The Perfect Theory (9 page)

After more than a decade of being misled by his own misguided intuition, Einstein finally saw the light. It was an interesting turn of events. The creator of the general theory of relativity hadn't been brave enough to accept the predictions that his theory made about the universe and had tried to fudge the answer by introducing a fix. It was only by embracing general relativity in its full mathematical glory that Friedmann and Lemaître had been able to propose an evolving, expanding universe, and the observational data had proved them right. Einstein's praise crowned Lemaître in the eyes of the popular press. Just as Einstein himself had been propelled into the limelight, Lemaître was now acclaimed as the “World's Leading Cosmologist.” Lemaître would go on to become one of the grand old men of modern cosmology. Along with those of Alexander Friedmann, his ideas set the scene for the revolution in cosmology that would take place almost thirty years later.

Chapter 4

R
OBERT OPPENHEIMER
wasn't particularly interested in the general theory of relativity. He believed in it, as any sensible physicist would, but he didn't think it was particularly relevant for physics at the time. Which makes it ironic that he would discover one of the strangest, most exotic predictions of Einstein's theory: the formation of black holes in nature.

Oppenheimer's interests lay in the
other
new theory that had taken off over the previous decade. He had cut his teeth and become famous as a quantum physicist, studying with the great and good of modern physics in Europe, and had eventually created the leading group in quantum physics in the United States, based at the University of California's Berkeley campus. To some extent, it was the rise of quantum physics and of men like Oppenheimer that was responsible for exiling Einstein's theory to a period of stagnation and isolation. Yet, in 1939, with his student Hartland Snyder, in trying to understand what would happen at the endpoint of the life cycle of heavy stars, Oppenheimer found a strange, incomprehensible solution to the general theory of relativity that had been lurking in the background for almost twenty-five years. Oppenheimer showed that if a star is big and dense enough, it will collapse out of sight. As he put it, after a while
“the star tends to close itself off from any communication with a distant observer; only its gravitational field persists.” It would seem as if a mysterious shroud had arisen around the collapsing ball of light and energy, hiding it from the outside world, and spacetime would wrap itself up in an impossibly tight knot. Nothing would be able to escape outside the shroud, not even light. Oppenheimer's result was yet another mathematical oddity that emerged from Einstein's equations, and many found it too difficult to stomach.

 

Almost a quarter of a century before Oppenheimer and Snyder found their result, the German astronomer Karl Schwarzschild had sent a letter to Einstein, signing off, “As you see, the war is kindly disposed toward me, allowing me, despite gunfire at a decidedly terrestrial distance, to take this walk into this your land of ideas.” It was December of 1915 and Schwarzschild was writing from the trenches on the eastern front. He had volunteered immediately after the outbreak of the First World War in 1914, even though, as the director of the Potsdam Observatory, he was not required to fight. But, as Eddington later said of him, “Schwarzschild's bent was more practical.” Like Friedmann, he had brought his ability as a physicist to bear on his military service, even submitting a paper to the Berlin Academy on “The Effect of Wind and Air-Density on the Path of a Projectile.”

While in Russia, Schwarzschild received the latest copy of the
Proceedings of the Prussian Academy of Sciences.
In it he found Einstein's brief but breathtaking presentation of his new general theory of relativity. He had set to work unpicking the field equations that Einstein was proposing, looking at the simplest, most physically interesting situation he could think of. Unlike Alexander Friedmann and Georges Lemaître, who would years later look at the universe as a whole, Schwarzschild decided to focus on something less grand: the spacetime around a spherical mass such as a planet or a star.

When tackling a tangled mess of equations like the ones Einstein proposed, it helps to simplify. By looking at the spacetime around a star, Schwarzschild could focus on finding solutions that were static and didn't evolve with time. Furthermore, he wanted a solution that looked exactly the same at the pole as near the equator so that all that should matter was the distance of any point in space from the center of the star.

Schwarzschild's solution was immensely simple, a condensed formula that took almost no time write down. And to some extent, it was obvious. If you were located a fair distance away from the star's center, its gravitational field behaved much as Newton centuries before had predicted—the gravitational attraction of the star would depend on its mass and would fall as the square of the distance. Schwarzschild's formula was different, true, but the differences were very small—just enough to explain the drift in Mercury's orbit that had been hovering over Einstein's whole endeavor.

But as you moved closer to the star, something very strange happened. If the star was small but heavy enough, it would be shrouded by a spherical surface that kept everything behind it hidden from sight—the same surface that Oppenheimer and Snyder would find many years later. This surface had a devastating effect on anything that tried to pass through it. If anything flew too close to the star and fell within that spherical boundary, it would never be able to get out again—it was a point of no return. To get out of Schwarzschild's magic sphere, you would need to travel at speeds greater than the speed of light. And that, according to Einstein's theory, was impossible. Schwarzschild had discovered what would, more than half a century later, be called black holes.

Schwarzschild rapidly wrote up his results and sent them to Einstein in a letter, asking him to present them at the Prussian Academy of Sciences. Einstein approved and responded by saying,
“I had not expected that one could formulate the exact solution of the problem in such a simple way.” In late January of 1916, Einstein presented Schwarzschild's solution to the world.

Schwarzschild would never get to explore his solution any further, let alone hear of Oppenheimer and Snyder's calculation. For a few months later, while still in Russia, Schwarzschild contracted pemphigus, a virulent blistering autoimmune disease. His own body turned against him, and he died in May 1916.

Schwarzschild's solution was rapidly adopted by Einstein and his followers. It was simple, easy to work with, and perfect for making predictions. It could be used, for example, in a model of the sun to work out the motion of the planets and make an accurate prediction of the precession of Mercury's orbit. It also accurately predicted the bending of light that Eddington set out to find in Príncipe. Schwarzschild's solution served the new relativists well, except for that unfathomable property of the strange surface shrouding the center of certain dense, small stars and keeping everything out.

There was no denying the surface was there in the equations and the solution. It was a valid solution of Einstein's general theory of relativity. But did it actually exist in nature?

 

During the 1920s, Arthur Eddington turned to figuring out how stars form and evolve. He wanted to completely characterize the structure of stars using fundamental laws of physics couched in the correct mathematical equations. He wrote,
“When we obtain by mathematical analysis an understanding of a result . . . we have obtained knowledge adapted to the fluid premises of a natural physical problem.” With the mathematics in hand, it would simply be a matter of solving equations, just as with general relativity. In 1926 Eddington published a book,
The Internal Constitution of the Stars,
which rapidly became the bible for stellar astrophysics. Not only was Eddington a world authority on general relativity; he was also the leading light on stars.

Stars had until then been a bit of a mystery. For a start, no one had a clear idea of how they could emit such copious amounts of energy. It was Eddington who came up with a plausible mechanism for how stars are fueled. To understand his idea, we need to take a close look at the simplest atoms. A hydrogen atom is made up of two particles, a proton (which is positively charged) and an electron (which is negatively charged). The proton and electron are held together by electromagnetic force, which causes opposite charges to attract one another. The proton is approximately two thousand times heavier than the electron and so makes up almost all the weight of the hydrogen atom.

A helium atom consists of two electrons and two protons. But it also contains two
neutral
particles at its core: neutrons, which have almost exactly the same weight as protons. A simple model of the helium atom shows a nucleus made up of two protons and two neutrons orbited by the two electrons. Almost all the weight of the helium atom is made up of the four particles in the nucleus, and one would expect helium to be four times heavier than hydrogen. But helium is slightly lighter, by about 0.7 percent, than the expected mass of four hydrogen atoms. Some of its mass seems to be missing. And where there is missing mass, according to Einstein's special theory of relativity, there is missing energy. This was Eddington's cue.

Eddington argued that the interconversion between hydrogen and helium might be the source of energy in stars. Hydrogen nuclei would slam together in the intense, hot inferno at the core of stars. Some of the protons, through radioactive decay, would transform into neutrons, and collectively the protons and neutrons would form helium nuclei. In the process, each atom would release a minute amount of energy. The combined energy released by the atoms would be enough to fuel the star and emit light. If most of the sun started in the form of hydrogen, it should be able burn for almost 9 billion years before its conversion into helium is complete. Given that the Earth is currently about 4.5 billion years old, the numbers seemed to add up.

In his book, Eddington created a whole edifice for explaining stellar astrophysics. After proposing a source for stars' energy, he explained why they didn't collapse: they could withstand the pull of gravity by radiating all the energy they produced outward. Stars were perfect physical systems that could be described in terms of his equations. Yet
The Internal Constitution of the Stars
told an incomplete story. Eddington could describe the life of stars in terms of his mathematical pyrotechnics, but he stopped short of explaining their death. His own rationale led to the logical conclusion that at some point a star's fuel would run out and the radiation preventing it from collapsing under the force of its own gravity would disappear. As he said in his book,
“It would seem that the star will be in an awkward predicament when its supply of subatomic energy ultimately fails. . . . It is a curious problem and one may make many fanciful suggestions as to what actually will happen.” And, of course, one possible fanciful suggestion would be to embrace Einstein's theory and Schwarzschild's solution so that, as Eddington wrote, “the force of gravitation would be so great that light would be unable to escape from it, the rays falling back to the star like a stone to the earth.” That was too far-fetched for Eddington, merely a mathematical result. For, as he declared,
“when we
prove
a result without understanding it—when it drops unforeseen out of a maze of mathematical formulae—we have no grounds for hoping that it will apply.”

Without being fanciful, then, what
would
happen when the fuel ran out? There were hints about the graveyard for stellar collapse in observations made in 1914. Astronomers had peered at the brightest star in the sky, Sirius, which is almost thirty times brighter than the sun, and observed an odd, dim companion orbiting it. Dubbed Sirius B, despite its dimness, it was incredibly hot and had remarkable properties: Sirius B had about the same mass as the sun, yet its radius was much smaller than Earth's. This meant that the companion star was very, very dense. By the early twenties, this object had been named a white dwarf and stood out as a mystery in the stellar zoo, a possible endpoint for the life cycle of a star. A key to explaining white dwarfs and their fate would come from the newfangled theory of quantum physics.

 

Quantum physics divided nature into its smallest constituents and put it back together in an outlandish way. It emerged from the bizarre phenomena that were being observed in the nineteenth century when physicists discovered that compounds and chemicals reemit or absorb light in a peculiar fashion. Rather than emitting or absorbing light in a continuous range of wavelengths, the substances would throw off light only in a discrete set of specific wavelengths, creating the bar-code-like spectra that would later reveal redshifting to Vesto Slipher and Milton Humason. The Newtonian physics that reigned at the time, allied with Maxwell's theory of electricity and light, couldn't explain this strange phenomenon.

During his miraculous year in 1905, Einstein had tackled another odd experimental fact: the photoelectric effect. If you bombard a metal with light, its atoms will soak up the light and sometimes release an electron. As the phenomenon's discoverer, Philipp Lenard, described it, “By mere exposure to ultraviolet light, metal plates give off negative electricity to the air.” You might think that all you need to do is blast enough light at the metal for this to happen, but that isn't the case. Only if the beam has exactly the right energy and frequency will an electron be emitted. Einstein looked at this effect and conjectured that light comes in chunks of energy, quantized in the same way that matter breaks down into fundamental particles. Only when one of these light particles has just the right frequency would the photoelectric effect come into play. Einstein called these particles “light quanta” and they later became known as photons.