## the magic of einstein's general theory of relativity -- 5/23/16

**Today's selection -- from Seven Brief Lessons on Physics by Carlo Rovelli.** The beauty and simplicity of Einstein's "General Theory of Relativity".

"But among the numerous leaps forward in our understanding that have succeeded one another over the course of history, Einstein's is perhaps unequaled. ...

"Newton had tried to explain the reason why things fall and the planets turn. He had imagined the existence of a 'force' that draws all material bodies toward one another and called it 'the force of gravity.' How this force was exerted between things distant from each other, without there being anything between them, was unknown -- and the great father of modern science was cautious of offering a hypothesis. Newton had also imagined that bodies move through space and that space is a great empty container, a large box that enclosed the universe, an immense structure through which all objects run true until a force obliges their trajectory to curve. What this 'space' was made of, this container of the world he invented, Newton could not say. But a few years before the birth of Einstein two great British physicists, Michael Faraday and James Maxwell, had added a key ingredient to Newton's cold world: the electromagnetic field. This field is a real entity that, diffused everywhere, carries radio waves, fills space, can vibrate and oscillate like the surface of a lake, and 'transports' the electrical force. Since his youth Einstein had been fascinated by this electromagnetic field that turned the rotors in the power stations built by his father, and he soon came to understand that gravity, like electricity, must be conveyed by a field as well: a 'gravitational field' analogous to the 'electrical field' must exist. He aimed at understanding how this 'gravitational field' worked and how it could be described with equations.

"And it is at this point that an extraordinary idea occurred to him, a stroke of pure genius: the gravitational field is not *diffused through space*; the gravitational field is that space itself. This is the idea of the general theory of relativity. Newton's 'space,' through which things move, and the 'gravitational field' are one and the same thing.

"It's a moment of enlightenment. A momentous simplification of the world: space is no longer something distinct from matter -- it is one of the 'material' components of the world. An entity that undulates, flexes, curves, twists. We are not contained within an invisible, rigid infrastructure: we are immersed in a gigantic, flexible snail shell. The sun bends space around itself, and Earth does not turn around it because of a mysterious force but because it is racing directly in a space that inclines, like a marble that rolls in a funnel. There are no mysterious forces generated at the center of the funnel; it is the curved nature of the walls that causes the marble to roll. Planets circle around the sun, and things fall, because space curves.

"How can we describe this curvature of space? The most outstanding mathematician of the nineteenth century, Carl Friedrich Gauss, the so-called prince of mathematicians, had written mathematical formulas to describe two-dimensional curvilinear surfaces, such as the surfaces of hills. Then he had asked a gifted student of his to generalize the theory to encompass spaces in three or more dimensions. The student in question, Bernhard Riemann, had produced an impressive doctoral thesis of the kind that seems completely useless. The result of Riemann's thesis was that the properties of a curved space are captured by a particular mathematical object, which we know today as Riemann's curvature and indicate with the letter R. Einstein wrote an equation that says that R is equivalent to the energy of matter [R=GE]. That is to say: space curves where there is matter. That is it. The equation fits into half a line, and there is nothing more. A vision -- that space curves -- became an equation.

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