The idea came to me thinking about the initial thread, "Special relativity question" What happens if a disk of radius R rotates with angular velocity, so that the periphery of the disc reaches the speed of light? The disc collapses in himself? Or also it curves to form a sphere? But if reduce the radius is reduced and peripheral speed! oohhhhh........... But if we rotate a sphere?We get an clepsydra? Or we never get so high peripheral speed because it reduce the radius and should increase the angular velocity but then reduce the radius even more. oohhh....ohhh.....I feel my mind explode. Any help?
There's a whole host of problems when one tries to naively work out the implications of a high-speed rotation in relativity. However, it's not a problem for the math of relativity. You are assuming the math of relativity plus the math of rigid motion, and you lead to logical contradictions. Therefore you can't use the math of both relativity and rigid motions. Or, in a universe with relativity, it is inconsistent to assume items are perfectly rigid. A full treatment based on the locally modeled properties of a more realistic material is possible, but since every point on the wheel is in a different state of instantaneous motion, the math gets tricky (in fact, this special relativity problem is best addressed with the tools of general relativity) and this problem has a long history (and a longer history of people getting it wrong). http://en.wikipedia.org/wiki/Ehrenfest_paradox
I learned math in the following way. You must be able to describe a real system in the form mathematics. You processed this mathematical system using mathematical device. The result you should be able to interpret it back into the real system. Not this is the role of mathematics? It's just an abstract science without regard to the exact sciences? what? "General relativitygeneralises special relativity and Newton's law of universal gravitation, providing a unified description of gravity as a geometric property of space and time, or spacetime. In particular, the curvature of spacetime is directly related to the four-momentum (mass-energy and linear momentum) of whatever matter and radiation are present. The relation is specified by the Einstein field equations, a system of partial differential equations." The universe is spinning, isn't it? If I'm closer to the center of rotation, and I look at an object that is farther from the center of rotation, I see it stationary and yet it has a speed different from mine. Since I'm revolve with the universe I do not to notice this rotation. (the reference system revolves together the universe) We can realize this only because the forces, especially centrifugal forces. Maybe that's why the universe is expanding. What angular speed of the universe must have that in the "region" of maximum speed reach the speed of light? The diameter of the observable universe is estimated to be about 28 billion parsecs (93 billion light-years).The speed of light value is 299,792,458 metres per second. If this "region" reaches the speed of light, what consequence has on the universe?
