Classical physics

Encyclopedia

What "

, 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.

:

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.

, then previous theory (or new theories based on the older paradigm) will often be referred to as "classical".

Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...

and

.

A

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 atom

s and molecule

s 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.

**classical physics**" refers to depends on the context. When discussing special relativitySpecial relativity

Special relativity is the physical theory of measurement in an inertial frame of reference proposed in 1905 by Albert Einstein in the paper "On the Electrodynamics of Moving Bodies".It generalizes Galileo's...

, it refers to the Newtonian physics which preceded relativity, i.e. the branches of physics

Physics

Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...

based on principles developed before the rise of relativity

Theory of relativity

The theory of relativity, or simply relativity, encompasses two theories of Albert Einstein: special relativity and general relativity. However, the word relativity is sometimes used in reference to Galilean invariance....

and quantum mechanics

Quantum mechanics

Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...

. When discussing general relativity

General relativity

General relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...

, it refers to the result of modifying Newtonian physics to incorporate special relativity. When discussing quantum mechanics

Quantum mechanics

Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...

, it refers to non-quantum physics, including special relativity, and general relativity.

## Overview

**Classical theory**has at least two distinct meanings in PhysicsPhysics

Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...

:

**In the context of quantum mechanics**, "classical theory" refers to theoriesQuantum mechanicsQuantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...TheoryThe English word theory was derived from a technical term in Ancient Greek philosophy. The word theoria, , meant "a looking at, viewing, beholding", and referring to contemplation or speculation, as opposed to action...

of physics that do not use the quantisationQuantization (physics)In physics, quantization is the process of explaining a classical understanding of physical phenomena in terms of a newer understanding known as "quantum mechanics". It is a procedure for constructing a quantum field theory starting from a classical field theory. This is a generalization of the...

paradigmParadigmThe word paradigm has been used in science to describe distinct concepts. It comes from Greek "παράδειγμα" , "pattern, example, sample" from the verb "παραδείκνυμι" , "exhibit, represent, expose" and that from "παρά" , "beside, beyond" + "δείκνυμι" , "to show, to point out".The original Greek...

, particularly Newtonian mechanics (which is also known as classical mechanicsClassical mechanicsIn physics, classical mechanics is one of the two major sub-fields of mechanics, which is concerned with the set of physical laws describing the motion of bodies under the action of a system of forces...

). General relativityGeneral relativityGeneral relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...

and special relativitySpecial relativitySpecial relativity is the physical theory of measurement in an inertial frame of reference proposed in 1905 by Albert Einstein in the paper "On the Electrodynamics of Moving Bodies".It generalizes Galileo's...

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 relativityPrinciple of relativityIn physics, the principle of relativity is the requirement that the equations describing the laws of physics have the same form in all admissible frames of reference....

. 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 aetherLuminiferous aetherIn the late 19th century, luminiferous aether or ether, meaning light-bearing aether, was the term used to describe a medium for the propagation of light....

.

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 shiftParadigm shift

A Paradigm shift is, according to Thomas Kuhn in his influential book The Structure of Scientific Revolutions , a change in the basic assumptions, or paradigms, within the ruling theory of science...

, then previous theory (or new theories based on the older paradigm) will often be referred to as "classical".

### Scope

Among the branches of theory included in classical physics are:- Classical mechanicsClassical mechanicsIn physics, classical mechanics is one of the two major sub-fields of mechanics, which is concerned with the set of physical laws describing the motion of bodies under the action of a system of forces...

- Newton's laws of motionNewton's laws of motionNewton's laws of motion are three physical laws that form the basis for classical mechanics. They describe the relationship between the forces acting on a body and its motion due to those forces...
- Classical LagrangianLagrangianThe Lagrangian, L, of a dynamical system is a function that summarizes the dynamics of the system. It is named after Joseph Louis Lagrange. The concept of a Lagrangian was originally introduced in a reformulation of classical mechanics by Irish mathematician William Rowan Hamilton known as...

and HamiltonianHamiltonian mechanicsHamiltonian mechanics is a reformulation of classical mechanics that was introduced in 1833 by Irish mathematician William Rowan Hamilton.It arose from Lagrangian mechanics, a previous reformulation of classical mechanics introduced by Joseph Louis Lagrange in 1788, but can be formulated without...

formalisms

- Newton's laws of motion
- Classical electrodynamics (Maxwell's EquationsMaxwell's equationsMaxwell's equations are a set of partial differential equations that, together with the Lorentz force law, form the foundation of classical electrodynamics, classical optics, and electric circuits. These fields in turn underlie modern electrical and communications technologies.Maxwell's equations...

) - Classical thermodynamicsThermodynamicsThermodynamics is a physical science that studies the effects on material bodies, and on radiation in regions of space, of transfer of heat and of work done on or by the bodies or radiation...
- Special relativitySpecial relativitySpecial relativity is the physical theory of measurement in an inertial frame of reference proposed in 1905 by Albert Einstein in the paper "On the Electrodynamics of Moving Bodies".It generalizes Galileo's...

and General relativityGeneral relativityGeneral relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics... - Classical chaos theoryChaos theoryChaos theory is a field of study in mathematics, with applications in several disciplines including physics, economics, biology, and philosophy. Chaos theory studies the behavior of dynamical systems that are highly sensitive to initial conditions, an effect which is popularly referred to as the...

and nonlinear dynamics

### Differences

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 soModern physics

The term modern physics refers to the post-Newtonian conception of physics. The term implies that classical descriptions of phenomena are lacking, and that an accurate, "modern", description of reality requires theories to incorporate elements of quantum mechanics or Einsteinian relativity, or both...

*always*includes quantum theoryQuantum mechanics

and

*may*include relativityTheory of relativity

The theory of relativity, or simply relativity, encompasses two theories of Albert Einstein: special relativity and general relativity. However, the word relativity is sometimes used in reference to Galilean invariance....

.

A

*physical system on the classical level*is a physical systemPhysical system

In physics, the word system has a technical meaning, namely, it is the portion of the physical universe chosen for analysis. Everything outside the system is known as the environment, which in analysis is ignored except for its effects on the system. The cut between system and the world is a free...

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 atom

Atom

The atom is a basic unit of matter that consists of a dense central nucleus surrounded by a cloud of negatively charged electrons. The atomic nucleus contains a mix of positively charged protons and electrically neutral neutrons...

s and molecule

Molecule

A molecule is an electrically neutral group of at least two atoms held together by covalent chemical bonds. Molecules are distinguished from ions by their electrical charge...

s 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

Electromagnetic radiation

Electromagnetic radiation is a form of energy that exhibits wave-like behavior as it travels through space...

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

Correspondence principle

In physics, the correspondence principle states that the behavior of systems described by the theory of quantum mechanics reproduces classical physics in the limit of large quantum numbers....

and Ehrenfest's theorem as a system becomes larger or more massive (action

Action (physics)

In physics, action is an attribute of the dynamics of a physical system. It is a mathematical functional which takes the trajectory, also called path or history, of the system as its argument and has a real number as its result. Action has the dimension of energy × time, and its unit is...

>> 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.

## See also

- Glossary of classical physicsGlossary of classical physicsThis article is a glossary of classical physics. It is some of the most common terms in classical physics and how they are used.- A :* Acceleration - the rate of change of velocity with respect to time...