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Symmetry (physics)

In physics, a symmetry of a physical system is a physical or mathematical feature of the system (observed or intrinsic) that is preserved or remains unchanged under some transformation. In physics, a symmetry of a physical system is a physical or mathematical feature of the system (observed or intrinsic) that is preserved or remains unchanged under some transformation. A family of particular transformations may be continuous (such as rotation of a circle) or discrete (e.g., reflection of a bilaterally symmetric figure, or rotation of a regular polygon). Continuous and discrete transformations give rise to corresponding types of symmetries. Continuous symmetries can be described by Lie groups while discrete symmetries are described by finite groups (see Symmetry group). These two concepts, Lie and finite groups, are the foundation for the fundamental theories of modern physics. Symmetries are frequently amenable to mathematical formulations such as group representations and can, in addition, be exploited to simplify many problems. Arguably the most important example of a symmetry in physics is that the speed of light has the same value in all frames of reference, which is known in mathematical terms as the Poincaré group, the symmetry group of special relativity. Another important example is the invariance of the form of physical laws under arbitrary differentiable coordinate transformations, which is an important idea in general relativity. Invariance is specified mathematically by transformations that leave some property (e.g. quantity) unchanged. This idea can apply to basic real-world observations. For example, temperature may be homogeneous throughout a room. Since the temperature does not depend on the position of an observer within the room, we say that the temperature is invariant under a shift in an observer's position within the room. Similarly, a uniform sphere rotated about its center will appear exactly as it did before the rotation. The sphere is said to exhibit spherical symmetry. A rotation about any axis of the sphere will preserve how the sphere 'looks'. The above ideas lead to the useful idea of invariance when discussing observed physical symmetry; this can be applied to symmetries in forces as well. For example, an electric field due to an electrically charged wire of infinite length is said to exhibit cylindrical symmetry, because the electric field strength at a given distance r from the wire will have the same magnitude at each point on the surface of a cylinder (whose axis is the wire) with radius r. Rotating the wire about its own axis does not change its position or charge density, hence it will preserve the field. The field strength at a rotated position is the same. This is not true in general for an arbitrary system of charges. In Newton's theory of mechanics, given two bodies, each with mass m, starting at the origin and moving along the x-axis in opposite directions, one with speed v1 and the other with speed v2 the total kinetic energy of the system (as calculated from an observer at the origin) is ​1⁄2m(v12 + v22) and remains the same if the velocities are interchanged. The total kinetic energy is preserved under a reflection in the y-axis.

[ "Spontaneous symmetry breaking", "Quantum mechanics", "Symmetry operation", "Monod-Wyman-Changeux model", "Eightfold Way", "Spontaneous symmetry breaking", "Chirality (mathematics)" ]
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