A Homogeneous Universe of Constant Mass and Increasing Radius
Space itself stretches; galaxies recede in proportion to distance.
The galaxies aren't flying through space away from us — space itself is stretching, carrying them along, and this is the paper that first said so.
The idea, unpacked
By the 1920s astronomers had a puzzle: nearly every distant galaxy's light was shifted toward the red, the colour you see when a source is moving away. It looked as if the whole sky were fleeing from us. Why should we be at the centre of a great exodus?
Lemaître's answer was to stop thinking of the galaxies as moving and start thinking of space itself as growing. Picture the space between galaxies quietly swelling, like dough rising. Nobody is at the centre; every observer sees everyone else drifting away. And the farther a galaxy is, the more swelling space lies between it and us, so the faster it appears to recede — velocity growing in step with distance.
Where it came from
Georges Lemaître was a Belgian priest and a trained physicist who had studied with Arthur Eddington in Cambridge and visited Hubble's and Slipher's circles in America. In 1927 he combined Einstein's general relativity with the new galaxy measurements and published the result in a small Belgian journal — in French, where almost no one in the wider community saw it.
He even pulled a first number out of the data: galaxies receding at about 625 kilometres per second for every megaparsec of distance. Two years later Edwin Hubble published the same velocity–distance relationship from his own observations, and it was Hubble's name that stuck to the law. Lemaître, characteristically, never pressed his claim.
Why it mattered
If space is expanding now, then run the film backwards and everything was once crammed together. That single thought — which Lemaître pursued into his 1931 idea of a 'primeval atom' — is the seed of the Big Bang, the modern account of how the universe began. The expanding universe also turned cosmology from philosophy into measurement: the rate of expansion became a number you could go out and pin down, and refining it is still front-line science a century later.
A loaf of raisin bread
Imagine raisins dotted through a loaf of dough as it bakes and rises. Each raisin is a galaxy; the dough is space. As the loaf swells, every raisin moves away from every other one — and a raisin twice as far has twice as much dough expanding between you and it, so it pulls away twice as fast. No raisin is the centre; the whole loaf is simply getting bigger. That is exactly Lemaître's picture, and you can drive it yourself below.
Where it sits
This note stands on Einstein's general relativity of 1915 and on Friedmann's 1922 mathematics, and it stares directly at Hubble's 1929 measurements — which is why the law is now officially the Hubble–Lemaître law. Looking forward, it opens onto the Big Bang and the 1965 discovery of the cosmic microwave background, the faint afterglow of that hot, dense beginning. The single number it first estimated, the Hubble constant, is still the most argued-over figure in cosmology today.
Each theory has its own advantage. One is in agreement with the observed radial velocities of nebulæ, the other with the existence of matter… It seems desirable to find an intermediate solution which could combine the advantages of both.
[v/c] measures the apparent Doppler effect due to the variation of the radius of the universe. It equals the ratio of the radii of the universe at the instants of observation and emission, diminished by unity.
…one finds a mean distance of 0.95 megaparsecs and a radial velocity of 600 Km/sec, i.e. 625 Km/sec at 10⁶ parsecs.
The recession velocities of extragalactic nebulæ are a cosmical effect of the expansion of the universe.