The Science of Discworld IV

detected distant nebulas, fuzzy wisps of light. In 1755 the philosopher Immanuel Kant called such nebulas ‘island universes’; eventually they became known as galaxies, from the Latin for ‘milk’. Charles Messier compiled the first systematic catalogue of nebulas (a few were genuine wisps, not galaxies) in 1774. A prominent one, in the constellation of Andromeda, was the 31st in his list, and it was therefore designated M31. It showed no parallax, so it was presumably a long way away. The big question was: how far?
    In 1924 Edwin Hubble showed that M31 lies far beyond the Milky Way, thanks to some brilliant work by Henrietta Leavitt, a human ‘computer’ hired to carry out the repetitive task of measuring and cataloguing how bright the stars were. At that time astronomerswere looking for a ‘standard candle’ – a type of star whose intrinsic brightness could be inferred from other observations. This could then be compared to its apparent brightness, and the way brightness decreases with distance could be used to calculate how far away the star was. Leavitt was observing Cepheid variables – stars whose light output changes in a periodic cycle – and in 1908 she discovered that the light output of a Cepheid is related to the period of its cycle. Therefore its intrinsic brightness can be calculated from observations, so it can be used as a standard candle. In 1924 Hubble observed Cepheid variables in M31, and calculated that this galaxy is a million light years away. The current estimate is 2.5 million light years.
    Most galaxies are much further away than that; so distant that there is no prospect of distinguishing Cepheids, indeed any individual stars. However, Hubble overcame this obstacle too. Vesto Slipher and Milton Humason discovered that the spectra of many galaxies were shifted towards the red end of the spectrum. The most plausible explanation was the Doppler effect, in which a wave changes frequency if its source moves. It is most familiar for sound waves: the pitch of a police car’s siren gets lower when it passes, changing from moving towards us to going away from us. The Doppler effect implies that the galaxies concerned must be receding at significant speeds. Hubble plotted the amount of redshift against estimates of distance for forty-six galaxies in which Cepheids had been spotted. The graph was approximately a straight line, suggesting that the velocity of recession (deduced from redshift) and distance were proportional. In 1929 he formulated this as a formula, which we now call Hubble’s law. The constant of proportionality, Hubble’s constant, is currently thought to be about 21 km/s per million light years. Hubble’s initial estimate was about seven times as big.
    It is now realised that the Swedish astronomer Knut Lundmark had the same idea in 1924, five years before Hubble. He used the apparent sizes of galaxies to infer how far away they were, and his figure for the ‘Hubble’ constant was within 1% of today’s – far betterthan Hubble’s. However, his work was ignored because his methods had not been cross-checked using independent measurements.
    These developments tied the size of the universe and its dynamic behaviour together, and led to a surprising inference. If all of the galaxies are moving away from us, then either the Earth is near the centre of some expanding region, or the entire universe is getting bigger.
    Astronomers were already aware that the universe might be expanding. Einstein’s field equations, the basis of general relativity, predicted it. In 1924 Aleksandr Friedmann derived three types of solution of the field equations, depending on whether the curvature of space is positive, zero or negative. Mathematicians working in non-Euclidean geometry had already discovered such spaces: respectively, they are said to be elliptic, Euclidean or hyperbolic (like the Escherverse). Elliptic space is finite, a hypersphere – like the surface of a sphere but three-dimensional. The other two are of infinite extent. (The Escherverse is like Roundworld: from the outside it appears to be finite, but from inside, measured using its own metric, it is infinite in extent. That’s how it can contain infinitely many angels or devils, all the same size.) The field equations specified a range of shapes for the universe, but did not pin the shape down uniquely.
    The field equations also allow the shape of the universe to change as time passes. In 1927 Georges Lemaître