Thought Experiment - Centripetal Force

[John_Dee]

Ok, so we know that if one were inside a donut-shaped spaceship that is rotating around it's axis, that the passengers will experience centripetal force. It seems obvious to say that the ship is rotating relative to the nearby stars and planets. So far, so good. But... what if we removed all matter from the universe, observable matter, dark matter, anything that warps spacetime, and left nothing but empty, flat spacetime. My question is, do the passengers still experience centripetal force? What is the ship rotating relative *TO*? How do the passengers know they are rotating if there are no stars whizzing by outside the window?

 

[PeroK]

There's nothing in rigid body dynamics that demands external matter for a body to rotate and experience the internal centripetal forces. A body's rotation may be measured without reference to anything external, so it's not rotating relative to anything, except itself.

 

[John_Dee]

A body's rotation may be measured without reference to anything external

Thanks, that sounds like it's probably right... but how exactly would one make such a reference-less measurement? Let's assume it's spinning at a fixed velocity. (no acceleration) If you're inside the ship rotating with it, then relative to you, it's stationary. I'm having a hard time wrapping my head around the idea that it is "rotating relative to itself"

 

[PeroK]

Thanks, that sounds like it's probably right... but how exactly would one make such a reference-less measurement? Let's assume it's spinning at a fixed velocity. (no acceleration) If you're inside the ship rotating with it, then relative to you, it's stationary. I'm having a hard time wrapping my head around the idea that it is "rotating relative to itself"

If something is rotating, then each particle is accelerating centripetally. That's how rotational motion is different from linear motion. Rotational motion involves measurable centripetal acceleration.

 

[John_Dee]

Ok, so if there is no measurable centripetal acceleration, then the object cannot be said to be "rotating". But in order for each particle to experience centripetal acceleration away from it's natural "straight line" path, mustn't it necessarily have linear velocity? And that linear velocity is where I'm getting "stuck" when I remove external references by which to measure it. Thanks for your patience. I may be trying hard to see something that isn't there, like a cool paradox about rotating bodies and different reference frames.

 

[PeroK]

Ok, so if there is no measurable centripetal acceleration, then the object cannot be said to be "rotating". But in order for each particle to experience centripetal acceleration away from it's natural "straight line" path, mustn't it necessarily have linear velocity?

If you adopt a reference frame in which the object is at rest, then you have no motion in that reference frame, but you still have the forces. Forces don't change by a change of reference frame. That why you can define an "inertial" reference frame: things at rest in an inertial reference frame have no forces on them.

Those forces are not dependent on relating motion to external objects. Those forces are real.

 

[Dale]

how exactly would one make such a reference-less measurement?

With a gyroscope or an inertial measurement unit or a Focault pendulum, or a ring interferometer. Or in a crude sense just with your own inner ear.

If you're inside the ship rotating with it, then relative to you, it's stationary.

It doesn’t matter. All of those methods detect your own proper rotation, regardless of the motion of the ship.

 

[anorlunda]

A very simple DIY way to measure that is to look at the surface of water in a bucket. If the axis of rotation is Z (as in the picture), then the XY surface is not flat.

 

[hutchphd]

If you wanted to be esoteric you could watch spatially separated clocks lose there synchrony.
The buckets may be easier.

 

[John_Dee]

Ok, what I'm getting from the responses seems to be that the answer to my thought experiment is YES, a rotating ship would experience centripetal force, even in an "empty" universe with no visible reference points. This makes me also think that if you rotated the entire universe around a non-rotating ship, that the ship would NOT experience centripetal force.

 

[PeroK]

This makes me also think that if you rotated the entire universe around a non-rotating ship, that the ship would NOT experience centripetal force.

That's not an experiment you can do in any meaningful sense. It's not clear how you would stop the ship rotating with the universe, even if a rotating universe makes sense.

 

[Dale]

Ok, what I'm getting from the responses seems to be that the answer to my thought experiment is YES, a rotating ship would experience centripetal force, even in an "empty" universe with no visible reference points. This makes me also think that if you rotated the entire universe around a non-rotating ship, that the ship would NOT experience centripetal force.

We don't have a lot of experimental data from empty universes. But in 100% of the universes that we have tested, you can determine the rotation of an object without using any visible reference points.

 

[John_Dee]

That's not an experiment you can do in any meaningful sense. It's not clear how you would stop the ship rotating with the universe, even if a rotating universe makes sense.

Perhaps not... but if you want to know my motivation for taking you all on this ride, it's because I got to reading about Mach's Principle, and the origin of inertia. Basically, the idea I got stuck in my head is this:

"What is the origin of inertia?

If the rest of the universe determines the inertial frames, it follows that inertia is not an intrinsic property of matter, but arises as a result of the interaction of matter with the rest of the matter in the universe."

This is what I was trying to "tease out" with my thought experiment.

 

[Dale]

Perhaps not... but if you want to know my motivation for taking you all on this ride, it's because I got to reading about Mach's Principle, and the origin of inertia. Basically, the idea I got stuck in my head is this:

"What is the origin of inertia?

If the rest of the universe determines the inertial frames, it follows that inertia is not an intrinsic property of matter, but arises as a result of the interaction of matter with the rest of the matter in the universe."

This is what I was trying to "tease out" with my thought experiment.

So far it is difficult to get experimental data for or against Mach's principle. But from the data that we do have it appears that the universe is not Machian. It is a nice philosophical idea, but doesn't seem to represent the real world well.

 

[PeroK]

Perhaps not... but if you want to know my motivation for taking you all on this ride, it's because I got to reading about Mach's Principle, and the origin of inertia.

Mach's principle, IMHO, is as much philosophy as physics. In any case, it's difficult to see how you ever settle the argument. You get into some deep waters, without any real prospect of being able to navigate them.

 

[gmax137]

Mach's principle, IMHO, is as much philosophy as physics. In any case, it's difficult to see how you ever settle the argument. You get into some deep waters, without any real prospect of being able to navigate them.

It is really interesting though.

 

[Nugatory]

This makes me also think that if you rotated the entire universe around a non-rotating ship, that the ship would NOT experience centripetal force.

That is indeed the prediction that General Relativity, which is our best current theory of gravity, makes. We cannot test this prediction (no spare otherwise empty universe available) but no one has been able to find a theory that says otherwise and works better than GR to describe the observations that we can make.

 

[John_Dee]

That is indeed the prediction that General Relativity, which is our best current theory of gravity, makes. We cannot test this prediction (no spare otherwise empty universe available) but no one has been able to find a theory that says otherwise and works better than GR to describe the observations that we can make.

Taking the idea of a rotating (non empty) universe further, I find it interesting that the galaxies would experience centrifugal force and tend to fly outward from the axis of rotation, while the non-rotating ship in the center would experience nothing. But like you said, since it's untestable I guess I'll have to just settle for the prediction of GR.

 

[PeroK]

Taking the idea of a rotating (non empty) universe further, I find it interesting that the galaxies would experience centrifugal force and tend to fly outward from the axis of rotation, while the non-rotating ship in the center would experience nothing. But like you said, since it's untestable I guess I'll have to just settle for the prediction of GR.

That's clearly not what anyone is saying. See, for example:

https://physics.stackexchange.com/questions/1048/what-if-the-universe-is-rotating-as-a-whole

 

[PeroK]

And, there was a discussion here recently:

https://www.physicsforums.com/threads/rotation-in-goedel-spacetime.999543/

 

[John_Dee]

And, there was a discussion here recently:

https://www.physicsforums.com/threads/rotation-in-goedel-spacetime.999543/

Thanks... this is going to keep me busy for a while!

 

[PeroK]

Thanks... this is going to keep me busy for a while!

This is an advanced topic: I think you need a graduate level understanding of GR to follow it.

 

[John_Dee]

This is an advanced topic: I think you need a graduate level understanding of GR to follow it.

I am just a few credits shy of a physics masters degree. Perhaps one day I'll finish it.