In physics, a conservation law states that a particular measurable property of an isolated physical system does not change as the system evolves. Any particular conservation law is a mathematical identity to certain symmetry of a physical system. The first few hydrogen atom electron orbitals shown as cross-sections with color-coded probability density. ...

Conservation Laws

A partial listing of conservation laws that are said to be exact laws, or more precisely have never been shown to be inexact:

• Conservation of energy
• Conservation of linear momentum
• Conservation of angular momentum
• Conservation of electric charge
• Conservation of color charge
• Conservation of probability

There are also approximate conservation laws. These are approximately true in particular situations, such as low speeds, short time scales, or certain interactions. Conservation of energy states that the total amount of energy (including potential energy) in a closed system remains constant. ... In classical mechanics, momentum (pl. ... Gyroscope. ... Electric charge is a fundamental conserved property of some subatomic particles, which determines their electromagnetic interactions. ... In quantum chromodynamics (QCD), color or color charge refers to a certain property of the subatomic particles called quarks. ... All the examples of continuity equations below express the same idea; they are all really examples of the same concept. ...

• Conservation of mass (applies for low speeds)
• Conservation of baryon number (See chiral anomaly)
• Conservation of lepton_number (In the Standard Model)
• Conservation of flavor (violated by the weak interaction)
• Conservation of parity
• CP symmetry

The law of conservation of mass/matter (The Lomonosov-Lavoisier law) states that the mass of a system of substances will remain constant, regardless of the processes acting inside the system. ... In particle physics, the baryon number is an approximate conserved quantum number. ... A chiral anomaly is the anomalous nonconservation of a chiral current. ... In high energy physics, the lepton number is the number of leptons minus the number of antileptons. ... The Standard Model of Fundamental Particles and Interactions The Standard Model of particle physics is a theory which describes the strong, weak, and electromagnetic fundamental forces, as well as the fundamental particles that make up all matter. ... In particle physics, flavor is a property of a fermion that identifies it, a label that specifies the name of the particle. ... The weak nuclear force or weak interaction is one of the four fundamental forces of nature. ... In physics, a parity transformation (also called parity inversion) is the simultaneous flip in the sign of all spatial coordinates: A 3×3 matrix representation of P would have determinant equal to –1, and hence cannot reduce to a rotation. ... CP is the product of two symmetries: C for charge conjugation, which transforms a particle into its antiparticle, and P for parity, which creates the mirror image of a physical system. ...

Global and local conservation laws

A conserved property of a physical system may be conserved either locally, or just globally. To be conserved locally, the property must flow from one place to another, and not just disappear one place and reappear another. On the other hand, if the conserved quantity is allowed to appear somewhere else, but with the total amount of the conserved quantity remaining the same, then we have a global conservation law.

A local symmetry has mediator particles and fields, like the electromagnetic field (photon) for the electric charge, which stems from a local U(1)-symmetry, the gauge freedom of the electrodynamics. There is a corresponding force, the Coulomb-force. In quantum physics, the photon (from Greek φως, phōs, meaning light) is the quantum of the electromagnetic field (light). ... In theoretical physics, gauge freedom is the ambiguity that makes the configurations related by gauge invariance indistinguishable. ... Electromagnetism is the physics of the electromagnetic field: a field, encompassing all of space, composed of the electric field and the magnetic field. ...

The angular momentum stems from a global rotation symmetry, and there is no interaction between two rotating bodies, which have their own angular momentum. Gyroscope. ...

Philosophy of conservation laws

Noether's theorem expresses the equivalence which exists between conservation laws and the invariance of physical laws with respect to certain transformations (typically called "symmetries") for systems which obey the Principle of least action and hence having a Lagrangian and a Hamiltonian (See Classical mechanics, Hamiltonian mechanics for details). For instance, time invariance implies that energy is conserved, translation invariance implies that momentum is conserved, and rotation invariance implies that angular momentum is conserved. Noethers theorem is a central result in theoretical physics that expresses the one-to-one correspondence between symmetries and conservation laws. ... Invariant may have meanings invariant (computer science), such as a combination of variables not altered in a loop invariant (mathematics), something unaltered by a transformation invariant (music) invariant (physics) conserved by system symmetry This is a disambiguation page — a navigational aid which lists other pages that might otherwise share the... This article or section does not cite its references or sources. ... The principle of least action was first formulated by Pierre-Louis Moreau de Maupertuis, who said that Nature is thrifty in all its actions. See action (physics). ... A Lagrangian of a dynamical system, named after Joseph Louis Lagrange, is a function of the dynamical variables and concisely describes the equations of motion of the system. ... Classical mechanics is a branch of physics which studies the deterministic motion of objects. ... Hamiltonian mechanics is a re-formulation of classical mechanics that was invented in 1833 by William Rowan Hamilton. ...

• Things that remain unchanged, in the midst of change

The idea that some things remain unchanging throughout the evolution of the universe has been motivating philosophers and scientists alike for a long time.

In fact, quantities that are conserved, the invariants, seem to preserve what some would like to call some kind of a 'physical reality' and seem to have a more meaningful existence than many other physical quantities. These laws bring a great deal of simplicity into the structure of a physical theory. They are the ultimate basis for most solutions of the equations of physics. In physics, invariants are usually quantities conserved (unchanged) by the symmetries of the physical system. ... The first few hydrogen atom electron orbitals shown as cross-sections with color-coded probability density. ...

See also

• Continuity equation
• Philosophy of physics
• Noether's theorem

All the examples of continuity equations below express the same idea; they are all really examples of the same concept. ... Philosophy of physics is the study of the fundamental, philosophical questions underlying modern physics, the study of matter and energy and how they interact. ... Noethers theorem is a central result in theoretical physics that expresses the one-to-one correspondence between symmetries and conservation laws. ...

Reference

• Stenger, Victor J., 2000. Timeless Reality: Symmetry, Simplicity, and Multiple Universes. Prometheus Books. Chpt. 12 is a gentle introduction to symmetry, invariance, and conservation laws.

External links

• Conservation Laws - an online textbook