General Relativity

[BravesFan]

What? Are you so dysfunctional that you actually believe that I said that? How absurd! Did you try to read my posts after a few martinis?


Are you still a freshman? Do you have any idea what you are saying?


I am not attempting to disprove anything. Yes, you are wonky, but it is caused by the confusion in your mind -- stay off those mushrooms! Why don't you just "hop" to debunk somewhere else!

annnd reported aaaand ignored. enjoy

 

[Ziggurat]

I thought you specified that they were touching.

No, there's no touching.

 

[BravesFan]

LOL, well played sir !!

 

[Perpetual Student]

annnd reported aaaand ignored. enjoy

Good idea!

 

[sol invictus]

I do not doubt that, but I have set my top in motion so that I see stuff flying off. There is no surrounding shell of mass in my experiment. As I understand GR, all frames of reference will confirm that stuff is flying off my top and since there is no surrounding mass, it must be that my top is absolutely rotating. Using a frame of reference where the top is still may have some value, but it will not negate the fact of its rotation.

It's true that if the universe is completely empty except for one top, and if we specify appropriate boundary conditions at infinity (roughly speaking, that infinity isn't rotating), then we can talk about whether or not the top is rotating. Formally, given that setup we can define a conserved angular momentum, and check whether or not it's zero. And when it's zero, it means the top will not be rotating in the natural coordinates that follow from those boundary conditions and the fact that the spacetime is otherwise empty.

But if instead we choose different boundary conditions (for instance, those that correspond to Zig's rigidly rotating sphere with a huge radius), the situation is inverted - a top that is static in the natural coordinates would have a non-zero angular momentum, and would feel centrifugal stresses.

In a more realistic situation - like the world we live in - we don't and cannot know what the boundary conditions are at infinity (or perhaps there is no infinity, because the space is bounded or compact). To make matters worse, the space we live in is not empty apart from the top but instead is curved in different ways at different places. Given that, it makes very little sense to talk about "really" rotating or not.

 

[ynot]

There is no disc in my scenario. There is only the top, and a surrounding spherical shell. Not a disc, a shell.
So here's the setup. We start with the top and the shell in an asymptotically flat space, with neither the top or the shell rotating with respect to each other or with respect to the local inertial reference frame. We place an observer at a distance, also stationary with respect to our top and our shell, far enough away that the gravity of the shell is negligible for that observer. Now we open up the shell, place the top in the center, and close the shell back up again. The top is inside the shell, but not in physical contact with the shell, everything is still stationary after that.

So we have a hollow sphere (shell) with a top somehow suspended at it's epicenter with each positioned so that if the sphere or top spin they do so on the same axis. There is no connection whatsoever between the sphere and top. Is this correct?

Now we start spinning the shell with respect to both the top and the distant observer. We can adopt a reference frame in which the shell is not rotating, but in this reference frame, the shell experiences centrifugal forces. So we conclude that the shell is "really rotating".

Seems to me that the only reference frame in which the sphere might not be rotating is the frame of the sphere. But everything in this frame would experience centrifugal forces.

But what about the top? Relative to the distant observer, the top is not spinning. And we never touched the top, so we didn't change its motion either. But in the reference frame where the top is not spinning, it now experiences centrifugal forces as well. So you tell me: is the top spinning or not? Because by the standard that Perpetual Student tried to establish, the top is spinning.

I don't understand why or how the top would experience centrifugal forces at all. On what basis do you say it would? Surely it would be non-spinning inside the spinning sphere and therefore experience no centrifugal forces.

 

[sol invictus]

I don't understand why or how the top would experience centrifugal forces at all. On what basis do you say it would?

That's what general relativity predicts, and the prediction has been confirmed experimentally (in a slightly different setup, but pretty close).

Surely it would be non-spinning inside the spinning sphere and therefore experience no centrifugal forces.

Nope.

The situation in GR is related to that in electricity and magnetism. If you take a spherical shell of charge, the electric field is zero inside the shell, so a charge inside feels no force so long as it stays inside. But if you spin the shell and let it rotate, a magnetic field develops inside it (as well as outside it). That means that any object with a non-zero magnetic dipole moment or any charge that moves will experience a stress, torque, or net force even when it's inside the shell.

Similarly, in GR mass is a bit like electric charge, and there is zero gravitational field inside a static non-rotating shell (just like in Newtonian gravity). But when you rotate the shell, a "gravitomagnetic" field develops inside it, and that field exerts forces and stresses on objects inside.

 

[Ziggurat]

So we have a hollow sphere (shell) with a top somehow suspended at it's epicenter with each positioned so that if the sphere or top spin they do so on the same axis. There is no connection whatsoever between the sphere and top. Is this correct?

Yes.

Seems to me that the only reference frame in which the sphere might not be rotating is the frame of the sphere. But everything in this frame would experience centrifugal forces.

Yes.

I don't understand why or how the top would experience centrifugal forces at all. On what basis do you say it would?

It's called frame dragging. And it's one of the stranger consequences of general relativity. The gravitational field of a spinning object is not the same as the gravitational field of a non-spinning object.

Surely it would be non-spinning inside the spinning sphere and therefore experience no centrifugal forces.

Making the shell spin would not make the inside top spin. That's not what I'm claiming. But it would still create centrifugal forces on the non-spinning top, because of frame dragging. In order to not experience these centrifugal forces, the top would need to rotate in the same direction as the spherical shell (though at a slower rate than the shell).

 

[Perpetual Student]

Originally Posted by Perpetual Student 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.

Sometimes it feels like I'm having a conversation with a bunch of mystics, which may be my fault. I have tried, but these claims about GR just make no sense. Maybe without understanding the mathematical bases of these effects, it simply can't be explained.
On the other hand, I'd like to keep trying, so could you please elaborate on your response. Perhaps this question about Newton's rotating spheres offers the best avenue. Why does it not work in GR "because there are no inertial frames"? If I rotate something in flat space (out somewhere between distant galaxies), why isn't it "good enough"?

 

[ynot]

It's called frame dragging. And it's one of the stranger consequences of general relativity. The gravitational field of a spinning object is not the same as the gravitational field of a non-spinning object.

If the gravitational field of the sphere (or frame) is having an effect on the top then surely it's "touching" the top and there is a form of connection between the two.

Making the shell spin would not make the inside top spin. That's not what I'm claiming. But it would still create centrifugal forces on the non-spinning top, because of frame dragging. In order to not experience these centrifugal forces, the top would need to rotate in the same direction as the spherical shell (though at a slower rate than the shell).

As Perpetual Student just said, it sounds more mystical than scientific. Or perhaps it''s more a mathematical "reality" than actual reality?

 

[ynot]

In order to not experience these centrifugal forces, the top would need to rotate in the same direction as the spherical shell (though at a slower rate than the shell).

Are you seriously claiming that the rotating top wouldn't experience centrifugal forces, or less centrifugal forces than when it was non-rotating? Or are you saying that the top would experience different centrifugal forces ("normal" rather than "frame drag")?

 

[Perpetual Student]

I think the issue of frame dragging complicates the question, which (simply put) is, "is rotation relative or absolute"?
So, my focus is on Newton's rotating spheres argument. For clarity, let's say the rotating spheres are out in one of the great voids far from any galaxy clusters so that any gravity from the rest of the universe is neutralized, which would be required since the universe has no center and all the mass of the universe should be more or less evenly distributed in all directions. So now, is the rotation absolute or not? Don't we know that it must be absolute because the string is taut? If the string were not taut and somehow the rest of the universe started to revolve around the spheres, it does not seem it could effect the spheres since there is no gravitational influence and hence no communication from the rest of the universe.
How could the mathematics of GR change this? It does not seem possible that rotational motion is not absolute.

 

[ynot]

I think the issue of frame dragging complicates the question, which (simply put) is, "is rotation relative or absolute"?

Is any form of acceleration relative or absolute?

 

[Ziggurat]

If the gravitational field of the sphere (or frame) is having an effect on the top then surely it's "touching" the top and there is a form of connection between the two.

There is an interaction, but only in the same sense that every mass interacts with every other mass through gravity. Does it make sense to say that you're touching the moon right now? Because that's a really strange way to define "touch", and it's certainly not the definition I've been using here.

As Perpetual Student just said, it sounds more mystical than scientific. Or perhaps it''s more a mathematical "reality" than actual reality?

It is neither mystical nor unreal math. It is exactly the physics measured by Gravity Probe B.

Are you seriously claiming that the rotating top wouldn't experience centrifugal forces, or less centrifugal forces than when it was non-rotating? Or are you saying that the top would experience different centrifugal forces ("normal" rather than "frame drag")?

If it rotated at the right speed, then yes, it would experience no centrifugal forces. This is what General Relativity tells us. And as mentioned above, this is exactly the effect that Gravity Probe B measured, but merely outside the spinning object rather than inside. The former is obviously easier to measure from a practical standpoint, but the latter is a little cleaner theoretically since the gravitational contribution that would exist without rotation is zero inside the sphere.

So if you don't believe that this is what happens, well, you're basically saying General Relativity is wrong (and Perpetual Student is claiming he accepts GR). That's conceivable, but one is currently left without any alternative way to explain quite a few experimental results if we abandon GR.

 

[ynot]

There is an interaction, but only in the same sense that every mass interacts with every other mass through gravity. Does it make sense to say that you're touching the moon right now? Because that's a really strange way to define "touch", and it's certainly not the definition I've been using here.

Thing is the sphere interacts with the top and has an effect on it (it's not magical) So I guess it's an induced centrifugal force.

If it rotated at the right speed, then yes, it would experience no centrifugal forces. This is what General Relativity tells us. And as mentioned above, this is exactly the effect that Gravity Probe B measured, but merely outside the spinning object rather than inside. The former is obviously easier to measure from a practical standpoint, but the latter is a little cleaner theoretically since the gravitational contribution that would exist without rotation is zero inside the sphere.

Would that be like not experiencing acceleration in freefall or the Earth not experiencing acceleration as it orbits the Sun?

So if you don't believe that this is what happens, well, you're basically saying General Relativity is wrong (and Perpetual Student is claiming he accepts GR). That's conceivable, but one is currently left without any alternative way to explain quite a few experimental results if we abandon GR.

Don't see why it has to be "If you're not with us you're against us".

 

[Ziggurat]

Thing is the sphere interacts with the top and has an effect on it (it's not magical)

Of course it isn't. This is all strictly vanilla General Relativity.

Would that be like not experiencing acceleration in freefall or the Earth not experiencing acceleration as it orbits the Sun?

Yes. In both cases, the local inertial reference frame doesn't match the distant inertial reference frame, and there is no global inertial reference frame. The only difference between this example and the example you give is that the mismatch isn't simply linear acceleration, but rotation. Your example is easier for people to accept and grasp since it still conforms roughly to Newtonian mechanics expectations, while the latter does not.

 

[sol invictus]

Perhaps this question about Newton's rotating spheres offers the best avenue. Why does it not work in GR "because there are no inertial frames"? If I rotate something in flat space (out somewhere between distant galaxies), why isn't it "good enough"?

Because you can't tell the difference between that thing rotating and a very distant shell of mass rotating (or the equivalent boundary conditions). So you can't decide if something is "really" rotating without information about the spacetime infinitely far away, which is impossible to ever have in practice.

 

[ynot]

If the top was experiencing induced centrifugal forces caused by a distant (or even close) shell of rotating mass why didn't it stand on it's end before it was spun?

How could two tops spinning side by side be doing so by way of a shell of rotating mass?

How could a spinning gyroscope precessing around a point be doing so by way of a shell of rotating mass?

What are the odds that any top would share the exact same axis as a distant shell of rotating mass?

 

[Ziggurat]

If the top was experiencing induced centrifugal forces caused by a distant (or even close) shell of rotating mass why didn't it stand on it's end before it was spun?

You're assuming that it wasn't spinning to begin with. But you don't know that. If it was spinning along with the internal inertial reference frame (which is itself spinning with respect to the external inertial reference frame), then you would see any centrifugal force.

How could two tops spinning side by side be doing so by way of a shell of rotating mass?

You're asking the wrong question. They aren't spinning or not spinning because of the external shell. The external shell merely defines the internal inertial reference frame. Whether or not they tops are spinning relative to the internal inertial reference frame is a separate question, and it's determined by their unique histories. But the inertial reference frame inside the shell is itself rotating with respect to what's outside the shell, so anything inside which rotates with that inertial reference frame won't feel the rotation, and anything which doesn't rotate with it will feel the difference in rotation.

 

[Farsight]

Sometimes it feels like I'm having a conversation with a bunch of mystics, which may be my fault. I have tried, but these claims about GR just make no sense. Maybe without understanding the mathematical bases of these effects, it simply can't be explained.

It isn't your fault, you are having a conversation with a bunch of mystics, and it can be explained. Do not fall for "that's what GR tells you" when it just isn't true. Here's an example:

Because you can't tell the difference between that thing rotating and a very distant shell of mass rotating (or the equivalent boundary conditions). So you can't decide if something is "really" rotating without information about the spacetime infinitely far away, which is impossible to ever have in practice.

You can tell the difference. You put a spoke in a wheel with a stick. And then you see that the spin of the rotating thing can change in an instant, whilst the rotation of a distant shell of mass cannot be altered faster than light can propagate. So you know that it's the thing rotating. At which point the mystics will huff and puff and say "you don't understand the math" or some other nonsense.