relativity, resulting in a set of intricate and beautiful equations that were ready to be let loose on the world. It was time for others to start figuring out what they meant.
Chapter 3
Correct Mathematics, Abominable Physics
E INSTEINâS FIELD EQUATIONS were complicated, a tangle of many unknown functions, yet they could in principle be solved by anyone with the right ability and determination. In the decades that followed Einsteinâs discovery, an eclectic Soviet mathematician and meteorologist named Alexander Friedmann and Abbé Georges Lemaître, a brilliant, determined Belgian priest, took the equations of general relativity and constructed a radical new view of the universe, a view that Einstein himself refused to accept for a very long time. Through their work, the theory gained a life of its own, beyond Einsteinâs control.
When Einstein first formulated his field equations in 1915, he had wanted to solve them himself. Finding a solution to his equations that could accurately model the whole universe seemed a good place to start. In 1917 he set about doing so, making some simple assumptions. In Einsteinâs theory, the distribution of matter and energy told spacetime what to do. To model the universe as a whole, he needed to consider
all
the matter and energy in the universe. The simplest and most logical assumption, and the one Einstein adopted in his first attempt, was that matter and energy are spread evenly throughout the whole of space. In doing so, Einstein was just continuing a line of reasoning that had transformed astronomy in the sixteenth century. Then, Nicolaus Copernicus had made the brave proposal that the Earth wasnât the center of the cosmos and that, in fact, it orbited around the sun. This âCopernicanâ revolution had succeeded throughout the centuries in making our place in the cosmos ever more insignificant. By the mid-nineteenth century, it became clear that not even the sun was of great import and lay somewhere nondescript in one of the spiral arms of the Milky Way, our galaxy. When Einstein tackled his equations, he was merely extending the idea that anywhere in the universe should look more or less the same to its logical consequences: there should be no preferred place or center that stands out.
The assumption that the universe was full of stuff, evenly spread out, made the field equations much simpler, but it also led to a very strange result: Einsteinâs equations predicted that such a universe would start to evolve. At some point, all the evenly distributed bits of energy and matter would start moving relative to each other in an organized manner. On the largest scales, nothing would stay still. Eventually everything could even fall in on itself, pulling spacetime along with it and causing the entire universe to collapse out of existence.
In 1916, astronomersâ general view of the cosmos was parochial at best. While they had a pretty good map of the Milky Way, there was little, if any, sense of what lay beyond it. No one had a clear indication of what the universe was doing as a whole. All observations seemed to show that stars were moving about a little bit, but not dramatically and definitely not in a concerted, organized manner on a large scale. To Einstein, as to most people, the sky seemed static, and there was no evidence that the universe was collapsing or expanding. Letting his physical intuition and prejudice get the better of him, Einstein proposed a fix to eradicate the evolving universe from his theory. He attached a new constant term to his field equations. This cosmological constant would stabilize the universe by exactly compensating for all the stuff in it. All the ordinary stuff, the energy and matter that Einstein had spread out evenly in the universe, tried to pull spacetime in on itself, and the cosmological constant pushed back, preventing the universe from collapsing. This push and pull kept the universe in a delicate,
Chapter 3
Correct Mathematics, Abominable Physics
E INSTEINâS FIELD EQUATIONS were complicated, a tangle of many unknown functions, yet they could in principle be solved by anyone with the right ability and determination. In the decades that followed Einsteinâs discovery, an eclectic Soviet mathematician and meteorologist named Alexander Friedmann and Abbé Georges Lemaître, a brilliant, determined Belgian priest, took the equations of general relativity and constructed a radical new view of the universe, a view that Einstein himself refused to accept for a very long time. Through their work, the theory gained a life of its own, beyond Einsteinâs control.
When Einstein first formulated his field equations in 1915, he had wanted to solve them himself. Finding a solution to his equations that could accurately model the whole universe seemed a good place to start. In 1917 he set about doing so, making some simple assumptions. In Einsteinâs theory, the distribution of matter and energy told spacetime what to do. To model the universe as a whole, he needed to consider
all
the matter and energy in the universe. The simplest and most logical assumption, and the one Einstein adopted in his first attempt, was that matter and energy are spread evenly throughout the whole of space. In doing so, Einstein was just continuing a line of reasoning that had transformed astronomy in the sixteenth century. Then, Nicolaus Copernicus had made the brave proposal that the Earth wasnât the center of the cosmos and that, in fact, it orbited around the sun. This âCopernicanâ revolution had succeeded throughout the centuries in making our place in the cosmos ever more insignificant. By the mid-nineteenth century, it became clear that not even the sun was of great import and lay somewhere nondescript in one of the spiral arms of the Milky Way, our galaxy. When Einstein tackled his equations, he was merely extending the idea that anywhere in the universe should look more or less the same to its logical consequences: there should be no preferred place or center that stands out.
The assumption that the universe was full of stuff, evenly spread out, made the field equations much simpler, but it also led to a very strange result: Einsteinâs equations predicted that such a universe would start to evolve. At some point, all the evenly distributed bits of energy and matter would start moving relative to each other in an organized manner. On the largest scales, nothing would stay still. Eventually everything could even fall in on itself, pulling spacetime along with it and causing the entire universe to collapse out of existence.
In 1916, astronomersâ general view of the cosmos was parochial at best. While they had a pretty good map of the Milky Way, there was little, if any, sense of what lay beyond it. No one had a clear indication of what the universe was doing as a whole. All observations seemed to show that stars were moving about a little bit, but not dramatically and definitely not in a concerted, organized manner on a large scale. To Einstein, as to most people, the sky seemed static, and there was no evidence that the universe was collapsing or expanding. Letting his physical intuition and prejudice get the better of him, Einstein proposed a fix to eradicate the evolving universe from his theory. He attached a new constant term to his field equations. This cosmological constant would stabilize the universe by exactly compensating for all the stuff in it. All the ordinary stuff, the energy and matter that Einstein had spread out evenly in the universe, tried to pull spacetime in on itself, and the cosmological constant pushed back, preventing the universe from collapsing. This push and pull kept the universe in a delicate,
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