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 = mc2) 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.4 After the first second, the remaining components of the cosmic soup were nucleons, electrons, and photons.g
GAMOW’S ALCHEMY
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 fo
r 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.5
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.”6
COSMIC MICROWAVES
The process of helium formation began at about 3 minutes A.B. and was complete in less than a minute. The universe was still expanding at a furious rate, and both the density and the temperature were dropping very rapidly. But after the first few minutes packed with action, the pace of the cosmic drama was getting slower. Very little was happening to the matter particles, and the most notable change was in the radiation component of the fireball.
At the microscopic, quantum level, the radiation consists of photons, but macroscopically it can be pictured as consisting of electromagnetic waves—oscillating patterns of electric and magnetic energy. The higher the frequency of oscillation, the more energetic the constituent photons. Waves of different frequency produce different physical effects, and we know them under different names. Visible light corresponds only to a narrow range of frequencies in the full electromagnetic spectrum. Higher frequency waves are called X rays, and still higher-frequency waves are called gamma rays. Going down in frequency, we encounter microwaves and still lower, radio waves. All these waves propagate at the speed of light.
As the fireball temperature declined, the intensity of the radiation tapered, and its frequency gradually shifted from gamma rays to X rays and then to visible light. An important event occurred at 300,000 years A.B., when the temperature got low enough for electrons and nuclei to combine into atoms. Prior to that, electromagnetic waves were frequently scattered by charged electrons and nuclei. However, the interaction of radiation with electrically neutral atoms is very weak, so that once atoms were formed, the waves propagated freely through the universe, with practically no scattering at all. In other words, the universe suddenly became transparent to light.
What happens to the cosmic radiation after that? Not much, except the frequencies of the electromagnetic waves, and the corresponding temperature, keep declining with the expansion of the universe. At the time of neutral atom formation, the temperature of the radiation was 4000 degrees, somewhat below that at the surface of the Sun. If we had been there, and could have tolerated such unhealthy conditions, we would have seen the universe ablaze with brilliant orange light. By the cosmic age of 600,000 years the light would change to red. At 1 million years, it would shift beyond the visible range, to the infrared part of the spectrum. So, as far as we’d have been concerned, the universe would have descended into complete darkness. Wave frequencies still continue to decline slowly: by the present time, corresponding to the cosmic age of about 14 billion years, they are down to the microwave range.
This history of the cosmic fireball was studied by Alpher and Herman, Gamow’s young collaborators. They followed it all the way to the present and reached a remarkable conclusion—that we should now be immersed in a sea of microwaves having the temperature of about 5 degrees kelvin.
Alpher and Herman’s work was published in 1948. You might think that it should have inspired a fair number of observers to search for cosmic microwaves. Indeed, the primeval radiation is a true smoking gun of the big bang, and its discovery should have a colossal significance. You might think also that, once the radiation is detected, a Nobel Prize would be awarded for its prediction. Alas, this is not how the events unfolded.
THE SMOKING GUN
Odd as it may seem, the prediction of cosmic radiation was
completely ignored for nearly two decades, until the radiation was accidentally discovered in 1965. Two radio astronomers, Arno Penzias and Robert Wilson, working at Bell Telephone Laboratories in New Jersey, detected a persistent noise in their sensitive radio antenna. The noise level could be characterized by a temperature of approximately 3 degrees kelvin and did not depend on the time of day or on the direction in which they pointed the antenna. Determined to get to the root of the problem, Penzias and Wilson painstakingly eliminated all possibilities they could think of. This included eviction of a pair of pigeons who were roosting in the antenna and removing what Penzias called the “white dielectric material” that was left after them. Nothing worked, however, and the origin of the noise remained enigmatic.
In the meantime, about 30 miles away, a group of physicists at Princeton University were busy building a radio detector of their own. The head of the group was Robert Dicke, an extraordinary physicist who was equally at home in theory and experiment. Dicke realized that a hot early stage in the history of the universe should have left an afterglow, and he designed an antenna to search for it. When the Princeton group were ready to start their measurements, they learned about Penzias and Wilson’s predicament. They knew immediately that the bothersome noise that Penzias and Wilson were working so hard to eliminate was precisely the signal of cosmic microwaves that they were hoping to detect!
It is a fascinating question why the cosmic radiation had to be discovered by accident. Why had nobody listened to Alpher and Herman? Even if their papers were somehow overlooked, why did it take more than fifteen years for someone else to come up with the same prediction? After all, cosmic radiation was a direct consequence of Gamow’s hot big bang model.
One reason, it seems, was that physicists simply did not believe that the early universe was for real. “This is often the way it is in physics,” wrote the Nobel Prize-winning physicist Steven Weinberg. “Our mistake is not that we take our theories too seriously, but that we do not take them seriously enough.”7 It did not help also that George Gamow was perhaps too colorful a character to be taken seriously by the physics community. A practical joker, composing “unprintable” limericks and often having one too many at the bar, he was surely not your typical physicist. Finally, by the mid-1950s neither Gamow nor Alpher and Herman were actively working on the big bang theory: Gamow was increasingly attracted to biology, where he suggested important insights into the genetic code, while Alpher and Herman left academia and moved on to careers in private industry. One cannot help thinking that lack of appreciation of their work must have played a role in those decisions. By the mid-1960s, when Penzias and Wilson were taking data from their antenna, the work of the Gamow group was all but forgotten.
Many Worlds in One: The Search for Other Universes Page 4