Human Universe. Andrew Cohen
chaos or order, from the waters or the sky or nothing at all – there exist as many creation myths as there are cultures. The impulse to understand the origin of the universe is clearly a powerful unifying idea, although the very existence of many different mythologies continues to be a source of division. It is an unfortunate testament to the emotional power of creation narratives that so much energy is spent arguing about old ones rather than using the increasingly detailed observational evidence available to twenty-first-century citizens to construct new ones. We live in a very privileged and exciting time in this sense, because observational evidence for creation stories was scant even a single lifetime ago. When my grandparents were born in Oldham at the turn of the twentieth century, there was no scientific creation story. Astronomers were not even aware of a universe beyond the Milky Way, which makes it all the more remarkable that the modern scientific approach to the description of the universe emerged almost fully formed from Einstein’s Theory of General Relativity before Edwin Hubble published the discovery of his Cepheid variable star in Andromeda and settled Shapley and Curtis’s Great Debate.
One of the beautiful things about mathematical physics is that equations contain stories. If you think of equations in terms of the nasty little things you used to solve at school on a damp autumn afternoon, then that may sound like a strange and abstract idea. But equations like Einstein’s field equations are much more complex animals. Recall that Einstein’s equations will tell you the shape of spacetime, given some distribution of matter and energy. That shape is known as a solution of the equations, and it is these solutions that contain the stories. The first exact solution to Einstein’s field equations was discovered in 1915 by the German physicist Karl Schwarzschild. Schwarzschild used the equations to calculate the shape of spacetime around a perfectly spherical, non-rotating mass. Schwarzschild’s solution can be used to describe planetary orbits around a star, but it also contains some of the most exotic ideas in modern physics; it describes what we now know as the event horizon of a black hole. The well-known tales of astronauts being spaghettified as they fall towards oblivion inside a supermassive collapsed star are to be found in Schwarzschild’s solution. The calculation was a remarkable achievement, not least because Schwarzschild completed it whilst serving in the German Army at the Russian Front. Shortly afterwards, the 42-year-old physicist died of a disease contracted in the trenches.
There were two ways of arriving at the truth; I decided to follow them both.
Georges Lemaître
The most remarkable stories waiting to be found inside Einstein’s equations reveal themselves when we take an audacious and seemingly reckless leap. Instead of confining ourselves to describing the spacetime around spherical blobs of matter, why not think a little bigger? Why not try to use Einstein’s equations to tell us about all of spacetime? Why can’t we apply General Relativity to the entire universe? Einstein noticed this as a possibility very early in the development of his theory, and in 1917 he published a paper entitled ‘Cosmological Considerations of the General Theory of Relativity’. It’s a big step, of course, from thinking about someone falling off a roof to telling the story of the universe, and Einstein appears to have been uncharacteristically wobbly. In a letter to his friend Paul Ehrenfest a few days before he presented his paper to the Prussian Academy, he wrote ‘I have … again perpetrated something about gravitation theory which somewhat exposes me to the danger of being confined in a madhouse.’
The universe modelled in Einstein’s 1917 paper is not the one we inhabit, but the paper is of interest for the introduction of what Einstein later came to view as a mistake. Einstein tried to find a solution to his equations that would describe a finite universe, populated by a uniform distribution of matter, and stable against gravitational collapse. At the time, this was a reasonable thing to do, because astronomers knew of only a single galaxy – the Milky Way – and the stars did not appear to be collapsing inwards towards each other. Einstein also seems to have had a particular story in mind; he felt that an eternal universe was more elegant than one that had a beginning, which left open the thorny question of a creator. He discovered, however, that General Relativity does not allow for a universe with stars, planets and galaxies to be eternal. Instead, his solution told the story of an unstable universe that would collapse inwards. Einstein tried to solve this unfortunate problem by adding a new term in his equations known as the cosmological constant. This extra term can act as a repulsive force, which Einstein adjusted to resist the tendency of his model universe to collapse under its own gravity. Later, he is famously said to have remarked to his friend George Gamow that the cosmological constant was his biggest blunder.
As physicists began to search for solutions to Einstein’s equations, more and more possible universes were discovered. None, with the exception of Einstein’s universe and a universe without matter and dominated by a (positive) cosmological constant discovered in 1917 by Willem de Sitter, was static. We will return to de Sitter’s universe in a moment, but in every other case, Einstein’s equations seemed to imply continual evolution, whereas Einstein himself felt that the universe should be unchanging and eternal. As more physicists worked with the equations, things only got worse for Einstein’s static, eternal universe.
The first exact cosmological solution of Einstein’s equations for a realistic universe filled with galaxies was discovered by Russian physicist Alexander Friedmann in 1922. He reached his result by assuming something that takes us all the way back to the beginning of this chapter: a Copernican universe in the sense that nowhere in space is special. This is known as the assumption of homogeneity and isotropy, and it corresponds to solving Einstein’s equations with a completely uniform matter distribution. This may seem to be a gross oversimplification, and in the early 1920s the extent to which this assumption agreed with the observational evidence – a universe seemingly containing just a single galaxy – was tenuous. From a theoretical perspective, however, Friedmann’s assumption makes perfect sense. It’s the simplest assumption one can make, and it makes it relatively easy to do the sums! So relatively easy, in fact, that Friedmann’s work was replicated and extended quite independently by a Belgian mathematician and priest named Georges Lemaître. Lemaître planted his flag firmly in the no-man’s-land between religion and science – a strip of intellectual land occupied, whether we like it or not, by cosmology. A student of Harlow Shapley, this deeply religious man never saw a conflict between these two very different modes of human thought. He embodies the much debated and criticised modern notion, introduced by the evolutionary biologist Stephen J. Gould, that science and religion are non-overlapping magesteria, asking the same questions but operating within separate domains. My view is that this is far too simplistic a position to take; questions concerning the origin of the physical universe are of the same character as questions about the nature of the gravitational force or the behaviour of subatomic particles, and answers will surely be found by employing the methodology of science. Having said that, I am willing to recognise that romance, or wonder, or whatever the term is for that deep feeling of awe when contemplating the universe in all its immensity, is a central component of both religious and scientific experience, and perhaps there is room for both in providing the inspiration for the exploration of nature.
At least this is what Lemaître felt, and he used his twin perspectives as a guide on his intellectual journey through the cosmos throughout his distinguished career. Ordained a priest in 1923 while studying at the Catholic University in Louvain, Lemaître studied physics and mathematics alongside some of the great physicists and astronomers of the time, including Arthur Eddington and Harlow Shapley, from the University of Cambridge to Harvard and MIT, before returning to Belgium in 1925 to work with Einstein’s General Relativity.
Lemaître never met Alexander Friedmann, who died from typhoid in 1925. They never spoke or corresponded, and Lemaître was almost certainly unaware of the obscure paper Friedmann had published describing a dynamic and changing universe. He followed the same intellectual path, however, assuming an isotropic and homogeneous distribution of matter in the cosmos, and searching for solutions to Einstein’s equations that describe the story of this smooth and uniform universe. And, of course, he came to the same conclusion: such a universe cannot be static – it must either expand or contract. Lemaître met Einstein at the 1927 Solvay Conference in Brussels, and told him of his conclusions. ‘Your calculations are correct, but your physics insight is abominable’, snapped the great man. Einstein was