古典力学
Not quite by the distinction between macroscopic and microscopic, classical and quantum mechanics are theories that are distinguished in a subtly different way. At first glance one might think of them as differing simply in the size of objects that they describe, classical objects being considered far larger as to mass and geometrical size than quantal objects, for example a football versus a fine particle of dust. More refined consideration distinguishes classical and quantum mechanics on the basis that classical mechanics fails to recognize that matter and energy cannot be divided into infinitesimally small parcels, so that ultimately fine division reveals irreducibly granular features. The criterion of fineness is whether or not the interactions are described in terms of Planck's constant. Roughly speaking, classical mechanics considers particles in mathematically idealized terms even as fine as geometrical points with no magnitude, still having their finite masses. Classical mechanics also considers mathematically idealized extended materials as geometrically continuously substantial. Such idealizations are useful for most everyday calculations, but may fail entirely for molecules, atoms, photons, and other elementary particles. In many ways, classical mechanics can be considered a mainly macroscopic theory. On the much smaller scale of atoms and molecules, classical mechanics may fail, and the interactions of particles are then described by quantum mechanics. Near the absolute minimum of temperature, the Bose–Einstein condensate exhibits effects on macroscopic scale that demand description by quantum mechanics.