Walter Isaacson - Einstein - His Life and Universe

One thing made Schwarzschild’s work very difficult. He had volunteered for the German military during the war, and when he read Einstein’s papers he was stationed in Russia, projecting the trajectory of artillery shells. Nevertheless, he was also able to find time to calculate what the gravitational field would be, according to Einstein’s theory, around an object in space. It was the wartime counterpart to Einstein’s ability to come up with the special theory of relativity while examining patent applications for the synchronization of clocks.

In January 1916, Schwarzschild mailed his result to Einstein with the declaration that it permitted his theory “to shine with increased purity.” Among other things, it reconfirmed, with greater rigor, the success of Einstein’s equations in explaining Mercury’s orbit. Einstein was thrilled. “I would not have expected that the exact solution to the problem could be formulated so simply,” he replied. The following Thursday, he personally delivered the paper at the Prussian Academy’s weekly meeting. 1

Schwarzschild’s first calculations focused on the curvature of space-time outside a spherical, nonspinning star. A few weeks later, he sent Einstein another paper on what it would be like inside such a star.

In both cases, something unusual seemed possible, indeed inevitable. If all the mass of a star (or any object) was compressed into a tiny enough space—defined by what became known as the Schwarzschild radius—then all of the calculations seemed to break down. At the center, spacetime would infinitely curve in on itself. For our sun, that would happen if all of its mass were compressed into a radius of less than two miles. For the earth, it would happen if all the mass were compressed into a radius of about one-third of an inch.

What would that mean? In such a situation, nothing within the Schwarzschild radius would be able to escape the gravitational pull, not even light or any other form of radiation. Time would also be part of the warpage as well, dilated to zero. In other words, a traveler nearing the Schwarzschild radius would appear, to someone on the outside, to freeze to a halt.

Einstein did not believe, then or later, that these results actually corresponded to anything real. In 1939, for example, he produced a paper that provided, he said, “a clear understanding as to why these ‘Schwarzschild singularities’ do not exist in physical reality.” A few months later, however, J. Robert Oppenheimer and his student Hart-land Snyder argued the opposite, predicting that stars could undergo a gravitational collapse. 2

As for Schwarzschild, he never had the chance to study the issue further. Weeks after writing his papers, he contracted a horrible auto-immune disease while on the front, which ate away at his skin cells, and he died that May at age 42.

As scientists would discover after Einstein’s death, Schwarzschild’s odd theory was right. Stars could collapse and create such a phenomenon, and in fact they often did. In the 1960s, physicists such as Stephen Hawking, Roger Penrose, John Wheeler, Freeman Dyson, and Kip Thorne showed that this was indeed a feature of Einstein’s general theory of relativity, one that was very real. Wheeler dubbed them “black holes,” and they have been a feature of cosmology, as well as Star Trek episodes, ever since. 3

Black holes have now been discovered all over the universe, including one at the center of our galaxy that is a few million times more massive than our sun. “Black holes are not rare, and they are not an accidental embellishment of our universe,” says Dyson. “They are the only places in the universe where Einstein’s theory of relativity shows its full power and glory. Here, and nowhere else, space and time lose their individuality and merge together in a sharply curved four-dimensional structure precisely delineated by Einstein’s equations.” 4

Einstein believed that his general theory solved Newton’s bucket issue in a way that Mach would have liked: inertia (or centrifugal forces) would not exist for something spinning in a completely empty universe.* Instead, inertia was caused only by rotation relative to all the other objects in the universe. “According to my theory, inertia is simply an interaction between masses, not an effect in which ‘space’ of itself is involved, separate from the observed mass,” Einstein told Schwarzschild. “It can be put this way. If I allow all things to vanish, then according to Newton the Galilean inertial space remains; following my interpretation, however, nothing remains.” 5

The issue of inertia got Einstein into a debate with one of the great astronomers of the time, Willem de Sitter of Leiden. Throughout 1916, Einstein struggled to preserve the relativity of inertia and Mach’s principle by using all sorts of constructs, including assuming various “border conditions” such as distant masses along the fringes of space that were, by necessity, unable to be observed. As de Sitter noted, that in itself would have been anathema to Mach, who railed against postulating things that could not possibly be observed. 6

By February 1917, Einstein had come up with a new approach. “I have completely abandoned my views, rightly contested by you,” he wrote de Sitter. “I am curious to hear what you will have to say about the somewhat crazy idea I am considering now.” 7It was an idea that initially struck him as so wacky that he told his friend Paul Ehrenfest in Leiden, “It exposes me to the danger of being confined to a madhouse.” He jokingly asked Ehrenfest for assurances, before he came to visit, that there were no such asylums in Leiden. 8

His new idea was published that month in what became yet another seminal Einstein paper, “Cosmological Considerations in the General Theory of Relativity.” 9On the surface, it did indeed seem to be based on a crazy notion: space has no borders because gravity bends it back on itself.

Einstein began by noting that an absolutely infinite universe filled with stars and other objects was not plausible. There would be an infinite amount of gravity tugging at every point and an infinite amount of light shining from every direction. On the other hand, a finite universe floating at some random location in space was inconceivable as well. Among other things, what would keep the stars and energy from flying off, escaping, and depleting the universe?

So he developed a third option: a finite universe, but one without boundaries. The masses in the universe caused space to curve, and over the expanse of the universe they caused space (indeed, the whole four-dimensional fabric of spacetime) to curve completely in on itself. The system is closed and finite, but there is no end or edge to it.

One method that Einstein employed to help people visualize this notion was to begin by imagining two-dimensional explorers on a two-dimensional universe, like a flat surface. These “flatlanders” can wander in any direction on this flat surface, but the concept of going up or down has no meaning to them.

Now, imagine this variation: What if these flatlanders’ two dimensions were still on a surface, but this surface was (in a way very subtle to them) gently curved? What if they and their world were still confined to two dimensions, but their flat surface was like the surface of a globe? As Einstein put it, “Let us consider now a two-dimensional existence, but this time on a spherical surface instead of on a plane.” An arrow shot by these flatlanders would still seem to travel in a straight line, but eventually it would curve around and come back—just as a sailor on the surface of our planet heading straight off over the seas would eventually return from the other horizon.

The curvature of the flatlanders’ two-dimensional space makes their surface finite, and yet they can find no boundaries. No matter what direction they travel, they reach no end or edge of their universe, but they eventually get back to the same place. As Einstein put it, “The great charm resulting from this consideration lies in the recognition that the universe of these beings is finite and yet has no limits. ” And if the flatlanders’ surface was like that of an inflating balloon, their whole universe could be expanding, yet there would still be no boundaries to it. 10