No one needs an astronomer to tell them that it is dark at night. Apart from the stars that dot the sky, the darkness is the night sky’s defining quality. Add an astronomer to the picture, however, and he or she will tell you that the darkness is actually one of the most profound observations you can make. It leads us to the idea that the Universe cannot have existed forever.
In astronomical circles the question “Why is it dark at night?” is known as “Olbers’ Paradox,” after German astronomer Heinrich Wilhelm Matthäus Olbers who popularized the discussion in 1823. Back then, the dark night sky was considered a paradox because the prevailing view was that the Universe had always existed and was infinite in size; stars were scattered throughout this unimaginable expanse and so in whatever direction we look, our line of sight should eventually intercept a star. Hence, the night sky should be starlit and as bright as day, not dark. Olbers was not the first to point out the problem. Before him, Thomas Digges in 1576, Johannes Kepler in 1610 and Edmond Halley in 1721 all puzzled over the darkness at night. It just did not fit their pictures of an infinitely old and vast Universe populated by a uniform collection of stars.
Various solutions were contemplated. It was a familiar fact, for example, that if you double the distance of a light source, you quarter its intensity (the inverse square law, see What is the Universe?). This means that distant objects will naturally fade from view. But this could not solve the paradox because the further you look the more stars seem to crowd together, compensating for the drop in individual brightness. So, astronomers were left with the paradox.
OLBERS PARADOX: IF THE UNIVERSE IS INFINITE, EVERY LINE OF SIGHT SHOULD REACH A STAR. SO WHY IS IT STILL DARK AT NIGHT?
The solution is to let go of the assumptions. If the Universe is not infinitely old, then the light from more distant stars would not have had time to reach the Earth. If the Universe is not static but expanding, this would have a weakening effect on distant light because of the redshift (see How Big is the Universe?). If the stars are not spread uniformly through space but are corralled into galaxies with voids between, this would affect the “line of sight” hypothesis. And we now know that there will never be enough stars in existence to fill the Universe with starlight because stars do not form fast enough or live long enough to release enough energy into space. Let us concentrate on the fundamental idea that the Universe is not infinitely old. This certainly helps to solve Olbers’ Paradox but it leaves us with a greater mystery: if the Universe is not infinitely old, how old is it?
In trying to work out the age of the Universe, an obvious starting point is that the Universe cannot be younger than the objects it contains. There have been various attempts to estimate the Earth’s age. The earliest were biblical in origin; theologians assumed that Man had always populated the planet and so counted the number of generations recorded in the Bible and used this to arrive at an estimate of the Earth’s age. By the 19th century such attempts had given way to more scientifically based methods, for example deducing the time it would take for the planet to cool down, supposing that it had solidified from a molten mass. The discovery of radioactivity in the late 19th century, by Antoine Henri Becquerel and independently by Marie Curie and her husband Pierre Curie, signaled the death of this approach because radioactivity in rocks provides a constant source of heat and so ruins the calculations of the cooling rate. However, far from demolishing our way to age the Earth, it was soon realized that radioactivity actually gave us the very best route of all.
“Man is slightly nearer to the atom than to the star . . . From his central position man can survey the grandest works of Nature with the astronomer, or the minutest works with the physicist.”
ARTHUR EDDINGTON 20TH CENTURY ASTROPHYSICIST
Radioactive elements decay from one element into another, giving out energy in the form of particles or rays. Different versions of the same element are called isotopes, and each radioactive isotope has a unique decay time. This is termed the “half-life” of the isotope because it measures the time taken for half the quantity to decay. After some ten half-lives there is hardly any of the original substance left. Some isotopes have relatively short half-lives (on a geological scale), such as carbon-14 at 6000 years. One isotope of uranium, uranium-235, decays with a half-life of 704 million years, into lead; uranium-238 has a half-life of 4.47 billion years, and decays into thorium. By analyzing a rock for its naturally occurring proportions of uranium, lead and thorium, geologists can estimate its age. If a wide enough range of samples is analyzed, this technique can give the definitive age of the Earth.
After a century of effort, geologists have now radioactively dated myriad Earth rocks, Moon rocks and meteorites. This has given an age, not just for the Earth but also for the whole Solar System, of 4.6 billion years, and represents a preliminary baseline for the age of the Universe. As it turns out, it is somewhat on the low side.
Looking further afield, isolated groups of stars known as “globular clusters” provide excellent candidates for estimating ages. Each large galaxy has a retinue of globular clusters; there are more than 150 known to be orbiting the center of the Milky Way Galaxy. The largest elliptical galaxies can possess more than 500. By studying the distribution of globular clusters, Harvard astronomer Harlow Shapley deduced in the early 20th century that the Sun was located far from the center of our Galaxy. Had we been in the center of the Galaxy, the globular clusters would have been distributed evenly around us. As it is, most of them gather tightly in the southern sky, revealing that we are seeing them from somewhere off-center.
Each globular cluster is a spherical collection of a few hundred thousand stars. The types of star it contains can indicate its age. Most stars in the Universe are called “main sequence” stars and this means that they are in the stable “middle-aged” phase of their existence. A star’s individual lifespan, and its characteristics, depend upon the amount of mass it contains. High-mass stars generate the most energy, have the hottest surfaces at more than 40,000 degrees Celsius, and give off blue-white light. They also have the shortest lifetimes—although a massive star has more fuel to burn, the extra weight pressing down on its core drives its nuclear reactions more quickly, so it runs out of fuel much faster than a smaller star. The highest-mass stars that astronomers have seen are about 100–200 times the mass of the Sun and are calculated to burn their fuel so furiously that they live for only a few million years. Less massive stars, conversely, generate energy more slowly and so live longer lives. They also have cooler surfaces and exhibit a different color. The Sun is a yellow star with a surface temperature of about 6000 degrees Celsius and it is estimated that it will live for approximately 10 billion years. The least massive main-sequence stars are the “red dwarfs.” With surface temperatures of less than 3000 degrees Celsius, they are so miserly with their nuclear fuel that calculations show the smallest of them may last for 100 billion years.
In an isolated stellar population, if no new stars are born the population becomes skewed toward low-mass stars because the higher-mass stars have lived and died off. Globular clusters are just such isolated systems. They formed their stars in one fell swoop at some point extremely far back in time, and have remained undisturbed since then. So a 10 billion-year-old globular cluster will contain only red dwarf stars because all the yellow and blue-white stars have already died. Astronomers can estimate the age of a globular cluster using a Hertzsprung-Russell diagram. Named after the Dane Ejnar Hertzsprung and the American Henry Norris Russell, the Hertzsprung-Russell diagram (or HR diagram for short) was developed in about 1920 and is a way of understanding the lives of stars. The diagram is a plot of the surface temperature of a star against its brightness; every star in the Universe can be placed somewhere on it.
THE HERTZSPRUNG-RUSSELL DIAGRAM: THE MAIN SEQUENCE TURN-OFF TELLS THE AGE OF A GLOBULAR CLUSTER
The surface temperature is linked to the color of the star, and the brightness is linked to its surface area. Most stars fall on a diagonal band across the diagram from which the “main sequence” stars take their name, massive blue stars to the left, red dwarf stars to the right and yellow medium-sized stars between the two. Only when a star begins to age and die does it move away from the main sequence, then becoming a red giant star. In the early lifetime of a globular cluster, blue stars would exist and would be becoming red giants. Later in the life of the cluster, there will be no blue stars left, and the smaller, yellow or red stars will be coming to the end of their lives on the main sequence. Hence, after plotting all the stars from a globular cluster onto an HR diagram, the point at which the main sequence turns off into the red giant region tells astronomers the cluster’s age.
Using this method, astronomers have estimated that the Universe must be older than 12 billion years because that is the average age of the Galaxy’s globular clusters. It means that at just 4.6 billion years old, our Solar System is a relative newcomer on the celestial scene.
It is not possible to do the H-R diagram analysis for the whole Galaxy because there are reservoirs of gas from which new stars are constantly being formed. Instead, astronomers have developed a different technique that relies on them scouring the Galaxy for the corpses of long-dead stars. These are known as “white dwarfs” and are remarkable celestial objects. Each contains roughly the mass of the Sun but compressed into an object the size of the Earth, making it extremely dense. The white dwarf was once the nuclear furnace at the heart of a star at temperatures of tens of millions of degrees, so it takes a considerable amount of time to cool down. To use white dwarfs as age indicators, astronomers look for the coolest ones they can find and calculate the time it has taken for them to cool to their current temperature. The coolest ones observed have surface temperatures of a few thousand degrees and it is thus estimated that they are between 11 and 12 billion years old. Because white dwarfs are so small, most of those found so far are within our own Galaxy. Recently, however, the Hubble Space Telescope has found a number in a nearby globular cluster. These too provide ages of 11–12 billion years. It is hugely encouraging that the age estimates from both HR diagrams for globular clusters and cooling of white dwarfs converge on 12 billion years. This reliably sets a minimum age for the Galaxy; the challenge remains to deduce an accurate age for the entire Universe.
The search for the age of the Universe received an enormous boost when Edwin Hubble discovered the expansion of the Universe in 1929 (see How Big is the Universe?), and it was confirmed that Albert Einstein’s General Theory of Relativity could explain the observed behavior. Einstein could have proposed the expanding Universe earlier, because his equations showed him that this movement was an intrinsic property of space. However, trapped by the old thinking that the Universe was infinite and static, Einstein had not believed his own work. Only Hubble’s observations of redshift convinced him.
A young Belgian mathematician, Georges Lemaître, was bolder and began seriously investigating the properties of an expanding Universe when it was just a numerical possibility. Two years before Hubble made his observations known, Lemaître published a paper predicting that the Universe would be found to be expanding. It led him to the solution of Olbers’ Paradox by making him contemplate the possibility of a creation event for the Universe. If the Universe was expanding today, then clearly it had to have been smaller in the past. To find out how much smaller, Lemaître used the mathematics of general relativity to model a reverse expansion, rather like a film running backward. This allowed him to investigate the behavior of the Universe at earlier and earlier times, when the celestial objects had been packed more closely together. He ran the cosmic clock all the way back until the entire Universe was compressed into a single, incredibly dense object that must have somehow exploded outward.
At the time, scientists were fascinated with the recently discovered radioactive elements that seemed to spontaneously split apart, and Lemaître proposed that the Universe had been born when some “primeval atom” spontaneously exploded. This was the beginning of what we now commonly call the Big Bang theory. Although scientists no longer think in terms of a primeval atom, much of cosmology today is concerned with understanding the nature of the Big Bang. To the astronomers in Lemaître’s time, this was an extraordinary concept. The prevailing wisdom was that space had always existed and would always exist—which was convenient because they would not have to explain how the Universe came about in the first place. But, as we have seen, this blind assumption was eroded by Olbers’ Paradox and then by Hubble’s discovery of the expanding Universe. In the end, astronomers had no choice but to accept Lemaître’s interpretation and, in the process, they realized that it gave them an extraordinarily simple way to estimate the age of the Universe.
The theory of the expanding Universe throws up a value for the expansion rate of the Universe, called the “Hubble constant.” Assuming that this has remained constant since the Big Bang event, cosmologists can use it to calculate the time it has taken for the Universe to expand to its present size. They call this the “Hubble time,” and using the presently accepted Hubble constant, it comes out at 13.7 billion years. But this is not quite the age of the Universe—it is an overestimate because of several factors that affect the expansion rate. One is the presence of matter. Matter produces gravity, which resists the expansion, and so astronomers have reasoned that the expansion rate will have slowed with time. Mathematical analysis of the expected slow-down shows that the actual age must be around two-thirds of the Hubble time, or just over 9 billion years. And that gives astronomers a huge problem because it conflicts with the ages of the globular clusters and the white dwarfs, which are both around 12 billion years. This conundrum is called the “age crisis” in cosmology.
“Theories crumble, but good observations never fade.”
HARLOW SHAPLEY 20TH CENTURY ASTRONOMER
Perhaps the calculation of the Hubble constant from galactic redshifts and standard candle distance markers (see How Big is the Universe?) was flawed. Astronomers developed a new way of estimating it from studying the microwave background radiation—a perpetual sleet of microwaves that fills the Universe, believed to be the afterglow of the Big Bang. They analyzed the pattern of hot and cool spots in this microwave background. Then, using general relativity and an estimate of how much matter and energy there is in the Universe, they deduced a Hubble constant—and this value was in excellent agreement with the traditional estimate.
A further refinement was then put into action, based on studies of patches in the microwave background created when the radiation collided with hot gas clouds deep in space. This value of the Hubble constant also agreed with the others. In one sense this is good news because all of the estimates are close to one another and reliably indicate a Hubble time of between 12 and 14 billion years, but the bad news is that it does not resolve the age crisis. Thankfully, an extraordinary solution appears to be at hand.
The question that cosmologists had to address was whether the presence of mass slows down the expansion over time as much as theory suggests. Recent redshift surveys have attempted to answer this. In the mid-1990s, two independent teams published their measurements and shocked everyone. Both teams found that the expansion rate is not decreasing at all. Somehow, the expansion of the Universe is accelerating. This finding went against all expectations and continues to fascinate and perplex in equal measure because no one knows what could be driving the acceleration. Some suspect it is a form of energy that Einstein originally toyed with during the development of general relativity, but this energy is difficult to conjure up from any modern theory. At present, there are no firm answers, and the mystery is encapsulated in the term “dark energy” (see What is Dark Energy?).
One thing, however, is certain: if the Universe expanded more slowly in the past, then it has taken longer to reach its current size than the Hubble time suggests, and the age crisis is averted. By all modern estimates, the Universe is around 13.7 billion years old.