The Broken Mirror
I. The Shape of Space
I don't recall the name of the professor who taught the course on Cosmology. I do recall he wore stiff suits and large spectacles and that he was British. Also, he kept his upper body completely fixed when he moved about. Scratching out equations on the chalkboard, for example, he would raise one hand and then bend his knees up and down to write. The effect, as seen from behind, was as if a large frog was anxiously stretching its legs against the front wall of the classroom. Meanwhile the professor/frog was also sagely informing us about the nature of stars and galaxies.
We were discussing the shape of space. Space can be negatively curved, positively curved or it can be flat. The verdict relies on understanding how much matter is in our Universe and whether it exceeds a theoretical critical number. This grand ratio is known as Omega. If Omega is greater than 1, then space is positively curved and the Universe is headed toward collapse. If Omega is less than 1, space is negatively curved and will expand forever.
The discussion turned philosophical. Astronomers had tried to measure Omega and values ranged from 0.001 to 1.2. Surely, our professor argued, this meant that the value was likely to be exactly 1. His argument was an aesthetic argument. An Omega of 1 was perfectly symmetrical. And if it were not 1, why would it be so tantalizingly close to 1? Omega could have been measured to be in the billions or a mere tiny billionth. But it was not.
The argument is alluring but it also recalls the struggle between idealizations of the natural world and the true natural world, that is bare reality, which obeys symmetry from a rough distance but, when magnified, obeys its own impenetrable logic. Planets do not move in perfect circles in a Ptolemaic harmonic symphony. They move in wobbly ellipses, tugged constantly in their orbits. The Earth is not a perfect sphere but an oblate spheroid, tilted sideways, drawn off-center by a heavily cratered moon.
Symmetry as an ordering principle is a rough guide. Inspected more closely, the Universe is riddled with tiny asymmetries. This seems obviously true on the larger scale; we all know there is no perfect circle or straightedge.
But it is also true in the idealized world of natural laws. Just when we believe we have fully understood some force or interaction or particle, just at the moment we are ready to formulate a Universal Law or Rule, we find one or two exceptions. Not thousands or millions of exceptions, but just a couple, a few... sometimes only one. But only one exception is needed to invalidate the rule altogether. It is a confounding feature of our world that every symmetry is broken, but only barely broken, it is like an otherwise perfect mirror with a hairline crack. A broken mirror, nonetheless.
With what I know now, it is obvious, contrary to what the professor was saying, that Omega may be slightly less than 1 or slightly greater than 1 but it is certainly not 1. That would make the Universe perfectly symmetrical in that respect. Such symmetry, as far as I know, is forbidden in this world.