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What "classical physics" refers to depends on the context. When discussing special relativity, it refers to the Newtonian physics which preceded relativity, i.e. the branches of physics based on principles developed before the rise of relativity and quantum mechanics. When discussing general relativity, it refers to the result of modifying Newtonian physics to incorporate special relativity. When discussing quantum mechanics, it refers to non-quantum physics, including special relativity, and general relativity.
Classical theory has at least two distinct meanings in Physics:
- In the context of quantum mechanics, "classical theory" refers to theories of physics that do not use the quantisation paradigm, particularly Newtonian mechanics (which is also known as classical mechanics). General relativity and special relativity are also considered to be "classical" in this sense.
- In the context of general and special relativity, "classical theory" refers to classical mechanics, and other theories which obey Galilean relativity. Light and other electromagnetic pheneomena cannot be correctly modeled in such a theory. Traditionally, light was reconciled with classical mechanics by assuming the existence of a "stationary" medium through which light propagated, the luminiferous aether.
The existence of these two distinct meanings of the term can lead to confusion: special relativity is a "classical theory" in the first sense, but its predictions are more accurate than "classical theory" in the second sense.
In other contexts, "classical theory" will have other meanings—if a current accepted theory is considered to be "modern", and its introduction represented a major paradigm shift, then previous theory (or new theories based on the older paradigm) will often be referred to as "classical".
Among the branches of theory included in classical physics are:
- Classical mechanics
- Classical electrodynamics (Maxwell's Equations)
- Classical thermodynamics
- Special relativity and General relativity
- Classical chaos theory and nonlinear dynamics
In contrast to classical physics, modern physics is a slightly looser term which may refer to just quantum physics or to 20th and 21st century physics in general and so always includes quantum theory and may include relativity.
A physical system on the classical level is a physical system in which the laws of classical physics are valid. There are no restrictions on the application of classical principles, but, practically, the scale of classical physics is the level of isolated atoms and molecules on upwards, including the macroscopic and astronomical realm. Inside the atom and among atoms in a molecule, the laws of classical physics break down and generally do not provide a correct description.
Moreover, the classical theory of electromagnetic radiation is somewhat limited in its ability to provide correct descriptions, since quantum effects are observable in more everyday circumstances than quantum effects of matter. Unlike quantum physics, classical physics is generally characterized by the principle of complete determinism (although the Many-worlds interpretation of quantum mechanics is in a sense deterministic).
Mathematically, classical physics equations are ones in which Planck's constant does not appear. According to the correspondence principle and Ehrenfest's theorem as a system becomes larger or more massive (action >> Planck's constant) the classical dynamics tends to emerge, with some exceptions, such as superfluidity. This is why we can usually ignore quantum mechanics when dealing with everyday objects; instead the classical description will suffice. However, one of the most vigorous on-going fields of research in physics is classical-quantum correspondence. This field of research is concerned with the discovery of how the laws of quantum physics give rise to classical physics in the limit of the large scales of the classical level.