The Hidden Reality_ Parallel Universes and the Deep Laws of the Cosmos - Brian Greene [12]
The Primeval Atom
It was against this backdrop that Lemaître approached Einstein at the 1927 Solvay Conference in Brussels, with his result that general relativity gave rise to a new cosmological paradigm in which space would expand. Having already wrestled with the mathematics to ensure a static universe, and having already dismissed Friedmann’s similar claims, Einstein had little patience for once again considering an expanding cosmos. He thus faulted Lemaître for blindly following the mathematics and practicing the “abominable physics” of accepting an obviously absurd conclusion.
A rebuke by a revered figure is no small setback, but for Lemaître it was short-lived. In 1929, using what was then the world’s largest telescope at the Mount Wilson Observatory, the American astronomer Edwin Hubble gathered convincing evidence that the distant galaxies were all rushing away from the Milky Way. The remote photons that Hubble examined had traveled to earth with a clear message: The universe is not static. It is expanding. Einstein’s reason for introducing the cosmological constant was thus unfounded. The big bang model describing a cosmos that began enormously compressed and has been expanding ever since became widely heralded as the scientific story of creation.8
Lemaître and Friedmann were vindicated. Friedmann received credit for being the first to explore the expanding universe solutions, and Lemaître for independently developing them into robust cosmological scenarios. Their work was duly lauded as a triumph of mathematical insight into the workings of the cosmos. Einstein, by contrast, was left wishing he’d never meddled with the third line of the general relativity tax form. Had he not brought to bear his unjustified conviction that the universe is static, he wouldn’t have introduced the cosmological constant and so might have predicted cosmic expansion more than a decade before it was observed.
Nevertheless, the cosmological constant’s story was far from over.
The Models and the Data
The big bang model of cosmology includes a detail that will prove essential. The model provides not one but a handful of different cosmological scenarios; all of them involve an expanding universe, but they differ with respect to the overall shape of space—and, in particular, they differ on the question of whether the full extent of space is finite or infinite. Since the finite-versus-infinite distinction will turn out to be vital in thinking about parallel worlds, I’ll lay out the possibilities.
The cosmological principle—the assumed homogeneity of the cosmos—constrains the geometry of space because most shapes are not sufficiently uniform to qualify: they bulge here, flatten out there, or twist way over there. But the cosmological principle does not imply a unique shape for our three dimensions of space; instead, it reduces the possibilities to a sharply culled collection of candidates. To visualize them presents a challenge even for professionals, but it is a helpful fact that the situation in two dimensions provides a mathematically precise analog that we can readily picture.
To this end, first consider a perfectly round cue ball. Its surface is two-dimensional (just as on earth’s surface, you can denote positions on the cue ball’s surface with two pieces of data—such as latitude and longitude—which is what we mean when we call a shape two-dimensional) and is completely uniform in the sense that every location looks like every other. Mathematicians call the cue ball’s surface a two-dimensional sphere and say that it has constant positive curvature. Loosely speaking, “positive” means that were you to view your reflection on a spherical mirror it would bloat outward, while “constant” means that regardless of where on the sphere your reflection is, the distortion appears the same.
Next, picture a perfectly smooth tabletop. As with the cue ball, the tabletop’s surface is uniform. Or nearly so. Were you an ant walking on the tabletop, the view from every point would indeed look like the view from every