Group:
philosophy of mathematics
Topic:
cosmology
Topic:
equal simplicity
Topic:
geometry
Topic:
law of nature
Topic:
physics
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Summary
Symmetry is an invariance under some transformation. For example, a circle has circular symmetry because it is invariant under rotation about its center. Group theory is the formalization of symmetry.
Modern geometry is based on transformation and symmetry. For example, a line is that which is preserved when flipping a plane.
In physics, a symmetry implies a conservation law. For example, quantum mechanical laws are invariant under spatial translation. This invariance is equavalent to the conservation of momentum. (cbb 4/06)
Subtopic: symmetry 
| Quote: something is symmetrical if it is invariant under some transformation; e.g., Newtonian laws are symmetrical under translation [»feynRP_1963]
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Subtopic: symmetry in physics
| Quote: the laws of physics contain many symmetries: translation in space and time, rotation, uniform velocity, reversal in space and time, interchange of identical atoms, phase, matter-antimatter [»feynRP_1963]
| | Quote: a physical system is symmetric with respect to an operation if the operation commutes with the passage of time [»feynRP_1965]
| | Quote: at the big bang, the universe revealed all the symmetries; then it 'crystallized' and lost symmetries [»ferrT9_1982]
| | Quote: partial symmetries such as neutrons/protons may arise out of complexity [»feynR_1965]
| | Quote: if the universe expanded more rapidly than the effect of physical processes; it could produce macroscopic information [»layzD12_1975]
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Subtopic: symmetry and conservation law
| Quote: Noether's theorem--a symmetry in nature implies a conservation law and vice versa [»creaRP_1986]
| | Quote: each of the symmetries in physical law corresponds to a conservation law: e.g., symmetry under translation is space means that momentum is conserved; e.g., conservation of energy, angular momentum, and electrical charge [»feynRP_1963]
| | Quote: symmetries are the basis of all conservation laws of quantum mechanics; e.g., conservation of energy, momentum, angular momentum, parity
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Subtopic: non symmetric
| Quote: computer science is messy because it lacks the locality, symmetry, and invariance to scale found in physics [»hillWD_1985]
| Quote: a relationship can be anti-symmetric
[»kentW_1978]
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Related Topics
Group: philosophy of mathematics (11 topics, 330 quotes)
Topic: cosmology (17 items)
Topic: equal simplicity (15 items)
Topic: geometry (33 items)
Topic: law of nature (28 items)
Topic: physics
(51 items)
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