# Classical physics

(Redirected from Physics in the Classical Limit)
The four major domains of modern physics

Classical physics refers to theories of physics that predate modern, more complete, or more widely applicable theories. If a currently accepted theory is considered to be "modern," and its introduction represented a major paradigm shift, then previous theories (or new theories based on the older paradigm) will often be referred to as "classical". As such, the definition of a classical theory depends on context. Classical physical concepts are often used when modern theories are unnecessarily complex for a particular situation.

## Overview

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 classical mechanics, including relativity.[1] Likewise, classical field theories, such as general relativity and classical electromagnetism, are those that do not incorporate any quantum mechanics.[2] In the context of general and special relativity, classical theories are those that obey Galilean relativity.[3]

Among the branches of theory included in classical physics are:

## Comparison with modern physics

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. Modern physics includes quantum theory and relativity, when applicable.

A physical system can be considered in the classical limit when they satisfy conditions such that the laws of classical physics are approximately valid. In practice, physical objects larger than atoms and molecules can be well-understood with classical mechanics, including the objects in the macroscopic and astronomical realm. Beginning at the atomic level, the laws of classical physics break down and generally do not provide a correct description of nature. Electromagnetic fields and forces can be described well by classical electrodynamics at length scales and field strengths large enough that quantum mechanical effects are negligible. Unlike quantum physics, classical physics is generally characterized by the principle of complete determinism, although deterministic interpretations of quantum mechanics do exist.

From the point of view of classical physics as non-relativistic physics, the predictions of general and special relativity are significantly different than those of classical theories, particularly concerning the passage of time, the geometry of space, the motion of bodies in free fall, and the propagation of light. Traditionally, light was reconciled with classical mechanics by assuming the existence of a stationary medium through which light propagated, the luminiferous aether, which was later shown not to exist.

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 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.

## Computer modeling and manual calculation, modern and classic comparison

A computer model would use only quantum theory and relativistic theory only

Today a computer performs millions of arithmetic operations in seconds to solve a classical differential equation, while Newton (the father of the differential calculus) would take hours to solve the same equation by manual calculation, even if he were the discoverer of that particular equation.

Computer modeling would use quantum and relativistics physics. Classic physics is considered the limit of quantum mechanics for large number of particles. On the other hand, classic mechanics (part of classic physics) is derived from relativistic mechanics. For velocities much smaller than that of light, one can neglect the terms with c2 and higher in the denominator. These formulas then reduce to the standard definitions of Newtonian kinetic energy and momentum. This is as it should be, for special relativity must agree with Newtonian mechanics at low velocities. Computer modeling has to be as real as possible. Classical physics would introduce an error as in the superfluidity case. In order to produce reliable models of the world, we can not use classic physics in today modeling. It is true that quantum theories consume time and computer resources which could be reduced by using classical equations, but we can not sacrifice reliability in order to save time.

Computer modeling would use only the energy criteria to determine which theory to use: relativity or quantum theory, when considering any object (the object can have any number of particles, and become a system of particles). The speed and size of an object (or a system of particles) are only used for academics purposes or engineer calculus (civil engineers use classical physics to build anything from a house to a bridge). A physicist would select a classical calculus at the beginning of a experiment to have an approximation before the real calculus process began (see again the four major domains of modern physics diagram).

In a computer model there is no need to use the speed of the object if classical physics is excluded. Low energy objects would be handled by quantum theory and high energy objects by relativity theory.[4][5][6] .

## References

1. ^ Morin, David (2008). Introduction to Classical Mechanics. New York: Cambridge University Press. ISBN 9780521876223.
2. ^ Barut, Asim O. (1980) [1964]. Introduction to Classical Mechanics. New York: Dover Publications. ISBN 9780486640389.
3. ^ Einstein, Albert (2004) [1920]. Relativity. Translated by Robert W. Lawson. New York: Barnes & Noble. ISBN 9780760759219.
4. ^ [Wojciech H. Zurek, Decoherence, einselection, and the quantum origins of the classical, Reviews of Modern Physics 2003, 75, 715 or http://arxiv.org/abs/quant-ph/0105127/>
5. ^ Wojciech H. Zurek, Decoherence and the transition from quantum to classical, Physics Today, 44, pp 36–44 (1991)
6. ^ Wojciech H. Zurek: Decoherence and the Transition from Quantum to Classical—Revisited Los Alamos Science Number 27 2002