Curved space?

Today, June 10, in 1854, a physicist named Georg Friedrich Bernhard Riemann gave a lecture in which he proposed that space might be curved and have extra dimensions. A weird concept to be sure, and it didn’t take off particularly quickly in the scientific community.

It took 12 more years, and two years after his death, until this work was finally published. Even then, it simply seemed to be an abstract concept and not justified by observations or general perception of space.

It wasn’t really until 1915 that we see the broader impact of his work in Einstein’s publication of his theory of General Relativity. Which proposes that space is indeed curved and has since been supported by extensive evidence. But what does the curvature of space actually mean?


Curved space and relativity

Einstein’s revolutionary theory of relativity claimed that space was not empty and constant, as was previously thought, but instead, that space and time were united and were warped by objects of mass. So big planets, stars and black holes, as well as smaller objects that you encounter in day to day life, all make indents in space time, like a heavy object on a trampoline, causing all the other objects on the trampoline to roll towards it (be attracted to it). For a fuller explanation, check out this whole post on relativity.

All well and good, space could be curved and that would describe planetary orbits and bending of light really, really well. But how could we actually express that in mathematical terms? How could we know how much an object would warp space and attract other objects to it?

And this was where Riemann came back in. His work on geometry of curved spaces formed the mathematical basis for formulating Einstein’s equations of relativity. However, despite his original work, it still took Einstein and his peers over a decade to work out the nitty-gritty of explaining spacetime.

It shows the genius of Riemann himself in how he developed this original geometry of curved spaces … and how without this lesser-known physicist/mathematician, we would not have an Einsteinian theory of relativity in 1915.

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