General Relativity

[W.D.Clinger]

My question is very simple. Is the earth really rotating or is the universe revolving around the earth? Does GR shed any light on that Question?

Yes. You've been objecting to the light.

We know when objects are rotating because there are forces associated with rotation. Put a loosely structured object into rotation and those forces will cause parts to fly off. When we are aware of these forces we can say something is really rotating. Is it really that difficult for you to understand?

Why do you speak of forces causing parts to fly off? Why don't you speak instead of the parts' inertia and of geodesics?

I am well aware of the history of Newton's bucket, Mach's thoughts and Einstein's inspiration and I don't think we need Ziggurat's Gedankenexperiment about frame dragging, when no one seems to be able to answer the question whether the earth is really rotating or is the universe revolving around the earth.

Why do you dismiss frame dragging as irrelevant?

You've been unwilling to consider what GR has to say about rotation. Now you're arguing that centrifugal forces have some kind of privileged reality.

In a certain coordinate system that's nearly at rest with respect to the cosmic microwave background, those centrifugal forces don't even exist. How do you reconcile that fact with your talk above of forces that cause parts to fly off?

 

[Perpetual Student]

You keep referring to bulges at the earth's equator and the stresses that rotating objects feel as though they had some relevance. They don't.

I don't think the statement "the earth is really rotating" means anything until you define it more carefully.

As I said above, we know when objects are rotating because there are forces associated with rotation. Put a loosely structured object into rotation and those forces will cause parts to fly off. When we are aware of these forces we can say something is really rotating. Even if it were the only thing in the universe, the parts would fly off telling us it is rotating. In contrast, if an object is not put into rotation (in a friction free situation), but an enclosure around it is set in rotation, those forces would not be felt by the object and parts will not fly off. Is it really that difficult to understand?

 

[Perpetual Student]

Well, my question was asking you which frame you consider to best describe what is "really happening". I know that all frames are equally valid in GR, but you have been saying that there must be a "preferred" one that somehow describes reality better than the others.

It is my understanding that under GR, all frames will do the job, but some may be more convenient than others. None tell us what is really happening.

Do you consider that a frame where the CMB is stationary is a naturally occurring preferred frame of reference for describing the motion of the top?

The CMB appears to be the best frame for understanding the real nature of the universe -- until a better one is revealed. The total motion of the top, moving along in some complex path with respect to the CMB tells the whole story. It will take into account its spinning on the table as well as all the other motions associated with the earth, solar system, galaxy, etc. The top is really spinning in all frames but the ones where we choose to look at it as stationary, which, I contend, may be convenient for some purpose, but is not a true representation of reality.

 

[edd]

The top is really spinning in all frames but the ones where we choose to look at it as stationary, which, I contend, may be convenient for some purpose, but is not a true representation of reality.

I'm not sure I understand your argument. How can it not be a true representation of reality when it represents the same reality with exactly the same observable results as the representation you think is true?

 

[Perpetual Student]

I'm not sure I understand your argument. How can it not be a true representation of reality when it represents the same reality with exactly the same observable results as the representation you think is true?

Isn't it obvious? Because the top is really rotating. We could detect that rotation with instruments on the top. Any frame where the top is stationary does not reveal that rotation. It may be a better frame for studying the molecular structure of the top, but it is quite poor for determining what is moving: the top or the universe?

 

[edd]

Isn't it obvious? Because the top is really rotating. We could detect that rotation with instruments on the top. Any frame where the top is stationary does not reveal that rotation.

But they do - the physics of the other frames make the same predictions for what the instruments on the top read.

 

[Perpetual Student]

But they do - the physics of the other frames make the same predictions for what the instruments on the top read.

Then you agree that we can say that the top is really rotating and we can say that the universe is not revolving around the top. We can say that is really what is happening! That is what I have been contending all along. Others have been saying that there is no distinction under GR between the top rotating and the universe revolving -- both perspectives are equally valid, even though we would need convoluted fictitious forces to have the universe revolving.

 

[edd]

Then you agree that we can say that the top is really rotating and we can say that the universe is not revolving around the top. We can say that is really what is happening! That is simply what I have been contending all along. Others have been saying that there is no distinction under GR between the top rotation and the universe revolving -- both perspectives are equally valid.

Maybe I should rephrase my earlier post. I'd have to give a bit more thought to how to better say it, but it's more likely one of the others here will clarify again.

 

[sol invictus]

As I said above, we know when objects are rotating because there are forces associated with rotation. Put a loosely structured object into rotation and those forces will cause parts to fly off. When we are aware of these forces we can say something is really rotating. Even if it were the only thing in the universe, the parts would fly off telling us it is rotating.

So if an object is surrounded by some masses that tend to cause it to stretch or fly apart, would you say it is therefore rotating?

In contrast, if an object is not put into rotation (in a friction free situation), but an enclosure around it is set in rotation, those forces would not be felt by the object and parts will not fly off. Is it really that difficult to understand?

It is hard to understand, mainly because it's false.

 

[Perpetual Student]

Yes. You've been objecting to the light.


Why do you speak of forces causing parts to fly off? Why don't you speak instead of the parts' inertia and of geodesics?


Why do you dismiss frame dragging as irrelevant?

You've been unwilling to consider what GR has to say about rotation. Now you're arguing that centrifugal forces have some kind of privileged reality.

In a certain coordinate system that's nearly at rest with respect to the cosmic microwave background, those centrifugal forces don't even exist. How do you reconcile that fact with your talk above of forces that cause parts to fly off?

I do not understand your point. Why can't we go with the simple question about the earth's rotation, which is evidenced by its equatorial bulge or a spinning top where instruments can reveal the forces associated with its rotation? These phenomena reveal true unambiguous rotation. If the universe consisted of only one single object, rotation could be detected by these forces. That is the point of Newton's "rotating spheres."

 

[sol invictus]

But they do - the physics of the other frames make the same predictions for what the instruments on the top read.

Then you agree that we can say that the top is really rotating and we can say that the universe is not revolving around the top. We can say that is really what is happening! That is what I have been contending all along.

How does edd's comment agree with that? Of course all the instruments read the same - that's the whole point. What an instrument on the top reads cannot depend on which set of coordinates you, Perpetual Student, choose to use to describe the whole situation with, any more than what they read depends on which language you use to explain the experiment to your friend.

 

[edd]

How does edd's comment agree with that? Of course all the instruments read the same - that's the whole point. What an instrument on the top reads cannot depend on which set of coordinates you, Perpetual Student, choose to use to describe the whole situation with, any more than what they read depends on which language you use to explain the experiment to your friend.

In fairness when I said "But they do" it would be understandable to think that I agreed with it. But as I said, I think I should rephrase that particular post - I'm in agreement with you, sol.

 

[Perpetual Student]

So if an object is surrounded by some masses that tend to cause it to stretch or fly apart, would you say it is therefore rotating?

No.

It is hard to understand, mainly because it's false.

What is false? The rotation of the enclosure will cause the non-spinning object to disintegrate?

 

[Perpetual Student]

In fairness when I said "But they do" it would be understandable to think that I agreed with it. But as I said, I think I should rephrase that particular post - I'm in agreement with you, sol.

Yes, by all means do not disagree with sol, otherwise you may fly apart like my spinning top.

 

[Perpetual Student]

OK, so what about Newton's "rotating spheres"? Is it a demonstration that rotation is not relative?

 

[sol invictus]

No.

Why not? It fits your definition of rotation.

What is false? The rotation of the enclosure will cause the non-spinning object to disintegrate?

Yes, potentially. The spacetime inside a rotating shell isn't flat, so there are stresses on objects inside one.

 

[sol invictus]

OK, so what about Newton's "rotating spheres"? Is it a demonstration that rotation is not relative?

Rotation isn't relative in Newtonian physics because there are a special class of coordinate systems - inertial frames - in which there are no "fictitious forces". One can then define rotation relative to those frames. Because the transformations between inertial frames don't involve rotation, all inertial frames agree on the degree of rotation (by contrast, velocity and position are relative).

That doesn't work in GR, because there are no inertial frames.

One can still define rotation (or really, angular momentum) of isolated objects in asymptotically flat spacetimes. But that's not going to be good enough for you.

 

[Perpetual Student]

Why not? It fits your definition of rotation.

Because you told me there is a gravitational force from some masses causing the disintegration of my top. In contrast, I set my top in motion where there are no such masses.

Yes, potentially. The spacetime inside a rotating shell isn't flat, so there are stresses on objects inside one.

So, if I have an object of some considerable mass (a 10 ton lead ball) at the center of a kilometer wide thin sphere of very thin low mass material like paper in otherwise empty space, there is no detectable difference between setting the central object in rotation and setting the paper sphere in rotation? I don't believe that. Prove it!

 

[W.D.Clinger]

Yes, by all means do not disagree with sol, otherwise you may fly apart like my spinning top.

FYI: I disagreed with sol invictus earlier this morning. Neither of us flew apart.

You've been unwilling to consider what GR has to say about rotation. Now you're arguing that centrifugal forces have some kind of privileged reality.

In a certain coordinate system that's nearly at rest with respect to the cosmic microwave background, those centrifugal forces don't even exist. How do you reconcile that fact with your talk above of forces that cause parts to fly off?

I do not understand your point.

My point was that you have contradicted yourself by saying both of these two things:

• Centrifugal forces have some kind of privileged, coordinate-independent reality.
• A coordinate system that's at rest with respect to CMB has some kind of privileged reality.

The proof of that contradiction is simple: In a CMB rest frame, the centrifugal forces don't exist (or are very small). The parts you described as flying off the rotating earth are just following their usual world lines. To recover centrifugal forces, you have to transform to a coordinate system that is not at rest with respect to the CMB. The parts will follow the same world lines with either coordinate system, but the more geocentric coordinate system will allow you to ascribe those world lines to centrifugal force.

Why can't we go with the simple question about the earth's rotation, which is evidenced by its equatorial bulge or a spinning top where instruments can reveal the forces associated with its rotation? These phenomena reveal true unambiguous rotation.

Really? It sounds to me as though you might need to think about what I wrote above.

If the universe consisted of only one single object, rotation could be detected by these forces. That is the point of Newton's "rotating spheres."

I don't think so. There are several people here (such as sol invictus) who understand GR a lot better than I do, so I'd prefer to let them take the lead in this discussion, but I'll drop a couple of hints.

There are many solutions to Einstein's field equations surrounding an isolated mass. The Schwarzschild solution is obtained by assuming a certain boundary condition. Part of that boundary condition says the isolated mass is not rotating with respect to spacetime at infinity.

The Kerr solution allows for rotation. Please study the Kerr solution, and ask yourself: Is the isolated mass rotating with respect to spacetime at infinity, or is spacetime at infinity rotating with respect to the isolated mass?

When you've figured that out, please let me know. I'd be very interested in the mathematical basis for your answer.

 

[Hellbound]

This may help a bit (and any errors made in this post are my own; I am not an expert, just a well-read layman).

If I'm setting at the precise axis of rotation of the Earth, and I spin my top at exactly 1 revolution every 24 hours in a direction opposite that of the Earth's rotation (assume a large enough top that it's stable at this rotaional speed)...does my top experience any force?

This, I think, drives home the point others are attempting to make. If the Earth is rotationg because of it's spin, then my top isn't...so it shouldn't experience any force. Yet it does. So then, my top is not experiencing rotational forces while nominal at rest. Or, you can say the Earth is at rest, but then why does it bulge at the equator?

A simple statement such as "but it's really rotating" immediately leads to situations where this type of contradiction arises.

What would be a centrifugal force in once set of coordinates dissappears in another, or becomes some other type of force. Einstein himself, in his book "Relativity", used the example of a spinning disc to elucidate some of the concepts (basically pointing out the inability to distinguish between certain types of forces and gravity fields and such...I can't recall the details currently, but I do recall the analogy...I'll have to look it up later and post details).

Just like unaccelerated motion, accelerated motion can only be defined by a reference frame. Rotating relative to something.