I continue my Spring Break posts on The Perfect Theory, a book on the general theory of relativity and its footprint on the last century. So far:
1. Einstein in 1907
1. I might have titled these thoughts on the second chapter, "Einstein in 1915." That is the year that Einstein delivered a short four page paper to the Prussian Academy of Sciences explaining how gravity fit with relativity and thus truly gave birth to the general theory of relativity (as opposed to the special theory he set out in 1905). The paper consisted of 10 field equations.
There is some debate whether Einstein actually put these equations in their final form first or whether David Hilbert did. Einstein was not a math-lover, particularly. To be sure, he was way ahead of most of us, but he considered math "superfluous erudition."
I have a hunch I know where he was coming from. He did not mean the calculus or algebra that we find so useful in engineering. I suspect he meant the drive to prove things that seem obvious. From what I can tell, Einstein was more of an intuitive soul, and the drive to mathematical minutia probably did not suit him well.
David Hilbert (University of Göttingen) was quite the opposite, with an agenda to solve 23 problems in the twentieth century. A quick perusal of the list and you might agree with Einstein. Hilbert wanted to "reduce every single mathematical fact in the universe from no more than half a dozen axioms" (76). Kurt Gödel would later demolish Hilbert's goal in 1931 with his incompleteness theorem.
Hilbert was extraordinarily more gifted at math than Einstein and Einstein ended up turning to him to help with non-Euclidean geometry, which was less than 100 years old. Euclid was Greek and had proposed, using common sense, that two parallel lines never meet. In the 1820s, Carl Friedrich Gauss had explored the rules of geometry on, say, curved sheets of paper, where Euclid's assumptions don't hold. On a sphere, parallel lines intersect and the angles of a triangle add up to 270 degrees. Bernhard Riemann in the 1850s had explored the rules of geometry into all sorts of non-Euclidean obscurity.
So in 1915, Einstein and Hilbert mailed back and forth, as Einstein tried to use Riemann's math to express gravity as a result of the curvature of space rather than as a force per se. It's still debated whether Hilbert beat Einstein, although Hilbert yielded to Einstein and Einstein usually gets the ultimate credit. It might be fair to say that neither would have come up with the answer without the other.
Einstein came up with 10 equations of 10 functions of the geometry of space and time in which "gravity is nothing more than objects moving in the geometry of spacetime. Massive objects affect the geometry, curving space and time" (21).
2. There is a second part to the chapter that relates to Arthur Eddington. There is often a politics and a history to science, as to any discipline, and it is seen in this book. In 1915, Europe was at war. In World War I, the Germans were fighting the English. Both many English scientists and German scientists went irrational, as war tends to make all of us. 93 German scientists (not Einstein) signed "An Appeal to the Cultured World" in support of the German government and rather bad on its facts. Meanwhile, Eddington's colleagues in England wanted to dismiss all German scientific thought as obviously inferior.
Eddington managed to convince the right people to let him head to the island of Principe in 1918 instead of to the war. His task? To measure where a certain set of stars appeared to be as their light passed by the sun during an eclipse. As Einstein's theory had predicted, their apparent position was off approximately what Einstein's theory said it would be due to the effect of the sun curving space because of its great mass.
In 1919 Eddington presented the results to the Royal Astronomical Society, "the most important result obtained in connection with the theory of gravitation since Newton's day," J. J. Thompson said (discoverer of the electron). Einstein was now a celebrity and Eddington the foremost authority on Einstein's theory in the English-speaking world.
The general theory of relativity has been substantiated time and time again ever since. Without taking such things into account, things like GPS wouldn't work.