The most famous goal of the Large Hadron Collider at CERN in Switzerland is detection of the Higgs boson. This particle's existence is wrapped up in a theory called spontaneous symmetry breaking. This concept, first elucidated in the context of condensed matter physics, won Philip Anderson the 1977 Nobel Prize.Outside the esoteric realm of high-energy physics, it's a surprisingly simple idea. Imagine a round pencil standing on its tip. If the pencil is symmetric, and the table smooth, and there is no breeze, the pencil won't fall. This is a consequence of symmetry: since there is no preferred direction for the pencil to fall in, it can't fall without breaking that symmetry. The symmetry is a reflection of the perfectly balanced forces acting on the pencil--and if they are balanced, the pencil can't fall.
Pencils do fall. Some slight movement of the air, some accretion of microscopic collisions of air molecules with the pencil will be enough to nudge it one direction or another, and the pencil will fall. The original symmetry, demoted, is not completely violated, though. If you stand up a vast number of pencils and measure their directions of fall, all directions will be equally represented. In the parlance of physics, this is now a hidden symmetry. For each pencil it is spontaneously broken by the smallest of imbalances--only to be revealed again en masse.
There are many other examples of spontaneous symmetry breaking in the world around us. Appropriate to the season is the growth of ice crystals on a window pane. The glass may initially seem symmetric, each point on its surface being like any other. Yet the crystals crawl slowly across the glass as if following a topographical map we can't see. Only when 50 or 100 or 1,000 windows are compared does the symmetry, the uniformity, reappear.
In the Gospel of John, Jesus' first sign is to turn gallon upon gallon of water into wine. We know nothing of who was being wed or their circumstances, only that Jesus, who apparently didn't start the day intending to transmute any liquid elements, put on the spot by his mother, gave one of the best wedding gifts ever.Why Cana? Why this wedding? This was surely a life-changing event for those who witnessed it. John says the purpose of the sign was to reveal Jesus' glory and bring about greater belief on the part of the disciples. But nothing about the couple or Cana or even the date of the event was apparently special. In that sense, there was a symmetry: there was nothing about the date and location of this wedding which would allow you to pick it from another. This symmetry was broken when Mary directed the servants to do what Jesus commanded. Like the falling pencil or the ice crystals, seemingly minor or arbitrary factors changed history.
In theology this is a form of what's called the scandal of particularity. The most common version of this is the question: If God were to save humanity, why through a single man, this man, why in the first century, why Palestine, and so on. Why was Jesus born when and where he was, to Mary and Joseph, and not some other couple? (Or, if you prefer, why were Mary and Joseph living where they were and not somewhere else?) To answer that this fulfills prophecy postpones the question without answering it.
This apparent paradox can undermine belief in a more general way. Why would God hear my prayers when so many others seem to have their prayers unanswered? We are tempted to conclude: my prayers are no different, and God doesn't play favorites, so when it appears a prayer is answered, it must just be coincidence.
When the pencil falls, there's a reason, though it may be submerged at a scale we can't perceive.
Why does God hear my prayers, and not those of someone else? God's varied responses to our pleas apparently break symmetry. What hidden symmetry awaits those with eyes to see?
