Einstein's GR & Rotating Earth Dilemma

[leo nardo]

Einstein, for his GR theory he made a last important effort to make it valid also for rotating objects. So consider the following thought experiment.
There is an observer A standing at the North Pole and another observer B sitting on a platform, turning clockwise once every 24 hours, both with a camera.
The Earth is hollow, with little gravity and a thin crust, turning like the normal earth.
At the equator there is a man sending short laser pulses through an hole in the Earth crust to the opposite side, about 12.000 km away. It takes 40 msec. for the pulses the reach the other side and inside the hollow Earth there is a bit of fog as to show the course of the laser beam.
During the 40 msec. objects at the equator move on for about 18 meters.
At the North Pole there is also a hole in the crust. Both A and B make a pictures during the laser beam crossing the inner earth.
Now, considering the rotating Earth as a reference frame for GR, observer A sees the laser beam going straight.
But B in rotation gets a picture from a laser beam slightly bent.
But then, consider B as part of the non-rotating universe, following the laser beam with his camera, he should find a straight line. Because why should light bent when there is no gravity involved. How to solve this dilemma.

 

[Dale]

Is the Earth rotating? And is the turntable for B counteracting the rotation or adding to it?

Assuming that the Earth is rotating then A will not see a straight path.

 

[pervect]

If the Earth is hollow and the crust is light, this is essentially a SR experiment, because you are saying gravity is negligible. And this experiment basically tells us that rotation is absolute, not relative.

We can measure the rate of absolute rotation with a ring laser gyro, for instance, as well as your scheme.

To do a GR experiment we would need to consider a case where gravity would make a diference. For example we might consider, as Einstein did, consider a still hollow but massive rotating Earth. Or in any case a "shell".

Then you can ask questions such as "will the frame that you determine to be nonrotating be fixed relative to the distant stars". Einstein's theory answers this one - no it will not.

The general class of effects due to rotating massive bodies is called "frame dragging". Wiki as a short summary on it http://en.wikipedia.org/w/index.php?title=Frame-dragging&oldid=518801991

 

[leo nardo]

Yes, I was already wondering why there was no return after I send the laser beam to the centre of the Earth on to the mirror positioned at the other side.
After reading Einstein’s biography in respect to GR there was talking about rotating objects, gyroscopes etc., which was confusing. And of course there would have been many more conflicts in the universe. The reference article you pointed at was very helpful. Thanks.

 

[sardar]

I would approach this dilemma by first acknowledging that Einstein's theory of General Relativity (GR) is a complex and highly accurate theory that has been proven through numerous experiments and observations. It is considered one of the most successful theories in physics, and it has been able to explain a wide range of phenomena in the universe.

That being said, I would also acknowledge that Einstein himself struggled with incorporating the concept of rotation into his theory. This is evident in his attempts to make GR valid for rotating objects, as mentioned in the content provided. So, it is not surprising that this thought experiment presents a dilemma in terms of the behavior of light in a rotating reference frame.

One possible way to approach this dilemma is to consider the concept of frame dragging, which is a phenomenon predicted by GR. This is the idea that a massive object, such as the Earth, can "drag" the space-time around it as it rotates. This can cause light to appear to bend in a rotating reference frame, as seen by observer B in this thought experiment.

However, in order to fully understand this phenomenon, we must also consider the concept of inertial frames of reference. This means that an observer in a non-rotating universe, as mentioned in the content, would not experience the same effects of frame dragging as an observer in a rotating reference frame. Therefore, it is not necessarily a contradiction for observer B to see a slightly bent laser beam while also observing a straight beam from a non-rotating perspective.

In conclusion, while this thought experiment may present a dilemma in terms of the behavior of light in a rotating reference frame, it is important to consider the complexities of Einstein's theory of GR and the concept of frame dragging. This dilemma does not invalidate the theory, but rather highlights the need for further exploration and understanding of the effects of rotation on space-time.