backgroundindependent

Background independence is a property of a physical theory in which the geometry of spacetime is not fixed in advance by the theory’s formulation; instead, the geometry is dynamical and determined by the theory’s fields through its equations of motion. In such theories, there is no background metric or structure that is presupposed a priori. Diffeomorphism invariance, which expresses the equivalence of different coordinate descriptions, is often cited as a mathematical manifestation of background independence.

General relativity is the paradigmatic example; the spacetime metric is a dynamical field governed by Einstein’s equations, and no fixed background spacetime is assumed. By contrast, many non-gravitational theories, such as quantum field theories defined on Minkowski space, rely on a fixed background metric and are therefore background dependent. String theory has traditionally been developed around perturbations about a given background, though some researchers pursue background-independent formulations or emergent spacetime; loop quantum gravity is explicitly built to be background independent, using quantized geometric excitations rather than a fixed spacetime.

Background independence raises conceptual and technical questions for quantum gravity, including how classical spacetime and time itself emerge from a more fundamental, non-fixed substrate—the so-called problem of time. It also motivates relational interpretations in which physical quantities are defined by relations among dynamical degrees of freedom rather than with respect to a fixed stage. The degree to which a theory is background independent is often debated, and a fully realized, predictive background-free quantum theory of gravity remains a central research goal.