#Symmetry #invariant #conservation Noether's theory, also known as [[Noether's theorem]], is a fundamental principle in physics that connects the concepts of symmetries and conservation laws. It was developed by the German mathematician [[Emmy Noether]] in 1915. Noether's theory states that for every continuous symmetry in a physical system, there is a corresponding conserved quantity. In simpler terms, if a physical system remains unchanged under certain transformations (symmetries), then there exists a quantity that remains constant throughout its evolution ([[Conservation Law|conservation law]]). Symmetries can take various forms such as spatial translation symmetry (system looks the same regardless of where it is located), rotational symmetry (system looks the same regardless of its orientation), time translation symmetry (system behaves the same at different times), and many others. Noether's theorem mathematically establishes this connection between symmetries and conservation laws. It demonstrates that for each symmetry of a physical system, there exists a corresponding conserved quantity known as a conserved charge or Noether charge. These charges can represent quantities like energy, momentum, angular momentum, and electric charge. For example, consider the conservation of linear momentum in classical mechanics. The fact that physical laws are invariant under spatial translation symmetry implies the conservation of linear momentum. Similarly, rotational symmetry leads to the conservation of angular momentum. Noether's theory has had significant implications across various branches of physics. It played a crucial role in the development of quantum field theory and helped unify different areas such as classical mechanics, electrodynamics, and general relativity. It has also found applications in particle physics where it relates symmetries with fundamental particles and their interactions. In summary, Noether's theory establishes a deep connection between symmetries and conservation laws. It provides a powerful tool for understanding fundamental principles governing physical systems and has greatly influenced our understanding of nature at both macroscopic and microscopic scales. # References ```dataview Table title as Title, authors as Authors where contains(subject, "Noether's theorem") or contains(subject, "Noether's theory") or contains(subject, "symmetry") sort title, authors, modified ```