The concept of "emergence" has become pervasive across philosophy, complex systems theory, and biology, yetsuffers from fundamental definitional ambiguity. Chalmers' influential distinction between "weak" and "strong"emergence fails to provide operational criteria: weak emergence conflates computational intractability withontological novelty, while strong emergence lacks empirical instantiation. This paper proposes a radicalredefinition grounded in physics: emergence is the appearance of a non-zero order parameter followingsymmetry-breaking phase transition at a critical point. Using the Landau-Ginzburg-Stuart framework as thecanonical form, we demonstrate that this definition provides measurable critical conditions, identifiable orderparameters, and traceable dynamics. Following Anderson's "More is Different" (1972) and Batterman's asymptoticanalysis (2002), we show that genuine novelty arises through symmetry breaking without violating physicalclosure. Butterfield's "emergence before the limit" (2011) addresses finite-size concerns. This unified frameworkrescues "emergence" from buzzword status and establishes it as a rigorous scientific concept with predictive power.Biological and social applications are developed in companion papers.