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In physics
Physics

Physics is the natural science which examines basic concepts such as energy, force, and spacetime and all that derives from these, such as mass, charge, matter and its Motion ....
 and mathematics
Mathematics

Mathematics is the study of quantity, structure, space, change, and related topics of pattern and form. Mathematicians seek out patterns whether found in numbers, space, natural science, computers, imaginary abstractions, or elsewhere....
, a sequence
Tuple

In mathematics, a tuple is a sequence of a specific number of values, called the components of the tuple. These components can be any kind of mathematical objects, where each component of a tuple is a value of a specified type....
 of N numbers can be understood to represent a location
Coordinate system

In mathematics and its applications, a coordinate system is a system for assigning an n-tuple of numbers or scalar to each Point in an n-dimensional space....
 in an N-dimensional space
Euclidean space

Around 300 Before Christ, the Ancient Greece mathematician Euclid undertook a study of relationships among distances and angles, first in a plane and then in space....
. When N=5, the space consisting of all locations with a nonzero fifth number is called the fifth dimension.

Abstract five-dimensional space occurs frequently in mathematics, and is a perfectly legitimate construct. Whether or not the real universe
Universe

The universe is defined as everything that physically exists: the entirety of space and time, all forms of matter, energy and momentum, and the physical laws and physical constants that govern them....
 in which we live is somehow five-dimensional is a topic that is debated and explored in several branches of physics, including astrophysics
Astrophysics

Astrophysics is the branch of astronomy that deals with the physics of the universe, including the physical properties of astronomical objects such as galaxy, stars, planets, exoplanets, and the interstellar medium, as well as their interactions....
 and particle physics
Particle physics

Particle physics is a branch of physics that studies the elementary particle constituents of matter and radiation, and the interactions between them....
.

In physics, the fifth dimension is a hypothetical extra dimension beyond the usual three spatial
Space

Space is the boundless, three-dimensional extent in which Physical body and events occur and have relative position and direction. Physical space is often conceived in three linear dimensions, although modern physics usually consider it, with time, to be part of the boundless four-dimensional continuum known as spacetime....
 dimensions and one time
Time

Time is a component of the measurement used to sequence events, to compare the durations of events and the intervals between them, and to quantify the motions of objects....
 dimension of Relativity.






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In physics
Physics

Physics is the natural science which examines basic concepts such as energy, force, and spacetime and all that derives from these, such as mass, charge, matter and its Motion ....
 and mathematics
Mathematics

Mathematics is the study of quantity, structure, space, change, and related topics of pattern and form. Mathematicians seek out patterns whether found in numbers, space, natural science, computers, imaginary abstractions, or elsewhere....
, a sequence
Tuple

In mathematics, a tuple is a sequence of a specific number of values, called the components of the tuple. These components can be any kind of mathematical objects, where each component of a tuple is a value of a specified type....
 of N numbers can be understood to represent a location
Coordinate system

In mathematics and its applications, a coordinate system is a system for assigning an n-tuple of numbers or scalar to each Point in an n-dimensional space....
 in an N-dimensional space
Euclidean space

Around 300 Before Christ, the Ancient Greece mathematician Euclid undertook a study of relationships among distances and angles, first in a plane and then in space....
. When N=5, the space consisting of all locations with a nonzero fifth number is called the fifth dimension.

Abstract five-dimensional space occurs frequently in mathematics, and is a perfectly legitimate construct. Whether or not the real universe
Universe

The universe is defined as everything that physically exists: the entirety of space and time, all forms of matter, energy and momentum, and the physical laws and physical constants that govern them....
 in which we live is somehow five-dimensional is a topic that is debated and explored in several branches of physics, including astrophysics
Astrophysics

Astrophysics is the branch of astronomy that deals with the physics of the universe, including the physical properties of astronomical objects such as galaxy, stars, planets, exoplanets, and the interstellar medium, as well as their interactions....
 and particle physics
Particle physics

Particle physics is a branch of physics that studies the elementary particle constituents of matter and radiation, and the interactions between them....
.

In physics, the fifth dimension is a hypothetical extra dimension beyond the usual three spatial
Space

Space is the boundless, three-dimensional extent in which Physical body and events occur and have relative position and direction. Physical space is often conceived in three linear dimensions, although modern physics usually consider it, with time, to be part of the boundless four-dimensional continuum known as spacetime....
 dimensions and one time
Time

Time is a component of the measurement used to sequence events, to compare the durations of events and the intervals between them, and to quantify the motions of objects....
 dimension of Relativity. The Kaluza-Klein theory used the fifth dimension to unify gravity with the electromagnetic force
Electromagnetic force

In physics, the electromagnetic force is the force that the electromagnetic field exerts on electrically charged particles. It is the electromagnetic force that holds electrons and protons together in atoms, and which hold atoms together to make molecules....
; e.g. Minkowski space
Minkowski space

In physics and mathematics, Minkowski space is the mathematical setting in which Albert Einstein theory of special relativity is most conveniently formulated....
 and Maxwell's equations in vacuum can be embedded in a 5-dimensional Riemann curvature tensor
Riemann curvature tensor

In the mathematical field of differential geometry, the Riemann curvature tensor or Riemann?Christoffel tensor is the most standard way to express curvature of Riemannian manifolds....
 ( eq. 37). Kaluza-Klein theory now is seen as essentially a gauge theory
Gauge theory

In physics, gauge theory is a quantum field theory where the Lagrangian is invariant under certain transformations.The transformations form a Lie group which is referred to as the symmetry group or the gauge group of the theory....
 with gauge group the circle group
Circle group

In mathematics, the circle group, denoted by T , is the multiplicative group of all complex numbers with absolute value 1, i.e., the unit circle in the complex plane....
. M-theory
M-theory

In theoretical physics, M-theory is a new limit of string theory in which 11 dimensions of spacetime may be identified. Because the dimensionality exceeds the dimensionality of five superstring theories in 10 dimensions, it was originally believed that the 11-dimensional theory is more fundamental and unifies all string theories ....
 suggests that space-time has eleven dimensions, seven of which are "rolled up" to below the subatomic level. Physicists have speculated that the graviton
Graviton

In physics, the graviton is a hypothetical elementary particle that mediates the force of gravity in the framework of quantum field theory. If it exists, the graviton must be Mass in special relativity and must have a spin of 2 ....
, a particle thought to carry the force of gravity, may "leak" into the fifth or higher dimensions which would explain how gravity is significantly weaker than the other three fundamental forces.

In 1993 the physicist Gerard 't Hooft put forward the holographic principle
Holographic principle

The holographic principle is a property of quantum gravity theories which resolves the black hole information paradox within string theory. First proposed by Gerard 't Hooft, it was given a precise string-theory interpretation by Leonard Susskind....
, which explains that the information about an extra dimension is visible as a curvature in a spacetime with one fewer dimensions. For example, holograms are three-dimensional pictures placed on a two-dimensional surface, which gives the image a curvature when the observer moves. Similarly, in general relativity, the fourth dimension is manifested in observable three dimensions as the curvature of path of a moving infinitesimal (test) particle. Hooft has speculated that the fifth dimension is really the spacetime fabric.

Since 2006, author Rob Bryanton
Rob Bryanton

Rob Bryanton is a Canadian author, composer, and sound designer. He lives and works in his home town of Regina, Saskatchewan Canada. He is the author and creator of the book and website, Imagining the Tenth Dimension....
 has been advancing the idea that the fifth dimension is also our universe's probability space
Probability space

A probability space, in probability theory, is the conventional mathematical model of randomness. This mathematical object, sometimes called also probability triple, formalizes three interrelated ideas by three mathematical notions....
, meaning that the fifth dimension contains the full amount of possibilities that could happen within the parallel universes of Everett's Many Worlds Interpretation. This idea requires an acceptance that time
Time

Time is a component of the measurement used to sequence events, to compare the durations of events and the intervals between them, and to quantify the motions of objects....
 is just one of the two possible directions in the fourth spatial dimension (as per the concept of time reversal symmetry), which makes this idea the subject of controversy at present.

Five-dimensional geometry


Polytopes


In five or more dimensions, only three regular polytope
Regular polytope

In mathematics, a regular polytope is a polytope whose symmetry is transitive on its flag , thus giving it the highest degree of symmetry. All its elements or j-faces — cells, faces and so on — are also transitive on the symmetries of the polytope, and are regular polytopes of dimension = n....
s exist. In 5 dimensions, they are:

  1. The hexateron
    Hexateron

    In Fifth dimension geometry, a hexateron, or hexa-5-tope, is a 5-simplex, a self-dual Regular polytope 5-polytope with 6 vertex , 15 Edge s, 20 triangle Face , 15 tetrahedral Cell , 6 5-cell hypercells....
     or 5-simplex, of the simplex
    Simplex

    In geometry, a simplex or n-simplex is an n-dimensional analogue of a triangle. Specifically, a simplex is the convex hull of a set of affine transformation Point s in some Euclidean space of dimension n or higher ....
     family, with 6 vertices, 15 edges, 20 faces (each an equilateral triangle
    Equilateral triangle

    In geometry, an equilateral triangle is a triangle in which all three sides are equal. In traditional or Euclidean geometry, equilateral triangles are also Equiangular polygon; that is, all three internal angles are also congruent to each other and are each 60?....
    ), 15 cells (each a regular tetrahedron
    Tetrahedron

    A tetrahedron is a polyhedron composed of four triangle faces, three of which meet at each vertex . A regular tetrahedron is one in which the four triangles are regular, or "equilateral", and is one of the Platonic solids....
    ), and 6 hypercells (each a pentachoron
    Pentachoron

    In geometry, the pentachoron is a fourth dimension object bounded by 5 tetrahedron. It is also known as the 5-cell, pentatope, or hyperpyramid....
    ).
  2. The penteract
    Penteract

    In Fifth dimension geometry, a penteract is a name for a Fifth dimension hypercube with 32 Vertex , 80 Edge s, 80 square Face , 40 cubic Cell , and 10 tesseract hypercells....
     or decateron, of the hypercube
    Hypercube

    In geometry, a hypercube is an n-dimensional analogue of a Square and a cube . It is a Closed set, Compact space, Convex set figure whose 1-skeleton consists of groups of opposite parallel line segments aligned in each of the space's dimensions, at right angles to each other and of the same length....
     family, with 32 vertices, 80 edges, 80 faces (each a square
    Square (geometry)

    In Euclidean geometry, a square is a regular polygon with four equal sides and four equal angles . A square with vertices ABCD would be denoted ....
    ), 40 cells (each a cube
    Cube

    A cube is a three-dimensional space solid object bounded by six square faces, facets or sides, with three meeting at each wikt:vertex. The cube can also be called a Regular polyhedron hexahedron and is one of the five Platonic solids....
    ), and 10 hypercells (each a tesseract
    Tesseract

    In geometry, the tesseract, also called an 8-cell or regular octachoron, is the Fourth dimension analog of the cube. The tesseract is to the cube as the cube is to the square ....
    ).
  3. The pentacross
    Pentacross

    In fifth dimension geometry, a pentacross, also called a triacontakaiditeron, is a five-dimensional polytope with 10 Vertex , 40 Edge s, 80 triangle Face , 80 octahedron Cell , 32 5-cell hypercells....
     or triacontakaiditeron, of the cross polytope family, with 10 vertices, 40 edges, 80 faces (each a triangle
    Triangle

    A triangle is one of the basic shapes of geometry: a polygon with three corners or wikt:vertex and three sides or edges which are line segments....
    ), 80 cells (each a tetrahedron
    Tetrahedron

    A tetrahedron is a polyhedron composed of four triangle faces, three of which meet at each vertex . A regular tetrahedron is one in which the four triangles are regular, or "equilateral", and is one of the Platonic solids....
    ), and 32 hypercells (each a pentachoron
    Pentachoron

    In geometry, the pentachoron is a fourth dimension object bounded by 5 tetrahedron. It is also known as the 5-cell, pentatope, or hyperpyramid....
    ).


The 5-simplex is self-dual
Dual polyhedron

In geometry, polyhedron are associated into pairs called duals, where the wikt:vertex of one correspond to the face s of the other. The dual of the dual is the original polyhedron....
, and the penteract and pentacross
Pentacross

In fifth dimension geometry, a pentacross, also called a triacontakaiditeron, is a five-dimensional polytope with 10 Vertex , 40 Edge s, 80 triangle Face , 80 octahedron Cell , 32 5-cell hypercells....
 are dual to each other.

The following are three projected images of the edges of a penteract
Penteract

In Fifth dimension geometry, a penteract is a name for a Fifth dimension hypercube with 32 Vertex , 80 Edge s, 80 square Face , 40 cubic Cell , and 10 tesseract hypercells....
:
2d of 5d 1
2d of 5d 2


Hypersphere

A hypersphere
Hypersphere

In mathematics, an n-sphere is a generalization of the surface of an ordinary sphere to arbitrary dimension. For any natural number n, an n-sphere of radius r is defined as the set of points in -dimensional Euclidean space which are at distance r from a central point, where the radius r may be any positive real num...
 in 5-space (also called a 4-sphere due to its surface being 4-dimensional) consists of the set of all points in 5-space at a fixed distance r from a central point P. The hypervolume enclosed by this hypersurface is:

The "Fifth dimension" in popular culture

  • In the fictitious universe of DC Comics
    DC Comics

    DC Comics is one of the largest and most popular American comic book and related media companies, along with Marvel Comics. A subsidiary of Warner Bros....
    , the "Fifth dimension" is the place from which Mister Mxyzptlk
    Mister Mxyzptlk

    Mr. Mxyzptlk , sometimes called Mxy, is a fictional supervillain who appears in DC Comics' Superman comic books.He was created by Jerry Siegel and Joe Shuster, and first appeared in Superman #30 ....
     comes.
  • In 1966, The Byrds
    The Byrds

    The Byrds were an American Rock music band. Formed in Los Angeles, California in 1964, The Byrds underwent several lineup changes, with frontman Roger McGuinn remaining the sole consistent member until the group's disbandment in 1973....
     released an album titled Fifth Dimension
    Fifth Dimension (album)

    Fifth Dimension is the third album by the United States Rock music band The Byrds, which was released in the summer of 1966 on Columbia Records, catalogue item CL 2549 in monaural, CS 9349 in stereo....
    , in which the fifth dimension is a metaphor for unexplored and unknown aspects of the universe and oneself.
  • The novel The Boy Who Reversed Himself
    The Boy Who Reversed Himself

    The Boy Who Reversed Himself is a science fiction novel by William Sleator. The novel deals with an exploration into other dimensions, and provides a journey into the world beyond our own....
     features four and five-dimensional space, referred to as 4-space and 5-space.
  • The characters in Madeleine L'Engle
    Madeleine L'Engle

    Madeleine L'Engle was an United States writer best known for her Young-adult fiction, particularly the Newbery Medal-winning A Wrinkle in Time and its sequels A Wind in the Door, A Swiftly Tilting Planet, Many Waters, and An Acceptable Time....
    's novel, "A Wrinkle In Time"
    A Wrinkle in Time

    A Wrinkle in Time is a science fantasy novel by Madeleine L'Engle, first published in 1962. The book won a Newbery Medal, Sequoyah Book Award, and Lewis Carroll Shelf Award, and was runner-up for the Hans Christian Andersen Award....
     use the fifth dimension to travel through space.
  • In the children's television program "Mona the Vampire
    Mona the Vampire

    Mona the Vampire is an animation children's TV based on the series Robyn le Vampire, directed by Louise Piche and Jean Caillon, originally based on the short stories by Sonia Halleyman and Hiawyn Oram....
    ", there is an amusement park ride called the "Fifth Dimensia".
  • Rob Bryanton
    Rob Bryanton

    Rob Bryanton is a Canadian author, composer, and sound designer. He lives and works in his home town of Regina, Saskatchewan Canada. He is the author and creator of the book and website, Imagining the Tenth Dimension....
    's book and animation "Imagining the Tenth Dimension" advances the idea that our fourth-dimensional "line of time" is being created one planck length at a time from the available probalistic branches within the fifth dimension.
  • The Fifth Dimension
    The Fifth Dimension

    The Fifth Dimension, also known as The 5th Dimension, is a multiple Grammy-winning United States popular music vocal group, whose repertoire also includes pop, Rhythm and blues, Soul music, and jazz....
     was a popular soul/pop group in the late 60's starring Marilyn McCoo and Billy Davis and featured such hits as "Wedding Bell Blues", Stoned Soul Picnic", "Up, Up, and Away", "Aquarius", and many others.
  • The fifth dimension of love of the Divine is termed by the Gaudiya Vaisnavas in Hindu philosophy as turyatita
    Turiya

    In Hindu philosophy, turiya is a state of pure consciousness, or the experience of ultimate reality and truth. It is a fourth state of consciousness that underlies and transcends the three common states of consciousness: the state of waking consciousness , the state of dreaming , and dreamless sleep ....
    , the dimension of the soul's Soul.
  • "Fifth Dimension" is a radio drama adaption of the short story "The Plattner Story" by H. G. Wells
    H. G. Wells

    Herbert George Wells , known by his pen name H. G. Wells, was an England author, best known for his work in the science fiction genre. Wells and Jules Verne are each sometimes referred to as "The Father of Science Fiction"....
    , produced by the Radio Tales
    Radio Tales

    Radio Tales is an United States drama anthology radio series produced by Generations Productions LLC. This award-winning anthology series adapted classic works of American and world literature, and was a recipient of funding from the National Endowment for the Arts....
     series for National Public Radio
    National Public Radio

    National Public Radio is a privately and publicly funded non-profit membership media organization that serves as a national Radio syndication to 797 public radio List of NPR stations in the United States....
    .


See also

  • Higher dimension
    Higher dimension

    Higher dimension as a term in mathematics most commonly refers to any number of spatial dimensions greater than three.The three standard dimensions are length, width, and breadth ....
  • 5-manifold
    5-manifold

    In mathematics, a 5-manifold is a 5-dimensional topological manifold, possibly with a piecewise linear structure or differential structure.Non-simply connected space 5-manifolds are impossible to classify, as this is harder than solving the word problem for groups....
  • List of regular 5-polytopes
    List of regular polytopes

    This page lists the regular polytopes in Euclidean geometry, spherical geometry and hyperbolic geometry spaces.The Schl?fli symbol notation describes every regular polytope, and is used widely below as a compact reference name for each....
  • Hypersphere
    Hypersphere

    In mathematics, an n-sphere is a generalization of the surface of an ordinary sphere to arbitrary dimension. For any natural number n, an n-sphere of radius r is defined as the set of points in -dimensional Euclidean space which are at distance r from a central point, where the radius r may be any positive real num...
  • Dimension
    Dimension

    In mathematics, the dimension of a space is roughly defined as the minimum number of coordinates needed to specify every point within it. For example: a point on the unit circle in the plane can be specified by two Cartesian coordinates but one can make do with a single coordinate , so the circle is 1-dimensional even though it exists in...
  • Fourth dimension
    Fourth dimension

    In physics and mathematics, a vector of n real number can be understood as a Coordinate system in an n-dimensional Euclidean space. When n = 4, the set of all such locations is called 4-dimensional Euclidean space....


External links