Three-dimensional analogy of space-time distortion. Matter changes the geometry of spacetime, this (curved) geometry being interpreted as gravity. Gravitation is a natural Phenomenon by which objects with Mass attract one another White lines do not represent the curvature of space, but instead represent the coordinate system imposed on the curved spacetime which would be rectilinear in a flat spacetime. In Mathematics and its applications a coordinate system is a system for assigning an n - Tuple of Numbers or scalars to each point

In physics, spacetime is any mathematical model that combines space and time into a single construct called the spacetime continuum. Physics (Greek Physis - φύσις in everyday terms is the Science of Matter and its motion. Note The term model has a different meaning in Model theory, a branch of Mathematical logic. Space is the extent within which Matter is physically extended and objects and Events have positions relative to one another In Physics, the treatment of Time is a central issue It has been treated as a question of Geometry. Continuum theories or models explain variation as involving a gradual quantitative transition without abrupt changes or discontinuities Spacetime is usually interpreted with space being three-dimensional and time playing the role of the fourth dimension. In Physics and Mathematics, a sequence of n numbers can be understood as a location in an n -dimensional space According to Euclidean space perception, the universe has three dimensions of space, and one dimension of time. The Universe is defined as everything that Physically Exists: the entirety of Space and Time, all forms of Matter, Energy In mathematics the dimension of a Space is roughly defined as the minimum number of Coordinates needed to specify every point within it By combining space and time into a single manifold, physicists have significantly simplified a large amount of physical theories, as well as described in a more uniform way the workings of the universe at both the supergalactic and subatomic levels. A manifold is a mathematical space in which every point has a neighborhood which resembles Euclidean space, but in which the global structure may be Theoretical physics employs Mathematical models and Abstractions of Physics in an attempt to explain experimental data taken of the natural world Physical cosmology, as a branch of Astronomy, is the study of the large-scale structure of the Universe and is concerned with fundamental questions about its Quantum mechanics is the study of mechanical systems whose dimensions are close to the Atomic scale such as Molecules Atoms Electrons

In classical mechanics, the use of Euclidean space instead of spacetime is appropriate, as time is treated as universal and constant, being independent of the state of motion of an observer. Classical mechanics is used for describing the motion of Macroscopic objects from Projectiles to parts of Machinery, as well as Astronomical objects In relativistic contexts, however, time cannot be separated from the three dimensions of space because the rate at which time passes depends on an object's velocity relative to the speed of light, and also the strength of intense gravitational fields which can slow the passage of time, and as such is dependent on the state of motion of the observer and is therefore not universal. This page is about the scientific concept of relativity for philosophical or sociological theories about relativity see Relativism. In Physics, velocity is defined as the rate of change of Position.

Concept with dimensions

The concept of spacetime combines space and time within a single coordinate system, typically with 4 dimensions: length, width, height, and time. Dimensions are components of a coordinate grid typically used to locate a point in space, or on the globe, such as by latitude, longitude and planet (Earth). Latitude, usually denoted symbolically by the Greek letter phi ( Φ) gives the location of a place on Earth (or other planetary body north or south of the Longitude (ˈlɒndʒɪˌtjuːd or ˈlɒŋgɪˌtjuːd symbolized by the Greek character Lambda (λ is the east-west Geographic coordinate measurement However, with spacetime, the coordinate grid is used to locate "events" (rather than just points in space), so time is added as another dimension to the grid.

Formerly, from experiments at slow speeds, time was believed to be a constant, which progressed at a fixed rate; however, later high-speed experiments revealed that time slowed down at higher speeds (with such slowing called "time dilation"). This article discusses a concept in physics For the concept in sociology see Time displacement. Many experiments have confirmed the slowing from time dilation, such as atomic clocks onboard a Space Shuttle running slower than synchronized Earth-bound clocks. An atomic clock is a type of Clock that uses an Atomic resonance Frequency standard as its timekeeping element NASA 's Space Shuttle, officially called the Space Transportation System ( STS) is the Spacecraft currently used by the United States Since time varies, it is treated as a variable within the spacetime coordinate grid, and time is no longer assumed to be a constant, independent of the location in space.

Note that treating spacetime events with the 4 dimensions (including time) is the conventional view; however, other invented coordinate grids treat time as 3 additional dimensions, with length-time, width-time, and height-time, to accompany the 3 dimensions of space. When dimensions are understood as mere components of the grid system, rather than physical attributes of space, it is easier to understand the alternate dimensional views, such as: latitude, longitude, plus Greenwich Mean Time (3 dimensions), or city, state, postal code, country, and UTC time (5 dimensions). Greenwich Mean Time ( GMT) is a term originally referring to mean solar time at the Royal Observatory in Greenwich, London The various dimensions are chosen, depending on the coordinate grid used.

The term spacetime has taken on a generalized meaning with the advent of higher-dimensional theories. How many dimensions are needed to describe the universe is still an open question. Speculative theories such as string theory predict 10 or 26 dimensions (with M-theory predicting 11 dimensions; 10 spatial and 1 temporal), but the existence of more than four dimensions would only appear to make a difference at the subatomic level. String theory is a still-developing scientific approach to Theoretical physics, whose original building blocks are one-dimensional extended objects called strings In Theoretical physics, M-theory is a new limit of String theory in which 11 dimensions of Spacetime may be identified A subatomic particle is an elementary or composite Particle smaller than an Atom.

Historical origin

The origins of this 20th century scientific concept began in the 19th century with fiction writers. Edgar Allan Poe stated in his essay on cosmology titled Eureka (1848) that "Space and duration are one. Edgar Allan Poe (January 19 1809 – October 7 1849 was an American poet, short-story Writer, editor and Literary critic, Eureka (1848 is a lengthy Non-fiction work by American author Edgar Allan Poe which he subtitled "A Prose Poem," though it has " This is the first known instance of suggesting space and time to be one thing. Poe arrived at this conclusion after approximately 90 pages of reasoning but employed no mathematics. In 1895, in his novel, The Time Machine, H.G. Wells wrote, “There is no difference between time and any of the three dimensions of space except that our consciousness moves along it. The Time Machine is a novella by H G Wells, first published in 1895 and later directly adapted into at least two Feature films of the same name as Herbert George Wells (21 September 1866 &ndash 13 August 1946 He was an outspoken socialist and a pacifist, his later works becoming increasingly political ” He added, “Scientific people…know very well that time is only a kind of space. ”

While spacetime can be viewed as a consequence of Albert Einstein's 1905 theory of special relativity, it was first explicitly proposed mathematically by one of his teachers, the mathematician Hermann Minkowski, in a 1908 essay ^[1] building on and extending Einstein's work. Albert Einstein ( German: ˈalbɐt ˈaɪ̯nʃtaɪ̯n; English: ˈælbɝt ˈaɪnstaɪn (14 March 1879 – 18 April 1955 was a German -born theoretical Year 1905 ( MCMV) was a Common year starting on Sunday (link will display full calendar of the Gregorian calendar (or a Common year starting Special relativity (SR (also known as the special theory of relativity or STR) is the Physical theory of Measurement in Inertial Hermann Minkowski ( June 22 1864 – January 12 1909) was a Russian born German Mathematician, of Jewish His concept of Minkowski space is the earliest treatment of space and time as two aspects of a unified whole, the essence of special relativity. In Physics and Mathematics, Minkowski space (or Minkowski spacetime) is the mathematical setting in which Einstein's theory of Special relativity Special relativity (SR (also known as the special theory of relativity or STR) is the Physical theory of Measurement in Inertial The idea of Minkowski Space also led to special relativity being viewed in a more geometrical way, this geometric viewpoint of spacetime being important in general relativity too. (For an English translation of Minkowski's article, see Lorentz et al. 1952. ) The 1926 thirteenth edition of the Encyclopedia Britannica included an article by Einstein titled "space-time". Year 1926 ( MCMXXVI) was a Common year starting on Friday (link will display the full calendar of the Gregorian calendar. The Encyclopædia Britannica is a general English-language encyclopaedia published by Encyclopædia Britannica Inc ^[2]

Basic concepts

Spacetimes are the arenas in which all physical events take place — an event is a point in spacetime specified by its time and place. For example, the motion of planets around the Sun may be described in a particular type of spacetime, or the motion of light around a rotating star may be described in another type of spacetime. A planet, as defined by the International Astronomical Union (IAU is a celestial body Orbiting a Star or stellar remnant that is The Sun (Sol is the Star at the center of the Solar System. Light, or visible light, is Electromagnetic radiation of a Wavelength that is visible to the Human eye (about 400–700 A star is a massive luminous ball of plasma. The nearest star to Earth is the Sun, which is the source of most of the Energy on Earth The basic elements of spacetime are events. In any given spacetime, an event is a unique position at a unique time. Examples of events include the explosion of a star or the single beat of a drum.

A spacetime is independent of any observer. ^[3] However, in describing physical phenomena (which occur at certain moments of time in a given region of space), each observer chooses a convenient coordinate system. In Mathematics and its applications a coordinate system is a system for assigning an n - Tuple of Numbers or scalars to each point Events are specified by four real numbers in any coordinate system. In Mathematics, the real numbers may be described informally in several different ways The worldline of a particle or light beam is the path that this particle or beam takes in the spacetime and represents the history of the particle or beam. In physics the world line of an object is the unique path of that object as it travels through 4- Dimensional Spacetime. The worldline of the orbit of the Earth is depicted in two spatial dimensions x and y (the plane of the Earth orbit) and a time dimension orthogonal to x and y. The orbit of the Earth is an ellipse in space alone, but its worldline is a helix in spacetime. A helix (pl helixes or helices) from the Greek word έλιξ, is a special kind of Space curve, i

The unification of space and time is exemplified by the common practice of expressing distance in units of time, by dividing the distance measurement by the speed of light. Measurement is the process of estimating the magnitude of some attribute of an object such as its length or weight relative to some standard ( unit of measurement) such as

Time-like interval

For two events separated by a time-like interval, enough time passes between them for there to be a cause-effect relationship between the two events. For a particle travelling less than the speed of light, any two events which occur to or by the particle must be separated by a time-like interval. Event pairs with time-like separation define a positive squared spacetime interval (s² > 0) and may be said to occur in each other's future or past.

The measure of a time-like spacetime interval is described by the proper time:

   (proper time). In relativity, proper time is Time measured by a single Clock between events that occur at the same place as the clock

The proper time interval would be measured by an observer with a clock traveling between the two events in an inertial reference frame, when the observer's path intersects each event as that event occurs. In Physics, an inertial frame of reference is a Frame of reference which belongs to a set of frames in which Physical laws hold in the same and simplest (The proper time defines a real number, since the interior of the square root is positive. In Mathematics, the real numbers may be described informally in several different ways )

Light-like interval

In a light-like interval, the spatial distance between two events is exactly balanced by the time between the two events. The events define a squared spacetime interval of zero (s² = 0).

Events which occur to or by a photon along its path (i. In Physics, the photon is the Elementary particle responsible for electromagnetic phenomena e. , while travelling at c, the speed of light) all have light-like separation. Given one event, all those events which follow at light-like intervals define the propagation of a light cone, and all the events which preceded from a light-like interval defined a second light cone. In Special relativity, a light cone (or null cone) is the pattern describing the temporal evolution of a flash of Light in Minkowski spacetime

Space-like interval

When a space-like interval separates two events, not enough time passes between their occurrences for there to exist a causal relationship crossing the spatial distance between the two events at the speed of light or slower. Causality (but not causation) denotes a necessary relationship between one event (called cause and another event (called effect) which is the direct consequence Generally, the events are considered not to occur in each other's future or past. There exists a reference frame such that the two events are observed to occur at the same time. See also Inertial frame A frame of reference in Physics, may refer to a Coordinate system or set of axes within which to

For these space-like event pairs with a negative squared spacetime interval (s² < 0), the measurement of space-like separation is the proper distance:

   (proper distance). In relativistic Physics, proper Length is an invariant quantity which is the rod Distance between Spacelike

Like the proper time of time-like intervals, the proper distance (Δσ) of space-like spacetime intervals is a real number value.

Space-time intervals

As can be seen, neither spacelike nor timelike intervals are invariant, but it is desirable to have invariants that can be used where events are not on light-like intervals. Spacetime entails a new concept of distance. Whereas distances in Euclidean spaces are entirely spatial and always positive, in special relativity the concept of distance is quantified in terms of the space-time interval between two events, which occur in two locations at two times:

   (spacetime interval),

where:

c is the speed of light,

Δt and Δr denote differences of the time and space coordinates, respectively, between the events.

(Note that the choice of signs for s² above follows the Landau-Lifshitz spacelike convention. In Physics, a sign convention is a choice of the signs (plus or minus of a set of quantities in a case where the choice of sign is arbitrary Other treatments, including some within Wikipedia, reverse the sign of s². )

Space-time intervals may be classified into three distinct types based on whether the temporal separation (c²Δt²) or the spatial separation (Δr²) of the two events is greater:

For special relativity, the spacetime interval is considered invariant across inertial reference frames. Special relativity (SR (also known as the special theory of relativity or STR) is the Physical theory of Measurement in Inertial In Mathematics and Theoretical physics, an invariant is a property of a system which remains unchanged under some transformation. In Physics, an inertial frame of reference is a Frame of reference which belongs to a set of frames in which Physical laws hold in the same and simplest

Certain types of worldlines (called geodesics of the spacetime) are the shortest paths between any two events, with distance being defined in terms of spacetime intervals. In physics the world line of an object is the unique path of that object as it travels through 4- Dimensional Spacetime. In Mathematics, a geodesic /ˌdʒiəˈdɛsɪk -ˈdisɪk/ -dee-sik is a generalization of the notion of a " straight line " to " curved spaces The concept of geodesics becomes critical in general relativity, since geodesic motion may be thought of as "pure motion" (inertial motion) in spacetime, that is, free from any external influences. General relativity or the general theory of relativity is the geometric theory of Gravitation published by Albert Einstein in 1916 A fictitious force, also called a pseudo force, d'Alembert force or inertial force, is an apparent Force that acts on all masses in a non-inertial

Mathematics of space-times

For physical reasons, a space-time continuum is mathematically defined as a four-dimensional, smooth, connected Lorentzian manifold (M,g). In Differential geometry, a pseudo-Riemannian manifold (also called a semi-Riemannian manifold) is a generalization of a Riemannian manifold. This means the smooth Lorentz metric g has signature . In Differential geometry, a pseudo-Riemannian manifold (also called a semi-Riemannian manifold) is a generalization of a Riemannian manifold. The metric determines the geometry of spacetime, as well as determining the geodesics of particles and light beams. In Mathematics, a geodesic /ˌdʒiəˈdɛsɪk -ˈdisɪk/ -dee-sik is a generalization of the notion of a " straight line " to " curved spaces About each point (event) on this manifold, coordinate charts are used to represent observers in reference frames. For other uses of "atlas" see Atlas (disambiguation. In Mathematics, particularly topology an atlas describes how Usually, Cartesian coordinates are used. Moreover, for simplicity's sake, the speed of light 'c' is usually assumed to be unity.

A reference frame (observer) can be identified with one of these coordinate charts; any such observer can describe any event p. Another reference frame may be identified by a second coordinate chart about p. Two observers (one in each reference frame) may describe the same event p but obtain different descriptions.

Usually, many overlapping coordinate charts are needed to cover a manifold. Given two coordinate charts, one containing p (representing an observer) and another containing q (another observer), the intersection of the charts represents the region of spacetime in which both observers can measure physical quantities and hence compare results. The relation between the two sets of measurements is given by a non-singular coordinate transformation on this intersection. In Mathematics, a singular point of an Algebraic variety V is a point P that is 'special' (so singular in the geometric sense that V The idea of coordinate charts as 'local observers who can perform measurements in their vicinity' also makes good physical sense, as this is how one actually collects physical data - locally.

For example, two observers, one of whom is on Earth, but the other one who is on a fast rocket to Jupiter, may observe a comet crashing into Jupiter (this is the event p). In general, they will disagree about the exact location and timing of this impact, i. e. , they will have different 4-tuples (as they are using different coordinate systems). Although their kinematic descriptions will differ, dynamical (physical) laws, such as momentum conservation and the first law of thermodynamics, will still hold. In fact, relativity theory requires more than this in the sense that it stipulates these (and all other physical) laws must take the same form in all coordinate systems. This introduces tensors into relativity, by which all physical quantities are represented. History The word tensor was introduced in 1846 by William Rowan Hamilton to describe the norm operation in a certain type of algebraic system (eventually

Geodesics are said to be timelike, null, or spacelike if the tangent vector to one point of the geodesic is of this nature. The paths of particles and light beams in spacetime are represented by timelike and null (light-like) geodesics (respectively).

Topology

Main article: Spacetime topology

The assumptions contained in the definition of a spacetime are usually justified by the following considerations. Spacetime topology, the topological structure of Spacetime, is a subject studied primarily in General relativity.

The connectedness assumption serves two main purposes. First, different observers making measurements (represented by coordinate charts) should be able to compare their observations on the non-empty intersection of the charts. If the connectedness assumption were dropped, this would not be possible. Second, for a manifold, the property of connectedness and path-connectedness are equivalent and one requires the existence of paths (in particular, geodesics) in the spacetime to represent the motion of particles and radiation. In Mathematics, a geodesic /ˌdʒiəˈdɛsɪk -ˈdisɪk/ -dee-sik is a generalization of the notion of a " straight line " to " curved spaces

Every spacetime is paracompact. In Mathematics, a paracompact space is a Topological space in which every Open cover admits an open locally finite refinement. This property, allied with the smoothness of the spacetime, gives rise to a smooth linear connection, an important structure in general relativity. In Mathematics, a connection is a device that defines a notion of Parallel transport on the bundle that is a way to "connect" or identify fibers over nearby Some important theorems on constructing spacetimes from compact and non-compact manifolds include the following:

• A compact manifold can be turned into a spacetime if, and only if, its Euler characteristic is 0. In Mathematics, and more specifically in Algebraic topology and Polyhedral combinatorics, the Euler characteristic is a Topological invariant
• Any non-compact 4-manifold can be turned into a spacetime.

Space-time symmetries

Main article: Spacetime symmetries

Often in relativity, space-times that have some form of symmetry are studied. Spacetime symmetries refers to aspects of Spacetime that can be described as exhibiting some form of Symmetry. As well as helping to classify spacetimes, these symmetries usually serve as a simplifying assumption in specialised work. Some of the most popular ones include:

• Axially symmetric spacetimes
• Spherically symmetric spacetimes
• Static spacetimes
• Stationary spacetimes

Causal structure

Main article: Causal structure

The causal structure of a spacetime describes causal relationships between pairs of points in the spacetime based on the existence of certain types of curves joining the points. A spherically symmetric spacetime is one whose Isometry group contains a subgroup which is isomorphic to the (rotation group SO(3 and the Orbits of In General relativity, a Spacetime is said to be static if it admits a global nowhere zero Timelike Hypersurface orthogonal Killing In General relativity, a Spacetime is said to be stationary if it admits a global nowhere zero Timelike Killing vector field. The causal structure of a Lorentzian manifold describes the causal relationships between points in the manifold

Spacetime in special relativity

Main article: Minkowski space

The geometry of spacetime in special relativity is described by the Minkowski metric on R⁴. In Physics and Mathematics, Minkowski space (or Minkowski spacetime) is the mathematical setting in which Einstein's theory of Special relativity In Physics and Mathematics, Minkowski space (or Minkowski spacetime) is the mathematical setting in which Einstein's theory of Special relativity This spacetime is called Minkowski space. The Minkowski metric is usually denoted by η and can be written as a four-by-four matrix:

where the Landau-Lifshitz spacelike convention is being used. In Physics, a sign convention is a choice of the signs (plus or minus of a set of quantities in a case where the choice of sign is arbitrary A basic assumption of relativity is that coordinate transformations must leave spacetime intervals invariant. Intervals are invariant under Lorentz transformations. In standard Physics, Lorentz covariance is a key property of Spacetime that follows from the Special theory of relativity, where it applies globally In Physics, the Lorentz transformation converts between two different observers' measurements of space and time where one observer is in constant motion with respect to This invariance property leads to the use of four-vectors (and other tensors) in describing physics. In relativity, a four-vector is a vector in a four-dimensional real Vector space, called Minkowski space.

Strictly speaking, one can also consider events in Newtonian physics as a single spacetime. This is Galilean-Newtonian relativity, and the coordinate systems are related by Galilean transformations. A principle of relativity is a criterion for judging physical theories, stating that they are inadequate if they do not prescribe the exact same laws of physics in The Galilean transformation is used to transform between the coordinates of two Reference frames which differ only by constant relative motion within the constructs of Newtonian However, since these preserve spatial and temporal distances independently, such a space-time can be decomposed into spatial coordinates plus temporal coordinates, which is not possible in the general case.

Spacetime in general relativity

In general relativity, it is assumed that spacetime is curved by the presence of matter (energy), this curvature being represented by the Riemann tensor. General relativity or the general theory of relativity is the geometric theory of Gravitation published by Albert Einstein in 1916 In the Mathematical field of Differential geometry, the Riemann curvature tensor or Riemann–Christoffel tensor is the most standard way to express In special relativity, the Riemann tensor is identically zero, and so this concept of "non-curvedness" is sometimes expressed by the statement "Minkowski spacetime is flat. "

Many space-time continua have physical interpretations which most physicists would consider bizarre or unsettling. For example, a compact spacetime has closed, time-like curves, which violate our usual ideas of causality (that is, future events could affect past ones). For this reason, mathematical physicists usually consider only restricted subsets of all the possible spacetimes. One way to do this is to study "realistic" solutions of the equations of general relativity. Another way is to add some additional "physically reasonable" but still fairly general geometric restrictions, and try to prove interesting things about the resulting spacetimes. The latter approach has led to some important results, most notably the Penrose-Hawking singularity theorems. The Penrose-Hawking singularity theorems are a set of results in General relativity which attempt to answer the question of whether gravity is necessarily singular

Quantized space-time

In general relativity, space-time is assumed to be smooth and continuous- and not just in the mathematical sense. In the theory of quantum mechanics, there is an inherent discreteness present in physics. In attempting to reconcile these two theories, it is sometimes postulated that spacetime should be quantized at the very smallest scales. Current theory is focused on the nature of space-time at the Planck scale. In Particle physics and Physical cosmology, the Planck scale is an Energy scale around 1 Causal sets, loop quantum gravity, string theory, and black hole thermodynamics all predict a quantized space-time with agreement on the order of magnitude. The causal sets programme is an approach to Quantum gravity. Its founding principle is that Spacetime is fundamentally discrete and that the spacetime points are related Loop quantum gravity (LQG, also known as loop gravity and Quantum geometry, is a proposed quantum theory of Spacetime which attempts to reconcile the theories String theory is a still-developing scientific approach to Theoretical physics, whose original building blocks are one-dimensional extended objects called strings In Physics, black hole thermodynamics is the area of study that seeks to reconcile the Laws of thermodynamics with the existence of Black hole Event In Physics, quantization is a procedure for constructing a Quantum field theory starting from a classical field theory. Loop quantum gravity makes precise predictions about the geometry of spacetime at the Planck scale.

Spiralization and Compression Theory

A recent development in physics is the theory of the spiralization and compression of space time, also known as the "Jack-in-the-box" theory. Physics (Greek Physis - φύσις in everyday terms is the Science of Matter and its motion. This theory was first put forth in 2006 by a group of scientists working in Portland, Oregon. Year 2006 ( MMVI) was a Common year starting on Sunday of the Gregorian calendar. Portland is a city located in the Northwestern United States, near the Confluence of the Willamette and Columbia rivers The theory speculates that over time, all the dimensions of space spiral inward until reaching a state of absolute compression. When complete compression is reached, space springs outward and expands rapidly, as with the big bang, before the cycle is begun again. The Big Bang is the cosmological model of the Universe that is best supported by all lines of scientific evidence and Observation. The highlight of this theory is the independence of time from the spiralization and compression of space. The impact of this theory on relativity and attempts at a unified field theory are yet unknown. In Physics, a unified field theory is a type of Field theory that allows all of the Fundamental forces between Elementary particles to be written However, it has been predicted, using the spiralization and compression theory, that the Large Hadron Collider will produce micro-universes.

Privileged character of 3+1 spacetime

A number of scientists and philosophers have written about spacetime, and concepts have evolved as more theories have been deduced and tested by mathematical analysis or experimentation.

Other writers have been limited by the scientific evidence available at the time. For example, in the latter 20th century, experiments with "atom-smasher" particle accelerators had revealed that individual protons accelerated to high speeds were gaining the mass equivalent to a car at rest, requiring ever-increasing amounts of energy to accelerate the protons even faster. While the passage of Time slowed at high speeds, the mass of the particles increased. Writers from previous eras were not aware of that evidence, so fanciful views are sometimes expressed in the writings that are described below.

Let dimensions be of two kinds: spatial and temporal. That spacetime, ignoring any undetectable compactified dimensions, consists of three spatial (bidirectional) and one temporal (unidirectional) dimensions can be explained by appealing to the physical consequences of differing numbers of dimensions. The argument is often of an anthropic nature. In Physics and Cosmology, the anthropic principle states that humans should take into account the constraints that human existence imposes on the kind of theoretical

Immanuel Kant argued that 3-dimensional Space was a consequence of the inverse square law of universal gravitation. Immanuel Kant (ɪmanuəl kant 22 April 1724 12 February 1804 was an 18th-century German Philosopher from the Prussian city of Königsberg Newton 's law of universal Gravitation is a physical law describing the gravitational attraction between bodies with mass While Kant's argument is historically important, John D. Barrow says of it that "we would regard this as getting the punch-line back to front: it is the three-dimensionality of Space that explains why we see inverse-square force laws in Nature, not vice-versa" (Barrow 2002). John David Barrow FRS (born November 29, 1952, London) is an English cosmologist, theoretical physicist, and This is because the law of gravitation (or any other inverse-square law) follows from the concept of flux, from Space having 3 dimensions, and from 3-dimensional solid objects having surface area proportional to the square of their size in one chosen dimension. In Physics, an inverse-square law is any Physical law stating that some physical Quantity or strength is inversely proportional In the various subfields of Physics, there exist two common usages of the term flux, both with rigorous mathematical frameworks In particular, a sphere of radius r has area of 4πr². Remote Authentication Dial In User Service ( RADIUS) is a networking protocol that provides centralized access authorization and accounting management for people or computers More generally, in a Space of N dimensions, the strength of the gravitational attraction between two bodies separated by a distance of r would be inversely proportional to r^N-1.

Fixing the number of temporal dimensions at 1 and letting the number of spatial dimensions N exceed 3, Paul Ehrenfest showed in 1920 that the orbit of a planet about its sun cannot remain stable, and that the same holds for a star's orbit around its galactic center. Paul Ehrenfest ( January 18, 1880 – September 25, 1933) was an Austrian Physicist and Mathematician, who In Physics, an orbit is the gravitationally curved path of one object around a point or another body for example the gravitational orbit of a planet around a star A planet, as defined by the International Astronomical Union (IAU is a celestial body Orbiting a Star or stellar remnant that is ^[4] Likewise, F. R. Tangherlini showed in 1963 that when N>3, electrons would not form stable orbitals around nuclei; they would either fall into the nucleus or disperse. An atomic orbital is a Mathematical function that describes the wave-like behavior of an electron in an atom The nucleus of an Atom is the very dense region consisting of Nucleons ( Protons and Neutrons, at the center of an atom Ehrenfest also showed that if N is even, then the different parts of a wave impulse will travel at different speeds. A wave is a disturbance that propagates through Space and Time, usually with transference of Energy. If N is odd and greater than 3, then wave impulses become distorted. Only when N=3 or 1 are both problems avoided.

Max Tegmark expands on the preceding argument in the following anthropic manner. Max Tegmark (born 5 May 1967) is a Swedish - American cosmologist. In Physics and Cosmology, the anthropic principle states that humans should take into account the constraints that human existence imposes on the kind of theoretical ^[5] If the number of Time dimensions differed from 1, the behavior of physical systems could not be predicted reliably from knowledge of the relevant partial differential equations. In Mathematics, partial differential equations ( PDE) are a type of Differential equation, i In such a universe, intelligent life capable of manipulating technology could not emerge. In addition, Tegmark maintains that protons and electrons would be unstable in a universe with more than one Time dimension, as they can decay into more massive particles (this is not a problem if the temperature is sufficiently low). The proton ( Greek πρῶτον / proton "first" is a Subatomic particle with an Electric charge of one positive The electron is a fundamental Subatomic particle that was identified and assigned the negative charge in 1897 by J If N>3, Ehrenfest's above argument holds; atoms as we know them (and probably more complex structures as well) could not exist. If N<3, gravitation of any kind becomes problematic, and the universe is probably too simple to contain observers. For example, nerves must intersect and cannot overlap.

In general, it is not clear how physical laws could operate if the number of Time dimensions T differed from 1. If T>1, individual subatomic particles, which decay after a fixed period, would not have much predictability because timelike geodesics would not be necessarily maximal. In Mathematics, a geodesic /ˌdʒiəˈdɛsɪk -ˈdisɪk/ -dee-sik is a generalization of the notion of a " straight line " to " curved spaces ^[6] N=1 and T=3 has the peculiar property that that the speed of light in a vacuum is a lower bound on the velocity of matter. Hence anthropic arguments rule out all cases except 3 spatial and 1 temporal dimensions--the description of the world in which we live.

Curiously, 3 and 4 dimensional spaces appear richest geometrically and topologically. For example, there are geometric statements whose truth or falsity is known for any number of spatial dimensions except 3, 4, or both.

For a more detailed introduction to the privileged status of 3 spatial and 1 temporal dimensions, see Barrow;^[7] for a deeper treatment, see Barrow and Tipler. ^[8] Barrow regularly cites Whitrow. ^[9]

In string theory, physicists are not constrained by notions limited to 3+1 dimensions, so coordinate grids of 10, or perhaps 26 dimensions, are used to describe the types and locations of the vibrating strings. String theory is a still-developing scientific approach to Theoretical physics, whose original building blocks are one-dimensional extended objects called strings String theory follows the notion that the "universe is wiggly" and considers matter and energy to be composed of tiny vibrating strings of various types, specified by some of the dimensions.

See also

References

• Ehrenfest, Paul, 1920, "How do the fundamental laws of physics make manifest that Space has 3 dimensions?" Annalen der Physik 61: 440. Paul Ehrenfest ( January 18, 1880 – September 25, 1933) was an Austrian Physicist and Mathematician, who
• Kant, Immanuel, 1929, "Thoughts on the true estimation of living forces" in J. Immanuel Kant (ɪmanuəl kant 22 April 1724 12 February 1804 was an 18th-century German Philosopher from the Prussian city of Königsberg Handyside, trans. , Kant's Inaugural Dissertation and Early Writings on Space. Univ. of Chicago Press.
• Lorentz, H. A., Einstein, Albert, Minkowski, Hermann, and Weyl Hermann, 1952. Hendrik Antoon Lorentz ( July 18, 1853 &ndash February 4, 1928) was a Dutch Physicist who shared the 1902 Nobel Albert Einstein ( German: ˈalbɐt ˈaɪ̯nʃtaɪ̯n; English: ˈælbɝt ˈaɪnstaɪn (14 March 1879 – 18 April 1955 was a German -born theoretical Hermann Minkowski ( June 22 1864 – January 12 1909) was a Russian born German Mathematician, of Jewish Hermann Klaus Hugo Weyl ( 9 November 1885 – 8 December 1955) was a German Mathematician. The Principle of Relativity: A Collection of Original Memoirs. Dover.
• Lucas, John Randolph, 1973. John Randolph Lucas FBA (born 18 June, 1929) is a British philosopher A Treatise on Time and Space. London: Methuen.
• Penrose, Roger (2004). Sir Roger Penrose, PhD, OM, FRS (born 8 August 1931) is an English Mathematical physicist and Emeritus The Road to Reality. The Road to Reality is a book on modern Physics by the British mathematical physicist Roger Penrose, published in 2004 Oxford: Oxford University Press.   Chpts. 17,18.
• Robb, A. A. (1936). Geometry of Time and Space. University Press.  

• Poe, Edgar A. (1848). Edgar Allan Poe (January 19 1809 – October 7 1849 was an American poet, short-story Writer, editor and Literary critic, Eureka; An Essay on the Material and Spiritual Universe. Eureka (1848 is a lengthy Non-fiction work by American author Edgar Allan Poe which he subtitled "A Prose Poem," though it has Hesperus Press Limited. ISBN 1-84391-009-8.  

• Schutz, J. W. (1997). Independent axioms for Minkowski Space-time. Addison-Wesley Longman.  

• Tangherlini, F. R. (1963). "Atoms in Higher Dimensions". Nuovo Cimento 14 (27): 636.  

• Taylor, E. F. ; Wheeler, John A. (1963). John Archibald Wheeler ( July 9, 1911 &ndash April 13, 2008) was an eminent American Theoretical physicist. Spacetime Physics. W. H. Freeman.  

• Wells, H.G. (2004). Herbert George Wells (21 September 1866 &ndash 13 August 1946 He was an outspoken socialist and a pacifist, his later works becoming increasingly political The Time Machine. The Time Machine is a novella by H G Wells, first published in 1895 and later directly adapted into at least two Feature films of the same name as New York: Pocket Books.   (pp. 5; 6)

External links

• Spacetime - Summary and collection of links to academic sites.