GR derived using spinning ride example?

In summary, Einstein used an example of a spinning wheel to demonstrate how matter curves space, which led to his theory of General Relativity. He was inspired by this example to frame the theory in terms of non-Euclidean geometry, but it is not a proof. The equivalence principle also plays a key role in understanding how the Lorentz effect and gravity are connected.
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Silverrida
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Hey, I'm new here, so I hope this hasn't already been posted, but I really need help with this question. There is a commonly used example to show how Einstein helped prove General Relativity through space curving due to different ratios in radians of a spinning wheel made to spin at the velocity in which it would feel like gravity was the only force acting upon you.

The experiment is as follows: one person measures the already spinning wheel's circumference and diameter from a stationary viewpoint, and finds the ratio to, of course, be 2pi. Now, the person in the wheel who believes he's at rest because he assumes gravity is acting upon and doesn't realize he's in a state of accelerated velocity does the same experiment, and due to the Lorentz contraction when measuring in the direction of acceleration, he will get the circumference to be greater than 2pi, as the circumference would be larger. Now, from this Einstein theorized that matter curved space to allow this change, and showed examples of how circle's circumferences change on curved surfaces.

My question is this: It seems like Einstein attributes the result of the Lorentz affect, which we know is due to accelerated motion, to a different cause, what we know of as General Relativity, or the affect mass and energy have on space-time. How is this attribution of affect possible? Is there a variable I am missing? Please explain this, it would be greatly appreciated.
 
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Hi, Selverrida -- Welcome to Physics Forums! This is a good question, and IMO shows that you're doing a good job of thinking about this subject.

There is a commonly used example to show how Einstein helped prove General Relativity through space curving
I would phrase this a little differently. Einstein was inspired by this example to try to frame GR as a theory involving non-Euclidean geometry. He didn't really use the example to prove anything. Here is an example of how Einstein presented it: http://hem.bredband.net/b153434/Works/Einstein.htm [Broken] This is the kind of thing physicists would generally refer to as a heuristic, or motivation for the theory -- not a proof.

It seems like Einstein attributes the result of the Lorentz affect, which we know is due to accelerated motion, to a different cause, what we know of as General Relativity,
I think the ingredient you're missing is the equivalence principle: http://en.wikipedia.org/wiki/Equivalence_principle The idea is that there is no way to distinguish between accelerated motion and gravity.
 
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1. What is GR and how is it derived using the spinning ride example?

GR, or General Relativity, is a theory in physics that describes the relationships between space, time, and gravity. It was developed by Albert Einstein in the early 20th century. The spinning ride example is often used to illustrate the concept of GR, as it demonstrates how objects with mass can affect the curvature of space-time.

2. How does the spinning ride example illustrate the curvature of space-time?

In the spinning ride example, the ride is constantly changing direction and velocity, causing the riders to experience a force pushing them towards the outer edge. This force is actually the result of the curvature of space-time caused by the ride's rotation. The faster the ride rotates, the greater the curvature of space-time and the stronger the force experienced by the riders.

3. How does GR differ from Newton's theory of gravity?

GR and Newton's theory of gravity are fundamentally different in their explanations of gravity. Newton's theory states that gravity is a force that exists between two objects with mass, while GR describes gravity as the curvature of space-time caused by the presence of mass. Additionally, GR accounts for the effects of acceleration and the speed of light, while Newton's theory does not.

4. Can GR be tested and proven using the spinning ride example?

Yes, GR has been extensively tested and confirmed through various experiments and observations. While the spinning ride example is a simplified demonstration, it does illustrate the concept of GR and the effects of gravity on the curvature of space-time.

5. What are some real-world applications of GR derived from the spinning ride example?

GR has numerous practical applications, including the accurate prediction of the orbits of planets, the ability to navigate spacecraft, and the use of gravitational lenses in astronomy. It also plays a crucial role in the development of technologies such as GPS and satellite communications.

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