General Relativity

[Ziggurat]

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?

It's not difficult to understand, it's just wrong. If a surrounding shell of mass is rotating (with respect to a stationary distant inertial observer), then your non-rotating interior object WILL feel forces which pull it apart. And those forces will behave exactly as if the shell wasn't there but the object was rotating.

 

[ynot]

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?

The "stretch" of the Earth is only one observable property that confirms it's spinning. The top is surrounded by the same mass regardless of whether it’s spinning or not but displays different properties when it (really) is spinning. A non-spinning top at the centre of a spinning disc doesn’t display the same properties as a top spinning at the centre of a disc (regardless of whether the disc is spinning or not).

 

[Farsight]

Perpetual Student: don't study the Kerr solution. Your top really is spinning. It's your top spinning, "not spacetime at infinity". You know this because you can change its rate of rotation. If you were changing the rotation of distant spacetime, you would be changing something at a great distance, instantly. That can't happen. Not unless you believe in magic.

You've doubtless learned a valuable lesson on this thread. But please don't think that GR is at fault. It's what crackpots say about it that's at fault.

 

[ynot]

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

I would like to know the answer to that.

 

[Ziggurat]

The "stretch" of the Earth is only one observable property that confirms it's spinning. The top is surrounded by the same mass regardless of whether it’s spinning or not but displays different properties when it (really) is spinning. A non-spinning top at the centre of a spinning disc doesn’t display the same properties as a top spinning at the centre of a disc (regardless of whether the disc is spinning or not).

A non-spinning top at the center of a rotating spherical shell (on a flat spacetime background) will feel the exact same forces as a spinning top not surrounded by anything. It's called frame dragging. The inertial reference frame inside the spherical shell is rotating with respect to the distant inertial reference frame, so not rotating with respect to the distant exterior means you ARE rotating with respect to the local inertial reference frame. And not rotating with respect to the interior inertial reference frame means you are rotating with respect to the distant inertial reference frame.

 

[Perpetual Student]

FYI:

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.

First off, I claim no expertise concerning GR. In fact, if you have followed this thread, you saw earlier that I am making an attempt to study the mathematics of GR, so hopefully I can better understand some of the more mysterious aspects of GR being discussed here. So, my comments come from the perspective of a layman trying to reconcile some seemingly contradictory things claimed about GR. I do not know if "centrifugal forces have some kind of privileged, coordinate-independent reality." But is seems to me that "a coordinate system that's at rest with respect to CMB has some kind of privileged reality."

Now, to my knowledge, if stuff comes flying off my spinning top because of its rotation, it will do so regardless of what frame of reference I use to examine my top. Choosing a frame of reference does not change reality. Does that translate to "centrifugal forces have some kind of privileged, coordinate-independent reality"? If so, I guess that's what I am saying. If you believe otherwise, I would like you to describe some coordinate system that will prevent the stuff from flying off my top.
I have already made my position clear as to why the CMB may give us information about reality. As a layman, it would be absurd for me to disbelieve or challenge GR. Of course, I accept that GR is mankind's best experimentally verified theory of gravity. My intention here is to probe the contention that there can be no preferred frame of reference in the universe because GR is the last and final word on that question.

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.

Is that some disingenuous attempt to expose my layman's status regarding GR? You have no need to do that; I have freely and repeatedly made it amply clear that I have an MS in mathematics (45 years ago) and have recently been trying to get up to speed with tensor calculus so perhaps I can eventually get a better handle on this. In any case, I may never be able to "figure that out."

 

[ynot]

A non-spinning top at the center of a rotating spherical shell (on a flat spacetime background) will feel the exact same forces as a spinning top not surrounded by anything. It's called frame dragging. The inertial reference frame inside the spherical shell is rotating with respect to the distant inertial reference frame, so not rotating with respect to the distant exterior means you ARE rotating with respect to the local inertial reference frame. And not rotating with respect to the interior inertial reference frame means you are rotating with respect to the distant inertial reference frame.

I don’t understand your language but if by “A non-spinning top at the center of a rotating spherical shell” you mean the top is spinning with something else (same speed, direction and axis), then it’s not non-spinning. A top spinning at the centre of a disc will display properties that it’s spinning regardless of whether the disc is spinning or not. That the disc may be spinning at the same speed and direction as the top is irrelevant.

 

[Perpetual Student]

It's not difficult to understand, it's just wrong. If a surrounding shell of mass is rotating (with respect to a stationary distant inertial observer), then your non-rotating interior object WILL feel forces which pull it apart. And those forces will behave exactly as if the shell wasn't there but the object was rotating.

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.

 

[Perpetual Student]

Perpetual Student: don't study the Kerr solution. Your top really is spinning. It's your top spinning, "not spacetime at infinity". You know this because you can change its rate of rotation. If you were changing the rotation of distant spacetime, you would be changing something at a great distance, instantly. That can't happen. Not unless you believe in magic.

You've doubtless learned a valuable lesson on this thread. But please don't think that GR is at fault. It's what crackpots say about it that's at fault.

I really don't understand the source of the dissonance here. I believe many people here are quite knowledgeable (even expert) in this field. Over time, I have gained a great deal of confidence in their knowledge and integrity and so they have gained my respect. They are not crackpots, but I am not a crackpot either.

 

[Farsight]

The source of the dissonance is that some people say "General relativity tells us x" when it doesn't, and when x is pseudoscience garbage. You're no crackpot, you're evidential and logical and rational. So don't allow yourself to be distracted by suggestions that you spend years learning differential calculus or that you spend months on the Kerr solution. Instead stick to your guns, and when you're winning the argument, then when you find yourself being called a crackpot by people who would tell you that the Sun goes round the Earth, we'll look again at your confidence in their knowledge and integrity.

You distinguish reality from observer effect by knowing that you can't change things faster than light can propagate. Accelerate towards a star and the distance to that star hasn't halved in a day. It's similar for tops.

 

[Ziggurat]

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.

No, you still don't get it. There is no such thing as "absolutely rotating". The closest you can get is to claim that you are (or are not) rotating with respect to a specific local inertial reference frame. But there is no such thing as a global inertial reference frame. And different local reference frames can rotate with respect to each other. So if you're rotating with respect to one local inertial reference frame but not with respect to some other local inertial reference frame, are you "absolutely rotating" or not? The term itself introduces contradictions.

 

[BravesFan]

Sometimes I suspect people should start with Colonel Relativity and work up from there

 

[BravesFan]

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?

Are attempting to rationalize universal rotation based on the fact that we don't go flying off of the surface of the earth as it rotates? Universal rotation (a pet project of min when I was a freshman) has been proven to be null. If it is rotating, it's less than a degree over the past 16 billion years or wtvr.

I don't understand how you can think that you have disproven a theory that has been proven via thousands of experiments to be true, by expressing a thought experiment that doesn't actually even pertain to the theory in which you hop to debunk....


Or has the confusing manner in which the claims are stated got me all wonky?

 

[Ziggurat]

I don’t understand your language but if by “A non-spinning top at the center of a rotating spherical shell” you mean the top is spinning with something else (same speed, direction and axis), then it’s not non-spinning. A top spinning at the centre of a disc will display properties that it’s spinning regardless of whether the disc is spinning or not. That the disc may be spinning at the same speed and direction as the top is irrelevant.

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.

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".

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.

 

[Ziggurat]

Sometimes I suspect people should start with Colonel Relativity and work up from there

I saw a kids' cartoon once while channel surfing that had two military characters: a General Specific, and a Private Public. Don't remember the cartoon, though, and it didn't look interesting otherwise.

 

[BravesFan]

No, the top is stationary relative to the shell as well as the reference frame. The shell is spinning. Now once might assert that if they shared a fulcrum, that if you grabbed the shell and stopped it spinning that you could transfer the spin to the top, which would mean it had the potential to spin. But it isn't spinning. No siree bob

 

[Perpetual Student]

Are attempting to rationalize universal rotation based on the fact that we don't go flying off of the surface of the earth as it rotates?

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?

Universal rotation (a pet project of min when I was a freshman) has been proven to be null. If it is rotating, it's less than a degree over the past 16 billion years or wtvr.

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

I don't understand how you can think that you have disproven a theory that has been proven via thousands of experiments to be true, by expressing a thought experiment that doesn't actually even pertain to the theory in which you hop to debunk....


Or has the confusing manner in which the claims are stated got me all wonky?

I am not attempting to disprove anything.

Edited by jhunter1163: 

Edited for Rule 0.

 

[Ziggurat]

No, the top is stationary relative to the shell as well as the reference frame.

There are multiple reference frames, so "the" reference frame doesn't mean anything. You need to specify which reference frame you are referring to.

And in this scenario, the top is NOT stationary relative to the shell. In the reference frame where the shell is stationary, the top and the distant observer are both rotating. In the reference frame where the distant observer is not rotating, the shell is rotating and the top is not. Yet the top still feels centrifugal forces.

The shell is spinning. Now once might assert that if they shared a fulcrum, that if you grabbed the shell and stopped it spinning that you could transfer the spin to the top, which would mean it had the potential to spin. But it isn't spinning. No siree bob

The top and the shell have no physical contact. I never touched the top. Relative to the distant observer, the top never moved. So there is no transfer of spin between anything and the top. Yet it still experiences centrifugal forces. This is not the case with Newtonian physics, it's very much a general relativity effect, so if you're trying to tease out how this can happen from Newtonian mechanics, you won't be able to get it. But it's exactly what GR predicts. And the effect has been observed (though under different conditions) with Gravity Probe B, so this isn't purely theoretical either.

 

[Astrodude]

"Complete nonsense" right back at you! I said nothing about changing coordinates. I said, if I put top in motion, it is actually rotating (it has angular momentum) and the universe is actually not revolving around my top. We can tell because we can trace the chain of causality that resulted in the top's motion.

You misunderstand the "equivalency principle", which implies that the motion of the universe that caused the top's motion is no different than moving your fingers to cause the tops motion. They are equivalent. When you move your fingers in opposing directions to spin the top, you're creating curvature in space time and this curvature results in the motion of the top. If the universe moved to cause the top's rotation, spacetime would curve the same way.

In short, saying the universe rotates around the center of the top in a certain way such that the relative angular momentum of the top increases with respect to the rest of the universe, and saying the top spins about its center ARE IDENTICAL STATEMENTS IN GR BECAUSE THEY BOTH DESCRIBE THE SAME CURVING OF SPACETIME.

You also need to understand that the top is not a rigid body in GR.

 

[BravesFan]

There are multiple reference frames, so "the" reference frame doesn't mean anything. You need to specify which reference frame you are referring to.

And in this scenario, the top is NOT stationary relative to the shell. In the reference frame where the shell is stationary, the top and the distant observer are both rotating. In the reference frame where the distant observer is not rotating, the shell is rotating and the top is not. Yet the top still feels centrifugal forces.



The top and the shell have no physical contact. I never touched the top. Relative to the distant observer, the top never moved. So there is no transfer of spin between anything and the top. Yet it still experiences centrifugal forces. This is not the case with Newtonian physics, it's very much a general relativity effect, so if you're trying to tease out how this can happen from Newtonian mechanics, you won't be able to get it. But it's exactly what GR predicts. And the effect has been observed (though under different conditions) with Gravity Probe B, so this isn't purely theoretical either.

I thought you specified that they were touching.