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Some people initially suggested that the big bang singularity was an artifact of the assumptions of exact homogeneity and isotropy that Friedmann adopted to solve Einstein’s equations. In a collapsing universe, if all galaxies were moving radially toward us, it would be no wonder that they would all crush together in a big crunch. But if the motion of galaxies were even slightly nonradial, one might think that they would bypass one another and start flying apart afterward. The singularity would then be avoided, and contraction would be followed by an expansion. Thus, one might hope to construct an oscillating model of the universe, without a beginning, with alternating periods of expansion and contraction.
It turns out, however, that the attractive nature of gravity makes this scenario impossible. The British physicist Roger Penrose and Stephen Hawking, who was a graduate student at the time, proved a series of theorems showing, under very general assumptions, that the cosmological singularity cannot be avoided. The main assumptions used in the proofs are that Einstein’s general theory of relativity is valid, and that matter has positive energy density and pressure everywhere in the universe. (More precisely, the pressure should not get so negative as to make gravity repulsive.) Thus, as long as we stay within the framework of general relativity and do not assume exotic repulsive-gravity matter, the singularity will be with us and the question of the initial conditions will remain unresolved.
The most notorious attempt to avoid the problem of the beginning was no doubt the steady-state theory, suggested in 1948 by the British astrophysicist Fred Hoyle and two Austrian refugees, Hermann Bondi and Thomas Gold, all at Cambridge University. They boldly asserted that the universe has always remained unchanged in its broad features, so that it looks more or less the same at all places and at all times. This view seems to be in glaring
contradiction with the expansion of the universe: If the distances between the galaxies grow, how can the universe remain unchanged? To compensate for the expansion, Hoyle and his friends postulated that matter is being continuously created out of the vacuum. This matter fills the voids opened by the receding galaxies, so that new galaxies can be formed in their place.
The Cambridge physicists admitted that they had no evidence for the spontaneous creation of matter, but the required creation rate was so low—a few atoms per cubic mile per century—that there was no evidence against it either. They further defended their theory by pointing out that continuous creation of matter, in their view, was no more objectionable than creation of all matter at once in the big bang. In fact, the term “big bang” was coined by Hoyle as he ridiculed the competing theory in a popular BBC radio talk show.
It did not take long, however, for the steady-state theory to run into serious problems. The most distant galaxies are seen as they were billions of years ago, because that is how long it takes for their light to reach us. If the steady-state theory is correct, and the universe at that time was the same as it is now, then these distant galaxies should look more or less the same as the galaxies we now see in our own neighborhood. With more data, however, it became increasingly clear that far-away galaxies are actually quite different and show distinct signs of their youth. They are smaller, have irregular shapes, and are populated with very bright, short-lived stars. Many of them are powerful sources of radio waves, a trait much less common among the older, nearby galaxies.
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There seemed to be no way in which the observations could be explained in terms of the steady-state theory.
As Sherlock Holmes used to say, “When you have eliminated the impossible, whatever remains, however improbable, must be the truth.”
7
The prospects of the steady-state theory were getting dimmer, and with no other viable alternative in sight, attitudes began to shift. Physicists were gradually coming to terms with the picture of an evolving universe that started with a bang.
The Modern Story of Genesis
The elements were cooked in less time than it takes to cook a dish of duck and roast potatoes.
—GEORGE GAMOW
T
he idea of the primeval fireball was born in the mind of George Gamow, a flamboyant Russian-born physicist whom we shall encounter more than once as our story develops. A fellow physicist, Leon Rosenfeld, described him as “a Slav giant, fair haired and speaking a very picturesque German; in fact he was picturesque in everything, even in his physics.”
1
Gamow took Friedmann’s course in general relativity in 1923-24, while he was a graduate student in Petrograd; thus he heard about the expanding universe solutions, so to say, from the horse’s mouth. He wanted to do research in cosmology under Friedmann, but this plan was ruined by Friedmann’s sudden death. Gamow ended up writing his thesis on the dynamics of a pendulum, a subject he characterized as “extremely dull.”
2
In 1928, at the instigation of his old professor, Orest Khvolson, Gamow was given a stipend to spend the summer at the University of Göttingen in Germany. That was the time when quantum mechanics was being developed, and Göttingen was one of the leading centers in this area of research. Physicists were trying to capture the essence of the new theory and to contribute
to its rapid advance. Discussions that started in seminar rooms during the day continued in the streets and cafés in the evenings, and it was hard not to be infected by this atmosphere of excitement and discovery. Gamow decided to investigate what quantum mechanics could say about the structure of atomic nuclei, and very quickly he made his mark. He used what is called the
tunneling
effect—the penetration of a barrier by a quantum particle—to explain the radioactive decay of nuclei. His theory was in beautiful agreement with the experimental data.
When the summer came to an end and it was time to return to Petrograd (now called Leningrad), Gamow decided to make a stop in Denmark and visit the legendary Niels Bohr, one of the founders of the quantum theory. He told Bohr about his work on radioactivity (which was not yet published), and Bohr was sufficiently impressed to offer Gamow a fellowship at his institute in Copenhagen. Of course, Gamow accepted with enthusiasm. He continued work in nuclear physics and soon became a recognized authority in this field.
In 1930 Gamow was invited to give a major talk at the International Congress on Nuclear Physics in Rome. He was already preparing to cross Europe on his little motorcycle when he learned from the Soviet embassy that his passport could not be extended and that he had to return to the Soviet Union before traveling anywhere else.
Back in Leningrad, Gamow immediately sensed that things had taken a drastic turn for the worse. The Stalinist regime was tightening its grip on the country. Science and art had to conform to the official Marxist ideology, and anyone accused of “bourgeois” idealistic views was severely persecuted. Quantum mechanics and Einstein’s theory of relativity were declared nonscientific and contrary to Marxism-Leninism. When Gamow mentioned quantum physics in a public lecture, a government representative interrupted the lecture and dismissed the audience. Gamow was warned that such mistakes were not to be repeated. Even before this incident, he was told he could forget about foreign travel and should not bother applying for a passport. The iron curtain was tightly closed. In Gamow’s mind, the writing was on the wall: he had to escape from the Soviet Union.
With his wife Lyuba, whom he had married soon after his return to Leningrad, Gamow was preparing for the escape. The plan was to cross the Black Sea from the Crimean Peninsula to Turkey. Childish as it may seem,
they wanted to do this in a kayak. They had a food supply for a week and a simple navigation plan: paddling straight to the south. But the Black Sea is not called black for nothing. Perfectly calm when the two adventurers left in the morning, the sea became increasingly rough toward the evening. During the night, it took all their efforts to keep the boat from turning over. Accepting defeat, they were now fighting to get back to the shore and felt fortunate when they finally made it the following day.
It was totally unexpected when in the summer of 1933 Gamow was informed that he had been appointed to represent the Soviet Union at the prestigious Solvay Congress on nuclear physics in Brussels. He was overjoyed, but had no idea what to make of it. The explanation came on arrival at the congress. When Gamow did not show up in Rome, Niels Bohr got concerned and wanted to see his old friend. He asked the French physicist Paul Langevin, a member of the French Communist Party, to use his connections to arrange Gamow’s appointment to the Solvay Congress. But, Gamow was horrified to find out, Bohr gave Langevin his personal assurance that Gamow was going to return to the Soviet Union! That evening at the dinner table Gamow sat next to Marie Curie, the famous discoverer of radium and plutonium, and told her about his impossible situation. Madame Curie knew Langevin very well (rumors said too well); she said she would talk to him. After a sleepless night and a day of anxious anticipation, Gamow finally heard from Curie that the issue was settled and he did not have to go back. The following year he accepted a professorship at George Washington University in the United States.
Gamow realized that the early universe was not only superdense, it was also superhot. The reason is that gases get hotter when they are compressed and cool down when they expand. (People who ride bicycles tell me that they know this property firsthand: a bicycle tire gets warm when you pump it with air. The compressed air heats up and the surface of the tire gets warmer as a result.)
To see why expansion causes a gas to cool down, consider a gas contained in a large box. You can picture the gas molecules as little balls bouncing off the walls of the box. Imagine now that the walls are moving apart,
so that the box is expanding. What effect will the recession of the walls have on the molecules? If you hit a tennis ball against a wall during a tennis practice, the ball comes back at you at the same speed. But imagine for a moment that the wall is moving away from you. The ball’s speed relative to the wall would then be smaller, and it would bounce back slower than you sent it off. Similarly, the molecules in an expanding box will slow down on each reflection from the walls. The temperature is proportional to the average energy of the molecules and will therefore decrease in the course of expansion. Of course, there are no moving walls in the expanding universe, but particles are reflected off one another, and the effect on the temperature is the same. The universe was getting progressively colder as it expanded. Thus, if we go back in time, the universe gets hotter and hotter, and it becomes infinitely hot if we extrapolate all the way back to the singularity.
At temperatures above a few hundred degrees kelvin,
f
the bonds holding atoms together inside molecules are not strong enough to withstand the heat, and the molecules decompose into separate atoms. Further increase of temperature leads to a progressive breakup of atoms. First, at about 3000 degrees kelvin, electrons are stripped off the atomic nuclei,
3
then at a billion degrees or so the nuclei fragment into protons and neutrons (collectively called
nucleons
), and finally at about a trillion degrees the nucleons break apart into their elementary constituents, called
quarks
.
Apart from matter particles that make up atoms, the fireball also contained vast quantities of radiation quanta, called
photons
. Photons are bundles of electric and magnetic energy; they are what ordinary visible light is made of. Moving charged particles emit and absorb photons, so equilibrium is quickly established where photons are absorbed at the same rate as they are emitted. The higher the temperature is, the higher are the average energy and the density of photons in equilibrium. The recipe for the hot cosmic soup thus appears to be very simple: break everything down to the smallest pieces, and then mix together and add a suitable quantity of photons. But there is more to it than that.
The further back in time we go, the more energetic the particles become. They are also more densely packed, and constantly bump into one another.
To understand the makeup of the fireball, we need to know what happens in such high-energy collisions. Smashing elementary particles is the favorite occupation of particle physicists. They build monstrous machines, called particle accelerators, where they boost particles to huge energies, let them collide, and see what happens. This is much more exciting than watching billiard balls collide, because particles often change their identity in collisions—it would be as if red and blue balls turned into yellow and green ones as they hit one another. The number of particles can also be altered: two initial particles can produce fireworks with dozens of new particles flying away from the collision point. This type of event was commonplace in the early moments after the big bang.
In such a collision, you cannot predict exactly what is going to happen. There is a large number of possible outcomes, and physicists use quantum theory to calculate their probabilities. But this is as far as you can go: there is no certainty in the quantum world. The range of possibilities is constrained by a few
conservation laws
, which are strictly enforced. Examples are energy and charge conservation: the total energy and the total electric charge should be the same before and after collision. Any process that is not forbidden by the conservation laws is thereby allowed and will occur with some nonzero probability. In the early universe, particles are incessantly hitting one another, and the fireball gets populated with all types of particles that can be created in these encounters.
For each type of particle, there exists an antiparticle of precisely the same mass and opposite electric charge. Particles and antiparticles are often created in pairs. For example, two photons with energies greater than that associated with the electron mass (through E = mc
2
) can collide and turn into an electron and its antiparticle, called a
positron
. The opposite process is
pair annihilation:
an electron and a positron smash into one another and turn into two photons.
At temperatures above 10 billion degrees, particle energies become large enough to produce electron-positron pairs. As a result, the fireball gets populated with a gas of electrons and positrons having about the same density as the gas of photons. At still higher temperatures, pairs of increasingly heavier particles make their appearance. Physicists have catalogued an extensive zoo of particles with a wide range of masses. At the top of this range are W and Z particles, which are about 300,000 times more massive than
electrons, and the
top quark
, about twice as heavy as W or Z. These are the heaviest particles that can currently be produced in particle accelerators. They existed in the fireball at temperatures above 3000 trillion degrees. As we approach these temperatures, our knowledge of particle physics becomes more and more sketchy and our understanding of the primeval fireball more and more uncertain.
Friedmann’s equations can be used to determine what temperature and density the fireball had at any given time. For example, at 1 second after the big bang, the temperature was 10 billion degrees and the density about 1 ton per cubic centimeter. (To avoid repeating “after the big bang,” I will use the abbreviation “A.B.”)
The most eventful part of the fireball history, marked by a rapid succession of exotic particle populations, occurred during the first second of its existence. The W, Z, and heavier particles were abundant only in the first 0.00000000001 second A.B. Muons—particles similar to electrons but 200 times heavier—and their antiparticles annihilated at 0.0001 second. At about the same time, triplets of quarks merged together to form nucleons. The last to annihilate were electron-positron pairs. They disappeared at 1 second A.B. There must have been a slight excess of quarks over antiquarks and of electrons over positrons to leave us with some electrons and nucleons at present.
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After the first second, the remaining components of the cosmic soup were nucleons, electrons, and photons.
g
Particles like quarks or W and Z were not known in Gamow’s day, and he was not even concerned about electron-positron pairs. His main interest was in the cosmic history after 1 second A.B. Early in his career Gamow became fascinated with the problem of the origin of atoms. There are ninety-two different types of atoms, or chemical elements, found in nature. Some of them, like hydrogen, helium, and carbon, are very abundant, while others, like gold and uranium, are extremely rare. Gamow wanted to know why this is so: What determined the element abundances?
In the Middle Ages alchemists tried to turn more abundant elements
into gold, but as we now know, there was a good reason why they did not succeed. In order to change one chemical element into another, one has to learn how to change the composition of atomic nuclei. But the particle energies needed for such nuclear transformations are millions of times greater than the energies typically involved in chemical reactions, far beyond what alchemists could achieve. Such energies are reached in a hydrogen bomb, but are not attained in any process naturally occurring on Earth. Thus, the element abundances we observe now are the same as they were 4.6 billion years ago, when the solar system was formed.
h
A natural place to look for the origin of elements is in the interiors of stars. Stars are giant, hot, gaseous spheres held together by gravity. Our Sun consists mainly of hydrogen—the simplest element whose nucleus is made of a single proton. The temperature in the central regions of the Sun is higher than 10 million degrees, high enough for nuclear reactions to occur. A chain of reactions transforms hydrogen into helium, releasing the energy that fuels the Sun. The theory of nuclear reactions in the Sun was developed in the late 1930s by Hans Bethe, a German-born physicist who was later awarded a Nobel Prize for this work. This theory, however, did very little to explain the elemental abundances. Helium production in stars can account for only a small fraction of the vast amounts of helium observed in the universe. Another puzzle is the presence of deuterium (heavy hydrogen), which has a very fragile nucleus. Deuterium is quickly destroyed in hot stellar interiors, and it is hard to see how it could ever be produced.
Gamow’s assessment of the situation was that stars were simply not hot enough to cook the elements, and he thought he had a better idea of what a suitable furnace could be: the entire universe shortly after the big bang. To investigate nuclear processes in the hot, early universe, Gamow enlisted the help of two young physicists, Ralph Alpher and Robert Herman. They considered a hot mixture of nucleons, electrons, and radiation uniformly filling the universe. When the universe cools down below 1 billion degrees kelvin, it becomes possible for a neutron and a proton to stick together and form a nucleus of deuterium (see
Figure 4.1
). Further attachment of protons and
neutrons quickly turns deuterium into helium (which has two protons and two neutrons in its nucleus). At this point, however, the buildup of nuclei essentially stops. The reason is that owing to some peculiarity of nuclear forces, there are no stable nuclei consisting of five nucleons, and simultaneous attachment of more than one nucleon is highly unlikely. This is what’s known as the five-nucleon gap. Calculations show that about 23 percent of all nucleons end up in helium, and almost all the rest in hydrogen. Small amounts of deuterium and lithium are also produced.
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Figure 4.1
.
Simplest atomic nuclei, with protons and neutrons represented by
p
and
n
, respectively.
Modern analyses, using the latest data on nuclear reactions and extensive computer power, give precise element abundances as they come out of the cosmic furnace. These calculations are in a very impressive agreement with astronomical observations. By studying the spectrum of light emitted by distant objects, astronomers can determine their chemical composition. A firm prediction of the hot big bang theory is that no galaxy in the universe should contain less than 23 percent of helium: helium produced in stars can only increase this primordial abundance. And indeed, no such galaxy has yet been found. The predicted abundance of deuterium is somewhat less than one part in 10,000, and the abundance of lithium is less than one part in a billion. It is quite remarkable that these vastly different amounts are confirmed
by observations. You might say that 23 percent of helium was a lucky guess, but the probability of a chance coincidence for the whole set of numbers is extremely low.
But what about the heavy elements? Despite all their efforts, Gamow and his crew could not find a way to bridge the five-nucleon gap. In the meantime, across the Atlantic, the chief proponent of the steady-state model, Fred Hoyle, was developing an alternative theory for the origin of elements. Hoyle was aware that stars, like our Sun, that burn hydrogen into helium are not hot enough to do the job. But what happens when a star runs out of its hydrogen? Then it can no longer support itself against gravity, so the stellar core begins to contract, with its density and temperature rising. When the central temperature reaches 100 million degrees, a new channel of nuclear reactions opens up: three helium nuclei stick together to form a nucleus of carbon. When all the helium in the central region is consumed, the star contracts further, until the temperature gets high enough to ignite carbon-burning nuclear reactions. As the process continues, a layered structure is formed with heavier elements closer to the center (since they require higher temperatures to be cooked). The process does not get very far in stars like the Sun, but in more massive stars it goes all the way to iron, which is the most stable of all nuclei. Beyond that, there is no more nuclear fuel to burn. Unsupported by nuclear reactions, the innermost core of the star collapses, reaching enormous densities and temperatures as high as 10 billion degrees. This triggers a gigantic explosion, known as a
supernova
, when all outer layers of elements are blown off into the interstellar space. Elements heavier than iron are formed during the core collapse and explosion. The enriched interstellar gas serves as a raw material for new stars and planetary systems. The resulting abundances of heavy elements, calculated by Hoyle and his collaborators, are in good agreement with observations.
Hoyle and Gamow were developing their ideas in the 1940s and ’50s, and at the time their theories were regarded as two competing models for the origin of elements. But in the end they both turned out to be right: light elements were formed predominantly in the early universe, and heavy elements in stars. Almost all known matter in the universe is in the form of hydrogen and helium, with heavy elements contributing less than 2 percent.
However, the heavy elements are crucial for our existence: Earth, air, and our bodies are made mostly of the heavy elements. As Cambridge astrophysicist Martin Rees wrote, “We are stardust—the ashes of long-dead stars.”
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