On November 25, 1915, Einstein presented his new equations to the Prussian Academy of Sciences in a short three-page paper,” this author tells us. Thus was the General Theory of Relativity born, after of course some years of gestation in Einstein’s remarkable brain.
With the centenary of that event almost upon us, a historical survey is in order. In The Perfect Theory, Pedro Ferreira, a professor of astrophysics at Oxford University, has supplied one.
I think most educated people know that Albert Einstein worked up two theories of relativity, the Special and the General. The Special Theory, published in 1905, rewrote the laws of physics for observers in uniform motion (constant speed in a straight line) relative to each other. It did so by uniting space and time in a 4-dimensional mathematical object, “spacetime,” with a very particular shape.
The General Theory, published ten years later, encompasses non-uniform motion by allowing spacetime to have any shape. The actual shape of a region of spacetime is determined by the gravitational forces present.
The Special Theory contains the famous equation E = mc2 — relating energy, mass, and the speed of light. By choosing suitable units of measurement the c2 can be made to disappear, leaving E = m. So mass is energy.
Much less well known is the key equation of General Relativity, G = 8πT. The boldface letters there are tensors, “packages” of measurements relative to some co-ordinate system. The numbers packaged in G, the Einstein tensor, define the shape of 4-dimensional spacetime: those in T, the energy-momentum tensor, list the local distribution of energy. So mass is energy is geometry!
Since G and T are packages of numbers, that key equation is actually a package of equations, commonly referred to in the plural as the field equations of General Relativity. The equations are interdependent; their solution depends on assumptions made about G and T. The equations were solved for particular simple assumptions while Einstein’s paper was still warm from the presses.
The case of a single point-sized gravitating particle in empty space, for example, was solved by Karl Schwarzschild, an artillery officer in the Kaiser’s forces on the Russian front. Schwarzschild’s solution not only explained oddities in the orbit of Mercury that had long baffled astronomers, it also predicted the existence of “black holes,” though physicists long resisted this particular conclusion and the phenomenon was not decisively named until 1967. Schwarzschild died in May 1916, a few weeks after his solution was published
General Relativity has had momentous consequences for cosmology. The very shape and fate of the universe is implicit in the field equations, and can be solved for once you have decided on the large-scale distribution of matter. Most broadly: Is the universe static, with the same overall appearance from one billion-year epoch to the next? Or is it evolving from this state to that different one? In 1916 all physicists, including Einstein, believed strongly in a static cosmos.
They also believed that the universe was, in Prof. Ferreira’s words, “full of stuff evenly spread out.” Feeding that assumption into the field equations, however, produced an evolving universe. To avoid this unhappy result, Einstein added a term Λg to the left-hand side of the tensor equation. That’s an upper-case Greek lambda, known to physicists as the “cosmological constant”; g is the fundamental geometric tensor from which G is derived.
When, in the 1920s, observations of distant galaxies showed that the universe is evolving after all, Λ had to be dropped, though the story that Einstein called Λ his “biggest blunder” is poorly sourced. For sixty years, Λ stayed dropped; then, following more accurate studies of very distant objects in the 1990s, Λ made a comeback and is now again included in statements of the field equations.
The curious history of Λ is only one of the threads from which Prof. Ferreira has woven his narrative. Quasars, pulsars, and dark matter have featuring roles. On the human side we read of the strange, sad career of Joseph Weber, nowadays handed out as a case study in Philosophy of Science courses. There is also good coverage of work on General Relativity done by great mid-twentieth-century Soviet physicists like Yakov Zel’dovich and Andrei Sakharov, whose stories are told at greater length in Istvan Hargittai’s Buried Glory.
There was a notion going around in the middle of the last century—I read it in one of Isaac Asimov’s articles at the time—that just as the years around 1700 belonged to chemistry, the years around 1800 to electricity, and the years around 1900 to radioactivity, so the years around 2000 would belong to gravitation; and that there would then emerge, later in the 21st century, a full-blown gravitational technology.
That hasn’t come to pass yet, but Prof. Ferreira’s closing two chapters hint at possibilities. (His last is titled: “Something is Going to Happen.”) If we do get gravitational technology, it will have taken its theoretical inspiration from those field equations Einstein cooked up a hundred years ago, and from the work of those who rose to their challenges—scholars whose stories are told here in The Perfect Theory, a strong candidate for pop-science Book of the Year.