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I am constructing a thought experiment about a spinning object that is floating in intergalactic space. I assume that this object is about the size of a planet so that it will have enough gravity so that a Foucault pendulum will work, although I'm not sure that this is necessary for the thought experiment.

I can easily determine that this object is spinning if I stand on the object and observe the galaxies around me rise and set. Similarly, I can determine the axis of rotation.

For simplicity, I go to one of the poles of my object, and I set up my Foucault pendulum. What will I see? And why will I see it? I assume that in intergalactic space, the gravity is very small (galaxies are very far away, and the mass of my object is very small compared to the mass of a galaxy) so that there will be little coupling between the gravitational field of my object and the gravitational field of the galaxies around me.

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Related: and links therein. More on Mach's principle. – Qmechanic Feb 24 at 17:06

This is indeed a Big Question; you have essentially stumbled into Mach's principle.

For an even more bewildering version: suppose that in that bit of intergalactic space, you have two spherical objects, which are rotating relative to each other about their separation axis, with the distant stars stationary with respect to object 1. Our current understanding of physics is very clear that a Foucault pendulum on object 1 will not precess, but if placed on a pole of object 2 it will precess relative to object 2 (and keep in plane with a pendulum on a pole of object 1). The reasons for this, however, are not as clear, and if I understand correctly they are still a matter of debate, but maybe someone closer to that field can clarify.

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There were some fairly insightful comments here that a moderator just unceremoniously dumped. – Robert Harvey Feb 25 at 21:55
@RobertHarvey yes, for two reasons: (1) the participants in the comment exchange indicated that it was concluded, and (2) some of the things said were slightly inappropriate and indicative of further inappropriate comments to come. If you think the insights brought up in the comments would constitute a good answer, or a followup question, feel free to post it. If you need to reference the comments to do so, I can undelete them for a short time so you can copy them into a text file. – David Z Feb 26 at 13:11
@DavidZ: It just seems aggressive, that's all I'm sayin'. On Stack Overflow, I delete comments ruthlessly, but if they have anything at all to do with the actual question content (and are reasonably civil), I don't feel the need. It's not like we're going to run out of bits. Nor do I base my decisions on predictions of what might happen in future commentary. No, I don't want to post an answer; why would I do that? I'm not a subject matter expert. In short, I save my guns for the real battles, which we never seem to be short of. ♦ – Robert Harvey Feb 26 at 15:48
@RobertHarvey probably a site culture difference. I've also posted a fair amount on SO, and I really do think we have more problems with comments here than you do there - though, admittedly, I don't see the junk that gets deleted on SO. Since it's a smaller site we get to know the frequent posters, and we notice a lot of the characteristic patterns that suggest an argument is about to break out, so it's easier to cut things off in advance. – David Z Feb 26 at 16:50
@DavidZ That's fair enough. – Robert Harvey Feb 26 at 16:53

While we may not be able to define a universal rest frame (Galilean invariance), we can still tell when frames are non-inertial. A spinning frame of reference is non-inertial, and thus there are non-inertial forces that arise, which we have ascribed to being "fictitious," which means that they are not fundamental, but rather a poor choice of reference. If we believe Newton's law to be what governs the universe, then we will always be able to tell a spinning frame. You can even tell how fast your frame is spinning just from local experiments, without needing an external reference frame such as the stars (e.g., the pendulum you mentioned). At either pole you will get a pendulum precession period equal to the rotation period of the planet.

Now the philosophical question about what is fundamental and what isn't, is essentially what I make of Mach's principle. And it's just that, a philosophical question.

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How does a spinning object know it is spinning?

Let's step back. How does an object spin? First imagine a rod, if you stretch (strain) the rod to be longer than its natural rest length then like a spring there is a force (stress) on the parts trying to compress it.

An object spins when it has some velocity in one direction and yet it the orthogonal direction it is too long (strained) so it has a stress in the orthogonal direction. You could imagine a spring with masses on the two ends. At rest it has a particular length.

When it spins it is longer and the two masses have a velocity orthogonal to the spring. It's literally longer and the parts are literally moving with respect to each other.

There is no way at all in which it is any way like the stationary spring. Just because it didn't stretch much doesn't mean it isn't stretched. A spinning object bulges at its equator, that's how it spins.

Now as for how you know. You could look at the parts and notice they are strained by measuring their separations between each other and considering the materials they are made of and how far apart their natural separations are you see that they are too far apart (that's measuring the strain). You can also measure the stress. You could also use the comoving coordinates of the parts as a reference frame and check to see if Newton's laws hold without fictional inertial forces (they won't). You could take something that moves through a vacuum at a steady speed such as light and send it around one way and then send it around another way and see if they get around in the same amount of time (they won't).

A rotating object and a not rotating object are different and there are thousands of ways to tell the difference. It's a bit absurd to even imagine they are similar in any way. Spin a spring and literally watch it get longer. What's confusing about that in the slightest?

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You're ignoring his question and saying "duh", restating the question as an assertion. That doesn't explain anything. Hey, it bothered Newton! – JDługosz Feb 24 at 21:21
@JDługosz What question am I ignoring? If you removed my ears and eyes and spun me, I'd still be able to feel it because I'd be stretched out. You are physically different when you are spinning. I disagreed with the OP that he could tell spin by looking at galaxies. Someone could have painted images on a large spherical shell and be spinning the shell. But you can tell when you spin. You can feel it when you are spinning because you are stressed when you spin. You can feel stress. – Timaeus Feb 24 at 21:28
"How does stuff tell that it's spinning?" "It does!" – JDługosz Feb 24 at 21:33
@JDługosz Did you read anything I wrote? If you had a cloud of dust, it can't have stress and it can't spin. It could orbit, but that's different (and the whole look at the sky wouldn't tell the difference), and the difference is essential. To spin, when the parts go in directions there is a stress. Stresses are literally what you feel. If you don't know how things feel, go learn, then you'll know what I'm talking about. Refuse to learn and you won't know. I can't make you learn. The stresses accelerate the parts, the acceleration of the parts is the spin. Feel the stress to know spin – Timaeus Feb 24 at 21:39
@JDlugosz: When I was a child, we did an experiment in which I was blindfolded, sat in a chair, and spun around. I could tell that I was spinning, not because I was stressed, but because of the semicircular canals in my skull, near the ears. This is a real concern for airplane pilots - the human ear is easily fooled, and that can lead to fatal airplane crashes. In my original question, I assumed that I was the observer, however, in thinking about your comments, I think that a cybernetic observer would be better - less prone to illusion. – user1928764 Feb 25 at 8:13

The basic rule is that space has no "origin", so only relative coordinates are possible. Thus, motion is relative and only meaningful with respect to other objects. Now we also have all directions being equivilent so you have no preferred axes, and orientation is only relative too.

But, starting with that, working out what are essentially Newton's laws of motion, you discover that angular velocity is not relative, as it links up with linear acceleration. That's the same thing: given no absolute position you find you also have no absolute motion (first derivitive) but do have absolute acceleration (second derivative).

Just start with the idea of no absolute position/direction and follow the math: when do absolute quantities pop out, and when do they not?

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I suspect you may have hit the source of the confusion here. Given that, apparently, the laws of physics are intrinsically invariant with respect to position, orientation and velocity (= the time derivative of position), it's somewhat surprising that they're not invariant with respect to angular velocity (= the time derivative of orientation). But of course, an extended object with non-zero angular velocity necessarily (either breaks apart or) experiences non-zero centripetal acceleration, which is also absolute. – Ilmari Karonen Feb 25 at 11:56

The obscure principle of angular energy will settle the matter.

The spinning object has angular momentum, which means that most of its particles have ordinary momentum about the center, which means they possess kinetic energy, and therefore by $E=mc^2$, we know they possess gravitational attraction what we can measure if we are precise enough.

Please note that we must use special relativity here only because we need mass-energy conversion. With pure Newtons mechanics we cannot easily prove mass-energy equivalence (I can get so far as $E=mk$ but it doesn't help because due to the way it is reached the formula no longer implies that $m$ further induces gravitational forces).

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I wouldn't even get so complicated as the other answers and would just consider the Coriolis effect on a pendulum. Or if you are trying to hit something with artillery.

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Trying to hit something with artillery? I'm gonna have to walk my shots. – DevSolar Feb 25 at 17:20

protected by Qmechanic Feb 24 at 20:39

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