by Michio Kaku
Progress in this direction was confusing, since now there were at least three cosmological models about how the universe should evolve (Einstein’s, de Sitter’s, and Friedmann-Lemaître’s). The matter rested until 1929, when it was finally settled by the astronomer Edwin Hubble, whose results were to shake the foundations of astronomy. He first demolished the one-galaxy universe theory by demonstrating the presence of other galaxies far beyond the Milky Way. (The universe, far from being a comfortable collection of a hundred billion stars contained in a single galaxy, now contained billions of galaxies, each one containing billions of stars. In just one year, the universe suddenly exploded.) He found that there were potentially billions of other galaxies, and that the closest one was Andromeda, about two million light-years from Earth. (The word “galaxy,” in fact, comes from the Greek word for “milk,” since the Greeks thought that the Milky Way galaxy was milk spilled by the gods across the night sky.)
This shocking revelation alone would have guaranteed Hubble’s fame among the giants of astronomy. But Hubble went further. In 1928, he made a fateful trip to Holland where he met de Sitter, who claimed that Einstein’s general relativity predicted an expanding universe with a simple relationship between red shift and distance. The farther a galaxy was from Earth, the faster it would be moving away. (This red shift is slightly different from the red shift considered by Einstein back in 1915. This red shift is caused by galaxies receding from Earth in an expanding universe. If a yellow star, for example, moves away from us, the speed of the light beam remains constant but its wavelength gets “stretched,” so that the color of the yellow star reddens. Similarly, if a yellow star approaches Earth, its wavelength is shrunken, squeezed like an accordion, and its color becomes bluish.)
When Hubble returned to the observatory at Mt. Wilson, he began a systematic determination of the red shift of these galaxies to see if this correlation held up. He knew that back in 1912, Vesto Melvin Slipher had shown that some distant nebulae were receding from Earth, creating a red shift. Hubble now systematically calculated the red shift coming from distant galaxies and discovered that these galaxies were receding from Earth—in other words, the universe was expanding at a fantastic rate. He then discovered that his data could fit the conjecture made by de Sitter. This is now called “Hubble’s law”: the faster a galaxy is receding from Earth, the farther it is (and vice versa).
Plotted on a curve, graphing distance versus velocity, Hubble found a near straight line, as predicted by general relativity, whose slope is now called “Hubble’s constant.” Hubble, in turn, was curious to know how his results would fit into Einstein’s. (Unfortunately, Einstein’s model had matter but no motion, and de Sitter’s universe had motion but no matter. His results did seem to agree with the work of Friedmann and Lemaître, which possessed both matter and motion.) In 1930, Einstein made the pilgrimage to the Mt. Wilson observatory, where he met Hubble for the first time. (When the astronomers there proudly boasted that their mammoth 100-inch telescope, the biggest in the world at that time, could determine the structure of the universe, Elsa was not impressed. She said, “My husband does that on the back of an old envelope.”) As Hubble explained the painstaking results he found from analyzing scores of galaxies, each one receding from the Milky Way, Einstein admitted that the cosmological constant was the greatest blunder of his life. The cosmological constant, introduced by Einstein to artificially create a static universe, was now dispensable. The universe did expand as he found a decade earlier.
Furthermore, Einstein’s equations gave perhaps the simplest derivation of Hubble’s law. Assume the universe is a balloon that is expanding, with the galaxies represented as tiny dots painted on the balloon. To an ant sitting on any one of these dots, it appears as if every other dot is moving away from it. Likewise, the farther a dot is away from the ant, the faster it is moving away, as in Hubble’s law. Thus, Einstein’s equations gave new insights into such ancient questions like, is there an end to the universe? If the universe ends with a wall, then we can ask the question, what lies beyond the wall? Columbus might have answered that question by considering the shape of the earth. In three dimensions, the earth is finite (being just a ball floating in space), but in two dimensions, it appears infinite (if one goes around and around its circumference) so anyone walking on the surface of the earth will never find the end. Thus, the earth is both finite and infinite at the same time, depending on the number of dimensions one measures. Likewise, one might state that the universe is infinite in three dimensions. There is no brick wall in space that represents the end of the universe; a rocket sent into space will never collide with some cosmic wall. However, there is the possibility that the universe might be finite in four dimensions. (If it were a four-dimensional ball, or hypersphere, you might conceivably travel completely around the universe and come back to where you started. In this universe, the farthest object you can see with a telescope is the back of your head.)
If the universe is expanding at a certain rate, then one can reverse the expansion and calculate the rough time at which the expansion first originated. In other words, not only did the universe have a beginning, but also one could calculate its age. (In 2003, satellite data showed that the universe is 13.7 billion years old.) In 1931, Lemaître postulated a specific origin to the universe, a super-hot genesis. If one took Einstein’s equations to their logical conclusion, they showed that there was a cataclysmic origin to the universe.
In 1949, cosmologist Fred Hoyle christened this the “big bang” theory during a discussion on BBC radio. Because he was pushing a rival theory, the legend got started that he coined the name “big bang” as an insult (although he later denied that story). However, it should be pointed out that the name is a complete misnomer. It was not big, and there was no bang. The universe started out as an infinitesimally small “singularity.” And there was no bang or explosion in the conventional sense, since it was the expansion of space itself that pushed the stars apart.
Not only did Einstein’s theory of general relativity introduce entirely unexpected concepts such as the expanding universe and the big bang, but also it introduced another concept that has intrigued astronomers ever since: black holes. In 1916, just one year after he published his theory of general relativity, Einstein was astonished to receive word that a physicist, Karl Schwarzschild, had solved his equations exactly for the case of a single pointlike star. Previously, Einstein had only used approximations to the equations of general relativity because they were so complex. Schwarzschild delighted Einstein by finding an exact solution, with no approximations whatsoever. Although Schwarzschild was director of the Astrophysical Observatory in Potsdam, he volunteered to serve Germany on the Russian front. Remarkably, as a soldier dodging shells bursting overhead, he managed against all odds to work on physics. Not only did he calculate the trajectory of artillery shells for the German army, he also calculated the most elegant, exact solution of Einstein’s equations. Today, this is called the “Schwarzschild solution.” (Unfortunately, he never lived long enough to enjoy the fame that his solution generated. One of the brightest stars emerging in this new field of relativity, Schwarzschild died at the age of forty-two, just a few months after his papers were published, from a rare skin disease he picked up while fighting on the Russian front, a waste for the world of science. Einstein delivered a moving eulogy for Schwarzschild, whose death only re-enforced Einstein’s hatred of the senselessness of war.)
The Schwarzschild solution, which created quite a sensation in scientific circles, also had strange consequences. Schwarzschild found that extremely close to this pointlike star, gravity was so intense that even light itself could not escape, so the star became invisible! This was a sticky problem not only for Einstein’s theory of gravity but also for the Newtonian theory. Back in 1783, John Michell, rector of Thornhill in England, posed the question whether a star could become so massive that even light could not escape. His calculations, using only Newtonian laws, could not be truste
d because no one knew precisely what the speed of light was, but his conclusions were hard to dismiss. In principle, a star could become so massive that its light would orbit around it. Thirteen years later, in his famous book Exposition du système du monde, mathematician Pierre-Simon Laplace also asked whether these “dark stars” were possible (but probably found the speculation so wild that he deleted it from the third edition). Centuries later, the question of dark stars came up again, thanks to Schwarzschild. He found that there was a “magic circle” surrounding the star, now called the “event horizon,” at which mind-bending distortions of space-time occur. Schwarzschild demonstrated that anyone unfortunate enough to fall past this event horizon would never return. (You would have to go faster than the speed of light to escape, which is impossible.) In fact, from inside the event horizon, nothing can escape, not even a light beam. Light emitted from this pointlike star would simply orbit around the star forever. From the outside, the star would appear shrouded in darkness.
One could use the Schwarzschild solution to calculate how much ordinary matter had to be compressed to reach this magic circle, called the “Schwarzschild radius,” at which point the star would completely collapse. For the sun, the Schwarzschild radius was 3 kilometers, or less than 2 miles. For the earth, it was less than a centimeter. (Since this compression factor was beyond physical comprehension in the 1910s, physicists assumed that no one would ever encounter such a fantastic object.) But the more Einstein studied the properties of these stars, later christened “black holes” by physicist John Wheeler, the stranger they became. For example, if you fell into a black hole, it would only take a fraction of a second to fall through the event horizon. As you briefly sailed past it, you would see light orbiting the black hole that was captured perhaps aeons—perhaps billions of years—ago. The final millisecond would not be a very pleasant one. The gravitational forces would be so great that the atoms of your body would be crushed. Death would be inevitable and horrible. But observers watching this cosmic death take place from a safe distance would see an entirely different picture. The light emitted from your body would be stretched by gravity, so it would appear as if you were frozen in time. To the rest of the universe, you would still be hovering over the black hole, motionless.
These stars, in fact, were so fantastic that most physicists thought they could never be found in the universe. Eddington, for example, said, “There should be a law of Nature to prevent a star from behaving in this absurd way.” In 1939, Einstein tried to show mathematically that such a black hole was impossible. He began by studying a star in formation, that is, a collection of particles circling around in space, gradually pulled in by their gravitational force. Einstein’s calculation showed that this circling collection of particles would gradually collapse, but would only come within 1.5 times the Schwarzschild radius, and hence a black hole could never form.
Although this calculation seemed airtight, what Einstein apparently missed was the possibility of an implosion of matter in the star itself, created by the crushing effect of the gravitational force overwhelming all the nuclear forces in matter. This more detailed calculation was published in 1939 by J. Robert Oppenheimer and his student Hartland Snyder. Instead of assuming a collection of particles circling in space, they assumed a static star, large enough so that its massive gravity could overwhelm the quantum forces inside the star. For example, a neutron star consists of a large ball of neutrons about the size of Manhattan (20 miles across) making up a gigantic nucleus. What keeps this ball of neutrons from collapsing is the Fermi force, which prevents more than one particle with certain quantum numbers (e.g., spin) from being in the same state. If the gravitational force is large enough, then one can overcome the Fermi force and thereby squeeze the star to within the Schwarzschild radius, at which point nothing known to science can prevent a complete collapse. However, it would be another three decades or so before neutron stars were found and black holes were discovered, so most of the papers on the mind-bending properties of black holes were considered highly speculative.
Although Einstein was still rather skeptical about black holes, he was confident that one day yet another of his predictions would come true: the discovery of gravity waves. As we have seen, one of the triumphs of Maxwell’s equations was the prediction that vibrating electric and magnetic fields would create a traveling wave that could be observed. Likewise, Einstein wondered if his equations allowed for gravity waves. In a Newtonian world, gravity waves cannot exist, since the “force” of gravity acts instantaneously throughout the universe, touching all objects simultaneously. But in general relativity, in some sense, gravity waves have to exist, as vibrations of the gravitational field cannot exceed the speed of light. Thus, a cataclysmic event, such as the collision of two black holes, will release a shock wave of gravity, a gravity wave, traveling at the speed of light.
As early as 1916, Einstein was able to show that with suitable approximations, his equations did yield wavelike motions of gravity. These waves spread across the fabric of space-time with the speed of light, as expected. In 1937, with his student Nathan Rosen, he was able to find an exact solution of his equations that gave gravity waves, with no approximations whatsoever. Gravity waves were now a firm prediction of general relativity. Einstein despaired, however, of ever being able to witness such an event. Calculations showed that it was far beyond the experimental capabilities of scientists at that time. (It would take almost eighty years, since Einstein first discovered gravity waves in his equations, for the Nobel Prize to be awarded to physicists who found the first indirect evidence for gravity waves. The first gravity waves may be directly detected perhaps ninety years after his first prediction. These gravity waves, in turn, may be the ultimate means by which to probe the big bang itself and find the unified field theory.)
In 1936, a Czech engineer, Rudi Mandl, approached Einstein with yet another idea concerning the strange properties of space and time, asking whether gravity from a nearby star could be used as a lens to magnify the light from distant stars, in the same way that glass lenses can be used to magnify light. Einstein had considered this possibility back in 1912, but, prodded by Mandl, calculated that the lens would create a ringlike pattern to an observer on Earth. For example, consider light from a faraway galaxy passing by a nearby galaxy. The gravity of the nearby galaxy might split the light in half, with each half going around the galaxy in opposite directions. When the light beams pass the nearby galaxy completely, they rejoin. From the earth, one would see these light beams as a ring of light, an optical illusion created by the bending of light around the nearby galaxy. However, Einstein concluded that “there is not much hope of observing this phenomenon directly.” In fact, he wrote that this work “is of little value, but it makes the poor guy [Mandl] happy.” Once again, Einstein was so far ahead of his time that it would take another sixty years before Einstein lenses and rings would be found and eventually become indispensable tools by which astronomers probe the cosmos.
As successful and far-reaching as general relativity was, it did not prepare Einstein in the mid-1920s for the fight of his life, to devise a unified field theory to unite the laws of physics while simultaneously doing battle with the “demon,” the quantum theory.
PART III
THE UNFINISHED PICTURE
The Unified Field Theory
CHAPTER 7
Unification and the Quantum Challenge
In 1905, almost as soon as Einstein worked out the special theory of relativity, he began to lose interest in it because he set his sights on bigger game: general relativity. In 1915, the pattern repeated itself. As soon as he finished formulating his theory of gravity, he began to shift his focus to an even more ambitious project: the unified field theory, which would unify his theory of gravity with Maxwell’s theory of electromagnetism. It was supposed to be his masterpiece, as well as the summation of science’s two-thousand-year investigation into the nature of gravity and light. It would give him the ability to “read the
Mind of God.”
Einstein was not the first to suggest a relationship between electromagnetism and gravity. Michael Faraday, working at the Royal Institution in London in the nineteenth century, performed some of the first experiments to probe the relationship between these two pervasive forces. He would, for example, drop magnets from the London Bridge and see if their rate of descent differed from that of ordinary rocks. If magnetism interacted with gravity, perhaps the magnetic field might act as a drag on gravity, making the magnets fall at a different rate. He would also drop pieces of metal from the top of a lecture room to a cushion on the floor, trying to see if the descent could induce an electric current in the metal. All his experiments produced negative results. However, he noted, “They do not shake my strong feeling of the existence of a relation between gravity and electricity, though they give no proof that such a relation exists.” Furthermore, Riemann, who founded the theory of curved space in any dimension, believed strongly that both gravity and electromagnetism could be reduced to purely geometric arguments. Unfortunately, he did not have any physical picture or field equations, so his ideas went nowhere.
