One example of an obvious symmetry is a snowflake, which looks the same when you rotate it one-sixth of a turn. Another is Einstein’s theory of relativity, which says the laws of physics are the same no matter what speed. However, in the 1960s, Dr. Nambu, inspired by studies of superconductivity, suggested that some symmetries in the laws of elementary particle physics might be hidden, or “broken” in actual practice. “You have to look for symmetries even when you can’t see them,” Dr. Turner said.

The principle of symmetry breaking is now embedded in all of modern particle physics. The $8 billion Large Hadron Collider, a giant particle accelerator soon to go into operation outside Geneva, was designed largely to find a particle known as the Higgs boson, which is theorized to be responsible for breaking the symmetry between electromagnetism and the so-called weak nuclear force, imparting mass to many particles that in theory are massless.

Imagine a pencil balanced on its point on a table  one of physicists’ favorite examples. To the pencil while it is still on its point, all directions along the table are the same. But the standing pencil is unstable and will eventually fall onto the table pointing in only one direction.

Applying this notion to a puzzle in the subatomic realm, Dr. Nambu explained why a particle known as the pion, which carries the strong nuclear force that holds atomic nuclei together, was much lighter than the protons and neutrons inside it. If it were not so light, the strong force would not extend far enough to stick nuclei heavier than hydrogen together, said Daniel Friedan, a physicist at Rutgers.

The fact that the pion is light, he said, explains why there is a variety of atoms in the world. “There is a variety of atoms because there is a variety of nuclei,” Dr. Friedan wrote in an e-mail message.