Bevarelseslover

Bevarelseslover is a term used in Scandinavian languages (most commonly Danish and Norwegian) to refer to conservation laws. These are statements in physics and mathematics asserting that certain quantities remain unchanged during the evolution of a system, given appropriate conditions. The plural form bevaringslover or befarelseslover is used for different conserved quantities, depending on the context.

Conservation laws can be global or local. A global law states that a total quantity is constant for an isolated system, while a local law expresses this constancy through a continuity equation, which relates the rate of change of density to the divergence of a flux. Local conservation laws are often written in forms that reveal how the quantity flows within space and time, and they are foundational in formulating physical theories.

Common examples include conservation of energy, linear momentum, angular momentum, and electric charge. In fluid dynamics, conservation of mass (or baryon number in certain contexts) is described by the continuity equation. In electromagnetism, charge conservation arises from Maxwell’s equations. In quantum mechanics, the evolution is unitary, which ensures probability conservation. In relativity, energy-momentum conservation follows from spacetime symmetries, as captured by Noether’s theorem, which links continuous symmetries to corresponding conservation laws.

Conservation laws serve as essential constraints in modeling physical systems, enabling predictions and checks on solutions and simulations. They may be exact in closed systems or approximately valid in open systems where exchanges with the environment are limited. See also Noether’s theorem, continuity equations, and invariants.