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Concept
Five-dimensional space
Résumé
A five-dimensional space is a space with five dimensions. In mathematics, a sequence of N numbers can represent a location in an N-dimensional space. If interpreted physically, that is one more than the usual three spatial dimensions and the fourth dimension of time used in relativistic physics. Whether or not the universe is five-dimensional is a topic of debate.
Much of the early work on five-dimensional space was in an attempt to develop a theory that unifies the four fundamental interactions in nature: strong and weak nuclear forces, gravity and electromagnetism. German mathematician Theodor Kaluza and Swedish physicist Oskar Klein independently developed the Kaluza–Klein theory in 1921, which used the fifth dimension to unify gravity with electromagnetic force. Although their approaches were later found to be at least partially inaccurate, the concept provided a basis for further research over the past century.
To explain why this dimension would not be directly observable, Klein suggested that the fifth dimension would be rolled up into a tiny, compact loop on the order of 10^-33 centimeters. Under his reasoning, he envisioned light as a disturbance caused by rippling in the higher dimension just beyond human perception, similar to how fish in a pond can only see shadows of ripples across the surface of the water caused by raindrops. While not detectable, it would indirectly imply a connection between seemingly unrelated forces. The KaluzaKlein theory experienced a revival in the 1970s due to the emergence of superstring theory and supergravity: the concept that reality is composed of vibrating strands of energy, a postulate only mathematically viable in ten dimensions or more. Superstring theory then evolved into a more generalized approach known as M-theory. M-theory suggested a potentially observable extra dimension in addition to the ten essential dimensions which would allow for the existence of superstrings. The other 10 dimensions are compacted, or "rolled up", to a size below the subatomic level.
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Cours associés (1)
ME-372: Finite element method
L'étudiant acquiert une initiation théorique à la méthode des éléments finis qui constitue la technique la plus courante pour la résolution de problèmes elliptiques en mécanique. Il apprend à applique
Séances de cours associées (2)
Éléments finis : Triangulaire vs Quadrangulaire
Compare les éléments finis triangulaires et quadrangulaires, en discutant de l'exhaustivité, de la continuité et de la précision.
Éléments finis : bases et précision
Explique les bases et la précision des éléments finis triangulaires et quadrangulaires.
Publications associées (7)
On vertices and facets of combinatorial 2-level polytopes
Yuri Faenza, Manuel Francesco Aprile, Alfonso Bolívar Cevallos Manzano
2-level polytopes naturally appear in several areas of mathematics, including combinatorial optimization, polyhedral combinatorics, communication complexity, and statistics. We investigate upper bounds on the product of the number of facets and the number ...
Springer2016Harmonic Holographic Microscopy Using Nanoparticles as Probes for Three-Dimensional Cell Imaging
Demetri Psaltis, Ye Pu, Rachel Grange, Chia-Lung Hsieh
We demonstrate the three-dimensional imaging capability of harmonic holographic microscopy by using the second harmonic generation from BaTiO3 nanoparticles as the signal. Three-dimensional distributions of the BaTiO3 nanoparticles in biological cells are ...
Ieee Service Center, 445 Hoes Lane, Po Box 1331, Piscataway, Nj 08855-1331 Usa2009Cascading gravity: Extending the Dvali-Gabadadze-Porrati model to higher dimension
We present a generalization of the Dvali-Gabadadze-Porrati scenario to higher codimensions which, unlike previous attempts, is free of ghost instabilities. The 4D propagator is made regular by embedding our visible 3-brane within a 4-brane, each with their ...
2008Concepts associés (6)
5-polytope
In geometry, a five-dimensional polytope (or 5-polytope) is a polytope in five-dimensional space, bounded by (4-polytope) facets, pairs of which share a polyhedral cell. A 5-polytope is a closed five-dimensional figure with vertices, edges, faces, and cells, and 4-faces. A vertex is a point where five or more edges meet. An edge is a line segment where four or more faces meet, and a face is a polygon where three or more cells meet. A cell is a polyhedron, and a 4-face is a 4-polytope.
Omnitruncated 5-simplex honeycomb
In five-dimensional Euclidean geometry, the omnitruncated 5-simplex honeycomb or omnitruncated hexateric honeycomb is a space-filling tessellation (or honeycomb). It is composed entirely of omnitruncated 5-simplex facets. The facets of all omnitruncated simplectic honeycombs are called permutahedra and can be positioned in n+1 space with integral coordinates, permutations of the whole numbers (0,1,..,n).
5-cube
thumb|Graphe d'un 5-cube. En cinq dimensions géométriques, un 5-cube est un nom pour un hypercube de cinq dimensions avec 32 sommets, 80 arêtes, 80 faces carrées, 40 cellules cubiques et 10 4-faces tesseracts. Il est représenté par le symbole de Schläfli {4,3,3,3}, réalisé sous la forme 3 tesseracts {4,3,3} autour de chaque arête cubique {4,3}. Il peut être appelé un penteract, ou encore un , étant un construit à partir de 10 facettes régulières. Il fait partie d'une famille infinie d'hypercubes.