**Space** is the boundless, three-dimensional extent in which

objectsIn physics, a physical body or physical object is a collection of masses, taken to be one...

and events occur and have relative position and direction. Physical space is often conceived in three

linearIn mathematics, a linear map or function f is a function which satisfies the following two properties:* Additivity : f = f + f...

dimensionIn physics and mathematics, the dimension of a space or object is informally defined as the minimum number of coordinates needed to specify any point within it. Thus a line has a dimension of one because only one coordinate is needed to specify a point on it...

s, although modern

physicistsPhysics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...

usually consider it, with

timeTime is a part of the measuring system used to sequence events, to compare the durations of events and the intervals between them, and to quantify rates of change such as the motions of objects....

, to be part of a boundless four-dimensional

continuumContinuum theories or models explain variation as involving a gradual quantitative transition without abrupt changes or discontinuities. It can be contrasted with 'categorical' models which propose qualitatively different states.-In physics:...

known as

spacetimeIn physics, spacetime is any mathematical model that combines space and time into a single continuum. Spacetime is usually interpreted with space as being three-dimensional and time playing the role of a fourth dimension that is of a different sort from the spatial dimensions...

. In

mathematicsMathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...

one examines "spaces" with different numbers of dimensions and with different underlying structures. The concept of space is considered to be of fundamental importance to an understanding of the physical

universeThe Universe is commonly defined as the totality of everything that exists, including all matter and energy, the planets, stars, galaxies, and the contents of intergalactic space. Definitions and usage vary and similar terms include the cosmos, the world and nature...

although disagreement continues between philosophers over whether it is itself an entity, a relationship between entities, or part of a

conceptual frameworkA conceptual framework is used in research to outline possible courses of action or to present a preferred approach to an idea or thought. For example, the philosopher Isaiah Berlin used the "hedgehogs" versus "foxes" approach; a "hedgehog" might approach the world in terms of a single organizing...

.

Debates concerning the nature, essence and the mode of existence of space date back to antiquity; namely, to treatises like the

*Timaeus* of

PlatoPlato , was a Classical Greek philosopher, mathematician, student of Socrates, writer of philosophical dialogues, and founder of the Academy in Athens, the first institution of higher learning in the Western world. Along with his mentor, Socrates, and his student, Aristotle, Plato helped to lay the...

, or

Socrates Socrates was a classical Greek Athenian philosopher. Credited as one of the founders of Western philosophy, he is an enigmatic figure known chiefly through the accounts of later classical writers, especially the writings of his students Plato and Xenophon, and the plays of his contemporary ...

in his reflections on what the Greeks called

*khora*Khôra is a philosophical term described by Plato in Timaeus as a receptacle, a space, or an interval. It is neither being nor nonbeing but an interval between in which the "forms" were originally held...

(i.e. "space"), or in the

*Physics* of

AristotleAristotle was a Greek philosopher and polymath, a student of Plato and teacher of Alexander the Great. His writings cover many subjects, including physics, metaphysics, poetry, theater, music, logic, rhetoric, linguistics, politics, government, ethics, biology, and zoology...

(Book IV, Delta) in the definition of

*topos* (i.e. place), or even in the later "geometrical conception of place" as "space

*qua* extension" in the

*Discourse on Place* (

*Qawl fi al-Makan*) of the 11th century Arab polymath Alhazen. Many of these classical philosophical questions were discussed in the Renaissance and then reformulated in the 17th century, particularly during the early development of

classical mechanicsIn physics, classical mechanics is one of the two major sub-fields of mechanics, which is concerned with the set of physical laws describing the motion of bodies under the action of a system of forces...

. In

Isaac NewtonSir Isaac Newton PRS was an English physicist, mathematician, astronomer, natural philosopher, alchemist, and theologian, who has been "considered by many to be the greatest and most influential scientist who ever lived."...

's view, space was absolute - in the sense that it existed permanently and independently of whether there were any matter in the space. Other natural philosophers, notably

Gottfried LeibnizGottfried Wilhelm Leibniz was a German philosopher and mathematician. He wrote in different languages, primarily in Latin , French and German ....

, thought instead that space was a collection of relations between objects, given by their

distanceDistance is a numerical description of how far apart objects are. In physics or everyday discussion, distance may refer to a physical length, or an estimation based on other criteria . In mathematics, a distance function or metric is a generalization of the concept of physical distance...

and direction from one another. In the 18th century, the philosopher and theologian

George BerkeleyGeorge Berkeley , also known as Bishop Berkeley , was an Irish philosopher whose primary achievement was the advancement of a theory he called "immaterialism"...

attempted to refute the "visibility of spatial depth" in his

*Essay Towards a New Theory of Vision*. Later, the metaphysician

Immanuel KantImmanuel Kant was a German philosopher from Königsberg , researching, lecturing and writing on philosophy and anthropology at the end of the 18th Century Enlightenment....

said neither space nor time can be empirically perceived, they are elements of a systematic framework that humans use to structure all experiences. Kant referred to "space" in his

*Critique of Pure Reason* as being: a subjective "pure

*a priori* form of intuition", hence it is an unavoidable contribution of our human faculties.

In the 19th and 20th centuries mathematicians began to examine non-Euclidean geometries, in which space can be said to be

*curved*, rather than

*flat*. According to

Albert EinsteinAlbert Einstein was a German-born theoretical physicist who developed the theory of general relativity, effecting a revolution in physics. For this achievement, Einstein is often regarded as the father of modern physics and one of the most prolific intellects in human history...

's theory of

general relativityGeneral relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...

, space around

gravitational fieldThe gravitational field is a model used in physics to explain the existence of gravity. In its original concept, gravity was a force between point masses...

s deviates from Euclidean space. Experimental

tests of general relativityAt its introduction in 1915, the general theory of relativity did not have a solid empirical foundation. It was known that it correctly accounted for the "anomalous" precession of the perihelion of Mercury and on philosophical grounds it was considered satisfying that it was able to unify Newton's...

have confirmed that non-Euclidean space provides a better model for the shape of space.

### Leibniz and Newton

In the seventeenth century, the

philosophy of space and timePhilosophy of space and time is the branch of philosophy concerned with the issues surrounding the ontology, epistemology, and character of space and time. While such ideas have been central to philosophy from its inception, the philosophy of space and time was both an inspiration for and a...

emerged as a central issue in

epistemology and

metaphysicsMetaphysics is a branch of philosophy concerned with explaining the fundamental nature of being and the world, although the term is not easily defined. Traditionally, metaphysics attempts to answer two basic questions in the broadest possible terms:...

. At its heart,

Gottfried LeibnizGottfried Wilhelm Leibniz was a German philosopher and mathematician. He wrote in different languages, primarily in Latin , French and German ....

, the German philosopher-mathematician, and

Isaac NewtonSir Isaac Newton PRS was an English physicist, mathematician, astronomer, natural philosopher, alchemist, and theologian, who has been "considered by many to be the greatest and most influential scientist who ever lived."...

, the English physicist-mathematician, set out two opposing theories of what space is. Rather than being an entity that independently exists over and above other matter, Leibniz held that space is no more than the collection of spatial relations between objects in the world: "space is that which results from places taken together". Unoccupied regions are those that

*could* have objects in them, and thus spatial relations with other places. For Leibniz, then, space was an idealised

abstractionAbstraction is a process by which higher concepts are derived from the usage and classification of literal concepts, first principles, or other methods....

from the relations between individual entities or their possible locations and therefore could not be continuous but must be discrete.

Space could be thought of in a similar way to the relations between family members. Although people in the family are related to one another, the relations do not exist independently of the people.

Leibniz argued that space could not exist independently of objects in the world because that implies a difference between two universes exactly alike except for the location of the material world in each universe. But since there would be no observational way of telling these universes apart then, according to the

identity of indiscerniblesThe identity of indiscernibles is an ontological principle which states that two or more objects or entities are identical if they have all their properties in common. That is, entities x and y are identical if any predicate possessed by x is also possessed by y and vice versa...

, there would be no real difference between them. According to the

principle of sufficient reasonThe principle of sufficient reason states that anything that happens does so for a reason: no state of affairs can obtain, and no statement can be true unless there is sufficient reason why it should not be otherwise...

, any theory of space that implied that there could be these two possible universes, must therefore be wrong.

Newton took space to be more than relations between material objects and based his position on

observationObservation is either an activity of a living being, such as a human, consisting of receiving knowledge of the outside world through the senses, or the recording of data using scientific instruments. The term may also refer to any data collected during this activity...

and

experimentAn experiment is a methodical procedure carried out with the goal of verifying, falsifying, or establishing the validity of a hypothesis. Experiments vary greatly in their goal and scale, but always rely on repeatable procedure and logical analysis of the results...

ation. For a

relationistRelationism can refer to:*In social thought, Karl Mannheim pioneered the idea of Relationism, in the development of his theories on the Sociology of Knowledge...

there can be no real difference between

inertial motionIn physics, an inertial frame of reference is a frame of reference that describes time homogeneously and space homogeneously, isotropically, and in a time-independent manner.All inertial frames are in a state of constant, rectilinear motion with respect to one another; they are not...

, in which the object travels with constant

velocityIn physics, velocity is speed in a given direction. Speed describes only how fast an object is moving, whereas velocity gives both the speed and direction of the object's motion. To have a constant velocity, an object must have a constant speed and motion in a constant direction. Constant ...

, and

non-inertial motionA non-inertial reference frame is a frame of reference that is under acceleration. The laws of physics in such a frame do not take on their most simple form, as required by the theory of special relativity...

, in which the velocity changes with time, since all spatial measurements are relative to other objects and their motions. But Newton argued that since non-inertial motion generates

forceIn physics, a force is any influence that causes an object to undergo a change in speed, a change in direction, or a change in shape. In other words, a force is that which can cause an object with mass to change its velocity , i.e., to accelerate, or which can cause a flexible object to deform...

s, it must be absolute. He used the example of

water in a spinning bucketIsaac Newton's rotating bucket argument was designed to demonstrate that true rotational motion cannot be defined as the relative rotation of the body with respect to the immediately surrounding bodies...

to demonstrate his argument.

WaterWater is a chemical substance with the chemical formula H2O. A water molecule contains one oxygen and two hydrogen atoms connected by covalent bonds. Water is a liquid at ambient conditions, but it often co-exists on Earth with its solid state, ice, and gaseous state . Water also exists in a...

in a

bucketA bucket, also called a pail, is typically a watertight, vertical cylinder or truncated cone, with an open top and a flat bottom, usually attached to a semicircular carrying handle called the bail. A pail can have an open top or can have a lid....

is hung from a rope and set to spin, starts with a flat surface. After a while, as the bucket continues to spin, the surface of the water becomes concave. If the bucket's spinning is stopped then the surface of the water remains concave as it continues to spin. The concave surface is therefore apparently not the result of relative motion between the bucket and the water. Instead, Newton argued, it must be a result of non-inertial motion relative to space itself. For several centuries the bucket argument was decisive in showing that space must exist independently of matter.

### Kant

In the eighteenth century the German philosopher

Immanuel KantImmanuel Kant was a German philosopher from Königsberg , researching, lecturing and writing on philosophy and anthropology at the end of the 18th Century Enlightenment....

developed a theory of

knowledgeKnowledge is a familiarity with someone or something unknown, which can include information, facts, descriptions, or skills acquired through experience or education. It can refer to the theoretical or practical understanding of a subject...

in which knowledge about space can be both

*a priori*The terms a priori and a posteriori are used in philosophy to distinguish two types of knowledge, justifications or arguments...

and

*synthetic*. According to Kant, knowledge about space is

*synthetic*, in that statements about space are not simply true by virtue of the meaning of the words in the statement. In his work, Kant rejected the view that space must be either a substance or relation. Instead he came to the conclusion that space and time are not discovered by humans to be objective features of the world, but are part of an unavoidable systematic framework for organizing our experiences.

### Non-Euclidean geometry

Euclid's

*Elements* contained five postulates that form the basis for Euclidean geometry. One of these, the

parallel postulateIn geometry, the parallel postulate, also called Euclid's fifth postulate because it is the fifth postulate in Euclid's Elements, is a distinctive axiom in Euclidean geometry...

has been the subject of debate among mathematicians for many centuries. It states that on any

planeIn mathematics, a plane is a flat, two-dimensional surface. A plane is the two dimensional analogue of a point , a line and a space...

on which there is a straight line

*L*_{1} and a point

*P* not on

*L*_{1}, there is only one straight line

*L*_{2} on the plane that passes through the point

*P* and is parallel to the straight line

*L*_{1}. Until the 19th century, few doubted the truth of the postulate; instead debate centered over whether it was necessary as an axiom, or whether it was a theory that could be derived from the other axioms. Around 1830 though, the

HungarianHungary , officially the Republic of Hungary , is a landlocked country in Central Europe. It is situated in the Carpathian Basin and is bordered by Slovakia to the north, Ukraine and Romania to the east, Serbia and Croatia to the south, Slovenia to the southwest and Austria to the west. The...

János BolyaiJános Bolyai was a Hungarian mathematician, known for his work in non-Euclidean geometry.Bolyai was born in the Transylvanian town of Kolozsvár , then part of the Habsburg Empire , the son of Zsuzsanna Benkő and the well-known mathematician Farkas Bolyai.-Life:By the age of 13, he had mastered...

and the

RussiaRussia or , officially known as both Russia and the Russian Federation , is a country in northern Eurasia. It is a federal semi-presidential republic, comprising 83 federal subjects...

n

Nikolai Ivanovich LobachevskyNikolai Ivanovich Lobachevsky was a Russian mathematician and geometer, renowned primarily for his pioneering works on hyperbolic geometry, otherwise known as Lobachevskian geometry...

separately published treatises on a type of geometry that does not include the parallel postulate, called

hyperbolic geometryIn mathematics, hyperbolic geometry is a non-Euclidean geometry, meaning that the parallel postulate of Euclidean geometry is replaced...

. In this geometry, an infinite number of parallel lines pass through the point

*P*. Consequently the sum of angles in a triangle is less than 180

^{o} and the ratio of a

circleA circle is a simple shape of Euclidean geometry consisting of those points in a plane that are a given distance from a given point, the centre. The distance between any of the points and the centre is called the radius....

's

circumferenceThe circumference is the distance around a closed curve. Circumference is a special perimeter.-Circumference of a circle:The circumference of a circle is the length around it....

to its

diameterIn geometry, a diameter of a circle is any straight line segment that passes through the center of the circle and whose endpoints are on the circle. The diameters are the longest chords of the circle...

is greater than

pi' is a mathematical constant that is the ratio of any circle's circumference to its diameter. is approximately equal to 3.14. Many formulae in mathematics, science, and engineering involve , which makes it one of the most important mathematical constants...

. In the 1850s,

Bernhard RiemannGeorg Friedrich Bernhard Riemann was an influential German mathematician who made lasting contributions to analysis and differential geometry, some of them enabling the later development of general relativity....

developed an equivalent theory of elliptical geometry, in which no parallel lines pass through

*P*. In this geometry, triangles have more than 180

^{o} and circles have a ratio of circumference-to-diameter that is less than pi.

Type of geometry |
Number of parallels |
Sum of angles in a triangle |
Ratio of circumference to diameter of circle |
Measure of curvature |
---|

Hyperbolic |
Infinite |
< 180^{o} |
> π |
< 0 |

Euclidean |
1 |
180^{o} |
π |
0 |

Elliptical |
0 |
> 180^{o} |
< π |
> 0 |

### Gauss and Poincaré

Although there was a prevailing Kantian consensus at the time, once non-Euclidean geometries had been formalised, some began to wonder whether or not physical space is curved.

Carl Friedrich GaussJohann Carl Friedrich Gauss was a German mathematician and scientist who contributed significantly to many fields, including number theory, statistics, analysis, differential geometry, geodesy, geophysics, electrostatics, astronomy and optics.Sometimes referred to as the Princeps mathematicorum...

, a German mathematician, was the first to consider an empirical investigation of the geometrical structure of space. He thought of making a test of the sum of the angles of an enormous stellar triangle and there are reports he actually carried out a test, on a small scale, by

triangulatingIn trigonometry and geometry, triangulation is the process of determining the location of a point by measuring angles to it from known points at either end of a fixed baseline, rather than measuring distances to the point directly...

mountain tops in Germany.

Henri PoincaréJules Henri Poincaré was a French mathematician, theoretical physicist, engineer, and a philosopher of science...

, a French mathematician and physicist of the late 19th century introduced an important insight in which he attempted to demonstrate the futility of any attempt to discover which geometry applies to space by experiment. He considered the predicament that would face scientists if they were confined to the surface of an imaginary large sphere with particular properties, known as a

sphere-worldThe idea of a sphere-world was constructed by Henri Poincaré who, while pursuing his argument for conventionalism , offered a thought experiment about a sphere with strange properties....

. In this world, the

temperatureTemperature is a physical property of matter that quantitatively expresses the common notions of hot and cold. Objects of low temperature are cold, while various degrees of higher temperatures are referred to as warm or hot...

is taken to vary in such a way that all objects expand and contract in similar proportions in different places on the sphere. With a suitable falloff in temperature, if the scientists try to use measuring rods to determine the sum of the angles in a triangle, they can be deceived into thinking that they inhabit a plane, rather than a spherical surface. In fact, the scientists cannot in principle determine whether they inhabit a plane or sphere and, Poincaré argued, the same is true for the debate over whether real space is Euclidean or not. For him, which geometry was used to describe space, was a matter of

conventionConventionalism is the philosophical attitude that fundamental principles of a certain kind are grounded on agreements in society, rather than on external reality...

. Since

Euclidean geometryEuclidean geometry is a mathematical system attributed to the Alexandrian Greek mathematician Euclid, which he described in his textbook on geometry: the Elements. Euclid's method consists in assuming a small set of intuitively appealing axioms, and deducing many other propositions from these...

is simpler than non-Euclidean geometry, he assumed the former would always be used to describe the 'true' geometry of the world.

### Einstein

In 1905,

Albert EinsteinAlbert Einstein was a German-born theoretical physicist who developed the theory of general relativity, effecting a revolution in physics. For this achievement, Einstein is often regarded as the father of modern physics and one of the most prolific intellects in human history...

published a paper on a special theory of relativity, in which he proposed that space and time be combined into a single construct known as

*spacetime*. In this theory, the

speed of lightThe speed of light in vacuum, usually denoted by c, is a physical constant important in many areas of physics. Its value is 299,792,458 metres per second, a figure that is exact since the length of the metre is defined from this constant and the international standard for time...

in a

vacuumIn everyday usage, vacuum is a volume of space that is essentially empty of matter, such that its gaseous pressure is much less than atmospheric pressure. The word comes from the Latin term for "empty". A perfect vacuum would be one with no particles in it at all, which is impossible to achieve in...

is the same for all observers—which has

the resultIn physics, the relativity of simultaneity is the concept that simultaneity–whether two events occur at the same time–is not absolute, but depends on the observer's reference frame. According to the special theory of relativity, it is impossible to say in an absolute sense whether two events occur...

that two events that appear simultaneous to one particular observer will not be simultaneous to another observer if the observers are moving with respect to one another. Moreover, an observer will measure a moving clock to

tick more slowlyIn the theory of relativity, time dilation is an observed difference of elapsed time between two events as measured by observers either moving relative to each other or differently situated from gravitational masses. An accurate clock at rest with respect to one observer may be measured to tick at...

than one that is stationary with respect to them; and objects are measured

to be shortenedIn physics, length contraction – according to Hendrik Lorentz – is the physical phenomenon of a decrease in length detected by an observer of objects that travel at any non-zero velocity relative to that observer...

in the direction that they are moving with respect to the observer.

Over the following ten years Einstein worked on a general theory of relativity, which is a theory of how gravity interacts with spacetime. Instead of viewing gravity as a

force fieldA force field, sometimes known as an energy shield, force shield, or deflector shield is a concept of a field tightly bounded and of significant magnitude so that objects affected by the particular force relating to the field are unable to pass through the central axis of the field and reach the...

acting in spacetime, Einstein suggested that it modifies the geometric structure of spacetime itself. According to the general theory, time

goes more slowlyGravitational time dilation is the effect of time passing at different rates in regions of different gravitational potential; the lower the gravitational potential, the more slowly time passes...

at places with lower gravitational potentials and rays of light bend in the presence of a gravitational field. Scientists have studied the behaviour of

binary pulsarA binary pulsar is a pulsar with a binary companion, often a white dwarf or neutron star. Binary pulsars are one of the few objects which allow physicists to test general relativity in the case of a strong gravitational field...

s, confirming the predictions of Einstein's theories and non-Euclidean geometry is usually used to describe spacetime.

## Mathematics

In modern mathematics

spacesIn mathematics, a space is a set with some added structure.Mathematical spaces often form a hierarchy, i.e., one space may inherit all the characteristics of a parent space...

are defined as sets with some added structure. They are frequently described as different types of

manifoldIn mathematics , a manifold is a topological space that on a small enough scale resembles the Euclidean space of a specific dimension, called the dimension of the manifold....

s, which are spaces that locally approximate to Euclidean space, and where the properties are defined largely on local connectedness of points that lie on the manifold. There are however, many diverse mathematical objects that are called spaces. For example,

vector spaceA vector space is a mathematical structure formed by a collection of vectors: objects that may be added together and multiplied by numbers, called scalars in this context. Scalars are often taken to be real numbers, but one may also consider vector spaces with scalar multiplication by complex...

s such as

function spaceIn mathematics, a function space is a set of functions of a given kind from a set X to a set Y. It is called a space because in many applications it is a topological space, a vector space, or both.-Examples:...

s may have infinite numbers of independent dimensions and a notion of distance very different to Euclidean space, and

topological spaceTopological spaces are mathematical structures that allow the formal definition of concepts such as convergence, connectedness, and continuity. They appear in virtually every branch of modern mathematics and are a central unifying notion...

s replace the concept of distance with a more abstract idea of nearness.

### Classical mechanics

Space is one of the few fundamental quantities in

physicsPhysics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...

, meaning that it cannot be defined via other quantities because nothing more fundamental is known at the present. On the other hand, it can be related to other fundamental quantities. Thus, similar to other fundamental quantities (like

timeTime is a part of the measuring system used to sequence events, to compare the durations of events and the intervals between them, and to quantify rates of change such as the motions of objects....

and

massMass can be defined as a quantitive measure of the resistance an object has to change in its velocity.In physics, mass commonly refers to any of the following three properties of matter, which have been shown experimentally to be equivalent:...

), space can be explored via

measurementMeasurement is the process or the result of determining the ratio of a physical quantity, such as a length, time, temperature etc., to a unit of measurement, such as the metre, second or degree Celsius...

and experiment.

### Relativity

Before Einstein's work on relativistic physics, time and space were viewed as independent dimensions. Einstein's discoveries showed that due to relativity of motion our space and time can be mathematically combined into one object —

spacetimeIn physics, spacetime is any mathematical model that combines space and time into a single continuum. Spacetime is usually interpreted with space as being three-dimensional and time playing the role of a fourth dimension that is of a different sort from the spatial dimensions...

. It turns out that distances in space or in time separately are not invariant with respect to Lorentz coordinate transformations, but distances in Minkowski space-time along space-time intervals are—which justifies the name.

In addition, time and space dimensions should not be viewed as exactly equivalent in Minkowski space-time. One can freely move in space but not in time. Thus, time and space coordinates are treated differently both in

special relativitySpecial relativity is the physical theory of measurement in an inertial frame of reference proposed in 1905 by Albert Einstein in the paper "On the Electrodynamics of Moving Bodies".It generalizes Galileo's...

(where time is sometimes considered an

imaginaryAn imaginary number is any number whose square is a real number less than zero. When any real number is squared, the result is never negative, but the square of an imaginary number is always negative...

coordinate) and in

general relativityGeneral relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...

(where different signs are assigned to time and space components of

spacetimeIn physics, spacetime is any mathematical model that combines space and time into a single continuum. Spacetime is usually interpreted with space as being three-dimensional and time playing the role of a fourth dimension that is of a different sort from the spatial dimensions...

metricIn the mathematical field of differential geometry, a metric tensor is a type of function defined on a manifold which takes as input a pair of tangent vectors v and w and produces a real number g in a way that generalizes many of the familiar properties of the dot product of vectors in Euclidean...

).

Furthermore, in Einstein's general theory of relativity, it is postulated that space-time is geometrically distorted-

*curved* -near to gravitationally significant masses.

Experiments are ongoing to attempt to directly measure

gravitational waveIn physics, gravitational waves are theoretical ripples in the curvature of spacetime which propagates as a wave, traveling outward from the source. Predicted to exist by Albert Einstein in 1916 on the basis of his theory of general relativity, gravitational waves theoretically transport energy as...

s. This is essentially solutions to the equations of general relativity, which describe moving ripples of spacetime. Indirect evidence for this has been found in the motions of the Hulse-Taylor binary system.

### Cosmology

Relativity theory leads to the

cosmologicalCosmology is the discipline that deals with the nature of the Universe as a whole. Cosmologists seek to understand the origin, evolution, structure, and ultimate fate of the Universe at large, as well as the natural laws that keep it in order...

question of what shape the universe is, and where space came from. It appears that space was created in the

Big BangThe Big Bang theory is the prevailing cosmological model that explains the early development of the Universe. According to the Big Bang theory, the Universe was once in an extremely hot and dense state which expanded rapidly. This rapid expansion caused the young Universe to cool and resulted in...

, 13.7 billion years ago and has been expanding ever since. The overall shape of space is not known, but space is known to be expanding very rapidly due to the

Cosmic InflationIn physical cosmology, cosmic inflation, cosmological inflation or just inflation is the theorized extremely rapid exponential expansion of the early universe by a factor of at least 1078 in volume, driven by a negative-pressure vacuum energy density. The inflationary epoch comprises the first part...

.

## Spatial measurement

The measurement of

*physical space* has long been important. Although earlier societies had developed measuring systems, the

International System of UnitsSi, si, or SI may refer to :- Measurement, mathematics and science :* International System of Units , the modern international standard version of the metric system...

, (SI), is now the most common system of units used in the measuring of space, and is almost universally used.

Currently, the standard space interval, called a standard meter or simply

meterThe metre , symbol m, is the base unit of length in the International System of Units . Originally intended to be one ten-millionth of the distance from the Earth's equator to the North Pole , its definition has been periodically refined to reflect growing knowledge of metrology...

, is defined as the

distance traveled by light in a vacuumThe speed of light in vacuum, usually denoted by c, is a physical constant important in many areas of physics. Its value is 299,792,458 metres per second, a figure that is exact since the length of the metre is defined from this constant and the international standard for time...

during a time interval of exactly 1/299,792,458 of a second. This definition coupled with present definition of the

secondThe second is a unit of measurement of time, and is the International System of Units base unit of time. It may be measured using a clock....

is based on the special theory of relativity in which the

speed of lightThe speed of light in vacuum, usually denoted by c, is a physical constant important in many areas of physics. Its value is 299,792,458 metres per second, a figure that is exact since the length of the metre is defined from this constant and the international standard for time...

plays the role of a fundamental constant of nature.

## Geographical space

GeographyGeography is the science that studies the lands, features, inhabitants, and phenomena of Earth. A literal translation would be "to describe or write about the Earth". The first person to use the word "geography" was Eratosthenes...

is the branch of science concerned with identifying and describing the

EarthEarth is the third planet from the Sun, and the densest and fifth-largest of the eight planets in the Solar System. It is also the largest of the Solar System's four terrestrial planets...

, utilizing spatial awareness to try to understand why things exist in specific locations.

CartographyCartography is the study and practice of making maps. Combining science, aesthetics, and technique, cartography builds on the premise that reality can be modeled in ways that communicate spatial information effectively.The fundamental problems of traditional cartography are to:*Set the map's...

is the mapping of spaces to allow better navigation, for visualization purposes and to act as a locational device.

GeostatisticsGeostatistics is a branch of statistics focusing on spatial or spatiotemporal datasets. Developed originally to predict probability distributions of ore grades for mining operations, it is currently applied in diverse disciplines including petroleum geology, hydrogeology, hydrology, meteorology,...

apply statistical concepts to collected spatial data to create an estimate for unobserved phenomena.

Geographical space is often considered as land, and can have a relation to

ownershipOwnership is the state or fact of exclusive rights and control over property, which may be an object, land/real estate or intellectual property. Ownership involves multiple rights, collectively referred to as title, which may be separated and held by different parties. The concept of ownership has...

usage (in which space is seen as

propertyProperty is any physical or intangible entity that is owned by a person or jointly by a group of people or a legal entity like a corporation...

or territory). While some cultures assert the rights of the individual in terms of ownership, other cultures will identify with a communal approach to land ownership, while still other cultures such as Australian Aboriginals, rather than asserting ownership rights to land, invert the relationship and consider that they are in fact owned by the land.

Spatial planningSpatial planning refers to the methods used by the public sector to influence the distribution of people and activities in spaces of various scales. Discrete professional disciplines which involve spatial planning include land use planning, urban planning, regional planning, transport planning and...

is a method of regulating the use of space at land-level, with decisions made at regional, national and international levels. Space can also impact on human and cultural behavior, being an important factor in

architectureArchitecture is both the process and product of planning, designing and construction. Architectural works, in the material form of buildings, are often perceived as cultural and political symbols and as works of art...

, where it will impact on the design of buildings and structures, and on farming.

Ownership of space is not restricted to land. Ownership of

airspaceAirspace means the portion of the atmosphere controlled by a country above its territory, including its territorial waters or, more generally, any specific three-dimensional portion of the atmosphere....

and of

watersThe terms international waters or trans-boundary waters apply where any of the following types of bodies of water transcend international boundaries: oceans, large marine ecosystems, enclosed or semi-enclosed regional seas and estuaries, rivers, lakes, groundwater systems , and wetlands.Oceans,...

is decided internationally. Other forms of ownership have been recently asserted to other spaces—for example to the

radioRadio is the transmission of signals through free space by modulation of electromagnetic waves with frequencies below those of visible light. Electromagnetic radiation travels by means of oscillating electromagnetic fields that pass through the air and the vacuum of space...

bands of the electromagnetic

spectrumA spectrum is a condition that is not limited to a specific set of values but can vary infinitely within a continuum. The word saw its first scientific use within the field of optics to describe the rainbow of colors in visible light when separated using a prism; it has since been applied by...

or to

cyberspaceCyberspace is the electronic medium of computer networks, in which online communication takes place.The term "cyberspace" was first used by the cyberpunk science fiction author William Gibson, though the concept was described somewhat earlier, for example in the Vernor Vinge short story "True...

.

Public spaceA public space is a social space such as a town square that is open and accessible to all, regardless of gender, race, ethnicity, age or socio-economic level. One of the earliest examples of public spaces are commons. For example, no fees or paid tickets are required for entry, nor are the entrants...

is a term used to define areas of land as collectively owned by the community, and managed in their name by delegated bodies; such spaces are open to all, while

private propertyPrivate property is the right of persons and firms to obtain, own, control, employ, dispose of, and bequeath land, capital, and other forms of property. Private property is distinguishable from public property, which refers to assets owned by a state, community or government rather than by...

is the land culturally owned by an individual or company, for their own use and pleasure.

Abstract spaceAbstract space, in geography, refers to a hypothetical space characterized by equal and consistent properties; a geographic space that is completely homogeneous. All movement and activity would be equally easy or difficult in all directions and all locations within this space...

is a term used in

geographyGeography is the science that studies the lands, features, inhabitants, and phenomena of Earth. A literal translation would be "to describe or write about the Earth". The first person to use the word "geography" was Eratosthenes...

to refer to a hypothetical space characterized by complete homogeneity. When modeling activity or behavior, it is a conceptual tool used to limit extraneous variables such as terrain.

## In psychology

Psychologists first began to study the way space is perceived in the middle of the 19th century. Those now concerned with such studies regard it as a distinct branch of

psychologyPsychology is the study of the mind and behavior. Its immediate goal is to understand individuals and groups by both establishing general principles and researching specific cases. For many, the ultimate goal of psychology is to benefit society...

. Psychologists analyzing the perception of space are concerned with how recognition of an object's physical appearance or its interactions are perceived, see, for example,

visual spaceVisual space is the perceptual space housing the visual world being experienced by an aware observer; it is the subjective counterpart of the space of physical objects before an observer's eyes.-Space of Physical Objects:...

.

Other, more specialized topics studied include

amodal perceptionAmodal perception is the term used to describe the perception of the whole of a physical structure when only parts of it affect the sensory receptors...

and

object permanenceObject permanence is the understanding that objects continue to exist even when they cannot be seen, heard, or touched. It is acquired by human infants between 8 and 12 months of age via the process of logical induction to help them develop secondary schemes in their sensori-motor coordination...

. The

perceptionPerception is the process of attaining awareness or understanding of the environment by organizing and interpreting sensory information. All perception involves signals in the nervous system, which in turn result from physical stimulation of the sense organs...

of surroundings is important due to its necessary relevance to survival, especially with regards to

huntingHunting is the practice of pursuing any living thing, usually wildlife, for food, recreation, or trade. In present-day use, the term refers to lawful hunting, as distinguished from poaching, which is the killing, trapping or capture of the hunted species contrary to applicable law...

and

self preservationSelf-preservation is behavior that ensures the survival of an organism. It is universal among living organisms. In some vertebrates, pain and fear are parts of this mechanism. Pain causes discomfort so that the organism is inclined to stop the pain...

as well as simply one's idea of

personal spacePersonal space is the region surrounding a person which they regard as psychologically theirs. Most people value their personal space and feel discomfort, anger, or anxiety when their personal space is encroached. Permitting a person to enter personal space and entering somebody else's personal...

.

Several space-related

phobiaA phobia is a type of anxiety disorder, usually defined as a persistent fear of an object or situation in which the sufferer commits to great lengths in avoiding, typically disproportional to the actual danger posed, often being recognized as irrational...

s have been identified, including

agoraphobiaAgoraphobia is an anxiety disorder defined as a morbid fear of having a panic attack or panic-like symptoms in a situation from which it is perceived to be difficult to escape. These situations can include, but are not limited to, wide-open spaces, crowds, or uncontrolled social conditions...

(the fear of open spaces), astrophobia (the fear of celestial space) and

claustrophobiaClaustrophobia is the fear of having no escape and being closed in small spaces or rooms...

(the fear of enclosed spaces).

## See also

- Absolute space and time
- Aether theories
Aether theories in early modern physics proposed the existence of a medium, the aether , a space-filling substance or field, thought to be necessary as a transmission medium for the propagation of electromagnetic waves...

- Cosmology
Cosmology is the discipline that deals with the nature of the Universe as a whole. Cosmologists seek to understand the origin, evolution, structure, and ultimate fate of the Universe at large, as well as the natural laws that keep it in order...

- General relativity
General relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...

- Personal space
Personal space is the region surrounding a person which they regard as psychologically theirs. Most people value their personal space and feel discomfort, anger, or anxiety when their personal space is encroached. Permitting a person to enter personal space and entering somebody else's personal...

- Shape of the universe
The shape of the universe is a matter of debate in physical cosmology over the local and global geometry of the universe which considers both curvature and topology, though, strictly speaking, it goes beyond both...

- Space exploration
Space exploration is the use of space technology to explore outer space. Physical exploration of space is conducted both by human spaceflights and by robotic spacecraft....

- Spatial-temporal reasoning
Spatial–temporal reasoning is used in both the fields of psychology and computer science.-Spatial–temporal reasoning in psychology:Spatial-temporal reasoning is the ability to visualize spatial patterns and mentally manipulate them over a time-ordered sequence of spatial transformations.This...

- Spatial analysis
Spatial analysis or spatial statistics includes any of the formal techniques which study entities using their topological, geometric, or geographic properties...

- Visual space
Visual space is the perceptual space housing the visual world being experienced by an aware observer; it is the subjective counterpart of the space of physical objects before an observer's eyes.-Space of Physical Objects:...