same cycle,” she said. “I’ll take the unknown.”
The light enveloped her, and for the first time in as long as she could remember, Alyssa felt truly free. Where she emerged, she did not know. But she carried with her the knowledge that she had broken free of eternity’s loop—and that, for now, was enough.
Here’s what Mr. Gippity came up with
If we wanted ChatGPT's opinion we can ask it ourselves.
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.
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.
> 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.
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.
> That result is terrifyingly boring in its implications though, which is why we try to avoid it.
What result? A result that the entire Universe is deterministic and already determined, like a movie already recorded to tape that we are somehow watching play from inside?
That could be one.
But I was referring to the possibility that it’s energetically impractical to ever get out of the solar system (or even travel within our solar system) in a way that any human is likely to ever want to do it. (Aka no FTL, or even near light speed)
And this likely applies to anything we’d call ‘life’ too.
And that time is actually one way, so no do overs, and no time travel. (Either because of the 2nd law of thermodynamics, or the 2nd law is an effect of this!)
If we accepted that, it would kill what - 95% of all Sci-fi ever?
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.
Wouldn't the fact that entropy must increase mean that you can never get to the exact same state as you were before?
Consider that Heisenberg's uncertainty theorem states that we cannot know precisely the position and velocity of a particle at the same time, not even in theory. Thus, they don't have precise values even in theory. Then how could you ever return back to the precisely same state which never had a precise value to begin with?
> Wouldn't the fact that entropy must increase mean that you can never get to the exact same state as you were before?
What you're running into is the observation that near closed timelike curves quantum mechanics inevitably becomes important.
> Consider that Heisenberg's uncertainty theorem states that we cannot know precisely the position and velocity of a particle at the same time, not even in theory. Thus, they don't have precise values even in theory.
This is a popular-level understanding of QM. The first sentence is true because it includes the all important 'at the same time'. The second is... trickier.
Position and momentum are observables, not state variables (unlike classical mechanics). They are incompatible so they suffer from Heisenberg uncertainty. But that doesn't mean a state can't have a definite position or momentum.
You can construct a wavefunction with a definite position. By Heinsenberg uncertainty, if you try to measure its momentum you can get any value. Likewise you can construct a wf with a definite momentum but if you measure its position you can get any value.
Nevertheless the system has a definite wf. For these two different wfs it is perfectly fair to say the first has a definite position and the second a definite momentum.
> Then how could you ever return back to the precisely same state which never had a precise value to begin with?
If the system goes around a CTC and returns to the same wavefunction it's the same. Quantum mechanical systems have definite states. But weirdly in QM position + momentum are not state variables.
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.
Thanks, that's what I get for skim-reading :)
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."
Seems like a typo in the first sentence of the abstract: "...close timelike curve..." vs "...closed timelike curve..."
Time is a flat circle.