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This has been messing with my head for a while.

The Cheela in/on Dragon's Egg book/planet, had their time move much faster, compared to the humans out in the space. This was explained as due to the extremely high gravity of their neutron star planet. What is the fictional physics occurring on Cheela to cause the time speed up?

But in reality AND any fictional universe that acts like reality, high gravity acts to slow time down. This effect was notably portrayed in Interstellar -- when the expedition party land on the watery planet that's extremely close to a black hole, their time is slowed down, compared to the human out in space.

I'm missing something simple here. Can someone help solve this for me please.

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    The answer given explains it. As you said, GR will slow down time -- with a factor of 1.7 to 1.4. But the fact that the cheela are made of nuclei and not of atoms means that their "chemistry" runs about a million times faster. So the chemistry speedup far outweighs the GR slowdown. Sep 28, 2022 at 19:22
  • @RossPresser Note that Dragon's Egg is not fully a neutron star (hence the quasi-atomic matter present on the surface) and is far more than 1.5 times the Schwarzchild radius; it's actually almost 7 times the Schwarzchild radius, so tau on the surface is only about 1.08.
    – DavidW
    Sep 28, 2022 at 22:28
  • Unfortunately, all your edit did was change this opinion-based (comparing two different series) to asking for real world science (comparing the fictional universe to our own). If you haven't yet, I'd suggest taking the tour and visiting the help center.
    – Skooba
    Sep 29, 2022 at 17:38
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    @Skooba Dragon's Egg made a big play of being hard science, being written by a professional physicist. Surely it is reasonable to ask what the in-universe explanation for an apparently paradoxical phenomenon is, given the hard science credentials. In particular the question is not asking for real-world physics answers, just the explanation given in the book. Sep 29, 2022 at 19:31
  • Lots of comments deleted following the edit to the question, making it about comparing Dragon's Egg to actual physics rather than comparing Dragon's Egg to Interstellar. I tried to leave the most still-relevant comments, but let me know if anything important has gone.
    – Rand al'Thor
    Sep 30, 2022 at 6:20

2 Answers 2

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You're mistaking the "living rate" of the Cheela against the Einsteinian General Relativity time dilation in Interstellar.

This was explained early in Dragon's Egg, during the exposition about how life evolved in the degenerate matter crust of a neutron star. The explanation was that, because degenerate matter is much more compact than normal matter (due to the electrons being not quite smashed into the nucleus, which would cause them to fuse with protons to produce neutronium), all the pseudo-chemical reactions between them proceed at thousands or tens of thousands of times the rate of reactions between normal matter atoms.

The time dilation effect of a neutron star would make perception of time there slow down (one year at the station in synchronous orbit with its orbiting monopolium tidal counterbalances would be something more than a year Earth time), just as it did deep down in the gravity well of Gargantua -- but living tens of thousands of times faster and in almost the same level of time dilation let the Cheela live and advance through hundreds of generations in the space of a few days of human time.

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  • I would disagree with "much more" -- the tau factor ranges from 1.7 to 1.4 depending on the ratio of the actual radius to the Schwarzchild radius. Sep 28, 2022 at 19:24
  • Thanks @Zeiss for the detailed explanation. I think I'll go reread that part from Dragon's Egg once again. I think I see where I got the wrong impression. Although the first paragraph answers my question, thank you very much for going into details. I needed that.
    – sharat87
    Sep 29, 2022 at 1:57
  • @RossPresser Edited -- you're right, tau 1.4-1.7 wouldn't give a HUGE differential. There would certainly be some differential between the surface and the human station, too, but the Cheela's "rate of living" grossly overrides that.
    – Zeiss Ikon
    Sep 29, 2022 at 11:08
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    @ZeissIkon I replied to Ross's similar comment on the main question, but it was removed. Maybe it will stick here. The tau factor of 1.4+ is based on a neutron star with a radius of approximately 1.5 times its Schwarzchild radius. We know the mass and radius of Dragon's Egg, and it's about 7 times its Schwarzchild radius, so tau will be much lower. I used a couple of online calculators and got approximately 1.08.
    – DavidW
    Sep 29, 2022 at 11:17
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    Ah , ok. The SR time dilation on the surface is negligible, around 1.0000044. The pseudo-chemical basis of the cheela biology is primarily based on the strong force, electromagnetic (and weak) interactions are (probably) irrelevant, as well as being glacially slow from the cheela's POV.
    – PM 2Ring
    Sep 29, 2022 at 16:42
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The "Technical Appendix" at the back of Dragon's Egg is very detailed in the description of the neutron star, the cheela, the Dragon Slayer's orbit, and everything else about the expedition.

The neutron star itself has half a solar mass (approximately 1e30 kg), a diameter of 10km and rotates every 0.1993s. A gravitational time dilation calculator says that tau on the surface would be approximately 1.083, and the rotational velocity (315 km/s) contributes no significant additional time dilation

The Dragon Slayer in turn is orbiting Dragon's Egg in a synchronous orbit at an altitude of 406km. It orbits every 0.1993s (the rotational speed of Dragon's Egg) or 5.018 orbits/s. The radius of Dragon's Egg is 10km, so the Slayer travels 416 * 2 * π * 5.018 = 13 116 km/s (4.375% c), which only gives a velocity time dilation of 1.00096. (Less than 1 in 1000.) The Egg has 0.5 solar masses, which at a distance of 416km gives a gravity time dilation of 1.00178, slightly less than twice the velocity time dilation.

I'm not sure these results can be added together, but in any event the total time dilation experienced by the crew on the Slayer will be less than half a percent. Over the course of the 8-day mission (which is cut short in any event) they would experience no more than an hour's difference from the crew on the St. George.

The cheela are a completely different story. Per the appendix, the Cheela live and experience time approximately a million times faster than we do.

The atomic nuclei that make up the cheela do not have captive electron clouds to keep them isolated from each other, but instead share a "sea" of free electrons. Because of the resulting close proximity of the nuclei, it is as easy for cheela nuclei to exchange neutrons as it is for human atoms to exchange electrons. The nuclei couple into "nuclear bonded molecules" by neutron exchange. Since the cheela use nuclear coupling instead of molecular coupling in their bodies, their rate of living is about one million times that of humans.

Dragon's Egg, "Technical Appendix"

Note that this has nothing to do with relativistic time dilation. It is purely because instead of (slow) chemical reactions, their bodies/metabolisms operate on strong nuclear reactions. So even if tau (on the surface of their star) is 1.083, it makes effectively no difference in how fast they experience time.

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  • Note that I'm explicitly ignoring Interstellar here because it's not necessary to answer the question and it's only causing a misunderstanding of gravitational time dilation.
    – DavidW
    Sep 29, 2022 at 20:31

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