In 1967 Dr. Sakharov laid out a prescription for how matter and antimatter could have survived their mutual destruction pact. One condition is that the laws of nature might not be as symmetrical as physicists like Einstein assumed.

In a purely symmetrical universe, physics should work the same if all the particles changed their electrical charges from positive to negative or vice versa — and, likewise, if the coordinates of everything were swapped from left to right, as if in a mirror. Violating these conditions — called charge and parity invariance, C and P for short — would cause matter and antimatter to act differently.

In 1957, Tsung-Dao Lee of Columbia University and Chen Ning Yang, then at Institute for Advanced Study, won the Nobel Prize in Physics for proposing something along these lines. They suggested that certain “weak interactions” might violate the parity rule, and experiments by Chien-Shiung Wu of Columbia (she was not awarded the prize) confirmed the theory. Nature, in some sense, is left-handed.

In 1964, a group led by James Cronin and Val Fitch, working at the Brookhaven National Laboratory on Long Island, discovered that some particles called kaons violated both the charge and parity conditions, revealing a telltale difference between matter and antimatter. These scientists also won a Nobel.

Hints of a discrepancy between matter and antimatter have since been found in the behavior of other particles called B mesons, in experiments at CERN and elsewhere.

“In the larger picture, CP violation is a big deal,” Dr. Turner of the Kavli Foundation said. “It is why we are here!”

Both kaons and B mesons are made of quarks, the same kinds of particles that make up protons and neutrons, the building blocks of ordinary matter. But so far there is not enough of a violation on the part of quarks, by a factor of a billion, to account for the existence of the universe today.