Quotes About Curvature

His head-snapping insight was that gravity could be defined as the curvature of spacetime, and thus it could be represented by a metric tensor.

That is a challenging concept. We can visualize a curved line or surface, but it is hard to imagine what curved three-dimensional space would be like, much less a curved four dimensions. But for mathematicians, extending the concept of curvature into different dimensions is easy, or at least doable. This involves using the concept of the metric, which specifies how to calculate the distance between two points in space.

Einstein's goal as he pursued his general theory of relativity was to find the mathematical equations describing two complementary processes: 1. How a gravitational field acts on matter, telling it how to move. 2. And in turn, how matter generates gravitational fields in spacetime, telling it how to curve. His head-snapping insight was that gravity could be defined as the curvature of spacetime, and thus it could be represented by a metric tensor. For more than three years he

The central idea of general relativity is that gravity arises from the curvature of spacetime

The mist just keeps on lifting and soon I'll be able to see all the way, as far as the earth's curvature allows. It's a blessing, that curvature, that hidden hemisphere-if we could take it all in at one, why move?

The infinite zero of a black hole-mass crammed into zero space, curving space infinitely-punches a hole in the smooth rubber sheet. The equations of general relativity cannot deal with the sharpness of zero. In a black hole, space and time are meaningless.

Gravity is the curvature of space.

The space that is added as the universe expands has the same properties-curvature, energy density-as the parent space.

Whether as a moral kink or a crooked twist given to the will, vice has often the appearance of a curvature for the soul.

Schwarzschild radius,

Most problems I work on are related to geometric structures on surfaces and their deformations.

Everything is different when the Earth is round.

This picture of matter curving space and curvaceous space dictating how matter and light will move has several striking features. It brings the non-Euclidean geometries that we talked about in the last chapter out from the library of pure mathematics into the arena of science. The vast collection of geometries describing spaces that are not simply the flat space of Euclid are the ones that Einstein used to capture the possible structures of space distorted by the presence of mass and energy.

Gravity acts on all forms of mass and energy, but energy comes in a host of very different forms that behave in peculiar ways that were not known in Newton's day. Wotst of all, gravity gravitates. Those waves of gravity that spread out, rippling the curvature of space, carry energy too and that energy acts as a source for its own gravity field. Gravity interacts with itself in a way that light does not.

Lying naked and cold beneath the perfect, whispering dark, I imagined I could feel the curve of the earth under my back, that I circled the whole planet so that my soles touched the top of my head and I blended with the dirt.

I find the satellite pictures and the curvature of the Earth very moving. So is it true that we live on the surface of a sphere, exposed to the gaze of the planets, left in a great void, where after the Fall the light was smashed to smithereens and blown apart? It is true. We should remember that every day, for we do tend to forget.

He (Riemann) showed that there are three main ways space can be curved- positive curvature, negative curvature, and zero curvature. Thes correspond respectively to elliptic, hyperbolic, and Euclidean flat geometries.