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]

Originally Posted by 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?

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]

Originally Posted by CurtC

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]

Originally Posted by 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.

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.

Originally Posted by davefoc

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]

Originally Posted by Yllanes

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]

Originally Posted by 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.

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]

Originally Posted by davefoc

...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]

Originally Posted by ceptimus

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]

Originally Posted by davefoc

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]

Originally Posted by 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?

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.

[Yllanes]

As I said before, maybe you are thinking something similar to Mach's principle, which says roughly (and the 'roughly' is the important part):

The inertia of a system is caused by its interaction with the rest of the universe, i.e., every particle in the universe eventually has an effect on every other particle.

According to Mach, if there were a single object in the universe, it would be impossible to determine whether it was rotating.

Einstein was inspired by these ideas when he developed GR, but the theory turned out to be quite anti-Mach. If we have an universe with a rotating bucket of water (Newton's thought experiment) it would feel centrifugal forces, even if it were otherwise completely empty (according to GR).

The real problem with Mach's principle is that it is so vague as to be be meaningless. You could try for a more precise formulation, but until you translate it to mathematical terms it means nothing. And translating it is not an easy problem. For the initiate, one book that discusses this is Gravitation and Inertia, by Ciufolini & Wheeer.

Originally Posted by davefoc

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.

You say, if the universe is otherwise completely empty and we can see no stars, what is the room rotating with respect to? The answer is that it is rotating with respect to the metric of spacetime. If you don't think that the metric is a 'real' concept, like a star, walk into a black hole... They are nothing but pure metric, no matter.

[screw_dog]

Originally Posted by ceptimus

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.

Originally Posted by epepke

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.

I'm sorry, but these two quotes appear to be in direct opposition.

Which is it? Can we tell if the windowless spaceship we are in is spinning?

[Yllanes]

Originally Posted by screw_dog

I'm sorry, but these two quotes appear to be in direct opposition.

He said a non rotating frame in a rotating universe is no different from a rotating frame in a non rotating universe. You can't tell between those two, so it makes no sense to speak of a rotating universe, but you can tell between a non rotating and a rotating frame in a non rotating universe.

Quote:

Which is it? Can we tell if the windowless spaceship we are in is spinning?

Yes.

[Budric]

I have a question about Newton's laws. Someone mentioned that you start getting ficticious forces in a rotating frame of reference. I keep thinking back to an old video in high school where they showed these two guys sitting at a table and pushing an object (ball or something) and it would not go in a straight line. Then the camera zoomed out and you see they're sitting on a platform that's rotating them and the table.

My question is why can I perform experiments at my table and things don't go in weird directions because the earth is rotating around the sun. Is it because the force is very small (large radius)? Or is it just my desk?

[Hellbound]

Budric:

The force is small. You can see this effect with long pendulums (One of the museums here has one, I wanna say the Smithsonian but I could be wrong).

Actually, the effect you see is due to the Earth rotating on it's axis; the effect from it's rotation around the sun would be so small as to be neglible (I think, not sure here).

You see some of this curving effect in weather patterns on the Earth, as well. THe major movements of air masses are, in part, driven by these effects.

The term for this is Coriolis Force. A quick google should bring you all kinds of info on it .

[Yllanes]

Originally Posted by Huntsman

Actually, the effect you see is due to the Earth rotating on it's axis; the effect from it's rotation around the sun would be so small as to be neglible (I think, not sure here).

Yes. The centrifugal acceleration due to the rotation is of the order of 0.01*cos d (in m/s/s, where d is the latitude). The effect of the rotation around the Sun is of the order of 0.0001 m/s/s. (Compare to gravity, ~10 m/s/s). It's an easy excercise to calculate the effect due to the rotation of the Solar System around the Galaxy (take 8 kpc as the radius of the orbit and 220 km/s as the speed).

Originally Posted by Budric

My question is why can I perform experiments at my table and things don't go in weird directions because the earth is rotating around the sun. Is it because the force is very small (large radius)? Or is it just my desk?

To further illustrate the point Huntsman made, notice that the Earth needs a whole day to complete a full rotation, so the effect of the rotation will only be significative in processes that take at least this time. The ball across the table takes a second, a hurricane takes more time. Storms in the Northern (Southern) hemisphere rotate counterclockwise (clockwise) for this reason. The other famous example is Foucault's pendulum, which Huntsman also mentioned. If you have a very big pendulum and let it oscillate, the plane of its motion will slowly rotate (we call this effect 'precession'). This was demonstrated by Foucault 150 years ago and was the first clear proof of the rotation of the Earth.

[epepke]

Originally Posted by screw_dog

I'm sorry, but these two quotes appear to be in direct opposition.

Which is it? Can we tell if the windowless spaceship we are in is spinning?

We are, after all, two different people. You can tell us apart with the naked eye.

Ceptimus, I think, is speaking from a Newtonian + Special Relativity perspective. In that framework, rotation isn't relative, and you can declare (in that framework) that you are spinning.

I am coming from a General Relativity perspective. In that framework, there is no way at all to tell the difference between the forces that you feel from spinning and the forces that you would feel from a gravitational field of the same shape, which would be a configuration of spacetime exactly the same as if space itself (and the associated inertial paths) were spinning around you. So under GR, you can tell that either you are spinning, or the universe is spinning around you, but you cannot tell which. The point is, under GR, it is equally valid to say that spacetime is rotating as it is to say that you are rotating. The mathematics comes out exactly the same no matter which way you do it. So you cannot say that you are absolutely rotating, just that you're rotating relative to spacetime (or it is rotating relative to you).

The point being that under the GR view, more is relative than in SR or Newtonian/Galilean mechanics. In N/G mechanics, velocity in a straight line is relative, and there is no way to build a local experiment that will tell you your velocity, but times and distances are not relative. SR adds optical experiments as well, and shows times and distances to be relative, though acceleration is not relative (with the cost that now the speed of light is now, in some sense, absolute). GR shows acceleration to be relative, in the sense that there is no way to distinguish acceleration from gravitational effects.

[ceptimus]

Objects in the rotating spaceship will tend to move further apart. It's difficult to see how to arrange gravity to do this, unless you allow negative gravity or negative time.
Also the rotating ship will have an axis of rotation, and the apparent forces on the objects in the ship depend on their distance from the axis. This is difficult to mimic with gravity: gravitational forces tend to act in a 3d spherical manner, rather than the more 2d cylindrical distribution that results from rotation.

[epepke]

Originally Posted by ceptimus

Objects in the rotating spaceship will tend to move further apart. It's difficult to see how to arrange gravity to do this, unless you allow negative gravity or negative time.
Also the rotating ship will have an axis of rotation, and the apparent forces on the objects in the ship depend on their distance from the axis. This is difficult to mimic with gravity: gravitational forces tend to act in a 3d spherical manner, rather than the more 2d cylindrical distribution that results from rotation.

I love these discussions, because I learn more and more about the difficulties in understanding this stuff.

See, within GR, there is no way at all to tell the difference between a rotating spaceship and a non-rotating universe and a non-rotating spaceship in a rotating universe.

I want to be very clear about that: no way at all. I think forgetting that is where people get hung up.

So if you put a spaceship, and you set it spinning, after it's spun up, there is no way at all to tell the difference between two. No way at all. If some aliens with infinite amounts of exotic matter or a warp drive or whatever set spacetime spinning around you, there would be no way at all of telling the difference.

Because there's no way at all, you can't even decide that there is a difference to tell in the first place. You could as easily say that when you span up the spaceship, you were really spinning up spacetime. The cases are in all ways equivalent under GR.

It's whether universe really "is" rotating or not rotating; there is no God with the universe in a little room to tell you the "real" answer. The only answers that exist are measurements from your frame of reference. Nothing else even has any meaning.

Now, it may be emotionally troubling or hard to think about, and one might not be able to think about the universe rotating without drinking a lot of beer first, but GR provides no way whatsoever to tell the difference.

[Dark Jaguar]

So the reason that model comes to that conclusion is because the model says a spinning universe would basically drag the stuff in our "non-spinning" space ship off to the sides of the ship, and not cause them to sort of veer clockwise/counterclockwise in relation to the "spin" of the universe? That seems like quite a strong gravitational effect for matter that's so far away it's gravity has no detectible effect on us at all (detectable as in every day experience, which being shoved up against the wall of a spinning spaceship would count as).

I'm fully willing to embrace the idea that centrifugal forces are essentially us being dragged around by the universe spinning around us (or whatever frame of reference you'd like, as they would in fact be identical), but it does seem like they are all a little far away to be having such a strong affect, but only in relation to spinning about. Or, is it more like the "straight paths" are determined by the net result of adding up all those gravitational effects, so the old classical "centrifugal force is caused by everything's straight direction constantly being redirected into a loop" is still in effect, but what is a straight path to take is being determined by the entire universe?

[epepke]

Originally Posted by Dark Jaguar

Or, is it more like the "straight paths" are determined by the net result of adding up all those gravitational effects, so the old classical "centrifugal force is caused by everything's straight direction constantly being redirected into a loop" is still in effect, but what is a straight path to take is being determined by the entire universe?

That's exactly correct, as near as I can tell.

The "straight paths" are called geodesics, and they're determined by the geometry of spacetime itself.

Theres a minor wrinkle, though. Minor conceptually, though it makes the mathematics huge. The geodesics are in spacetime, not just in space. It's important, because you might think that something that isn't moving in your frame of reference isn't going to start moving, just because some lines get bent. But it is moving: it's moving through time. Its odometer might not be changing, but its clock is.

[Dark Jaguar]

Ah, there's an interesting wrinkle! But I think I'll stick with fully wrapping myself around geodesics first. It's just great to finally get a handle on the GR equivilant of centrifugal force.

I'll add it's nice because this way centrifugal forces aren't any "special thing" that has to have it's own solution any more to me. It's now just a natural consequence and just a particular arrangement of things in GR as I had understood it before, but just hadn't properly been applying to that situation.

[Art Vandelay]

Originally Posted by Yllanes

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).

Well, a metric is a function on the entire space, and here we'll talking about a three-dimensional subspace, so that's not exactly an appropriate term. Also, we're not in a different space, we're in a different frame of reference.

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

The term "triangle" is not well-defined.

Originally Posted by davefoc

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?

Of course not. In order for you to tell the difference between different frames of reference, you must exist. And if you exist, then space is not void (it has you in it).

Originally Posted by epepke

I am coming from a General Relativity perspective. In that framework, there is no way at all to tell the difference between the forces that you feel from spinning and the forces that you would feel from a gravitational field of the same shape, which would be a configuration of spacetime exactly the same as if space itself (and the associated inertial paths) were spinning around you.

Wait- are you saying that gravity normally works like a rotating reference frame, or are saying that it's theoretically possible for there to be a configuration of gravity that acts like a rotating reference frame? I don't think you've been quite clear about this.

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GR shows acceleration to be relative, in the sense that there is no way to distinguish acceleration from gravitational effects.

Locally.

Originally Posted by Yllanes

You say, if the universe is otherwise completely empty and we can see no stars, what is the room rotating with respect to? The answer is that it is rotating with respect to the metric of spacetime.

I think that a more direct answer is that it's rotating with respect to itself. If you're in a room, then there isn't just one object in the universe. There's you, the ceiling, the floor, the four walls, etc. All of these are moving with respect to each other.

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If you don't think that the metric is a 'real' concept, like a star, walk into a black hole... They are nothing but pure metric, no matter.

Are you saying that blacks holes are not made up of matter?

Originally Posted by Budric

My question is why can I perform experiments at my table and things don't go in weird directions because the earth is rotating around the sun.

The Earth is not rotating around the sun. The Earth is revolving around the sun, which isn't quite the same thing. If you look at a rotating table, the ball's route is taking up a significant portion of the table, so the rotation of the table is significant. The table doesn't take up a significant portion of the Earth, so the Earth's rotation doesn't cause significant effects. Hurricanes do take up a significant portion of the Earth, so the Earth's rotation affects them, but the Earth's revolution doesn't. To be affected by the Earth's revolution, something would have to be not merely a significant portion of the Earth, but of the Earth's orbit.

Also, the orbit of the Earth involves gravity, which obviously counterbalances the centrifugal force (otherwise, it wouldn't be an orbit). Locally, the Earth's frame is actually inertial (ignoring the Earth's gravity). You only see the effect of the sun in tidal forces.

Originally Posted by Huntsman

The force is small. You can see this effect with long pendulums (One of the museums here has one, I wanna say the Smithsonian but I could be wrong).

Actually, I don't think you'd really see it at all. As I said, the rotation and the sun's gravity cancel each other out.

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Actually, the effect you see is due to the Earth rotating on it's axis; the effect from it's rotation around the sun would be so small as to be neglible (I think, not sure here).

Its.

[epepke]

Originally Posted by Art Vandelay

Wait- are you saying that gravity normally works like a rotating reference frame, or are saying that it's theoretically possible for there to be a configuration of gravity that acts like a rotating reference frame? I don't think you've been quite clear about this.

It doesn't matter, at all, how gravity normally works. GR is based on the equivalence principle. The effects of acceleration (or, as I said, more accurately, resistance to acceleration) are gravity.

And GR has solutions for every possible configuration. That's why the equations are so big and hard to solve.

[Art Vandelay]

Originally Posted by epepke

It doesn't matter, at all, how gravity normally works. GR is based on the equivalence principle. The effects of acceleration (or, as I said, more accurately, resistance to acceleration) are gravity.

No, it's not. Gravity is the curvature of space time. Acceleration is the curvature of a path. The priciple of equivalence says that spacetime is locally indistinguishable from a flat spacetime. Come to think of it, it's a rather vacuous statement. The actual spacetime can be locally approximated by an uncurved spacetime. I.e., it's differentiable.

[epepke]

Originally Posted by Art Vandelay

No, it's not. Gravity is the curvature of space time. Acceleration is the curvature of a path. The priciple of equivalence says that spacetime is locally indistinguishable from a flat spacetime. Come to think of it, it's a rather vacuous statement. The actual spacetime can be locally approximated by an uncurved spacetime. I.e., it's differentiable.

Art, I can only answer questions. I cannot cure your mental disorder, whatever it may be.

[Yllanes]

Originally Posted by Art Vandelay

Well, a metric is a function on the entire space, and here we'll talking about a three-dimensional subspace, so that's not exactly an appropriate term. Also, we're not in a different space, we're in a different frame of reference.

That doesn't make sense. Of course you can talk about the metric of a rotating disk, or a cylinder, or a sphere, why wouldn't you? And you can talk about the spatial part of the metric of spacetime, what do you think we are doing when we talk about cosmology and the different universes (open,closed, flat)?

We can define a metric in a very general class of manifolds. And a manifold is a very general concept. For example, the configuration space (the set of all posible positions of a system of particles) in classical mechanics is a manifold. The space of all velocities at all points is its tangent bundle and the phase space (momenta and positions) its cotangent bundle. You can very well define a metric, through the mass tensor (kinetic energy), as a diffeomorphism between the two.

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The term "triangle" is not well-defined.

Why not? It has three sides, which are straight lines. The straight lines are not the ones you would find on a plane, but that doesn't matter.

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Are you saying that blacks holes are not made up of matter?

In a sense they aren't. Once they are formed, they are a singularity and a metric. They are not matter in the sense stars are. Black holes are pure gravitation, one of the reasons theoretical physicists like them so much. Once you have a star, you need an astrophysicist to tell you the equation of state. With black holes there's only geometry to worry about.

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Actually, I don't think you'd really see it at all. As I said, the rotation and the sun's gravity cancel each other out.

I don't know what you are saying here. Foucault's pendulum is an observable non inertial effect of the rotation of the Earth around its axis. It doesn't take a significant part of the surface, by the way, it just takes time, which, as I said before, is the important thing.

[Hellbound]

Originally Posted by Yllanes

I don't know what you are saying here. Foucault's pendulum is an observable non inertial effect of the rotation of the Earth around its axis. It doesn't take a significant part of the surface, by the way, it just takes time, which, as I said before, is the important thing.

I think he responded before reading farther in my post, where I pointed out that the effect was due to the Earth's rotation, rather than it's orbit around the Sun.

[Yllanes]

Originally Posted by Huntsman

I think he responded before reading farther in my post, where I pointed out that the effect was due to the Earth's rotation, rather than it's orbit around the Sun.

That's what I thought, but he also said: 'Actually, I don't think you'd really see it at all. As I said, the rotation and the sun's gravity cancel each other out'. He made a point of distinguishing between 'revolving' and 'rotating'.

And, anyway, the effect of the orbit around the Sun is minute, but that doesn't mean it is cancelled by gravity.

[davefoc]

Well, I am almost off on a little mini-vacation but I wanted to take a moment to post my incomplete thoughts about all this.

I thought Ceptimus did a good job of expressing the reason that if you just think about Newton's laws of motion then it becomes obvious that you don't need any special property of space to figure out when something is rotating and when it is not.

But then I go back to the notion of the merry-go-round rotating, but rotating relative to what? If the universe was rotating at the same rate as the rotating merry-go-round we would judge the merry-go-round as not rotating. It seems difficult to reconcile the two views.

I think now that the reason for the apparent conflict is that we tend to assume that the notion of a straight line is absolute. An object without any forces acting on it moves in a straight line.

But it is actually the universe that controls our ability to judge what is straight. If the universe rotated differently than however it happens to be rotating now we wouldn't know it because we would judge the path of an object without external forces on it as straight in that other hypothetical universe. But in fact the straight in the hypotheical universe would not be the same as straight in the current universe.

I was hoping to think this out a little better before I posted, but I am about to leave so I decided to post now. I think it is very possible that what I have said above as already been said, and I just didn't quite understand it. I also think that maybe I am just wrong here and still don't quite get it.