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General Relativity, 100 Years On



One hundred years ago, on Nov. 25, 1915, 36-year old Albert Einstein made history when he redefined gravity in his fourth and final lecture to the Prussian Academy of Sciences in Berlin on "The Field Equations of Gravitation." In a word, or at least an equation, Einstein proposed that Gαβ = Tαβ. That's it ... sort of. The equation is a really shorthand version of the paper published by the academy a week after his lecture.

Start off with the notion, developed by Einstein 10 years earlier, that we live in a four-dimensional fabric called spacetime ("A Matter of Some Gravity," March 7, 2013). Three of these dimensions are spatial (up/down, left/right, forward/back), the fourth being time (past/future). Now look at the equation:

On left side, Gαβ (aka the "Einstein tensor," comprising 10 independent components) is a quick and dirty way of describing curvature, that is, how the geometry of spacetime fabric is warped by massive objects. From our point of view, this warping manifests as gravity: The apple falls from the tree, not because of mutual attraction between the apple and the planet, but because the apple free-falls along spacetime curved by the mass of the Earth.

Tαβ is the "stress energy tensor" or, informally, matter content, and is a shorthand way of describing how objects move in a gravitational field.

(Which is all the math you'll get out of me, other than to note, for purists, that I skipped a parameter by making 8πG/c^4 = 1 on the right side of the equation. For more on gravity, check out "Gravity 101," April 16, 2009.)

That equation is the core of the Theory of General Relativity, in which the do-si-do between geometry and motion can be summarized in the words of the late American physicist John Archibald Wheeler: Matter tells spacetime how to curve, and spacetime tells matter how to move.

The usual analogy is to imagine a heavy ball, standing in for the sun, sitting in the middle of — and deforming — an elastic sheet (that is, the ball "tells" the sheet, or space, how to curve). A smaller ball — think of Earth — rolls around the heavier ball in an elliptical orbit (the curvature of the sheet "telling" it how to move). Of course, the smaller ball also deforms the sheet as it orbits the "sun" — hence the moon's orbit around the Earth.

What's missing in this analogy is any feel for the vastness of the theory. The spacetime fabric extends, unbroken, throughout the entire universe. And it's dynamic, continuously rippling and bending in response to the movement of massive bodies both near and far: Everything is connected to everything else.

OK, so what? What's general relativity good for? Well, it's really good — essential, actually — for GPS, not to mention our understanding of nuclear reactions, magnetism and light. Without relativity, cosmology — the science that deals with the origin and history of the universe — would be dead in the water, with the Big Bang and black holes lost in space, as it were. But what it's really good for is that it gives us the tools, along with the other two Great Ideas of the last 200 years — evolution and quantum mechanics — to discuss, investigate and explore the biggest questions of all about the cosmos and our place in it.

Barry Evans ( knows that he is, therefore he thinks.

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