# conservation laws

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## conservation laws

**conservation laws,**in physics, basic laws that together determine which processes can or cannot occur in nature; each law maintains that the total value of the quantity governed by that law, e.g., mass or energy, remains unchanged during physical processes. Conservation laws have the broadest possible application of all laws in physics and are thus considered by many scientists to be the most fundamental laws in nature.

### Conservation of Classical Processes

### Conservation of Elementary Particle Properties

^{31}years. Two partial conservation laws, governing the quantities known as strangeness and isotopic spin, have been discovered for elementary particles. Strangeness is conserved during the so-called strong interactions and the electromagnetic interactions, but not during the weak interactions associated with particle decay; isotopic spin is conserved only during the strong interactions.

### Conservation of Natural Symmetries

One very important discovery has been the link between conservation laws and basic symmetries in nature. For example, empty space possesses the symmetries that it is the same at every location (homogeneity) and in every direction (isotropy); these symmetries in turn lead to the invariance principles that the laws of physics should be the same regardless of changes of position or of orientation in space. The first invariance principle implies the law of conservation of linear momentum, while the second implies conservation of angular momentum. The symmetry known as the homogeneity of time leads to the invariance principle that the laws of physics remain the same at all times, which in turn implies the law of conservation of energy. The symmetries and invariance principles underlying the other conservation laws are more complex, and some are not yet understood.

Three special conservation laws have been defined with respect to symmetries and invariance principles associated with inversion or reversal of space, time, and charge. Space inversion yields a mirror-image world where the “handedness” of particles and processes is reversed; the conserved quantity corresponding to this symmetry is called space parity, or simply parity, *P.* Similarly, the symmetries leading to invariance with respect to time reversal and charge conjugation (changing particles into their antiparticles) result in conservation of time parity, *T,* and charge parity, *C.* Although these three conservation laws do not hold individually for all possible processes, the combination of all three is thought to be an absolute conservation law, known as the *CPT* theorem, according to which if a given process occurs, then a corresponding process must also be possible in which particles are replaced by their antiparticles, the handedness of each particle is reversed, and the process proceeds in the opposite direction in time. Thus, conservation laws provide one of the keys to our understanding of the universe and its material basis.

### Bibliography

See R. P. Feynman, *The Character of Physical Law* (1967); M. Gardner, *The Ambidextrous Universe: Left, Right, and the Fall of Parity* (rev. ed. 1969); S. Glashow, *The Charm of Physics* (1991).

## Conservation laws (physics)

Principles which state that the total values of specified quantities remain constant in time for an isolated system. Conservation laws occupy enormously important positions both at the foundations of physics and in its applications.

#### Realization in classical mechanics

There are three great conservation laws of mechanics: the conservation of linear momentum, often referred to simply as the conservation of momentum; the conservation of angular momentum; and the conservation of energy.

The linear momentum, or simply momentum, of a particle is equal to the product of its mass and velocity. It is a vector quantity. The total momentum of a system of particles is simply the sum of the momenta of each particle considered separately. The law of conservation of momentum states that this total momentum does not change in time. *See* Conservation of momentum, Momentum

The angular momentum of a particle is more complicated. It is defined by the vector product of the position and momentum vectors. The law of conservation of angular momentum states that the total angular momentum of an isolated system is constant in time. *See* Angular momentum

The conservation of energy is perhaps the most important law of all. Energy is a scalar quantity, and takes two forms: kinetic and potential. The kinetic energy of a particle is defined to be one-half the product of its mass and the square of its velocity. The potential energy is loosely defined as the ability to do work. The total energy is the sum of the kinetic and potential energies, and according to the conservation law it remains constant in time for an isolated system.

The essential difficulty in applying the conservation of energy law can be appreciated by considering the problem of two colliding bodies. In general, the bodies emerge from the collision moving more slowly than when they entered. This phenomenon seems to violate the conservation of energy, until it is recognized that the bodies involved may consist of smaller particles. Their random small-scale motions will require kinetic energy, which robs kinetic energy from the overall coherent large-scale motion of the bodies that are observed directly. One of the greatest achievements of nineteenth-century physics was the recognition that small-scale motion within macroscopic bodies could be identified with the perceived property of heat. *See* Conservation of energy, Energy, Kinetic theory of matter

#### Position in modern physics

As physics has evolved, the great conservation laws have likewise evolved in both form and content, but have never ceased to be important guiding principles.

In order to account for the phenomena of electromagnetism, it was necessary to go beyond the notion of point particles, to postulate the existence of continuous electric and magnetic fields filling all space. To obtain valid conservation laws, energy, momentum, and angular momentum must be ascribed to the electromagnetic fields. *See* Electromagnetic radiation, Maxwell's equations, Poynting's vector

In the special theory of relativity, energy and momentum are not independent concepts. Einstein discovered perhaps the most important consequence of special relativity, that is, the equivalence of mass and energy, as a consequence of the conservation laws. The “law” of conservation of mass is understood as an approximate consequence of the conservation of energy. *See* Conservation of mass, Relativity

A remarkable, beautiful, and very fruitful connection has been established between symmetries and conservation laws. Thus the law of conservation of linear momentum is understood as a consequence of the homogeneity of space, the conservation of angular momentum as a consequence of the isotropy of space, and the conservation of energy as a consequence of the homogeneity of time. *See* Symmetry laws (physics)

The development of general relativity, the modern theory of gravitation, necessitates attention to a fundamental question for the conservation laws: The laws refer to an “isolated system,” but it is not clear that any system is truly isolated. This is a particularly acute problem for gravitational forces, which are long range and add up over cosmological distances. It turns out that the symmetry of physical laws is actually a more fundamental property than the conservation laws themselves, for the symmetries remain valid while the conservation laws, strictly speaking, fail.

In quantum theory, the great conservation laws remain valid in a very strong sense. Generally, the formalism of quantum mechanics does not allow prediction of the outcome of individual experiments, but only the relative probability of different possible outcomes. One might therefore entertain the possibility that the conservation laws were valid only on the average. However, momentum, angular momentum, and energy are conserved in every experiment. *See* Quantum mechanics, Quantum theory of measurement

#### Conservation laws of particle type

There is another important class of conservation laws, associated not with the motion of particles but with their type. Perhaps the most practically important of these laws is the conservation of chemical elements. From a modern viewpoint, this principle results from the fact that the small amount of energy involved in chemical transformations is inadequate to disrupt the nuclei deep within atoms. It is not an absolute law, because some nuclei decay spontaneously, and at sufficiently high energies it is grossly violated. *See* Radioactivity

Several conservation laws in particle physics are of the same character: They are useful even though they are not exact because, while known processes violate them, such processes are either unusually slow or require extremely high energy. *See* Elementary particle