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211 | Solo: Secrets of Einstein's Equation
Sean Carroll's Mindscape: Science, Society, Philosophy, Culture, Arts, and Ideas
The Curvature of an Arbitrary Space Time
Professor Riemann and his successors said we can specify the curvature of an arbitrary space time. For every point in space for every line segment I could draw, there is yet another vector which tells me how the two initially parallel lines are moving apart or moving together or twisting. So it turns out that all of this complicated information is summed up in yet another tensor. But this tensor is not 4x4. Like the metric tensor in spacetime is 4x4 array of numbers because it's four dimensions of space, four components. The Riemann tensor is 4X4x4x4. And who says you have to be in four dimensions, right?
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