by Adam Frank
The disc-like geometry of the spiral nebula hit a strong note of recognition for some astronomers. Discs of stars had already made a significant appearance in the realms of cosmological conjecture. As far back as 1785, the philosopher Immanuel Kant had offered an influential model of cosmic history by predicting that the Milky Way was formed from a giant spinning cloud of gas that had collapsed under its own gravity. Kant hypothesized that a disc-shaped Milky Way would be a natural result of such a collapse.19 By the early twentieth century, a growing body of observations led many astronomers who recalled Kant’s theories to imagine spiral nebulae to be separate systems of stars like our own Milky Way. If they were the same size as the Milky Way, these island universes, called galaxies, must be at great distances to appear so small in the sky. Opponents of the island universe hypothesis dismissed this interpretation of spiral nebulae, arguing that the required distances were so great as to be unimaginable. The universe, in their vision, could not be that big. The spiral nebulae, they argued, must be nothing more than interestingly shaped clouds of gas and stars embedded much closer to home within the Milky Way.
FIGURE 6.2. Astronomer Edwin Hubble and the powerful Hooker telescope. Hubble’s work with the electrically powered Hooker allowed him to greatly expand the scale of the universe by showing galaxies as distant star systems and to discover cosmic expansion.
The argument came to a head in the confrontation between two well-known astronomers, Harlow Shapley and Heber Curtis. The debate occurred in a packed auditorium at the 1920 meeting of the National Academy of Sciences in Washington, D.C.20 Shapley, formerly the director of the Mount Wilson Observatory, opened the argument by sharply attacking the island universe theory. He had developed his own model in which the universe was one “enormous all-comprehending galactic system”.21 Curtis, a prominent astronomer from the Lick Observatory, defended the island universe theory by presenting multiple lines of evidence that spiral nebulae were distant, separate galaxies.22
The debate ended without a knockout. Both men were struggling with biases and incorrect assumptions that no one understood at the time. What is truly remarkable about this Great Debate, however, is its historical moment. As late as 1920, a time when aeroplanes and radios were becoming commonplace, science had yet to determine the nature of our own galaxy or prove the existence of others. The true dimensions of galactic space, and of the universe itself, would not be resolved until the appearance of Edwin Hubble.
At the time of the Great Debate, Hubble was not yet the towering figure in astronomy he would one day become, but he had already made impressions on the community. Tall and handsome, the young Hubble arrived in Pasadena (the home of Caltech and the offices of the Mount Wilson Observatory) in 1919.23 He was fresh from serving in World War I and, after spending time in Oxford on a Rhodes Scholarship, had taken somewhat unsuccessfully to English affectations.24 While Shapley was firm in his conviction that spiral nebulae lay inside the Milky Way, Hubble favoured the island universe theory.25 Hubble decided to mount his own attack on the issue, but to solve the riddle of the spirals he would need a reliable means of measuring their distance.
Distance vexes astronomers. There is no way to run a tape measure to the stars. Astronomers must find proxy measurements to convert into distance. Measurements of brightness can, in special circumstances, fit the bill. The apparent brightness of any light source decreases with distance. That is both basic physics and common experience. Car headlights are painfully bright up close but those same headlights will appear faint from a mile away on a dark night. Thus if you know the intrinsic brightness of the source—like knowing a lightbulb burns at one hundred watts—you can use this dimming effect to find its distance.
By comparing how bright an object appears to be with how bright you know it to be intrinsically, its distance can be directly computed. The problem for astronomers is that stars, and other celestial sources, do not come with “100 watts” printed on the side. Luckily, certain classes of celestial objects have properties that let astronomers deduce their all-important intrinsic brightness. These are called “standard candles” and they are worth their weight in gold. Once identified, a standard candle makes determining distance as simple as measuring brightness.
By the 1920s a special class of pulsating star called Cepheid variables had already been firmly identified as a standard candle. Cepheids are pulsating stars. They brighten and dim in cycles over a period of days or weeks. In 1908 the astronomer Henrietta Leavitt discovered a direct relationship between a Cepheid’s pulsation period and its average intrinsic brightness.26 In essence, Leavitt found a way to read the “100 watt” label printed on stars. Because of her work, once an astronomer found a Cepheid variable and measured its period, he or she could quickly compute the star’s distance (and the distance to any objects around it).27
The Hooker telescope was big enough to let astronomers see individual stars in the bigger spiral nebulae. On October 5, 1923, Hubble spent the night probing the great spiral nebula in Andromeda for signposts he could use for gauging its distance.28 The next day while comparing his night’s work with previous observations he found what he was looking for on his photographic plates. To his surprise and delight he had come across a Cepheid variable in Andromeda. With a few simple lines of maths Hubble used the newly discovered standard-candle star to sweep away one hundred years of debate.
Using the Cepheid variable, Hubble calculated that Andromeda was almost a million light-years from the Earth. This was far larger than any astronomer’s estimate for the Milky Way’s outer boundary and implied that the spiral nebula in Andromeda could not live within the Milky Way; it was without doubt a spiral galaxy. Harlow Shapley had by this time moved on to Harvard but he had not given up on his belief that spiral nebulae were part of the Milky Way. On receiving news of Hubble’s discovery, Shapley (who nursed an intense dislike of the younger man) told a student, “Here is the letter that has destroyed my universe.”29
Hubble’s result showed astronomers that spirals were indeed galaxies and, more important, that the universe was far larger than anyone had imagined. From Hubble’s discovery onward the measure of space would be taken in terms of galaxies and their measurable cosmic distribution. Cosmology was leaving its era of philosophical speculation and entering its astrophysical age.
BUILDING UNIVERSES: THE GAME BEGINS
True scientific cosmology demanded a theory of the universe as a whole, a complete and all-encompassing mathematical description of space and time. Such a theory would be a model, a mathematical representation capable of describing everything that happened in the cosmos. The model must also tell scientists what to expect while making their observations and allow the raw data of astronomical investigation to be compared with theoretical expectations.
If cosmology was finally to move from the realm of quasi-philosophical speculation to the firmer ground of science, it would need a testable account of the universe. It would have to become a branch of physics and astrophysics. The universe would have to be treated like everything else physics studies: an atom, a rock, a cow. But the universe contains all atoms, all rocks, all cows and all physicists. It not only contains everything like a giant box, it is the box. How could scientists describe the totality of existence from the inside?
In many ways cosmology was waiting for Einstein. He and his general theory of relativity found a way to make the theoretical description possible.
All earlier attempts to build models of the universe were hobbled because they lacked Einstein’s great insight into the nature of space-time. The first step towards a successful model was the special theory of relativity, as it swept aside Newton’s divine sensorium of absolute time and space and replaced it with a unified 4-D space-time. The task was completed when general relativity linked the flexible fabric of this space-time to the large-scale distribution of mass-energy. In this way, gravity was recognized as nothing more than the malleable fabric of space-time, with mass-energy acting as the agent driving s
pace-time’s gravitational distortions.
It did not take long for Einstein to begin using his field equations, linking space-time to mass-energy, to construct cosmological models. But the effort required one critical assumption that all his work, and the work of others that followed, would have to accept. To derive a mathematical description for the universe as a whole, Einstein had to assume the universe was perfect in one key sense of the word—it had to be very smooth and very symmetric. The technical terms are homogeneity and isotropy, but the meaning is simple: on cosmic scales everything has to look the same from every perspective. Einstein could not use his equations to derive cosmological models unless he assumed that the universe was perfectly symmetric on the largest scales.
A perfectly smooth ping-pong ball looks the same no matter what angle you view it from. Thus physicists say that perfect spheres, like ideal ping-pong balls, are maximally symmetric. Likewise, if you examine a perfect sphere by standing on its surface and wandering around, your location should not matter for the description—every location looks the same. By assuming that the real universe was maximally symmetric, a description of a small region of space-time in Einstein’s equations could become a description of all space-time—a mathematical description of the entire universe.
With this assumption in hand, cosmic history and cosmic architecture became accessible for Einstein to explore. The ancient questions of cosmology still remained. Did the universe have a beginning or had it always existed? Was space infinite or was it somehow bounded? But with his newly formulated relativistic cosmology, Einstein had the conceptual tools needed to provide mathematically definite answers to many of the great questions.
FIGURE 6.3. Einstein’s first universe. In Einstein’s first cosmological model, the whole of cosmic space was spherical. 3-D space wrapped back on itself the way the 2-D surface of a balloon is without edges or boundaries. Objects (such as the depicted ants) are constrained to move through space according to its shape.
The limits of cosmic time and space were tackled first. Newton had accepted a spatially infinite universe but, with his biblical bias, he could not accept one that was eternal in time. Unlike Newton, Einstein wanted an eternal universe. Like most scientists of his day, Einstein believed the universe had always existed and always would exist, which led him to search for solutions to his equations that would represent a finite, closed and eternal universe. Finite means there is only so much space to go around, only so many cubic centimetres existing in the cosmos. In this context, closed means that space has no edges, no brick walls for starships to bang into when they arrive at the end of creation.
To understand what this looks like, imagine the surface of our own planet. The Earth has a finite surface area (as we are becoming painfully aware). It is also unbounded. Head west for long enough and you will come back around from the east after travelling in an extended circle. This familiar example shows us that the 2-D surface of a sphere, like the Earth, is a curved space that is both finite and unbounded. General relativity, with its curved space-time, allowed Einstein to create a universe with just these kinds of properties, only in higher dimensions. The 3-D space of Einstein’s first model of the universe was hyperspherical—it was the 3-D version of a 2-D spherical surface.
Let’s stay with the analogy of the 2-D spherical surface for a moment longer. It will give us some insight into the critical issue of dimensionality, which will be important in the chapters to come.
Imagine a spherical balloon. Like the Earth’s surface, the balloon’s fabric defines a 2-D space (the technical term for space here is a manifold). We can imagine an entire 2-D universe defined by the balloon’s surface. This universe might include 2-D creatures cheerfully unaware that there are any higher dimensions extending beyond their world. Thinking cosmologically, we can see that for these creatures there is no “inside” or “outside” of the balloon. As higher-dimensional creatures, we 3-D beings can see the balloon is curved. We can see that it separates an inside from an outside. But that privileged distinction exists only in a space with more than two dimensions. For the 2-D creatures, no such extra space exists or needs to exist.
Remember that the total 4-D space-time of general relativity is reality. It is all there is. In Einstein’s first cosmological model, the 3-D spatial part of space-time was curved like the balloon’s surface. There was no 3-D “inside” or “outside”. If you had a starship, you could head off in any direction and, after a very long time, return to where you started from the opposite compass point. In this way the long-standing paradox of boundaries in space—“brick walls” at the edge of the universe—had been resolved. In thinking about the standard idea of cosmic edges, or boundaries, Einstein wrote to a friend, “If it were possible to regard the universe as a continuum which is finite (closed) with respect to its spatial dimension, we should have no need at all of any such boundary conditions.”30 With curved space Einstein could build a finite but unbounded universe as a solution to the equations of general relativity. Time presented a different problem.
Einstein was searching for solutions to his equations that described a static universe. When he looked more closely at his solution—the model universe predicted by his equations—Einstein saw that it was unstable. A little nudge and his closed, hyperspherical universe began to contract or expand, just like a balloon withering under deflation or stretching under inflation.
This gravitational instability was somewhat similar to the one Newton had discovered two hundred years before for his smooth, infinite distribution of stars.31 Einstein was convinced that both contraction and expansion were absurd possibilities. To protect his universe from any kind of evolution, the great scientist fudged. He added an extra term to his equations called a cosmological constant. The cosmological constant filled all space with a kind of antigravity that locked the universe into rigidity. It was an act of cosmic meddling he would soon come to regret.
Within just a few years Einstein had company in his cosmological sandpit. Equations in mathematical physics are like Lego sets. Just because you built a tractor with your box of Lego doesn’t mean someone else can’t use the same bricks to make an aeroplane. Almost immediately after Einstein published his model universe, Willem de Sitter, a professor of physics in the Netherlands, found an entirely different cosmological solution to the equations of general relativity. The de Sitter universe also appeared static, stable and closed. When confronted with de Sitter’s work Einstein saw that it too represented a valid solution to his equations. But there were aspects of de Sitter’s model that struck Einstein as deeply flawed. Most important was that de Sitter assumed a universe was empty of matter. When Einstein chided de Sitter on this point, the Dutchman responded that “empty” could be interpreted simply as an approximation to a very low density of matter.
De Sitter’s universe had another strange property that would prove far more important for history. In his solution, time ran slower for distant observers than for those nearby. One consequence of this cosmic time dilation was that light emitted by distant sources would stretch as it travelled through space-time. Wavelengths would elongate, making light from distant sources shift from the shorter, bluer end of the spectrum to the longer wavelengths at its red end. It was puzzling behaviour. Eventually the true reason for the redshift would emerge as de Sitter’s cosmological solution was recognized as a universe that moved.32 It took some time for astronomers to recognize this point, but once they did, it was clear that de Sitter’s space represented an expanding space. Expansion was an idea that would soon be on everyone’s mind.
THE EXPANDING UNIVERSE IN LIGHT AND MIND
“Nobody who hasn’t done it could ever realize how cold it was”, Milton Humason, the mule driver turned astronomer, later said of his long nights of astronomical observation.33 Humason had arrived at Mount Wilson as a teamster when the Hooker telescope was still under construction. Eventually he found work as an electrician at the observatory and when his skills guiding the telescope were re
cognized he eventually was made a full-fledged member of the astronomical staff. Together, Milton Humason and Edwin Hubble would spend countless hours in the tiny cage perched atop the 2.5-metre telescope. But it took many nights of training the giant instrument on individual galaxies to get accurate readings of their light and extract a measure of their motion. The effort would prove worthy of frozen hands, as motion had become the central question of cosmology circa 1930.34
Even before Hubble discovered that galaxies were separate star systems, the motion of spiral nebulae had been a contentious subject. Astronomers can measure a celestial object’s motion towards or away from the Earth by looking for changes in the light the object emits. Changes in the wavelength of light are like cosmic speed guns for astronomers, allowing them to chart cosmic motions and map out cosmic architecture. The secret lies in the fingerprints of the universe’s elements.
Heat any element, such as a tube of hydrogen gas, and it will glow with a few very narrow and precisely defined bands of colour (this is the physics behind colourful neon lights). These emission lines, as the bands of light are called, form a unique elemental fingerprint of colours (i.e., wavelengths). When astronomers look at a distant object they use a spectrograph to break light up into its component colours. These spectra allow astronomers to see exactly how much energy arrives at each different wavelength. In the early years of the twentieth century, astronomers began collecting a menagerie of galaxy spectra, which would open a new door on cosmic evolution.
