Describing General Relativity Thought Experiments

[romesh]

I have aquestion regarding the topic.

 

We say that the earth rotates on its axis which causes a bulge in its shape.

 

Conversely we can say that the gravitational effects of the motion of whole of the universe causes the bulge. But will not the distant stars of the universe cross the restricted speed of light c in the process?

 

How can we explain this phenomenon?

 

 

[mathematic]

I have aquestion regarding the topic.

 

We say that the earth rotates on its axis which causes a bulge in its shape.

 

Conversely we can say that the gravitational effects of the motion of whole of the universe causes the bulge. But will not the distant stars of the universe cross the restricted speed of light c in the process?

 

How can we explain this phenomenon?

 

 

Could you elaborate on your question (Conversely ...)?

[IM Egdall]

I believe romesh is referring to frame dragging in general relativity. We can think about the bulge of the Earth from two points of view:

 

1) Reference frame above Earth. Here the Earth is seen to rotate, and this rotation results in the bulge at its center.

 

2) Reference frame on Earth. Here the Earth is stationary and the rest of the universe is rotating. So from this point of view, the Earth's bulge is caused by the rotation of the rest of the universe.

 

 

I think this is romesh's question: As we consider stars farther and farther away from the Earth, from the Earth reference frame they are rotating faster and faster. A star far enough away appears to be rotating faster than the speed of light.

 

But there is no information here which is traveling at the speed of light, so it does not violate special relativity.

 

Did I get this right?

Edited August 25, 2012 by IM Egdall

[romesh]

You got my question right IM Egdall.

 

But Einstein's special relativity restricts speed of any object by speed of light.

 

The stars which are far enough from the earth would certainly revolve around the earth at or greater than c if we take earth as the frame of reference.

 

Let me explain my question further.

 

If there is a star, 2 light years away from the earth, then it has to complete the revolution,of 2*3.14*2 light years, around the earth in 24 hrs.

 

This star would definately cross the restricted speed of c.

 

How can this phenomenon be explained?

[IM Egdall]

You got my question right IM Egdall.

 

But Einstein's special relativity restricts speed of any object by speed of light.

 

The stars which are far enough from the earth would certainly revolve around the earth at or greater than c if we take earth as the frame of reference.

 

Let me explain my question further.

 

If there is a star, 2 light years away from the earth, then it has to complete the revolution,of 2*3.14*2 light years, around the earth in 24 hrs.

 

This star would definately cross the restricted speed of c.

 

How can this phenomenon be explained?

 

One thing comes to mind: Special relativity applies to objects in uniform motion, that is objects which travel at a constant speed and in a constant direction. A star as seen in the Earth frame of reference is rotating around the Earth. Its direction is constantly changing. So special relativity does not apply here.

 

Non-uniform motion is the venue of general relativity, where there is no speed of light restriction.

Edited August 26, 2012 by IM Egdall

[mathematic]

There is a much simpler explanation for this business of stars motion in the earth's frame. A good example would show what is going on. Take a very bright flashlight on shine it on a distant object. Rotate the flashlight and if the object is far enough away, the light spot will move faster than the speed of light. The speed limit of relativity refers to the speed of information transfer.

 

Note: the speed limit for light holds in general relativity as well.

[romesh]

There is a much simpler explanation for this business of stars motion in the earth's frame. A good example would show what is going on. Take a very bright flashlight on shine it on a distant object. Rotate the flashlight and if the object is far enough away, the light spot will move faster than the speed of light. The speed limit of relativity refers to the speed of information transfer.

 

Note: the speed limit for light holds in general relativity as well.

 

 

But the light spot isn't a material object unlike the stars. The spot is just a geometric spot which is moving.

 

And the restriction to the speed of light applies to general relativity as well.

 

One thing comes to mind: Special relativity applies to objects in uniform motion, that is objects which travel at a constant speed and in a constant direction. A star as seen in the Earth frame of reference is rotating around the Earth. Its direction is constantly changing. So special relativity does not apply here.

 

Non-uniform motion is the venue of general relativity, where there is no speed of light restriction.

 

 

This is baseless.

 

You mean to say that if we keep on accelerating an object then, we could reach the speed of light c or even beyond it! Now if we stop accelerating, our uniform speed can come c or even more than c!

Edited August 27, 2012 by romesh

[J.C.MacSwell]

I have aquestion regarding the topic.

 

We say that the earth rotates on its axis which causes a bulge in its shape.

 

Conversely we can say that the gravitational effects of the motion of whole of the universe causes the bulge. But will not the distant stars of the universe cross the restricted speed of light c in the process?

 

How can we explain this phenomenon?

 

in an inertial frame nothing can exceed the speed of light. The Earth frame is not an inertial frame, so that limit does not apply.

[ACG52]

The earth rotating, and a stationary earth with the universe rotating around it, are not equivalent frames. The rotating earth is an accelerated frame, and the stationary earth is a non-accelerated frame. Since in the physical universe, the earth is a rotating frame, the premise in the OP is faulty.

[altergnostic]

Also, the bulge is caused by centrifugal forces due to the fact that the equator moves faster than the poles. To create the same effect from outside gravitational forces, you would need the equivalent difference in mass distribution around the universe, and we would see more stars above the equator than above the poles. Rotation wouldn't even matter. If you rotate an evenly distributed amount of stars around the earth, the gravitational effects would be the same as if they were not moving at all.

 

And regarding c, it is a limit only for inertial frames. It is possible for an inertial frame to calculate speeds up to 2c (emiting 2 photons in opposite directions at c each and applying the addition of velocities equation) but you will not measure a single body moving at any speed higher than c because light moves at c and you see everything with light. That's why information can't be transmitted faster than light.

 

Bringing rotation into play adds acceleration to the problem, and we are no longer dealing with inertial frames, and c is not the limit anymore, but how would you measure the speed of the revolving stars relative to the earth? Simply define a reference point and measure the motion of the stars relative to it. You will see that the stars move way slower than c. The distance of 2 lightyears for any particular star does not enter this calculation. It could only enter the problem if you were measuring the speed of revolution relative to a fixed background rotating with the earth, but such background is a mathematical abstraction, so you will never physically measure such speeds.

From the point of view of this distant star, the earth would be spinning at speed that is equal to the speed of the star relative to some point of reference at the surface of the earth, measured in the earth's frame. Hence, this is a correct velocity, measurable in both frames. The other speed is only apparent, it is a visual effect, not a physical velocity, no body is moving faster than c.

 

To understand this, just think about turning your head very fast from left to right. Are you compelled to say that everything else moved at enormous speeds relative to your face? Or even, spin a coin and move away. Is there any change in any speeds?