Friday, May 11, 2007

The Broken Mirror: II

II Through the Looking-Glass

"One hopes that nature possesses an order that one may aspire to comprehend. When we arrive at an understanding, we shall marvel how neatly all the elementary particles fit into the great scheme."
-Madame Chien-Shiung Wu

If you look into a mirror, you look out into a reversed world. Left and Right are interchanged but otherwise the world in the mirror looks much like our own.

What about the Laws of Physics? Are they the same in the mirror-world? It appears so. If I throw a ball in the air, my double in the mirror also throws up a ball and both fall according the same law of gravity. I can play with magnets or tops or engines and again the actions of my double are also possible in this world.

Chemists work with the notion of Chirality. The left-right orientation of molecules has a profound impact on their properties. So a left-hand molecule in our world becomes its right-hand counterpart in the mirror world which, according to chemical precepts, is an entirely different molecule. But all of this is surprisingly irrelevant. Since every other molecule in the mirror-world has also changed its handedness, any chemical experiments our double performs are also possible in our world.

So it would seem that if we, like Alice, were unsure whether we were inside a mirror there would be no way for us to discover the truth. Or so it seemed, even to physicists, who refer to this mirror-symmetry property of the Universe as "Parity Conservation."

In 1956, an incredible (and vastly under-appreciated) experiment was performed whose purpose was in fact to determine on which side of the Looking-Glass we live in. The more prosaic intent was to determine the Question of Parity Conservation. The experimenter was a Chinese-born woman - Madame Chien-Shiung Wu.

Her fellow physicists, T.D. Lee and C.N. Yang, had predicted that there might be certain interactions among subatomic particles whose mirror was improbable or did not exist at all. Parity tests such as these had already been performed for a wide variety of interactions and so most physicists were dubious but intrigued.

It was Madame Wu, setting up a laboratory at the National Bureau of Standards in Washington, who set out to confirm or disprove their hunch. The key was in how one particular atom, cobalt-60, decayed. Unlike other atoms studied it decayed (ejecting pieces of itself in the form of beta particles) in an asymmetric manner. The mirror-image of this process was not one that was observed.

If you had placed a large mirror against one wall of Madame Wu's laboratory, her double in the mirror was performing a similar experiment but obtaining results which do not appear in our Universe. The mirror world is not our world merely reconfigured, it is a distinct and alternate reality. Deep within the subtle textures of the Universe there is indeed a small asymmetry, a telltale, a crack, which can be used to distinguish ourselves from the mirror world.

The result was completely unexpected. Mirror-symmetry appeared to be true and appeared to continue to hold true across thousands of other experiments. Looking upon this event, the fall of Parity, the physicist I. Rabi remarked "A rather complete theoretical structure has been shattered at the base and we are not sure how the pieces will be put together"

Wednesday, May 09, 2007

The Broken Mirror: I

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.