Classical limit
Encyclopedia
The classical limit or correspondence limit is the ability of a physical theory
to approximate or "recover" classical mechanics
when considered over special values of its parameters. The classical limit is used with physical theories that predict non-classical behavior. A postulate called the correspondence principle
was introduced to quantum theory
by Niels Bohr
; it states that, in effect, some kind of continuity argument should apply to the classical limit of quantum systems as the value of Planck's constant tends to zero.
In quantum mechanics
, due to Heisenberg's
uncertainty principle
, an electron
can never be at rest; it must always have a non-zero kinetic energy
, a result not found in classical mechanics. For example, if we consider something very large relative to an electron, like a baseball, the uncertainty principle predicts that it cannot have zero kinetic energy, but the uncertainty in kinetic energy is so small that the baseball can appear to be at rest, and hence appears to obey classical mechanics. In general, if large energies and large objects (relative to the size and energy levels of an electron) are considered in quantum mechanics, the result will appear to obey classical mechanics. It is unclear how the classical limit applies to chaotic systems, a field known as quantum chaos
.
In general
and special relativity
, if we consider flat space, small masses, and small speeds (in comparison to the speed of light), we find that objects once again appear to obey classical mechanics.
Theoretical physics
Theoretical physics is a branch of physics which employs mathematical models and abstractions of physics to rationalize, explain and predict natural phenomena...
to approximate or "recover" classical mechanics
Classical mechanics
In 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...
when considered over special values of its parameters. The classical limit is used with physical theories that predict non-classical behavior. A postulate called 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....
was introduced to quantum theory
Bohr model
In atomic physics, the Bohr model, introduced by Niels Bohr in 1913, depicts the atom as a small, positively charged nucleus surrounded by electrons that travel in circular orbits around the nucleus—similar in structure to the solar system, but with electrostatic forces providing attraction,...
by Niels Bohr
Niels Bohr
Niels Henrik David Bohr was a Danish physicist who made foundational contributions to understanding atomic structure and quantum mechanics, for which he received the Nobel Prize in Physics in 1922. Bohr mentored and collaborated with many of the top physicists of the century at his institute in...
; it states that, in effect, some kind of continuity argument should apply to the classical limit of quantum systems as the value of Planck's constant tends to zero.
In 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...
, due to Heisenberg's
Werner Heisenberg
Werner Karl Heisenberg was a German theoretical physicist who made foundational contributions to quantum mechanics and is best known for asserting the uncertainty principle of quantum theory...
uncertainty principle
Uncertainty principle
In quantum mechanics, the Heisenberg uncertainty principle states a fundamental limit on the accuracy with which certain pairs of physical properties of a particle, such as position and momentum, can be simultaneously known...
, an electron
Electron
The electron is a subatomic particle with a negative elementary electric charge. It has no known components or substructure; in other words, it is generally thought to be an elementary particle. An electron has a mass that is approximately 1/1836 that of the proton...
can never be at rest; it must always have a non-zero kinetic energy
Kinetic energy
The kinetic energy of an object is the energy which it possesses due to its motion.It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes...
, a result not found in classical mechanics. For example, if we consider something very large relative to an electron, like a baseball, the uncertainty principle predicts that it cannot have zero kinetic energy, but the uncertainty in kinetic energy is so small that the baseball can appear to be at rest, and hence appears to obey classical mechanics. In general, if large energies and large objects (relative to the size and energy levels of an electron) are considered in quantum mechanics, the result will appear to obey classical mechanics. It is unclear how the classical limit applies to chaotic systems, a field known as quantum chaos
Quantum chaos
Quantum chaos is a branch of physics which studies how chaotic classical dynamical systems can be described in terms of quantum theory. The primary question that quantum chaos seeks to answer is, "What is the relationship between quantum mechanics and classical chaos?" The correspondence principle...
.
In general
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...
and special relativity
Special 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...
, if we consider flat space, small masses, and small speeds (in comparison to the speed of light), we find that objects once again appear to obey classical mechanics.
See also
- Quantum limitQuantum limitQuantum limit in physics refers to a limit on measurement accuracy at quantum scales.It may refer to the minimum level of quantum noise which is obtainable without squeezed states. For instance, the sensitivity of optical measurements has a standard quantum limit...
- Relativistic limit
- Modern physicsModern physicsThe 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...