The Science of Discworld IV

derived an expanding universe from Einstein’s field equations, and estimated the rate of expansion. His 1931 paper ‘A homogeneous universe of constant mass and growing radius accounting for the radial velocity of extragalactic nebulae’ went largely unread, because he published it in an obscure Belgian journal, but eventually it became a classic.
    Lemaître’s solution conflicted with the prevailing cosmological wisdom, but the popular (and populist) astronomer Sir Arthur Eddington believed that Lemaître’s theory solved many of the major problems in cosmology. In 1930 he invited Lemaître to a meeting in London about physics and spirituality. By then, Lemaître hadrealised that if you ran the universe’s expansion backwards, everything converged to a single point some lengthy period into the past. fn1 He called this initial singularity the primeval atom, and published the idea in the leading scientific journal
Nature
. A huge controversy ensued. Lemaître may not have helped his cause by referring to the idea as ‘the Cosmic Egg exploding at the moment of the creation’.
    Much later Fred Hoyle, by then a leading advocate of the steady-state theory – that the universe is in equilibrium, aside from local fluctuations, and it has always been that way – dismissed Lemaître’s theory as the ‘Big Bang’. The name stuck. So did the theory, to Hoyle’s discomfort. Hoyle had developed the steady-state theory in 1948, aided by Thomas Gold, Hermann Bondi and others. It required matter to be continuously created, gently, particle by particle, in the voids between the stars, to prevent the density of matter decreasing as the universe got bigger. The necessary rate of production was low, about one hydrogen atom per cubic metre every billion years.
    Unfortunately for Hoyle, indirect evidence against the steady-state theory, and in favour of the Big Bang, kept piling up. The smoking gun was the discovery of cosmic background radiation in 1965 – a sizzle of random radio noise that we now think originated when the universe first became transparent to radio waves, shortly after the Big Bang. Moreover, its temperature agreed with theory. Hawking has called this observation ‘the final nail in the coffin of the steady-state theory’.
    Einstein, in private, was unimpressed by Lemaître’s expanding-universe solution. He accepted the mathematics, but not the physical reality. But when Hubble’s results were published two years later, Einstein immediately changed his mind and gave Lemaître strong public support. In 1935 Howard Robertson and Arthur Walker proved that every homogeneous, isotropic universe – one that isthe same at every point and in every direction – corresponds to a particular family of solutions of Einstein’s field equations. The resulting universes could be static, expanding or contracting; their topology could be simple or complex. The family is called the Friedmann-Lemaître-Robertson-Walker metric, or the ‘standard model of cosmology’ if that’s too big a mouthful. It now dominates mainstream cosmological thinking.
    Narrativium now took over, and led many cosmologists into the realms of scientific mythology. The correct statement that ‘there exist solutions of Einstein’s field equations corresponding to the classical non-Euclidean geometries’ transmogrified into the false statement ‘these are the only possible solutions of constant curvature’. The mistake may have arisen because mathematicians weren’t paying enough attention to astronomy and astronomers weren’t paying enough attention to mathematics. Robertson and Walker’s uniqueness theorem proves that the
metric
is unique, and it is easy to imagine that the space must also be unique. After all, doesn’t the metric define the space?
    No, it doesn’t.
    The metric is local; the space is global. Both infinite Euclidean space and the flat torus have the same metric, because the geometry of small regions is identical. The computer screen remains flat; what changes are the rules about going off the edge. But globally, the flat torus has special geodesics – ones that form closed loops – whereas Euclidean space does not. So the metric does not define the space. But cosmologists thought it did. In 1999, writing in
Scientific American
, Jean-Pierre Luminet, Glenn Starkman, and Jeffrey Weeks, wrote: ‘The decades from 1930 to 1990 were the dark ages of the subject. Most astronomy textbooks, quoting one another for