The Curvature of an Arbitrary Space Time

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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?

My little pandemic-lockdown contribution to the world was a series of videos called The Biggest Ideas in the Universe. The idea was to explain physics in a pedagogical way, concentrating on established ideas rather than speculations, with the twist that I tried to include and explain any equations that seemed useful, even though no prior mathematical knowledge was presumed. I’m in the process of writing a series of three books inspired by those videos, and the first one is coming out now: The Biggest Ideas In The Universe: Space, Time, and Motion. For this solo episode I go through one of the highlights from the book: explaining the mathematical and physical basis of Einstein’s equation of general relativity, relating mass and energy to the curvature of spacetime. Hope it works!

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