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23. April 2011, 13:36:48
Übergeek 바둑이 
Thema: Re: am simply admitting to my inability to understand everything from the limited perspective of being a creature who cannot hope to "see" how it all works, but must by neccessity rely on my ability to understand it.
Verändert von Übergeek 바둑이 (23. April 2011, 14:07:15)
Iamon_lyme:

> I did try to visualize what a space time curviature might look like.

Just remember, when they talk of curvature, they are not talking of the one-dimensional curvature of a two-dimensional curve (for example, the curvature of a circle is the reciprocal of its radius). We can visualize the "curvature" of a line or a sphere. To us curvature is what we see in Euclidean space.

The curvature they talk about is higher dimensional. In three dimensions curvature cannot be visualized so simply. It is expressed as the product of a matrix with orthonormal columns and a three dimenisonal vector. In higher dimensions curvature is expressed as the products of tensors in Riemann manifolds. It is too complex to be visualized in terms our brain can understand. It is understood only in mathematical terms, and therefore, it is an abstract concept. To make it short, Einstein used tensor calculus for his theory of relativity. If you are familiar with the math and the theorems of course it makes sense. If you are like most of us, it is all another language entirely.

> Try envisioning a vacuum within a vacuum

We forget sometimes that "vacuum" is a human concept to indicate the absense of matter in some enclosed space. In reality most of space is made of "vacuum" (for example, atoms have a tiny nucleus and even tinier electrons in orbit around it). However, elementary particles (like electrons, protons, etc.) have a dual character of a particle and a wave. That is the product of the quantum mechanical description of matter.

The real problem that physicists have is that quantum mechanics and relativity theory don't "mix", meaning that there is no exact solution when trying to solve relativistic quantum mechanics (like the Schroedinger equation) into higher dimensions. The attempts at these solutions is what things like superstring theory tries to do. Relativity is good at describing the universe in the huge scale of stars, galaxies, etc. While quantum mecahnics is good at describing the universe in the tiny scale of atoms and molecules. However, there is no unified theory thaht describes the two of them with the same math.

However, some day we will have a prodigy (maybe this gifted child) who will be able to do so. He has the potential and he will do well as long as he is allowed to be a child, and unrealistic expectations are not put upon him.

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