by George Rhee
Hubble’s observations implied that, in the past, galaxies were closer together. In other words, when the universe was younger, it had a higher mean density. The universe began in a state of very high density and has been expanding and decreasing in density ever since. This is the idea at the heart of the Big Bang theory.
How We Use Redshifted Light to Look Back in Time
Imagine the universe is a loaf of bread with raisins embedded in it. If the loaf of bread expands, the raisins move farther apart from each other. We measure how much the loaf (space) has expanded using a quantity called the expansion factor. If the expansion factor doubles over a given time interval, then the distance between any two raisins (galaxies) has also doubled. The concept of expansion factor gives us another way of thinking about the redshift.
Let us imagine that at a certain time light is emitted from a distant galaxy with a wavelength λ 1. We receive the light in our telescope at a later time when the light has a longer wavelength λ 2. We calculate the redshift from the ratio of the two wavelengths λ 2 and λ 1. The ratio of the two wavelengths is just the amount by which the universe has expanded during the time the light traveled from the distant galaxy to Earth. If the universe expanded by a factor 2, the wavelengths will have stretched by a factor 2. We believe the universe to have been expanding since the Big Bang, so the expansion factor has always increased. Our current belief is that the expansion will go on forever. In fact, in a few billion years astronomers in our own milky way galaxy (which will have merged with the neighboring Andromeda galaxy) will not even be able to see any galaxies at all with their telescopes.
There is a simple relation between expansion factor and redshift. The expansion factor is equal to one plus the redshift. If we observe a galaxy at a redshift of 5, we can say that the universe has expanded by a factor 6 in the time since the light from that galaxy started on its way to us. This provides us with another way of thinking of the redshift. Rather than think of galaxies moving away at tremendous speeds, we can think of the wavelength of the emitted light increasing as the light travels on its journey to us. Since we are not at the center of the universe, one might think that certain galaxies should have blueshifts as they move away from the center toward us. In fact, if we consider a string of equally spaced galaxies in a line that appear to obey Hubble’s law as seen from one, then an observer on any of these galaxies will think that he is at the center of the universe. This is an application of the cosmological principle, which states that the universe, on average, looks the same to any observer located within it.
The redshift is an observable quantity, which we can calculate using a galaxy spectrum obtained at a telescope (see Fig. 2.2). Using our models we can compute the age of the universe at the time redshifted light set off on its journey to us. Figure 2.3 illustrates the relation between the redshift and the age of the universe at the time the light was emitted. As the redshifts increase we can look back over aeons of time to a period when the universe was a small fraction of its present age. With our telescopes we can see galaxies out to redshifts of about 8 corresponding to a time when the universe was about 600 million years old, about 5 % of its present age. The Earth is about 4.6 billion years old, and the oldest rocks on Earth are about 2 billion years old. These rocks, therefore, tell us what conditions were like on our planet when it was slightly over half of its present age. We astronomers, however, can look back in time and see objects as they looked long before the Earth or the Sun had even formed. There is a price we have to pay for this amazing view of the universe. The light of stars like our Sun that peaks in the visible part of the spectrum gets shifted in wavelength into the infrared part of the spectrum for high redshifts. To explore the high redshift universe we need infrared detectors on the largest ground based telescope and also in space.
Fig. 2.3A timeline of the universe comparing the age of the universe with redshift. The redshift measures how much the light emitted by a distant galaxy has been shifted towards the red due to the expansion of the universe. Galaxies which emit light at very early times have very high redshifts. The redshift is an observable quantity. Using known values for the Hubble constant and the density of the universe we can reliably estimate the age of the universe at the time the redshifted light was emitted. The goal of observational cosmology is to explore with observations the area between redshift 6 and redshift 14. We want to know how and when the first stars and galaxies formed in the first billion years after the Big Bang (Credit: Rychard Bouwens)
When we look at the Moon we see it as it was 1 s ago, because that is how long light takes to reach us from the Moon. When we look at the Sun, we see it as it was 8 min ago, because that is how long it takes for light to travel the distance from the Sun to the Earth. The nearest star is 4 light years away. In the movie Contact, Jodie Foster used a radio telescope to detect a signal from an alien civilization. The aliens had received our first TV broadcast made in the 1930s and beamed it back to us. Since we received the broadcast 60 years after it was first beamed into space, and assuming the aliens beamed it right back, we could conclude that the aliens were located 30 light years away from us. Imagine a phone conversation where you had to wait 60 years to get a reply! The light travel time to the large spiral galaxy nearest to us, the Andromeda nebula, is 2 million years. You can see this object with your naked eye on a dark night. Keep in mind that the light that hits your eye is 2 million years old. The light from the most distant galaxies that we can see was emitted so long ago that these objects would look quite different if we could see them as they are today.
Astronomy has something in common with geology. Both disciplines deal with an “experiment” that has been run once. Both study the past over immense expanses of time. Geologists do this by studying rocks and fossils, astronomers use telescopes to actually look into the past. Just as geologists see that species in the past were different from the species we see around us today, astronomers see that very distant galaxies look different from nearby galaxies. The distant galaxies are seen as they were when they were young. Indeed, our journey back in time through the universe is like a journey through the strata of the Earth.
The Second Pillar of the Big Bang: The Cosmic Background Radiation
In 1967, the discovery of the cosmic background radiation provided strong support for the Big Bang theory. In fact the radiation’s existence had been predicted 20 years earlier. To understand the importance of the background radiation we have to first consider what happens to matter in the early universe.
The density of the universe was higher in the past than it is today since objects were closer together. But just what do we mean by the density of the universe? To estimate the density of the universe, we take a large volume of space–say a cube 100 million light years on a side–and estimate how much mass lies in this volume. The density is obtained by dividing the mass by the volume. If we add up the amount of mass in stars and the gas between the galaxies, we arrive at an average density of 0.1 atoms per cubic meter. When we go back to a redshift of five (the redshift of distant galaxies), the expansion factor has shrunk by a factor six, so the volume of the cube will have shrunk by a factor 63 or ∼ 200. The density of the universe would thus be 20 atoms per cubic meter at that time. When we look back at a galaxy of redshift five, we know that the density of the universe at the time that light was emitted was about 200 times the density of the universe today.
Atoms such as hydrogen and helium only account for a few percent of the total observed density of the universe. Most of the mass in the universe is in a form other than atomic matter. Dark matter plays such an important role in cosmology that it will be the subject of Chap. 4. We shall also encounter a mysterious substance called dark energy. Brian Schmidt, Saul Perlmutter and Adam Riess, the leaders of the two teams that proved the existence of dark energy were awarded the 2011 Nobel prize for physics.
The origin of the cosmic background radiation lies in the interaction of light and matter. Metal objects that ar
e heated to a sufficiently high temperature start to glow. Radiation emitted by objects of known temperature is called black body radiation. The color of that radiation is determined by the temperature. For example, the surface of the Sun appears yellow to us because the Sun’s surface has a temperature of about 6,000 K. If the Sun were hotter it would appear bluer, if it were cooler it would appear redder. As the emitting object gets hotter, the radiation it emits shifts to shorter wavelengths. The radiation also has a well defined spectrum (light intensity of its various colors) that has a shape known as the black-body curve. One can show that, in an expanding universe, black body radiation will retain the shape of its spectrum, and appear to us as radiation of a lower temperature. The temperature of the black body radiation falls as the universe expands because the wavelength of the light shifts to longer wavelengths.
Although the cosmic background radiation was detected in 1967, its existence had, in fact, been predicted by George Gamow and collaborators in the 1940s. Gamow assumed that, at some point in its history, the universe was hot enough and dense enough for nuclear fusion reactions to take place, and predicted that the afterglow from this period should be detectable today as cosmic background radiation.
The background radiation left over from the Big Bang lets us see the universe in its early stage of evolution and gives us a window into the origin of structures that will later become the galaxies we see around us. The radiation shows us what the universe must have looked like long ago before galaxies and stars existed, it is in some sense a distant mirror. We will discuss the clues about our past revealed by the radiation in Chap. 7.
In his classic of popular science writing entitled The First Three Minutes, Steven Weinberg noted that the existence of this radiation could have been confirmed experimentally at the time the prediction was made. The Big Bang theory at the time was sufficiently removed from mainstream science that people did not think it worth their while to carry out experiments to confirm or deny it. The absorption of light by cyanogen molecules implied a temperature of 2.3 K for the coldest clouds of molecular gas in our galaxy. The Kelvin temperatures are quoted relative to absolute zero (). This 2.3 K temperature measurement dated from the 1940s and was quoted in a famous textbook in the 1950s, which stated that the temperature arrived at had a “very restricted meaning.” In fact, it was an unwitting measurement of the temperature of the cosmic radiation left over from the Big Bang.
The Third Pillar of the Big Bang: The Abundances of Deuterium and Helium
If in some cataclysm, all of scientific knowledge were to be destroyed, and only one sentence passed on to the next generations of creatures, what statement would contain the most information in the fewest words? Everything is made of atoms.
Richard Feynman
We know that close to 90 % of all atoms in the universe are hydrogen atoms. The other 10 % are almost all helium atoms. The Big Bang theory explains why this is the case. In fact the Big Bang theory provides an accurate explanation for the relative amounts or abundances of the lighter atoms (hydrogen, deuterium, helium and lithium) that we see in the universe. How are the helium and deuterium observed? Helium was first discovered in the Sun in 1868 and later observed on Earth. Helium abundances can be determined in the spectra of hot stars, in the upper solar atmosphere, and in the solar wind. One can also indirectly infer the helium abundance by comparing theoretical model predictions for the temperatures and luminosities of stars. Deuterium abundances are even more difficult to measure. Interstellar molecules composed of hydrogen, or deuterium, carbon and nitrogen are used to estimate deuterium abundances.
As Feynman points out, “The most remarkable discovery in all astronomy is that the stars are made of atoms of the same kind as those on Earth”. In 1835 the French philosopher Auguste Comte stated that “we shall never be able by any means to study the chemical composition of the stars”. However, in the early 1920s, methods became available for calculating the abundances of elements in a gas by observing its spectrum. In 1925, using these methods, Cecilia Payne analyzed the spectrum of the Sun and reached the conclusion that hydrogen and helium make up 98 % of the mass of the Sun. This result surprised people who expected the composition of the Sun to be similar to that of the Earth which is made mostly of iron. The stars were thought to have the same mix of elements as the Sun, so this discovery suggested that the stars were also made mostly of hydrogen and helium. The precise conclusion is that for every 10,000 atoms of hydrogen in the universe there are 975 atoms of helium, 6 atoms of oxygen and 1 of carbon. All the other elements are present in smaller quantities than 1 atom per 10,000 hydrogen atoms. A more detailed look suggested that the abundances of the elements reflected the properties of atomic nuclei. Maybe nuclear physics processes were responsible for producing the abundances of the elements.
Already in 1903 Rutherford and Soddy had hinted that nuclear processes were responsible for generating energy in the Sun;
The maintenance of solar energy, for example, no longer presents any fundamental difficulty if the internal energy of the component elements is considered to be available, that is, if processes of subatomic change are going on.
When this question was examined by von Weizacker he found that many different sets of conditions were required to produce the mix of elements that we see in nature.
The Sun produces energy by turning hydrogen into helium. So, why can’t nuclear fusion in stars be used to account for all the helium in the universe? There is not enough time. The stars can only account for about 2 % of the helium production in the universe. To create elements from hydrogen requires extremely high temperatures. If the stars cannot do the job, where can we find another furnace hot enough to form helium?
George Gamow was the first to explore the idea that nuclear processes could have taken place in the first few minutes of the Big Bang when it was hot enough for nuclear fusion to occur. The physicists Alpher and Herman worked out the details and found that nuclear processes which we will discuss below produced just the right abundance of helium to match that seen in stars. These processes also account for lithium and deuterium abundances. The inescapable conclusion is that only the very lightest atoms were created during the hot Big Bang. The heavier elements it turns out are made inside stars and during supernova explosions.
To understand more of the workings of nuclear alchemy we need to explore the properties of atoms. Atoms are made from particles called electrons, neutrons, and protons. The neutrons and protons form the nucleus, and the electrons orbit the nucleus. In this sense, the atom resembles the solar system. In the solar system, most of the mass resides in the Sun; in atoms most of the mass resides in the nucleus. There are certain allowed orbits or energy levels for electrons in atoms. These can be precisely calculated using the formalism of quantum theory, which was developed in the 1920s. The electron can jump from one level to another by emitting or absorbing light of known energy and wavelength (i.e. color). This is a crucial property of atoms, which astronomers make use of to measure redshifts as we have seen. Without sending a probe to the Sun, we can tell which elements are present in the Sun. The absorption lines in the Sun’s spectrum occur because atoms near the Sun’s surface absorb some of the light generated in the Sun’s interior. The absorption occurs because electrons in these atoms jump up from one energy level to another and absorb light in the process.
You are no doubt familiar with the concept of chemical elements, such as carbon, nitrogen, and so on. What differentiates one element from another is the number of protons in the atomic nucleus. Hydrogen, the simplest atom, consists of one electron orbiting one proton. The helium atom consists of two protons and two neutrons in the nucleus with two electrons in orbit. The number of protons in the nucleus determines how many electrons are present in each atom. This is because atoms have no net charge; the negative charge of the electrons is needed to balance the positive charge of the protons. It is the properties of the electron orbits that determine the chemical properties of t
he elements. The periodic table of the elements is an ordering of elements according to the number of protons in their nucleus which in turn determines their chemical properties.
It is a triumph of physics to have explained the properties of the periodic table in terms of the structure of atoms. This structure is determined by some simple fundamental equations. The power of physics lies in the ability to unify seemingly unrelated phenomena using simple underlying principles. A number of key discoveries about atoms and their constituent particles were made at the Cavendish Laboratory in Cambridge, England. The discovery of the electron, the neutron, and the atomic nucleus were all made at the Cavendish Laboratory. Ernest Rutherford, who discovered the atomic nucleus, was once asked how it was that he always seemed to be riding the crest of the wave in nuclear research. His answer was characteristic “I created the wave.” Immodesty aside, this is an attribute of great men, they create the environment in which their and other talents can flourish. Niels Bohr did this to great effect in Copenhagen in the 1920s and 1930s. Many great physicists of that period passed through Bohr’s institute.
