Microcausality Condition

a requirement that the causality condition (which states that cause must precede effect) be satisfied down to an arbitrarily small distance and time interval. The microcausality condition usually refers to distances ≲ 10^-14 cm and to times ≲ 10^-24 sec.

It is shown in the theory of relativity that the assumption of the existence of physical signals that propagate with a velocity greater than the velocity of light leads to violation of the causality requirement. Thus, the microcausality condition prohibits the propagation of signals at a velocity greater than the velocity of light “in the small.”

In quantum theory, where operators correspond to physical quantities, the microcausality condition requires the interchangeability of any operators that pertain to two points of space-time if these points cannot be linked by a light signal. This interchangeability means that the physical quantities to which these operators correspond can be precisely determined independently and simultaneously. The microcausality condition is important in quantum field theory, especially in the dispersion and axiomatic approaches; these approaches are not based on specific model concepts of interaction and therefore can be used for direct verification of the microcausality condition. In the most highly developed branch of quantum field theory—quantum electrodynamics—the microcausality condition has been experimentally verified for distances ≲10^~15 cm (and, correspondingly, for times ≲10^~25 sec).

The violation of the microcausality condition would make it necessary to radically alter the method of describing physical processes and to reject the dynamic description used in modern theories, in which the state of a physical system at a given moment of time (the effect) is determined by the states of the system at preceding times (the cause).