Laws of Conservation

Common conservation laws

• Energy — total energy (including kinetic, potential, thermal, mass–energy) is conserved in closed systems; conservation is central to mechanics, thermodynamics, and relativity.
• Linear momentum — momentum of a closed system is unchanged in the absence of external forces, governing collisions and motion.
• Angular momentum — rotational analog of linear momentum; conserved when no external torque acts.
• Electric charge — net electric charge is conserved in all observed processes.
• Quantum numbers — quantities such as baryon number, lepton number, parity, and others are conserved in many reactions though some are only approximately conserved or violated under specific interactions.

Theoretical basis and history

Historically, conservation principles emerged from empirical observations (for example, conservation of mass in chemistry). In the 20th century, Emmy Noether provided a unifying theorem: continuous symmetries of a physical system imply conserved quantities. For instance, time-translation symmetry implies energy conservation; spatial translation implies linear momentum conservation.

Forms, locality, and applications

Conservation laws are often expressed locally as continuity equations relating a density and a flux, meaning conservation holds at every point in space when no sources or sinks are present. They underpin engineering calculations, astronomical dynamics, chemical reactions, and particle interactions. In modern physics they guide the construction of theories and the interpretation of experimental results.

Notable distinctions include exact versus approximate conservation (some quantum processes may violate a classical conservation law under special conditions) and global versus local formulations. Conservation laws remain central organizing principles across the physical sciences.