Editing Dimension (section)

== In physics ==

===Spatial dimensions===
Classical physics theories describe three [[size|physical dimension]]s: from a particular point in [[space]], the basic directions in which we can move are up/down, left/right, and forward/backward. Movement in any other direction can be expressed in terms of just these three. Moving down is the same as moving up a negative distance. Moving diagonally upward and forward is just as the name of the direction implies ''i.e.'', moving in a [[linear combination]] of up and forward. In its simplest form: a line describes one dimension, a plane describes two dimensions, and a cube describes three dimensions. (See [[Space]] and [[Cartesian coordinate system]].)

{| class="wikitable" style="margin:auto;text-align:center;"
|-
!style="width:5em;"| {{longitem|Number of <br />dimensions}}
! Example co-ordinate systems
|-
| [[One-dimensional space|1]] ||
{| border="0"
|- style="vertical-align:bottom;line-height:2.0em;"
!style="padding-right:1.0em;"| [[File:Coord NumberLine.svg|120px|Number line]]<br />[[Number line]]
! [[File:Coord Angle.svg|120px|Angle]]<br />[[Angle]]
|}
|-
| [[Plane (mathematics)|2]] ||
{|
|- style="line-height:3.0em;"
!style="padding:1.0em 1.0em 0 0;"| [[File:Coord-XY.svg|120px]]<br />[[Cartesian coordinate system|Cartesian]]&nbsp;<span style="font-size:90%;font-weight:normal;">(two-dimensional)</span>
!style="padding:1.0em 1.0em 0 0;"| [[File:Coord Circular.svg|120px|Polar system]]<br />[[Polar coordinate system|Polar]]
!style="padding:1.0em 1.0em 0 0;"| [[File:Coord LatLong.svg|120px|Geographic system]]<br />[[Geographic coordinate system|Latitude and longitude]]
|}
|-
| [[Three-dimensional space|3]] ||
{| border="0"
|- style="line-height:3.0em;"
!style="padding:1.0em 1.0em 0 0;"| [[File:Coord XYZ.svg|120px|Cartesian system (3d)]]<br />Cartesian&nbsp;<span style="font-size:90%;font-weight:normal;">(three-dimensional)</span>
!style="padding:1.0em 1.0em 0 0;"| [[File:Cylindrical Coordinates.svg|120px|Cylindrical system]]<br />[[Cylindrical coordinate system|Cylindrical]]
!style="padding:1.0em 1.0em 0 0;"| [[File:Spherical Coordinates (Colatitude, Longitude).svg|120px|Spherical system]]<br />[[Spherical coordinate system|Spherical]]
|}
|}

===Time<!--'Temporal dimension' and 'Temporal dimensions' redirect here-->===
A '''temporal dimension''', or '''time dimension''',<!--boldface per WP:R#PLA--> is a dimension of time. Time is often referred to as the "[[Spacetime|fourth dimension]]" for this reason, but that is not to imply that it is a spatial dimension{{citation needed|date=February 2024}}. A temporal dimension is one way to measure physical change. It is perceived differently from the three spatial dimensions in that there is only one of it, and that we cannot move freely in time but subjectively move [[Arrow of time|in one direction]].

The equations used in physics to model reality do not treat time in the same way that humans commonly perceive it. The equations of [[classical mechanics]] are [[T-symmetry|symmetric with respect to time]], and equations of quantum mechanics are typically symmetric if both time and other quantities (such as [[C-symmetry|charge]] and [[Parity (physics)|parity]]) are reversed. In these models, the perception of time flowing in one direction is an artifact of the [[laws of thermodynamics]] (we perceive time as flowing in the direction of increasing [[entropy]]).

The best-known treatment of time as a dimension is [[Henri Poincaré|Poincaré]] and [[Albert Einstein|Einstein]]'s [[special relativity]] (and extended to [[general relativity]]), which treats perceived space and time as components of a four-dimensional [[manifold]], known as [[spacetime]], and in the special, flat case as [[Minkowski space]]. Time is different from other spatial dimensions as time operates in all spatial dimensions. Time operates in the first, second and third as well as theoretical spatial dimensions such as a [[Four-dimensional space|fourth spatial dimension]]. Time is not however present in a single point of absolute infinite [[Singularity (mathematics)|singularity]] as defined as a [[geometric point]], as an infinitely small point can have no change and therefore no time. Just as when an object moves through [[Position (geometry)|positions]] in space, it also moves through positions in time. In this sense the [[force]] moving any [[Physical object|object]] to change is ''time''.<ref>{{cite arXiv| eprint = math/0702552| last1 = Rylov| first1 = Yuri A.| title = Non-Euclidean method of the generalized geometry construction and its application to space-time geometry| year = 2007}}</ref><ref>{{Cite book|chapter-url=https://link.springer.com/chapter/10.1007/978-3-319-17046-6_8|chapter=Definitions for The Fourth Dimension: A Proposed Time Classification System1|first1=Paul M.|last1=Lane|first2=Jay D.|last2=Lindquist|title=Proceedings of the 1988 Academy of Marketing Science (AMS) Annual Conference|series=Developments in Marketing Science: Proceedings of the Academy of Marketing Science|editor-first=Kenneth D.|editor-last=Bahn|date=May 22, 2015|publisher=Springer International Publishing|pages=38–46|via=Springer Link|doi=10.1007/978-3-319-17046-6_8|isbn=978-3-319-17045-9}}</ref><ref>{{Cite journal|url=http://www.jstor.org/stable/20022840|title=The Space-Time Manifold of Relativity. The Non-Euclidean Geometry of Mechanics and Electromagnetics|author1=Wilson, Edwin B.|author2=Lewis, Gilbert N.|year=1912|journal=Proceedings of the American Academy of Arts and Sciences|volume=48|issue=11|pages=389–507|doi=10.2307/20022840|jstor=20022840}}</ref>

===Additional dimensions===

In physics, three dimensions of space and one of time is the accepted norm. However, there are theories that attempt to unify the four [[fundamental forces]] by introducing [[extra dimensions]]/[[hyperspace]]. Most notably, [[superstring theory]] requires 10 spacetime dimensions, and originates from a more fundamental 11-dimensional theory tentatively called [[M-theory]] which subsumes five previously distinct superstring theories. [[Supergravity theory]] also promotes 11D spacetime = 7D hyperspace + 4 common dimensions. To date, no direct experimental or observational evidence is available to support the existence of these extra dimensions. If hyperspace exists, it must be hidden from us by some physical mechanism. One well-studied possibility is that the extra dimensions may be "curled up" ([[Compactification (physics)|compactified]]) at such tiny scales as to be effectively invisible to current experiments.
[[File:Calabi-Yau.png|thumb|upright=0.7|Illustration of a Calabi–Yau manifold]]
In 1921, [[Kaluza–Klein theory]] presented 5D including an extra dimension of space. At the level of [[quantum field theory]], Kaluza–Klein theory unifies [[gravity]] with [[Gauge theory|gauge]] interactions, based on the realization that gravity propagating in small, compact extra dimensions is equivalent to gauge interactions at long distances. In particular when the geometry of the extra dimensions is trivial, it reproduces [[electromagnetism]]. However, at sufficiently high energies or short distances, this setup still suffers from the same pathologies that famously obstruct direct attempts to describe [[quantum gravity]]. Therefore, these models still require a [[UV completion]], of the kind that string theory is intended to provide. In particular, superstring theory requires six compact dimensions (6D hyperspace) forming a [[Calabi–Yau manifold]]. Thus Kaluza-Klein theory may be considered either as an incomplete description on its own, or as a subset of string theory model building.

In addition to small and curled up extra dimensions, there may be extra dimensions that instead are not apparent because the matter associated with our visible universe is localized on a {{nowrap|(3 + 1)-dimensional}} subspace. Thus, the extra dimensions need not be small and compact but may be [[large extra dimensions]]. [[D-brane]]s are dynamical extended objects of various dimensionalities predicted by string theory that could play this role. They have the property that open string excitations, which are associated with gauge interactions, are confined to the [[brane]] by their endpoints, whereas the closed strings that mediate the gravitational interaction are free to propagate into the whole spacetime, or "the bulk". This could be related to why gravity is exponentially weaker than the other forces, as it effectively dilutes itself as it propagates into a higher-dimensional volume.

Some aspects of brane physics have been applied to [[Brane cosmology|cosmology]]. For example, brane gas cosmology<ref>{{cite journal |last1=Brandenberger |first1=R. |last2=Vafa |first2=C. |title=Superstrings in the early universe |journal=Nuclear Physics B |volume=316 |issue=2 |pages=391–410 |year=1989 |doi=10.1016/0550-3213(89)90037-0 |bibcode=1989NuPhB.316..391B}}</ref><ref>Scott Watson, [http://www-astro-theory.fnal.gov/Conferences/cosmo02/poster/watson.pdf Brane Gas Cosmology]. {{webarchive|url=https://web.archive.org/web/20141027144123/http://www-astro-theory.fnal.gov/Conferences/cosmo02/poster/watson.pdf|date=2014-10-27}} (pdf).</ref> attempts to explain why there are three dimensions of space using topological and thermodynamic considerations. According to this idea it would be since three is the largest number of spatial dimensions in which strings can generically intersect. If initially there are many windings of strings around compact dimensions, space could only expand to macroscopic sizes once these windings are eliminated, which requires oppositely wound strings to find each other and annihilate. But strings can only find each other to annihilate at a meaningful rate in three dimensions, so it follows that only three dimensions of space are allowed to grow large given this kind of initial configuration.

Extra dimensions are said to be [[universal extra dimension|universal]] if all fields are equally free to propagate within them.