Physics from Symmetry

Schwichtenberg, Jakob

doi:10.1007/978-3-319-66631-0

Cited by 28 publications

(35 citation statements)

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“…The textbooks will not be split into individual visual cues that have to be integrated when a hypothetical binding problem is solved for each symmetrical object and when multiple objects are organized into a scene. Such a perception textbook will be a coherent presentation that can be titled “perception from symmetry,” the same way a modern physics textbook is titled “physics from symmetry” (Schwichtenberg, 2018 ). Our proposal should not be surprising if we remember that perception is a cognitive capacity to acquire information about the physical world, rather than an analysis of sensory cues isolated from the physical environment.…”

Section: Summary and Directions For Future Researchmentioning

confidence: 99%

The Concept of Symmetry and the Theory of Perception

Pizlo

Barros

2021

Front. Comput. Neurosci.

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Perceptual constancy refers to the fact that the perceived geometrical and physical characteristics of objects remain constant despite transformations of the objects such as rigid motion. Perceptual constancy is essential in everything we do, like recognition of familiar objects and scenes, planning and executing visual navigation, visuomotor coordination, and many more. Perceptual constancy would not exist without the geometrical and physical permanence of objects: their shape, size, and weight. Formally, perceptual constancy and permanence of objects are invariants, also known in mathematics and physics as symmetries. Symmetries of the Laws of Physics received a central status due to mathematical theorems of Emmy Noether formulated and proved over 100 years ago. These theorems connected symmetries of the physical laws to conservation laws through the least-action principle. We show how Noether's theorem is applied to mirror-symmetrical objects and establishes mental shape representation (perceptual conservation) through the application of a simplicity (least-action) principle. This way, the formalism of Noether's theorem provides a computational explanation of the relation between the physical world and its mental representation.

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Section: Summary and Directions For Future Researchmentioning

confidence: 99%

The Concept of Symmetry and the Theory of Perception

Pizlo

Barros

2021

Front. Comput. Neurosci.

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“…The link between unitary groups and division algebras n has been diffusely studied [31][32][33] . Unitary groups are the fundamental bricks to build the particle Standard Model, because each fundamental force can be described by a unitary or special unitary group 1,[34][35][36][37] , being G = SU(3) × SU(2) × U(1) the SM group of strong SU(3), weak SU(2) and hypercharge U(1) interactions 1 . Besides its symmetry, the SM includes three fermions families: between these three generations, particles differ by their flavour quantum number and mass, but their interactions are identical.…”

Section: Fundamental Forces From Division Algebras Automorphismsmentioning

confidence: 99%

An exceptional G(2) extension of the Standard Model from the correspondence with Cayley–Dickson algebras automorphism groups

Masi

2021

Sci Rep

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In this article I propose a new criterion to extend the Standard Model of particle physics from a straightforward algebraic conjecture: the symmetries of physical microscopic forces originate from the automorphism groups of main Cayley–Dickson algebras, from complex numbers to octonions and sedenions. This correspondence leads to a natural enlargement of the Standard Model color sector, from a SU(3) gauge group to an exceptional Higgs-broken G(2) group, following the octonionic automorphism relation guideline. In this picture, an additional ensemble of massive G(2)-gluons emerges, which is separated from the particle dynamics of the Standard Model.

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“…In special relativity, the observers (coordinate systems) move at constant relative velocity with respect to each other, and the symmetries are global [6]. The spacetime is viewed as a four-dimensional real vector space, equipped with a diagonal metric of signature (1, 3, 0), called the Minkowski metric [17]. The Poincaré group is the full symmetry group of special relativity [17].…”

Section: Local Symmetries In Physicsmentioning

confidence: 99%

“…The spacetime is viewed as a four-dimensional real vector space, equipped with a diagonal metric of signature (1, 3, 0), called the Minkowski metric [17]. The Poincaré group is the full symmetry group of special relativity [17].…”

Section: Local Symmetries In Physicsmentioning

confidence: 99%

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Global Symmetries, Local Symmetries and Groupoids

Petitjean

2021

Symmetry

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Local symmetries are primarily defined in the case of spacetime, but several authors have defined them outside this context, sometimes with the help of groupoids. We show that, in many cases, local symmetries can be defined as global symmetries. We also show that groups can be used, rather than groupoids, to handle local symmetries. Examples are given for graphs and networks, color symmetry and tilings. The definition of local symmetry in physics is also discussed.

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Physics from Symmetry

Cited by 28 publications

References 0 publications

The Concept of Symmetry and the Theory of Perception

The Concept of Symmetry and the Theory of Perception

An exceptional G(2) extension of the Standard Model from the correspondence with Cayley–Dickson algebras automorphism groups

Global Symmetries, Local Symmetries and Groupoids

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