Classical limit

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.

See also

• Quantum limit
• Relativistic limit
• Modern physics