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I'm having trouble reconciling my astronaut space ship's spinning centrifugal gravity system in an otherwise empty universe.

My intrepid astronaut has been transported far beyond normal time scales and now exists at the true Heat Death of the Universe. This is the 'true' actual heat death - ie, not just after black holes evaporated, but even after that. All the universe is at virtually maximum entropy - for all intents and purposes it might as well not exist.

Her spaceship is still held together and has active systems inside. I want her spaceship to be already spinning to create normal gravity.

As there is no 'magical' axis about which the universe exist and there is no effective remainder of the universe and thus no meaningful other point of reference: Can spin gravity still apply and what measurement/experiment can be used to determine its rate of spin in an empty fully entropic universe?

For story related purposes:

  • My astronaut is having trouble as she looks out the window and sees 'nothing', how indeed she can measure spin when there is nothing to measure against? she asks. She also asks 'Where does the energy go on my spinning spaceship that gives constant gravity and will it spin forever?'
  • My astronaut will attempt to change the spin, and also accelerate her space ship (I don't yet know how to describe this sensation) in a post-Heat-Death universe later.
  • She would have existential thoughts eventually, based on basic principles of physics, but for all intents and purposes she begins with a very methodical approach. She has a fully working physical spaceship.
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You're assuming that the condition of the universe would have any affect on her space ship ... it wouldn't

The heat death of the universe is not an area-of-effect event. It isn't defined by some artifact that causes everything to (simplifying!) stop vibrating. It's defined as the moment when the atomic structure of everything that naturally exists stops vibrating/moving/etc.1

Bing! Your astronaut's space ship suddenly appears in the universe. It's entirely and completely unaffected by the condition of the universe just as the universe is entirely and completely unaffected by the presence of the ship. Just because the ship's lights come on doesn't mean the universe hasn't experienced heat death and vice-versa.2

Said in a much simpler way: you're imposing a problem where no problem exists.

The ship's centrifugal gravity works just fine. It's measured just fine. The gravimeter used to measure it works just fine. If you want to know the rate of spin, spray paint a line across the proverbial spindle and bearings of the spinning section and use a stop watch to determine how long it takes for the outside to rotate around to the line on the inside once.

In like manner, your ship can accelerate just fine and that can be measured with an accelerometer (a specialized form of gravimeter) just fine.

As you've asked about in at least one previous question, the problem is navigation. That's when your astronaut must actually care about things outside the ship.

NOTE: It's really important to understand that the universe won't be trying to force something onto the ship... kinda. That well-balanced end-of-life condition would want the ship to be part of the well-balanced system. But it's not an overwhelming force. How far away is your ship from a big, lifeless, unmoving, cold rock in space? Does it matter? Does your ship have a Quetta-ton nuclear bomb? Would detonating it re-ignite a star? So what? Your ship can move around just fine and anything it can do to the universe compared to the universe itself would be so factually small and short-lived that it would be irrelevant. In the end, unless you bring some Clarkean Magic to bear, your astronaut will go stark raving mad from boredom — not because there's nothing to do (like ship maintenance), but because there's no reason to do it (nowhere to go and nothing to do when you get there).

1 This is a huge over-simplification of what scientists hypothesize is the ultimate fate of the universe. Maximum entropy. No heat, no motion, no nuthin'. I wouldn't lose too much sleep over it, though.

2 An argument could be made that the sudden presence of the ship would destabilize the balance of gravity, causing things to move ever so slightly and, thereby, back the universe away from it's heat death (etc.). Giving it a last breath of life, so to speak. Yup! Irrelevant. The piddly amount of injected energy due to the mass of the ship, it's waste byproducts, light streaming from its view ports, etc. is so infuriatingly small compared to the well-balanced nothing that exists at the HDOtU that everything will re-balance almost instantly (on an astronomical time scale...) as if the ship had never existed. So say we all.

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  • $\begingroup$ Your line-painting experiment wouldn't work because you don't know if the spindle is truly sitting still. Your distance from it and the Gravimeter would be able to give you a precise answer (though with an annoying amount of extra math). Besides this minor point, perfect answer imho $\endgroup$ Commented yesterday
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    $\begingroup$ @QuestionablePresence If it's relevant that the spindle is or isn't sitting still the ship is badly designed. Gyroscopic stabilization would be designed into the system precisely to stop that problem. However, in the case when the whole ship is spinning (no spindle), your point makes good sense. $\endgroup$ Commented yesterday
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The reference frame is only a modelling artifact used by us human in mathematically describing a certain behavior. It's not a conditio sine qua non for the actual occurrence of the described phenomenon, centrifugal gravity in this case.

If your astronaut wants to measure their rotation rate change, they can simply leave an object outside of the change domain and use it as reference point, in the same way as one would leave a sign on a wall to know where they have been while moving in an otherwise empty room.

What would actually concern me is how to keep the entire spaceship as such without decaying in an environment which is at its minimum free energy level. Many times more difficult than keeping a cup of hot coffee hot while standing outside in winter in Siberia.

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    $\begingroup$ An ideal environment to do some scientific experiments on gravity in. Too bad anything discovered will be never shared with anyone... $\endgroup$ Commented yesterday
  • $\begingroup$ Given that most spaceships are largely concerned with getting rid of their (waste) heat, I'd say that not even that really matters, our regular "space" is already closer to "nothing" than to "survivable" so insulation is already well in place. Maybe turn down the radiators to 98% $\endgroup$ Commented yesterday
  • $\begingroup$ @QuestionablePresence it's not discarding heat. It's keeping all the matter making the spaceship as matter, rather than having it decay to whatever protons and electrons decay at that moment in the universe life $\endgroup$ Commented yesterday
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    $\begingroup$ @L.Dutch Protons and electrons don't magically just start decaying in a matter of seconds or years or centuries once the Universe's warranty expires. Just because the rest of the universe has been sitting around for however many googolplex years it takes for it to decay, doesn't mean the spaceship won't take just as long to decay once you drop it in. The astronaut will have exactly as much trouble stopping her ship from undergoing proton decay at the End Of All Things as she will in 2026: it will inevitably happen, but it will happen long after anything she could possibly care about is over. $\endgroup$ Commented yesterday
  • $\begingroup$ @L.Dutch ah I wasn't thinking about vacuum decay or similar phenomenon $\endgroup$ Commented yesterday
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The ship don't need to spin relative to anything, but as you note it could be tricky to determine exactly how quickly it's spinning without visual references.

The method your protagonist would use depends on which tools are available.

If the protagonist can move about the entire ship, measure all distances and measure acceleration everywhere, there are other approaches, but I don't see why you necessarily could. For all I know, the protagonist sits in a capsule joined to a counterweight by a wire, the two spinning around their centre of gravity. In that case, it's harder to know the relevant measurements with any accuracy, especially if there are no windows in that direction.

If you can measure distances, forces and angles (where the latter can be accomplished by distance measurements and trigonometry), you could still find various "vertical" lines and use trigonometry to see how far away they intersect. You need to be able to determine or a kilogram or a Newton to start out with, to have some reference.

If you can't measure the centrifugal force accurately, but can measure time, the easiest way of determining that you are in fact spinning is to measure the Coriolis force. Lift an object, drop it and note how far off from the point "directly below it" it lands. The point "directly below" could be determined by tying a weight to a string, and you could simply note how fast the falling object deviates from the plumb line.

The math isn't terribly difficult, but the linked Wikipedia page is a nice place to start and get some formulas!

If the spinning is too slow, in terms of revolutions per second, your protagonist could put up a Foucault pendulum. This would give her a rather accurate idea about how fast she's spinning.

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  • $\begingroup$ I was about so suggest yeeting something out the airlock but this is the far better approach to getting that data $\endgroup$ Commented yesterday
  • $\begingroup$ With an accelerometer and a known measurement for the distance from the ship's rotation axis to the floor (the latter will probably be harder to come by), you could also get the centrifugal force and extrapolate the angular velocity. Alternatively, if reaction control still works, you could have the ship measure how long it takes with known RCS forces to bring it back to equilibrium. $\endgroup$ Commented yesterday
  • $\begingroup$ @controlgroup Why do assume the protagonist can measure a distance to the axis, or even know where the axis is? $\endgroup$ Commented yesterday
  • $\begingroup$ @EdvinW We are talking about a starship which has somehow reached the Heat Death, either by sheer godtech or by surviving some incomprehensible spacetime effect. It seems odd that it wouldn't -- either on paper or on a computer somewhere -- have a technical diagram of itself, in case the astronaut onboard might need to measure something. Certainly, the people on the ISS are able to check how far apart two spots in two different modules are while onboard. Unless this ship is somehow less advanced than the ISS, our protagonist should be able to as well. $\endgroup$ Commented yesterday
  • $\begingroup$ Finding the axis is actually rather trivial. It's the one set of points in the ship where centrifugal gravity is zero. (Or, if that lies outside the ship, the line that all other centrifugal acceleration vectors point away from.) That is if the ship can't tell for itself with a simple gyroscope. $\endgroup$ Commented yesterday
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In short:

Rotation is absolute. It is not relative to anything. The rate of spin can easily be determined by measuring the size of the ship with a meter stick and the apparent weight of a kilogram of water with a spring scale.

A kilogram is the mass of one cubic decimeter of water. A decimeter is one tenth of the length of the meter stick.

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Time to bring forth the good ol' Mach's principle. If the inertia is determined by the distribution of mass in the Universe, and there is no mass anymore, then indeed you cannot distinguish rotating and non-rotating scenarios.

Note that Mach's principle is controversial to say the least; simple Newtonian geometric arguments suggest the rotation is absolute - but again, if the inertia of items inside of your ship is determined by the ship itself, the argument does not hold.

Also note that a post-heat death universe is not necessarily "empty". If anything, there is still vacuum, and vacuum has energy. And maybe there is also cosmological constant, dark energy and stray (very) long wavelength photons around. "bare" ≠ empty.

And maybe the arrow of time (if it is indeed entropic) itself will re-orient when the ship appears and time starts ticking again. Everything is in the fine details.

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