Curiously however, Krauss does not list what I believe was Einstein's biggest failure after quantum mechanics: his refusal to accept the reality of black holes. This failure is especially staggeringly ironic, since the gravitational waves which were discovered this week (which he did predict and which further confirmed his theory) came from the collision of two black holes (entities whose existence he explicitly rejected).

Months after Einstein put the capstone on his general theory of relativity, a German mathematical physicist serving in the First World War named Karl Schwarzschild applied his theory to the simple case of spacetime around a spherical star. Schwarzschild found that as you approached closer to the star, for a star massive enough you would encounter a region where gravity was so strong that you could not escape from it unless you were moving at the speed of light. Schwarzschild sent his calculations to Einstein who curiously accepted them without protest; they seemed simple and logical.

And yet Einstein never really explored the physical structure of Schwarzschild's solution, nor did he ever accept its profound implications. He regarded the solution mainly as a mathematical abstraction, much as some who did not quite believe in Copernicus's heliocentric model and regarded it only as a mathematical construction. Schwarzschild sadly died of an autoimmune disease on the Russian front in 1916. Einstein himself did not return to Schwarzschild's discovery, and it fell to a succession of young physicists unaffected by the biases of the old guard to investigate it to its logical conclusion.

The most famous among these were Subrahmanyan Chandrasekhar and Robert Oppenheimer. Chandrasekhar's (or Chandra as everyone called him) story is well known. While crossing the ocean from India to England in 1930, the 19 year old Chandra worked out what would happen when white dwarfs exceed a certain mass. This mass, now called the Chandrasekhar limit, would be the limiting mass for a white dwarf to support itself against its internal gravitational pull. Chandra found his own skeptical Einstein in the famous English astronomer Arthur Eddington, who in a meeting in 1935 excoriated him for developing a model of a star which did not make physical sense (to Eddington). Chandra who knew better than to waste his time battling the establishment wisely moved on, seeing his ideas vindicated half a century later.

Oppenheimer turned to gravitational collapse almost as a temporary diversion when he wanted to explore the ramifications of a theory of neutron cores set forth by the Soviet physicist Lev Landau. It was Oppenheimer who first worked out the full implications of a star which was so massive that it could not achieve any kind of steady state against gravitational collapse. In a seminal paper in 1939, Oppenheimer also introduced the now familiar idea of an observer falling past the so-called event horizon. Without calling them as such, Oppenheimer had discovered black holes and singularities, regions of spacetime where gravitational fields becomes infinite.

Ironically, in the same year that Oppenheimer published his calculations Einstein wrote a paper in the journal

*Annals of Mathematics*titled "A Stationary System with Spherical Symmetry Consisting of Many Gravitational Masses". The paper - published only a month after Oppenheimer's - argued against Schwarzschild's conception of singularities. In it he tried to get away from the idea that a single body could create a gravitational field strong enough to cause such a prohibitive warping of spacetime. Instead he tried to replace such a single body with a collection of bodies exhibiting spherical symmetry. The crux of Einstein's argument that such a system would have to rotate at the speed of light in order to exhibit singularities. Needless to say Einstein was deeply mistaken, and the 1939 paper displayed exactly the kind of mathematical modeling free of physical reality that he thought Schwarzschild's equations for singularities did.

After the war both Oppenheimer and Einstein worked together at the Institute for Advanced Study in Princeton. There is no evidence indicating that they ever discussed black holes or their respective papers from 1939; there is no evidence that Oppenheimer objected to Einstein's paper or that Einstein explicitly told Oppenheimer that he rejected his conclusions. But what was happening was worse than opposition: it was indifference. Just like Einstein Oppenheimer lost all interest in black holes after 1939 and refused to have any discussion about them, although as their inventor he putatively at least believed in them. The two physicists who had been scientific revolutionaries in their younger days became arch conservatives in their older years.

It is a delicious reversal of fortune that the same black holes that Einstein explicitly rejected have been found to contain some of the deepest mysteries of physics, encompassing not just relativity but also quantum mechanics, thermodynamics and information theory. And now with the discovery of gravitational waves from colliding black holes, the scientific children which Einstein disowned have come back to smile at their father and say, "I told you so." This is irony of the highest order, and I suspect that Einstein with his great sense of irony about science and history would actually have enjoyed it.

It seems an exaggeration to say that Einstein opposed quantum mechanics. I believe he opposed only the Copenhagen interpretation.

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