Massive Rotating Solids...

[alien_inc]

Hi all,

 

I was just was wondering how relativity would view a system consisting of a massive, large radius, rotating solid. Now I'm ignoring the possibility of gravitational collapse, and I'm unsure if doing so affects this thought experiment.

 

Anyway, as we increase the rotational speed of the object, the matter at the "equator" of the sphere would approach the speed of light much faster then the matter on the interior of the sphere. And as we know, the closer you get to c, the more time dilation you get between the center and surface of the object. Would this cause a "swirl" effect within the structure of the object, due to the dilation of time between the center and surface of the solid? Or does the solid maintain its structural integrityand just appear to swirl due to the warpage of spacetime?

 

 

Thanks for any input on this question.

 

Regards,

Joe

 

 

 

 

[swansont]

For a real material — like the earth — you will get a bulge when it rotates, which is dependent on the gravitation. The result is that the gravitational and kinematic time dilation terms cancel on the surface. There is no effect to worry about over the surface — all clocks run at the same rate.

 

I don't know what you mean by a swirl under the surface, or how you would see it. Are you thinking of frame-dragging?

http://en.wikipedia.org/wiki/Frame-dragging

[alien_inc]

Sorry, I should have been more detailed in my original post.

 

I'm specifically talking about the time dilation between the surface at the equator (having the most angular velocity) and the center of the sphere. So what I'm imagining is you take a cross-section of the sphere, perpendicular to the axis of rotation, through the center to the surface.

 

When approaching c at the surface, the matter at the center is moving considerably slower then matter at the surface, thus producing a time dilation between the surface and center.

 

My question is does the warpage of spacetime at the surface of the sphere;

 

a) actually tare the sphere apart, producing a swirl like pattern when looking at the above mentioned cross-section, or

b) does it just look like that if viewing the object from an external point of view and locally no change is detected, or

c) there is no swirl, no taring, no time dilation between the surface and center.

 

 

Does this clear things up a little?

[swansont]

There is time dilation, but I can't think of a reason why there would be a swirl.

[altergnostic]

The logic for a swirl is that the outer sections of the body would lag behind the inner ones, like a drain, where water closer to the center spins relatively faster than water further away. The first post was clear enough.

 

I would only add two things:

Time dilation due to velocity is frame dependant, meaning, the surface would see the center time dilated due to velocity the same amount as if measurements were done the other way around.

Another problem is that the body is spinning, so the frame is not innertial. Any curve already represents an acceleration, as spin does.

 

I'd say that, if the rotation is applied from the center, you don't need relativity to cause a swirl. From any point, really. Torque, you know.

[swansont]

The logic for a swirl is that the outer sections of the body would lag behind the inner ones, like a drain, where water closer to the center spins relatively faster than water further away. The first post was clear enough.

 

But that doesn't depend on time dilation — that depends on the material, and we're talking about a solid. The rotation speed measured by any observer doesn't care about the time dilation. As you say below, this is from a torque.

 

 

I would only add two things:

Time dilation due to velocity is frame dependant, meaning, the surface would see the center time dilated due to velocity the same amount as if measurements were done the other way around.

Another problem is that the body is spinning, so the frame is not innertial. Any curve already represents an acceleration, as spin does.

 

I'd say that, if the rotation is applied from the center, you don't need relativity to cause a swirl. From any point, really. Torque, you know.

[altergnostic]

But that doesn't depend on time dilation that depends on the material, and we're talking about a solid. The rotation speed measured by any observer doesn't care about the time dilation. As you say below, this is from a torque.

 

 

Yes, precisely. I was trying to translate what I thought was the OP's logic. He is probably considering the dilated time and assuming it will cause distortion.

 

[alien_inc]

Yes, precisely. I was trying to translate what I thought was the OP's logic. He is probably considering the dilated time and assuming it will cause distortion.

 

Yes, thats what I was thinking of... And I see where I was going wrong in my thinking.

 

Thanks for the response, it was very much appreciated.