PARITY

in physics, property important in the quantum-mechanical description of a physical system. In most cases, it relates to the symmetry of the wave function representing a system of fundamental particles. A parity transformation replaces such a system with a type of mirror image. Stated mathematically, the spatial coordinates describing the system are inverted through the point at the origin; that is, the coordinates x, y, and z are replaced with -x, -y, and -z. In general, if a system is identical to the original system after a parity transformation, the system is said to have even parity. If the final formulation is the negative of the original, its parity is odd. For either parity the physical observables, which depend on the square of the wave function, are unchanged. A complex system has an overall parity that is the product of the parities of its components. Until 1956 it was assumed that when an isolated system of fundamental particles interacts the overall parity remains the same, or is conserved. This conservation of parity implied that, for fundamental physical interactions, it is impossible to distinguish right from left and clockwise from counterclockwise. The laws of physics, it was thought, are indifferent to mirror reflection and could never predict a change in parity of a system. This law of the conservation of parity was explicitly formulated in the early 1930s by the Hungarian-born physicist Eugene P. Wigner and became an intrinsic part of quantum mechanics. In attempting to understand some puzzles in the decay of particles called K mesons, the Chinese-born physicists Tsung-Dao Lee and Chen Ning Yang proposed in 1956 that parity is not always conserved. For subatomic particles, three basic interactions are important: electromagnetic, strong, and weak. Lee and Yang showed that there was no evidence that parity conservation applies to the weak interaction. The fundamental laws governing weak interactions should not be indifferent to mirror reflection, and, therefore, weak interactions should show some measure of built-in right- or left-handedness that might be experimentally detectable. In experiments conducted by the Chinese-born physicist Chien-Shiung Wu in 1956 and announced by her in 1957, it was conclusively proved that the electrons ejected along with antineutrinos from certain unstable cobalt nuclei in the process of beta decay, a weak interaction, are predominantly left-handedthat is to say, the spin rotation of the electrons is that of a left-handed screw. Nevertheless, it is believed on strong theoretical grounds (i.e., the CPT theorem) that when the operation of parity reversal P is joined with two others, called charge conjugation C and time reversal T, the combined operation does leave the fundamental laws unchanged. in economics, equality in price, rate of exchange, purchasing power, or wages. In international exchange, parity refers to the exchange rate between the currencies of two countries making the purchasing power of both currencies substantially equal. Theoretically, exchange rates of currencies can be set at a parity or par level and adjusted to maintain parity as economic conditions change. The adjustments can be made in the marketplace, by price changes, as conditions of supply and demand change. These kinds of adjustment occur naturally if the exchange rates are allowed to fluctuate freely or within wide ranges. If, however, the exchange rates are stabilized or set arbitrarily (as by the Bretton Woods Conference of 1944) or are set within a narrow range, the par rates can be maintained by intervention of national governments or international agencies (e.g., the International Monetary Fund). In U.S. agricultural economics, the term parity is used for a system of regulating the prices of farm commodities, usually by government price supports and production quotas, in order to provide farmers with the same purchasing power that they had in a selected base period. For most farm commodities the base period has been 191014. For example, the average price received per bushel of wheat during 191014 was 98 cents; if the prices paid by farmers for other goods quadrupled, the parity price for wheat would be $3.92 per bushel. Parity is also used in personnel administration in establishing equitable wage schedules between certain classes of employees. A parity ratio may be set, for instance, between the salaries of police officers and the salaries of firefighters.