what's the deal with rotating frames of reference

[davefoc]

It seems that it is possible to tell the difference between a rotating frame of reference and a non-rotating frame of reference even if those frames of reference are in an area of space where no stars are visible for reference.

Objects fixed in the rotating frame of reference will experience centripetal force. Objects fixed in the non-rotating frame of reference won't experience centripetal force.

What's going on here? I understand this problem is addressed in general relativity but can the answer be boiled down so that even I could understand it? If space is a completely empty void then would it be possible to tell the difference between a rotating and a non-rotating frame of reference? What in the void would there be to interact with the matter within it to let the matter sense whether it is rotating or not?

I understand that I might be wildly confused here, but I am curious enough about what is going on to allow my ignorance to become more widely known. So please feel free to allude to my lack of insight or to mention it directly.

 

[Yllanes]

Forget relativity for the moment. Newton's laws only work in inertial (non-accelerating) reference frames. Whenever you are in a non-inertial frame, pseudoforces appear (centrifugal force, Coriolis force, azimutal force, drag force). This means that in that frame F =/= m a, you have to add all these terms.

Now consider this. Imagine a group of people on a mery-go-round and take into account special relativity. The platform its measured, first at rest. We get, not surprisingly, 2*pi*r = l. Now it starts rotating at relavistic speed. A man in the centre measures it again. The value for its radius is the same as before, because the velocity is perpendicular to the radius, so there is no measured contraction. However, the circunference is tangential to velocity, so it is contracted. This means that, for this rotating platform, 2*pi*r =/= l. You could say that there is another metric at work, we are no longer in Euclidean space, but in a hyperbolic geometry (notice that we haven't talked about a graviation, just acceleration in special relativity). Incidentally, we know that the centripetal acceleration on the disk is not gravity, because it doesn't go to zero at infinity. Exercise: Would the angles of a triangle sum more or less than 180º on this platform?

 

[CurtC]

I think davefoc's question has to do with what is "space"? Most of us have an intuitive idea that it's just how objects are arranged with respect to each other, but he's asking, if there are no other objects in our thought experiment, what then does space describe? It has to be more than that, because obviously enough you can still tell the difference between rotating and non-rotating frames.

I guess the answer is that space is more than the description of where stuff is. The laws of physics depend on space, independently of other bodies in the universe. Truly understanding this might require mind-altering substances.

 

[Ririon]

One of these days I will get a good relativity book, a comfortable and undisturbed place to read and some tea and shortbread.

 

[davefoc]

Forget relativity for the moment. Newton's laws only work in inertial (non-accelerating) reference frames. Whenever you are in a non-inertial frame, pseudoforces appear (centrifugal force, Coriolis force, azimutal force, drag force). This means that in that frame F =/= m a, you have to add all these terms.

Now consider this. Imagine a group of people on a mery-go-round and take into account special relativity. The platform its measured, first at rest. We get, not surprisingly, 2*pi*r = l. Now it starts rotating at relavistic speed. A man in the centre measures it again. The value for its radius is the same as before, because the velocity is perpendicular to the radius, so there is no measured contraction. However, the circunference is tangential to velocity, so it is contracted. This means that, for this rotating platform, 2*pi*r =/= l. You could say that there is another metric at work, we are no longer in Euclidean space, but in a hyperbolic geometry (notice that we haven't talked about a graviation, just acceleration in special relativity). Incidentally, we know that the centripetal acceleration on the disk is not gravity, because it doesn't go to zero at infinity. Exercise: Would the angles of a triangle sum more or less than 180º on this platform?

Ylanes, thank you for your answer. I am not sure I understood it well enough to know whether you have addressed the basic idea of my question. If the merry go round is floating in space completely devoid of all references and completely devoid of all external gravitational effects people on the merry go round can still tell if its spinning or not. It seems that there is something in the void they are floating in that interacts with the matter of the riders and the matter of the merry go round such that it is possible to tell the difference between spinning and not spinning. If this were not so they might just be able to change their frame of reference to one that is spinning at the same rate they are and then they would think they are not spinning.

 

[kuroyume0161]

I guess the answer is that space is more than the description of where stuff is. The laws of physics depend on space, independently of other bodies in the universe. Truly understanding this might require mind-altering substances.

But don't cause confusion that 'space independent of other bodies in the universe' is an absolute frame of reference.

 

[davefoc]

I think davefoc's question has to do with what is "space"? Most of us have an intuitive idea that it's just how objects are arranged with respect to each other, but he's asking, if there are no other objects in our thought experiment, what then does space describe? It has to be more than that, because obviously enough you can still tell the difference between rotating and non-rotating frames.

I guess the answer is that space is more than the description of where stuff is. The laws of physics depend on space, independently of other bodies in the universe. Truly understanding this might require mind-altering substances.

CurtC, thanks for the answer. You seem to be suggesting that this is just an unresolved issue in physics. It is interesting that so much is understood, but this seemingly simple issue isn't.

I would not have independently recognized it as an issue. For me there was spinning and not spinning and I never thought about how the issue forces a non-rotating frame of reference on the problem before one can make calculations that predict the orbits of planets and the forces on the merry go round riders. I have been reading through an elementary book on relativity and they mentioned the issue without providing an explanation that I understood.

One obvious possibility that you allueded to is that a vacuum is not really devoid of some kind of structure. Would it be wrong to think of this as some sort of aether? You may remember that I mentioned that I thought that there must be some kind of aether because of the fact that a light beam travels at the same speed with respect to another light beam traveling in the same direction. That is a light beam neither gains nor loses distance with respect to another light beam traveling in the same direction. This suggests to me that an aether does exist even if it is not the simple aether originally envisioned that didn't explain time and distance contraction from observers in different inertial frames of reference.

It seems that modern physics instruction is pretty much devoted to shooting down the idea of an aether which tends to make me think that I have entered kook land with my thinking on this.

 

[Yllanes]

What I meant is that rotating frames are easy to identify, because Newton's second law is not satisfied in them. Things accelerate that shouldn't, etc.

If this were not so they might just be able to change their frame of reference to one that is spinning at the same rate they are and then they would think they are not spinning.

Again, I'm not sure what you mean. If you are in a rapidly rotating room, even if there is nothing at all outside, you will stick to the walls. For you the room is not rotating.

 

[roger]

Dave, it has nothing to do with any property of space. It's Newton's laws. An object in motion stays in motion, and an object at rest stays at rest. Recall the (non-relativistic) equation F=MA. This tells us that if there is acceleration, you will feel force,and if you apply force, there will be an acceleration.

So, adding all that up. Take a stick, and rotate it around it's center, like a helicopter blade. Without reference to any other object in the universe, you see that the tip is continuously changing position and direction of motion with relation to the stick's center point. Hence, the tip is undergoing acceleration. If you were sitting on that tip, you would feel that acceleration as a force (due to F=MA).

Now, if it was a big stick floating in empty space you would not be able to tell what that force was coming from. You wouldn't perceive the stick as rotating, but you would feel the force. Move around on the stick and you could probably surmise what was happening and where the rotation point was because the forces would change as you move closer to and away from the center of rotation.

 

[Ziggurat]

Another way to think about it is to start with a SINGLE reference frame (which we index with some x,y,z,t coordinates), and assume Newton's laws hold in that frame (that is, force causes acceleration, no acceleration means no force), but without prior knowledge of what happens in any other reference frames. We can do experiments in this reference frame, we can throw balls around, play with masses on springs, etc. and confirm that Newton's laws hold in this single frame. Now the question becomes: what happens if we CHANGE reference frames? In other words, instead of (x,y,z,t), what happens if we use some other coordinates (x',y',z',t')?

Well, all you really need to do is plug in the transformations for (x,y,z,t) -> (x',y',z',t') into your equations of motion (Newton's laws), and you can find out what the equations of motion in your new reference frame look like. And it turns out that if Newton's laws hold in ONE reference frame, they will also hold in any other frame which differs from the first by some constant rate of translation (that is, a moving, non-accelerating frame). This is classical Galilean relativity. But there are SOME coordinate transformations under which your equations of motion DO change. Those include frames which are rotating and frames which are accelerating. But we can get the equations of motion for the new reference frame to LOOK like the original equations of motion by separating it into a component which is the same as before (acceleration = force/mass) plus whatever is different for this new frame (the so-called fictitious forces, such as centrifugal and corriolis forces).

You can do the same process with special relativity with a few adjustments. Classically, Newton's second law is often written as F = m d^2x/dt^2 (acceleration as the second derivative of position with respect to time). In SR, this is replaced with F = dp/dt (where p is the momentum) - this substitution makes no difference classically (where p = m dx/dt), but it does matter in relativity (since p is a little more complicated). But given that substitution, you can establish that only a certain class of coordinate transformations (Lorentzian boosts) will leave your equations of motion the same, and other transformations (such as rotations, or galilean boosts) will not.

 

[jj]

Exercise: Would the angles of a triangle sum more or less than 180º on this platform?

Top or bottom?

 

[Alkatran]

I'd like to point out another reason you can tell rotation from linear movement: it takes at least 2 particles to get rotation. It only takes 1 particle to move in a straight line.

If there was only one particle in the universe there would be no way to measure anything. With 2 particles you can measure things like relative distance, speed and acceleration. Being able to measure relative acceleration, along with a bit of knowledge of how things move around, is all you need to figure out if rotation is happening.

 

[epepke]

It seems that it is possible to tell the difference between a rotating frame of reference and a non-rotating frame of reference even if those frames of reference are in an area of space where no stars are visible for reference.

Objects fixed in the rotating frame of reference will experience centripetal force. Objects fixed in the non-rotating frame of reference won't experience centripetal force.

What's going on here? I understand this problem is addressed in general relativity but can the answer be boiled down so that even I could understand it? If space is a completely empty void then would it be possible to tell the difference between a rotating and a non-rotating frame of reference? What in the void would there be to interact with the matter within it to let the matter sense whether it is rotating or not?

I understand that I might be wildly confused here, but I am curious enough about what is going on to allow my ignorance to become more widely known. So please feel free to allude to my lack of insight or to mention it directly.

It sounds as if your understanding is pretty good.

Note that this thought experiment is pretty old. Einstein himself thought about it and even vacillated. So you're in good company.

However, I think it has been resolved.

In Special Relativity, there's no problem. SR only applies to inertial frames. A rotating reference frame is undergoing acceleration. Rotation is not relative under SR. So there you have it.

In General Relativity, it's a bit trickier. The forces that you feel in a rotating frame (or, more precisely, inertial resistance to those forces), are not only like gravity, they are gravity. If you declare the universe as non-rotating and the frame rotating, then it reduces to the SR case. If you declare the frame non-rotating and the universe rotating, then the rotation of the universe creates a gravitational field.

This is, I think, why people are talking about space and spacetime here. This can be hard to think about, because space doesn't seem like it has stuff in it, if there's nothing else in the universe. There are no little wires or dots that you would be able to see, so there's no stuff that it's easy to see that would cause this. (If you get into quantum behavior, there's reason to believe that there's a lot of stuff in the vacuum, but let's not go there.)

However, spacetime does have some properties. There's a relationship between space and time given by c. There are also things called geodesics, which are inertial paths and correspond to what in flat spacetime (SR) would be called straight lines. Light travels along geodesics, too, and they're called null geodesics.

Now, why spacetime works like this, nobody knows, at least from a classical view. (QED, as I've mentioned, explains the geodesics rather nicely, but let's not go there.) What is important is that the mathematics of a rotating frame in a non-rotating universe, and the mathematics of a non-rotating frame in a rotating universe are exactly the same, and so there is no way at all to distinguish between them.

At this point, if you still have emotional difficulties, you might want to go into the relativistic quantum field theories, such as QED, in which there is stuff everywhere, and you can't have an otherwise empty universe. Even if there is just a single electron in the universe, it has amplitudes everywhere.

 

[Yllanes]

Davefoc, my connection broke when I was editing a previous post. I wanted to add that maybe I took your question at a more basic level than it was intended. Google for "Mach's Principle", maybe this is what you meant (the Wikipedia article on this is not very complete, and I don't have time right now to explain it in detail myself).

 

[davefoc]

I have just read through several of the posts. I don't have time to understand them all right now, but my initial reaction is that only epepke has really understood what I am talking about (that is not to say that I understand exactly what epepke is talking about yet).

Let me say this.
There are two ways we know that something is rotating.
1. We assume some non-rotating frame of reference and notice that the object is moving with respect to the non-rotating frame of reference we assumed.
2. The forces and motions that we calculate and or sense for the object are consistent with Newton's laws of motion in the particular non-rotating frame we assumed.

For instance consider the earth rotating around the sun. How do we know that the earth is rotating around the sun rather than they are both fixed in some frame of reference?

The answer seems pretty obvious. We look at the background stars and make a pretty good guess as to how a non-rotating frame of reference is oriented and we notice the earth is moving a lot and the sun is moving a little bit too in that frame of reference.

Ahah we say, our guess as to what the non-rotating frame of reference must be pretty good because when we make calculations on the earth and sun's motions based on Newton's equations we come up with a pretty good description of how the sun and the earth are actually moving through the non-rotating reference frame we assumed. Further we might even refine our idea of exactly how the non-rotating reference frame is oriented by working backward from the motions of the earth and sun that are observed.

But the thing that is not obvious is that we have had to assume that there is such a thing as a non-rotating frames of reference in the vacuum of space to make all this work out. And that seems to suggest (to me at least) that there is something going on with respect to the interaction between mass and a vacuum that has some directional properties that allows us to detect whether we are rotating or not.

 

[ceptimus]

...we have had to assume that there is such a thing as a non-rotating frames of reference in the vacuum of space to make all this work out.

I don't think so. If we are able to observe centripetal forces at work, then we know a system is rotating. If we don't observe any such forces then we know it isn't. You could be placed inside a spaceship, with no windows and no means of observing anything outside, and with a few simple experiments you'd be able to tell if the spaceship was rotating or not.

 

[davefoc]

I don't think so. If we are able to observe centripetal forces at work, then we know a system is rotating. If we don't observe any such forces then we know it isn't. You could be placed inside a spaceship, with no windows and no means of observing anything outside, and with a few simple experiments you'd be able to tell if the spaceship was rotating or not.

You would use one of the two ways of detecting rotation that I mentioned previously. You would detect the forces causes by rotation and deduce that you are rotating. You could also establish you rate of rotation with respect to a hypothetical non-rotating frame. So far I am with you I think. And if you looked outside your spaceship you'd probably feel like you did a pretty good job of deciding what the non-rotating frame was because you'd observe the stars and see that your hypothetical non-rotating frame wasn't rotating with respect to them.

OK, but my question goes to why there should be a special non-rotating frame at all if the space you are floating in consists of a complete nothingness that is incapable of interacting at all with your ship.

 

[ceptimus]

Imagine you are in the spaceship in zero-G and objects are just hanging motionless (with respect to the ship and each other). We would normally conclude this was a non-rotating system. But if you say that there is nothing outside the ship for it to rotate 'with respect to' and therefore you might just as well consider that it is rotating, then you would have to come up with a whole new physics to explain why objects with no forces acting on them move in circles.

I think the apparent paradox of 'what is the system rotating with respect to?' is just a trick of our way of thinking. Objects don't care whether they're in a rotating frame of reference or not - they just obey their nature and move in straight lines unless a force causes them to deviate. The 'frame of reference' thing is just an analytical concept that exists in the minds of humans. It has no basis in reality.

 

[Ziggurat]

OK, but my question goes to why there should be a special non-rotating frame at all if the space you are floating in consists of a complete nothingness that is incapable of interacting at all with your ship.

To a certain extent, I'm not sure a satisfactory answer exists. Take things to an elementary enough level, and I don't think you can answer the "why should they" questions, but only the "do they" questions.

 

[epepke]

I have just read through several of the posts. I don't have time to understand them all right now, but my initial reaction is that only epepke has really understood what I am talking about (that is not to say that I understand exactly what epepke is talking about yet).

Let me say this.
There are two ways we know that something is rotating.
1. We assume some non-rotating frame of reference and notice that the object is moving with respect to the non-rotating frame of reference we assumed.
2. The forces and motions that we calculate and or sense for the object are consistent with Newton's laws of motion in the particular non-rotating frame we assumed.

For instance consider the earth rotating around the sun. How do we know that the earth is rotating around the sun rather than they are both fixed in some frame of reference?

Stick to the carousel in space, or a rotating space station. That's clearer. Something rotating, but held together with wires and girders and stuff so that its bits don't fly off into space.

The situation of a planet revolving around the sun or even rotating about its axis is a bit hairier, because you have to deal with gravity as keeping the system together as well as the gravitational effects of rotation. This gets tricky and confusing almost instantly.

Much better to have the thing kept together with wires. Assume the mass of the carousel or space station is small enough that the gravitational effects of that mass is negligible, so we can concentrate on the gravitational effects of the rotation.