[HN Gopher] Life on a Closed Timelike Curve
___________________________________________________________________
Life on a Closed Timelike Curve
Author : the_mitsuhiko
Score : 88 points
Date : 2025-01-12 21:33 UTC (3 days ago)
(HTM) web link (iopscience.iop.org)
(TXT) w3m dump (iopscience.iop.org)
| heisenzombie wrote:
| 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.
| jeroenvlek wrote:
| 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?
| dvh wrote:
| 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.
| evanb wrote:
| 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.
| ben_w wrote:
| "A" universe, but not "the" (i.e. our) universe.
|
| Specifically: https://en.wikipedia.org/wiki/Godel_metric
|
| It's specifically a universe where time travel definitely
| happens.
| codethief wrote:
| 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.
| ben_w wrote:
| Thanks, that's what I get for skim-reading :)
| lmm wrote:
| > 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.
| the_mitsuhiko wrote:
| > 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.
| goatlover wrote:
| 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.
| red75prime wrote:
| 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."
| lazide wrote:
| 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.wik
| ipedia.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.
| lupire wrote:
| > 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?
| tingletech wrote:
| Seems like a typo in the first sentence of the abstract:
| "...close timelike curve..." vs "...closed timelike curve..."
| Klaster_1 wrote:
| Do Greg Egan books have a DOI?
| A_D_E_P_T wrote:
| Some of them should. _Permutation City_ and the 3-Adacia series
| of short stories are worth a spot in anybody 's reference
| library.
| NoMoreNicksLeft wrote:
| 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?
| cosmos0072 wrote:
| 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 wrote:
| > 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...
| the_mitsuhiko wrote:
| This paper (among some others that are referenced in this
| Wikipedia article) are also cited here and referenced.
| zozbot234 wrote:
| 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 wrote:
| 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 wrote:
| 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).
| moralestapia wrote:
| >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.
| Sharlin wrote:
| 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.
| PaulHoule wrote:
| 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.
| zmgsabst wrote:
| 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.
| vyrotek wrote:
| This reminds me of comic strips where someone interacts with an
| adjacent frame.
| pdonis wrote:
| _> 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 wrote:
| also a good example is the movie Triangle
| lupire wrote:
| And the TV show Dark
| cgh wrote:
| 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.
| harrison_clarke wrote:
| futurama solved that: fry travelled back and became his
| grandfather's younger self, rather than his own younger self
| A_D_E_P_T wrote:
| > "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 wrote:
| 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 wrote:
| 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 wrote:
| 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 wrote:
| > 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
| dustingetz wrote:
| 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
| the_mitsuhiko wrote:
| > What about entropy?
|
| Look at 3.1. "spontaneous recombination of an unstable
| particle" for how this works.
| dustingetz wrote:
| 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...
|
| _SS11. 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
| lupire wrote:
| 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.
| dustingetz wrote:
| Yes but mirror boxes are not real, except maybe the case
| of quark color confinement inside a proton?
| Rygian wrote:
| 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?
| 3ple_alpha wrote:
| 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.
| zombot wrote:
| 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.
| dmor wrote:
| 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#...
| tizio13 wrote:
| Thank you for this suggestion. Here's what Mr. Gippity came up
| with: *Title: The Loops of Eternity*
|
| In the heart of a Godel-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.
| novemp wrote:
| _Here's what Mr. Gippity came up with_
|
| If we wanted ChatGPT's opinion we can ask it ourselves.
| carabiner wrote:
| Time is a flat circle.
| rtxgucci wrote:
| 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.
| neonate wrote:
| https://web.archive.org/web/20241223001630/https://iopscienc...
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