Nonlocal

Nonlocal describes dependence or influence that extends beyond a local neighborhood or immediate vicinity. In many fields, the term signals that a property, operator, or effect cannot be fully understood from information at a single point or small region alone.

In quantum physics, nonlocality denotes correlations between distant systems that cannot be explained by signals traveling within the light cone. Entangled states exhibit correlations that violate local realism, as formalized by Bell's theorem. Experiments testing Bell inequalities have provided strong evidence for nonlocal quantum correlations, while preserving the no-signalling principle that forbids faster-than-light communication.

In mathematics and analysis, nonlocal operators depend on the values of a function in a broad region, not just near a point. Examples include integral operators and the fractional Laplacian, which model long-range interactions. Nonlocal models arise in diffusion, phase transitions, and image processing, and often involve nonlocal boundary conditions that couple distant regions.

In programming languages such as Python, a nonlocal statement designates that a name refers to a binding in the nearest enclosing scope rather than the global module scope, allowing nested functions to assign to variables defined in an outer function. This contrasts with global variables and supports closures that modify enclosing environments.