I recently read on recommendation a SciFi novel about life evolving on a neutron star or its crust. One thing that puzzled me was the assertion the neutron star life was living roughly a million times faster than some human astronauts who visited the wandering star (but orbit hundreds of Km above to avoid the extreme gravitational tides or something like that). However, I think I understand that the extreme gravity of the neutron star - 67 billion Gs I think in the story - should have extreme effects on relative flow of time. While reading this bothered me as the novel was otherwise trying to be super hard scifi.
Question: what would be the time effects between normal G and 67 billion Gs (if this question is properly formulated, maybe not)?
I entered some numbers into this online calculator, using 2.8 x 1030 kg as a typical neutron star mass, 10 km as a typical neutron star radius, and having the astronauts orbit 1000 km from the neutron star (I left the other parameters unchanged).
The calculator spat out a time dilation factor of ~0.2341 for an object on the surface of the neutron star, meaning for every year that passes for the astronauts, an object on the surface would only age ~0.8103 years.
I also found a StackExchange post that claims the theoretical maximum possible time dilation factor for a neutron star is ~2.29. So it looks like the novel’s assertion that neutron star life is living “a million times faster” is outrageous bunk.
I think, if it’s the story I’m thinking of, it’s not time dilation, but that the physiology of the neutron star creatures is so different that they live much faster than we do.
Nothing to do with time dilation. The factor of a million in processes there is because “chemical” reactions are mediated by the strong nuclear force rather than EM.
What do you think is being wrongly ignored exactly? Time dilation is not significant relative to the factor of a million in the speed of the chemical processes that dictate the rate at which events proceed for the Cheela.
In the movie Interstellar, I remember that the team of astronauts drop onto a planet with very strong gravity. IIRC it was the one with the huge tidal wave. When they return to the ship, they see that one astronaut who stayed on the ship aged significantly. So is this bad science, since a neutron star would presumably have considerably more gravity than any planet?
The time dilation wasn’t due to the planet’s gravity IIRC it was due to the gravity of the supermassive black hole it was in orbit around.
IANAPhysicist but if I’m remembering right the numbers for interstellar work out, but they had to give their black hole an extremely rapid spin to get the desired time dilation (as spinning black holes have different properties than nonspinning ones)
I love “hard” science fiction. Arthur C. Clarke had a number of such stories, an old classic example being Technical Error, in which a technician in the core of a huge generator is suddenly subject to enormous electromagnetic forces with … unpredictable results.
But the idea of life on a neutron star seems to be beyond far-fetched. Not even atoms can exist on a neutron star, let alone molecules. So the possibility of the kinds of complex structures necessary for life being formed from a homogenous mass of neutrons and a few stray unassociated electrons and protons seems rather silly.
I saw Interstellar but it’s been a while. There is nothing magical about a black hole. If you were in orbit around a black hole, it wouldn’t be a different experience than orbiting a large body of the same mass. I don’t know anything orbital mechanics but I’m guessing that if they could establish a stable orbit around a black hole they couldn’t have been close enough for significant time dilation, any more than what the astronauts on the Space Shuttle experience.
I agree on the silliness, but the surface of a neutron star will have quite a few protons, not just a scattering. In fact, the crust of a neutron star should be made of “normal” matter. Well, not strictly normal, but of normal nuclei in a sea of electrons. As you go deeper, the atomic numbers and weights of the nuclei increase, with increasing number of neutrons in them as well as free neutrons that the pressure prevents the decay of. Similarly, a lot of the heavy nuclei would quickly decay in our environment, but be stable in that environment.
The strong force is far more complicated than electromagnetism. If electromagnetism-based life is plausible, then strong-force-based-life is even more so. Heck, it might even be possible to get “living glueballs”, life composed entirely of strong-carrier-particles, without even needing protons and neutrons (a trick which has no equivalent for electromagnetism).
It’s true that if the Sun was replaced today by a black hole of the same mass, the Earth would go on orbiting merrily in its path without being affected. But that’s only because we’re relatively far away from the Sun.
In Newtonian gravity (pre-Einstein), the only limit on how closely you can orbit an object is the physical size of the object itself (i.e., don’t run into the thing.) If “point masses” existed, you could whip around them 1 mm away so long as you were going fast enough. At least, that’s what Newton thought.
In Einstein’s GR, though, if you try to orbit a non-spinning compact object very closely, it turns out that there is distance called the ISCO (innermost stable circular orbit). This orbital distance works out to be 3 times the size of the black hole itself. IIRC you end up with a time-dilation factor of √2 for a planet in such an orbit (though don’t quote me on that.) This wouldn’t be large enough to give you a time-dilation factor like that shown on the water planet in Interstellar.
However, if you have a rotating black hole, it turns out that you can orbit it stably at a much closer radius—arbitrarily close to the event horizon, in fact. This in turn allows you to get arbitrarily large time dilation, though you have to get the black hole spinning stupidly fast to get the magnitude of the time dilation as large was shown in Interstellar.