correspondence principle
The correspondence principle, formulated by Niels Bohr, demands that any new quantum theory must reproduce the well-tested predictions of classical physics in the regime where classical physics works — typically for large systems, large quantum numbers, or wherever the graininess set by h becomes negligible. It is a guardrail: a quantum theory may be strange, but it cannot contradict the everyday world that classical physics already describes correctly.
Bohr used it as a practical tool while building his atom. For an electron in a very high orbit, far from the nucleus, his quantum jumps had to blend smoothly into the continuous radiation that classical electromagnetism predicts for an orbiting charge. By insisting that the two pictures agree in that limit, he could fix details of his model that the bare quantum rules left undetermined, such as the values of certain constants.
More broadly, the principle is a statement of intellectual humility and consistency. A bridge does not behave quantum-mechanically in any noticeable way, and a successful deeper theory must explain why the older theory worked so well, not merely declare it obsolete. Quantum mechanics passes this test: averaged over many particles or taken to large scales, its predictions melt back into Newton and Maxwell.
In the large-scale limit, quantum predictions must melt back into familiar classical physics.
Correspondence is a necessary check, not a derivation: agreeing with classical physics in the right limit does not by itself prove a quantum theory correct, and not every classical concept survives the transition into the quantum world.