Genius_ The Life and Science of Richard Feynman - James Gleick [198]
The understanding of symmetry also became an understanding of symmetry’s imperfections, for, as symmetry laws came to dominate, they also began to break down. One of the most obvious of all symmetries led the way: the symmetry of left and right. Humans seem mostly symmetrical, but not perfectly so. The symmetry is “broken,” as a modern physicist would say, by an off-center heart and liver and by more subtle or superficial differences. We learn to break the symmetry ourselves by internalizing an awareness of the difference between left and right, although sometimes this is not so easy. Feynman himself confessed to a group gathered around the coffee pot in a Caltech laboratory that even now he had to look for the mole on the back of his left hand when he wanted to be sure. As early as his MIT fraternity days he had puzzled over the classic teaser of mirror symmetry: why does a mirror seem to invert left and right but not top and bottom? That is, why are the letters of a book backward but not upside down, and why would Feynman’s double behind the mirror appear to have a mole on his right hand? Was it possible, he liked to ask, to give a symmetrical explanation of what a mirror does—an explanation that treats up-and-down no differently from left-and-right? Many logicians and scientists had debated this conundrum. There were many explanations, some of them correct. Feynman’s was a model of clarity.
Imagine yourself standing before the mirror, he suggested, with one hand pointing east and the other west. Wave the east hand. The mirror image waves its east hand. Its head is up. Its west hand lies to the west. Its feet are down. “Everything’s really all right,” Feynman said. The problem is on the axis running through the mirror. Your nose and the back of your head are reversed: if your nose points north, your double’s nose points south. The problem now is psychological. We think of our image as another person. We cannot imagine ourselves “squashed” back to front, so we imagine ourselves turned left and right, as if we had walked around a pane of glass to face the other way. It is in this psychological turnabout that left and right are switched. It is the same with a book. If the letters are reversed left and right, it is because we turned the book about a vertical axis to face the mirror. We could just as easily turn the book from bottom to top instead, in which case the letters will appear upside down.
Our own asymmetries—our blemishes, hearts, handednesses—arise from contingent choices nature made in the process of building up complicated organisms. A preference for right or left appears in biology all the way down to the level of organic molecules, which can be right- or left-handed. Sugar molecules have this intrinsic corkscrew property. Chemists can make them with either handedness, but bacteria digest only “right-handed” sugar, and that is the kind that sugar beets produce. Earthly sugar beets, that is—for evolution might just as well have chosen a left-handed pathway, just as the industrial revolution might have settled on left-threaded rather than right-threaded screws.
On still smaller scales, at the level of elementary particle interactions, physicists assumed that nature would not distinguish between right and left. It seemed inconceivable that the laws of physics would change with mirror reflection, any more than they change when an experiment is conducted at a different place or