# GR derived using spinning ride example?

1. Feb 9, 2010

### Silverrida

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.

2. Feb 9, 2010

### bcrowell

Staff Emeritus
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.

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.

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.

Last edited by a moderator: May 4, 2017