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Jump to navigationJump to searchNew page: Image:lighterstill.jpg In the most general sense, '''symmetry''' can be defined as a property that an entity has whereby it preserves some of its aspects under certain actual or possi...
[[Image:lighterstill.jpg]]
In the most general sense, '''symmetry''' can be defined as a property that an entity has whereby it preserves some of its aspects under certain actual or possible transformations. A sphere is symmetrical because a rotation about its axis preserves its shape. A crystal [[structure]] is symmetrical with respect to certain translations in [[space]]. The existence of symmetries in natural [[phenomena]] and in human artifacts is pervasive. However, nature also displays important violations of symmetry: Some organic molecules come only or predominantly in left-handed varieties; the bilateral symmetry of most organisms is at best only approximate.
==General==
The general [[concept]] of symmetry applies not only to objects and their collections, but also to properties of objects, to processes they may undergo, as well as to more abstract entities such as mathematical structures, scientific [[law]]s, and [[symbol]]ic and conceptual systems, including [[myth]]ology and [[religion]]. Symmetry symbols pervade ancient [[cosmology|cosmologies]]. Thus the concept of ''axis mundi'' (the world axis) is a famous mytho-poetic [[archetype]] expressing the [[idea]] of centrality in the arrangement of the [[Cosmos]]. Whether axis mundi is represented as a sacred mountain, tree, or ladder, it invariably signifies a possibility for [[human]]s to connect with [[heaven]]. The central image of [[Christianity]], the cross, belongs in the same broad category, as far as its symbolic connotations are concerned. The concept of triadicity so essential to many religions is closely linked to symmetry considerations.
==Abstract==
The abstract notion of symmetry also lies at the very foundation of [[Natural Sciences|natural science]]. The fundamental significance of symmetries for [[physics]] came to the fore early in the twentieth century. Prior developments in mathematics contributed to this. Thus, in his Erlangen Program (1872), the German mathematician [[Felix Klein]] (1849–1925) proposed interpreting [[geometry]] as the study of spatial properties that are invariant under certain groups of transformations (translations, rigid rotations, reflections, scaling, etc.). Emmy Noether (1882–1935) applied Klein's approach to theoretical physics to establish in 1915 a famous theorem relating physical conservation laws (of energy, momentum, and angular momentum) to symmetries of [[space]] and [[time]] (homogeneity and isotropy). By that time, [[Albert Einstein]]'s (1879–1955) [[Theory of Relativity]] had engendered the notion of relativistic invariance, the kind of symmetry all genuine physical laws were expected to possess with respect to a group of coordinate transformations known as the ''Lorentz-Poincaré group''. With this came the realization that symmetry (invariance) is a clue to [[reality]]: Only those physical properties that "survive" unchanged under appropriate transformations are real; those that do not are merely perspectival manifestations of the underlying reality.
==Particle Physics==
With the development of particle physics the [[concept]] of symmetry was extended to internal degrees of freedom (quantum numbers), such as C (charge conjugation, the replacement of a particle by its antiparticle) and isospin (initially the quantum number distinguishing the proton from the neutron). Along with P (parity, roughly a mirror [[reflection]] of particle processes) and T (time-reversal operation), these were long believed to be exact symmetries, until the discovery in 1956 of C- and P-symmetry violations in certain weak interactions, and the [[discovery]] in 1964 of the violation of the combined CP-symmetry. However, theoretical considerations preclude violation of the more complex CPT-symmetry.
The emergence of quantum electrodynamics (QED), the first successful quantum relativistic theory describing the interaction of electrically charged spin-1/2 particles with the electromagnetic field, made the notion of [[gauge symmetry]] central to particle physics. The exact form of interaction turns out to be a consequence of imposing a local gauge invariance on a free-particle Lagrangian with respect to a particular group (U(1) in the case of QED) of transformations of its quantum state. Extending this principle to other interactions led to the unification of electromagnetic and weak forces in the Weinberg-Salam-Glashow theory on the basis of the symmetry group SU(2) × U(1) and to quantum chromodynamics (a theory of strong [[quark]] interactions based on the group SU(3)), and eventually paved the way for the ongoing search for a theory unifying all physical forces.
==Reference==
Source Citation: BALASHOV, YURI V. "Symmetry." Encyclopedia of Science and Religion. Ed. J. Wentzel Vrede van Huyssteen. Vol. 2. New York: Macmillan Reference USA, 2003. 852-853. 2 vols. Gale Virtual Reference Library. Gale. University of the South. 1 Mar. 2009
[http://find.galegroup.com/gvrl/infomark.do?&contentSet=EBKS&type=retrieve&tabID=T001&prodId=GVRL&docId=CX3404200495&source=gale&userGroupName=tel_a_uots&version=1.0]
In the most general sense, '''symmetry''' can be defined as a property that an entity has whereby it preserves some of its aspects under certain actual or possible transformations. A sphere is symmetrical because a rotation about its axis preserves its shape. A crystal [[structure]] is symmetrical with respect to certain translations in [[space]]. The existence of symmetries in natural [[phenomena]] and in human artifacts is pervasive. However, nature also displays important violations of symmetry: Some organic molecules come only or predominantly in left-handed varieties; the bilateral symmetry of most organisms is at best only approximate.
==General==
The general [[concept]] of symmetry applies not only to objects and their collections, but also to properties of objects, to processes they may undergo, as well as to more abstract entities such as mathematical structures, scientific [[law]]s, and [[symbol]]ic and conceptual systems, including [[myth]]ology and [[religion]]. Symmetry symbols pervade ancient [[cosmology|cosmologies]]. Thus the concept of ''axis mundi'' (the world axis) is a famous mytho-poetic [[archetype]] expressing the [[idea]] of centrality in the arrangement of the [[Cosmos]]. Whether axis mundi is represented as a sacred mountain, tree, or ladder, it invariably signifies a possibility for [[human]]s to connect with [[heaven]]. The central image of [[Christianity]], the cross, belongs in the same broad category, as far as its symbolic connotations are concerned. The concept of triadicity so essential to many religions is closely linked to symmetry considerations.
==Abstract==
The abstract notion of symmetry also lies at the very foundation of [[Natural Sciences|natural science]]. The fundamental significance of symmetries for [[physics]] came to the fore early in the twentieth century. Prior developments in mathematics contributed to this. Thus, in his Erlangen Program (1872), the German mathematician [[Felix Klein]] (1849–1925) proposed interpreting [[geometry]] as the study of spatial properties that are invariant under certain groups of transformations (translations, rigid rotations, reflections, scaling, etc.). Emmy Noether (1882–1935) applied Klein's approach to theoretical physics to establish in 1915 a famous theorem relating physical conservation laws (of energy, momentum, and angular momentum) to symmetries of [[space]] and [[time]] (homogeneity and isotropy). By that time, [[Albert Einstein]]'s (1879–1955) [[Theory of Relativity]] had engendered the notion of relativistic invariance, the kind of symmetry all genuine physical laws were expected to possess with respect to a group of coordinate transformations known as the ''Lorentz-Poincaré group''. With this came the realization that symmetry (invariance) is a clue to [[reality]]: Only those physical properties that "survive" unchanged under appropriate transformations are real; those that do not are merely perspectival manifestations of the underlying reality.
==Particle Physics==
With the development of particle physics the [[concept]] of symmetry was extended to internal degrees of freedom (quantum numbers), such as C (charge conjugation, the replacement of a particle by its antiparticle) and isospin (initially the quantum number distinguishing the proton from the neutron). Along with P (parity, roughly a mirror [[reflection]] of particle processes) and T (time-reversal operation), these were long believed to be exact symmetries, until the discovery in 1956 of C- and P-symmetry violations in certain weak interactions, and the [[discovery]] in 1964 of the violation of the combined CP-symmetry. However, theoretical considerations preclude violation of the more complex CPT-symmetry.
The emergence of quantum electrodynamics (QED), the first successful quantum relativistic theory describing the interaction of electrically charged spin-1/2 particles with the electromagnetic field, made the notion of [[gauge symmetry]] central to particle physics. The exact form of interaction turns out to be a consequence of imposing a local gauge invariance on a free-particle Lagrangian with respect to a particular group (U(1) in the case of QED) of transformations of its quantum state. Extending this principle to other interactions led to the unification of electromagnetic and weak forces in the Weinberg-Salam-Glashow theory on the basis of the symmetry group SU(2) × U(1) and to quantum chromodynamics (a theory of strong [[quark]] interactions based on the group SU(3)), and eventually paved the way for the ongoing search for a theory unifying all physical forces.
==Reference==
Source Citation: BALASHOV, YURI V. "Symmetry." Encyclopedia of Science and Religion. Ed. J. Wentzel Vrede van Huyssteen. Vol. 2. New York: Macmillan Reference USA, 2003. 852-853. 2 vols. Gale Virtual Reference Library. Gale. University of the South. 1 Mar. 2009
[http://find.galegroup.com/gvrl/infomark.do?&contentSet=EBKS&type=retrieve&tabID=T001&prodId=GVRL&docId=CX3404200495&source=gale&userGroupName=tel_a_uots&version=1.0]
