Group: philosophy of mathematics
Topic: cosmology
Topic: equal simplicity
Topic: geometry
Topic: law of nature
Topic: physics
 
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]
 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, matterantimatter [»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]
 Subtopic: symmetry and conservation law
Quote: Noether's theorema 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
 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 antisymmetric [»kentW_1978]

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)
