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Space


 
 

Space is the boundless extent within which matterMatter

In physics, matter is commonly defined as the substance of which physical objects are composed, not counting the contributio...
 is physically extended and objectsPhysical body

In physics, a physical body is a collection of masses, taken to be one....
 and eventEvent Overview

The word event can have several meanings:...
s have positions relative to one another. Physical space is often conceived in three linearLinear

The word linear comes from the Latin word linearis, which means created by lines....
 dimensionDimension

In common usage, a dimension is a parameter or measurement required to define the characteristics of an object—i.e....
s, although modern physicistsPhysics

Physics , the most fundamental physical science, is concerned with the underlying principles of the natural world....
 usually consider it, with timeTime

Two distinct views exist on the meaning of time....
, to be part of the boundless four-dimensional continuum known as spacetimeFacts About Spacetime

In physics, spacetime is a mathematical model that combines three-dimensional space and one-dimensional time into a single c...
. In mathematicsMathematics Summary

Mathematics is the discipline that deals with concepts such as quantity, structure, space and change....
 spaces with different numbers of dimensions and with different underlying structures can be examined. The concept of space is considered to be of fundamental importance to an understanding of the universeUniverse

The term universe has a variety of meanings, based on the context in which it is used....
 although disagreement continues between philosophersPhilosophy

Philosophy is a field of study that includes diverse subfields such as aesthetics, epistemology, ethics, logic, and metaphys...
 over whether it is itself an entity, a relationship between entities, or part of a conceptual frameworkConceptual framework

A conceptual framework is used in research to outline possible courses of action or to present a preferred approach to a sys...
.

Many of the philosophical questions arose in the 17th century, during the early development of classical mechanicsClassical mechanics Overview

Classical mechanics is used to describe the motion of macroscopic objects, from projectiles to parts of machinery, as well a...
. In Isaac Newton'sIsaac Newton

[[[Old Style and New Style dates|OS]]: [[25 December]] [[1642]] [[20 March]] [[1727]]] was an [[England|English]] [[physics|physicist,]]...
 view, space was absolute - in the sense that it existed permanently and independently of whether there were any matter in the space. Other natural philosophersNatural philosophy

Natural philosophy or the philosophy of nature, known in Latin as philosophia naturalis, is a term applied to the ...
, notably Gottfried LeibnizGottfried Leibniz

Gottfried Wilhelm Leibniz was a German polymath who wrote mostly in French and Latin....
, thought instead that space was a collection of relations between objects, given by their distanceDistance

Distance is a numerical description of how far apart things lie....
 and direction from one another. In the 18th century, Immanuel KantImmanuel Kant

Immanuel Kant , was a German philosopher from Knigsberg in East Prussia ....
 described space and time as elements of a systematic framework which humans use to structure their experience.

In the 19th and 20th centuries mathematicians began to examine non-Euclidean geometriesNon-Euclidean geometry

----The term non-Euclidean geometry describes hyperbolic, elliptic and absolute geometry, which are contrasted with Euclid...
, in which space can be said to be curved, rather than flat. According to Albert Einstein'sAlbert Einstein

Albert Einstein was a German-born theoretical physicist....
 theory of general relativity, space around gravitational fieldGravitational field

A gravitational field is a model used within physics to explain how gravity exists in the universe....
s deviates from Euclidean space. Experimental tests of general relativityTests of general relativity

Tests of Einstein's general theory of relativity did not provide an experimental foundation for the theory until well after ...
 have confirmed that non-Euclidean space provides a better model for explaining the existing laws of mechanicsMechanics

Mechanics is the branch of physics concerned with the behaviour of physical bodies when subjected to forces or displacement...
 and opticsOptics

Optics is a branch of physics that describes the behavior and properties of light and the interaction of light with matter....
.

=Philosophy of space=

Leibniz and Newton

In the seventeenth century, the philosophy of space and timePhilosophy of space and time

Philosophy of space and time is a branch of philosophy which deals with issues surrounding the ontology, epistemology and ch...
 emerged as a central issue in epistemologyEpistemology

Epistemology or theory of knowledge is the branch of philosophy that studies the nature and scope of knowledge....
 and metaphysicsMetaphysics

Metaphysics is the branch of philosophy concerned with explaining the nature of the world....
. At its heart, Gottfried Leibniz, the German philosopher-mathematician, and Isaac Newton, the English physicist-mathematician, set out two opposing theories of what space is. Rather than being an entity which 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 which could have objects in them and thus spatial relations with other places. For Leibniz, then, space was an idealised abstractionAbstraction

Abstraction is the process of reducing the information content of a concept, typically in order to retain only information w...
 from the relations between individual entities or their possible locations and therefore could not be continuous but must be discreteDiscrete

The word discrete comes from the Latin word discretus which means separate....
.
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 would imply that there would be 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 indiscerniblesIdentity of indiscernibles

The identity of indiscernibles is an ontological principle that states that if there is no way of telling two entities apart...
, there would be no real difference between them. According to the principle of sufficient reasonPrinciple of sufficient reason

The principle of sufficient reason states that anything that happens does so for a definite reason....
, any theory of space which 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

Observation is an activity of a sapient or sentient living being, which senses and assimiliates the knowledge of a phenomeno...
 and experimentExperiment

In the scientific method, an experiment , is a set of actions and observations, performed in the context of solving a partic...
ation. For a relationistRelationism

Relationism can refer to a framework of social thought governing political, economic and social behaviour; or to a particula...
 there can be no real difference between inertial motionInertial frame of reference

An inertial reference frame is a coordinate system in which Newton's first and second laws of motion are valid —ie....
, in which the object travels with constant velocityVelocity

The velocity of an object is simply its speed in a particular direction....
, and non-inertial motionNon-inertial reference frame

A non inertial frame of reference is one in which a body violates Newton's Laws of Motion, mainly the First Law....
, 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 forceForce

In physics, force is that which changes or tends to change the state of rest or motion of a body....
s, it must be absolute. He used the example of water in a spinning bucketBucket argument

Isaac Newton's rotating bucket argument attempts to show that true rotational motion cannot be defined as the relative rotat...
 to demonstrate his argument. WaterWater

Water is a tasteless, odorless substance that is essential to all known forms of life and is known as the universal solve...
 in a bucketFacts About Bucket

A bucket, also called a pail, is a watertight, vertical cylinder or truncated cone, with an open top and a flat bottom...
 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 Kant developed a theory of knowledgeKnowledge

Knowledge is what is known. Like the related concepts truth, belief and wisdom....
 in which knowledge about space can be both a prioriA priori and a posteriori (philosophy)

The terms "a priori" and "a posteriori" are used in philosophy to distinguish between two different types of p...
and synthetic. In Kant's view, knowledge about space is a priori, in that it is held independently of experience. His reasoning was that it is impossible to imagine the axiomAxiom

An axiom is a sentence or proposition that is accepted as the first and last line of a one-line proof and is considered ...
s of geometry not being true. For example, intuitionIntuition

Intuition has many related meanings, including:...
 seems to give us complete certainty that there is one and only one straight lineLine (mathematics)

A line, or straight line, can be described as an infinitely thin, infinitely long, perfectly straight curve....
 through two pointsPoint (geometry) Overview

A spatial point is an entity with a location in space but no extent....
. Since the theoremTheorem Overview

A theorem is a proposition that has been or is to be proved on the basis of explicit assumptions....
s of Euclidean geometryEuclidean geometry

Euclidean geometry is a mathematical system attributed to the Greek mathematician Euclid of Alexandria....
 are logically derived from the axioms, space can therefore be completely understood without one having to observe it. According to Kant, knowledge about space is also synthetic, in that statements about space are not simply true by virtue of the meaning of the words in the statement. In other words, since, in his view, the theorems of geometry describe the actual structure of the world, one can make factual statements about space. For instance, if one inspects a triangleTriangle

A triangle is one of the basic shapes of geometry: a polygon with three vertices and three sides which are straight line seg...
, its angleAngle

An angle is the figure formed by two rays sharing a common endpoint, called the vertex of the angle....
s always seem to sum to 180°. Whereas scientific lawScientific law

A scientific law, is a law-like statement that generalizes across a set of conditions....
s have to be justified by experience and could be falsifiedFalsification

Falsification may mean:*The act of disproving a proposition, hypothesis, or theory....
 at any moment, it is inconceivable that geometrical laws could be violated. Alongside arithmeticArithmetic

Arithmetic or arithmetics is the oldest and simplest branch of mathematics, used by almost everyone, for tasks rangin...
, geometry provided Kant with one of his chief examples of synthetic a priori knowledge. 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 a systematic framework for organizing our experiences.

Non-Euclidean geometry

Euclid's Elements contained five postulates which form the basis for Euclidean geometry. One of these, the parallel postulateParallel postulate

In geometry, the parallel postulate, also called Euclid's fifth postulate since it is the fifth postulate in Euclid's ...
 has been the subject of debate among mathematicians for many centuries. It states that on any planePlane (mathematics)

In mathematics, a plane is a fundamental two-dimensional object....
 on which there is a straight line L1 and a point P not on L1, there is only one straight line L2 on the plane which passes through the point P and is parallel to the straight line L1. 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 which could be derived from the other axioms. Around 1830 though, the HungarianHungary

Hungary , officially the Republic of Hungary , is a landlocked country in Central Europe, bordered by Austria, Slovaki...
 János BolyaiJános Bolyai

Jnos Bolyai was a Hungarian mathematician, known for his work in non-Euclidean geometry....
 and the RussiaRussia

Russia , also the Russian Federation , is a country that stretches over a vast expanse of Eurasia....
n Nikolai Ivanovich LobachevskyNikolai Ivanovich Lobachevsky

Nikolai Ivanovich Lobachevsky was a Russian mathematician. ...
 separately published treatises on a type of geometry which does not include the parallel postulate, called hyperbolic geometryHyperbolic geometry

Hyperbolic geometry is a non-Euclidean geometry, meaning that the parallel postulate of Euclidean geometry is rejected....
. In this geometry, there are an infinite number of parallel lines which pass through the point P. Consequently the sum of angles in a triangle is less than 180o and the ratio of a circleCircle

In Euclidean geometry, a circle is the set of all points in a plane at a fixed distance, called the radius, from a fixed poi...
's circumferenceCircumference

The circumference is the distance around a closed curve....
 to its diameterDiameter

n geometry, a diameter of a circle is any straight line segment that passes through the center and whose endpoints are on t...
 is greater than piPi

The mathematical constant p is an irrational real number, approximately equal to 3.14159, which is the ratio of a circle's c...
. In the 1850s, Bernhard RiemannBernhard Riemann

Georg Friedrich Bernhard Riemann was a German mathematician who made important contributions to analysis and differential ...
 developed an equivalent theory of elliptical geometry, in which there are no parallel lines which pass through P. In this geometry, triangles have more than 180o and circles have a ratio of circumference to diameter which 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 < 180o > p < 0
Euclidean 1 180o p 0
Elliptical 0 > 180o < p > 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 GaussCarl Friedrich Gauss Summary

Carl Friedrich Gauss was a German mathematician and scientist of profound genius who contributed significantly to many fie...
, the 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 triangulatingTriangulation

In trigonometry and elementary geometry, triangulation is the process of finding coordinates and distance to a point by calc...
 mountain tops in Germany.

Henri PoincaréHenri Poincaré

Jules Henri Poincar , generally known as Henri Poincar, was one of France's greatest mathematicians and theoretical ...
, a French mathematician and physicist of the late 19th century introduced an important insight which attempted to demonstrate the futility of any attempt to discover by experiment which geometry applies to space. He considered the predicament which would face scientists if they were confined to the surface of an imaginary large sphere with particular properties, known as a sphere-worldSphere-world

The idea of a sphere-world was constructed by Henri Poincar while pursuing his argument for conventionalism, offered a thou...
. In this world, the temperatureTemperature

In thermodynamics, temperature is a measure of the tendency of an object or system to spontaneously give up energy....
 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, it was a matter of conventionFacts About Conventionalism

Conventionalism is the philosophical attitude that fundamental principles of a certain kind are grounded on agreements in s...
 which geometry was used to describe space. Since Euclidean geometry 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

Albert Einstein was a German-born theoretical physicist....
 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 lightSpeed of light

The speed of light in a vacuum is an important physical constant denoted by the letter c for constant or the Latin w...
 in a vacuumFacts About Vacuum

A vacuum is a volume of space that is substansively empty of matter, so that gaseous pressure is much less than standard atm...
 is the same for all observers - which has the resultRelativity of simultaneity

The relativity of simultaneity is the dependence of the notion of simultaneity on the observer....
 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 slowlyTime dilation

Time dilation is the phenomenon whereby an observer finds that the rate at which time passes for an object moving relative t...
 than one which is stationary with respect to them; and objects are measured to be shortenedLength contraction

Length contraction, according to Albert Einstein's special theory of relativity, is the decrease in length observed in objec...
 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 fieldForce field Overview

Force field may refer to:* Force field...
 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

Gravitational time dilation is a consequence of Albert Einstein's theories of relativity and related theories under which a ...
 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 pulsarBinary pulsar

A binary pulsar is a pulsar with a binary companion, often another pulsar, white dwarf or neutron star....
s, confirming the predictions of Einstein's theories and Non-Euclidean geometry is usually used to describe spacetime.

=Mathematics=
In modern mathematics, spaces are frequently described as different types of manifoldManifold

A manifold is an abstract mathematical space in which every point has a neighborhood which resembles Euclidean space, but in...
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.

=Physics=

Classical mechanics

Space is one of the few fundamentalFundamental

Fundamental:* Fundamental frequency, a concept in music or phonetics, often referred to as simply a fundamental....
 quantities in physicsPhysics

Physics , the most fundamental physical science, is concerned with the underlying principles of the natural world....
, 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

Two distinct views exist on the meaning of time....
 and massMass

Mass is a property of a physical object that quantifies the amount of matter and energy it is equivalent to....
), space can be explored via measurementMeasurement

Measurement is the estimation or determination of extent, dimension or capacity, usually in relation to some standard or uni...
 and experiment.

Astronomy

AstronomyAstronomy

Astronomy is the science of celestial objects and phenomena that originate outside the Earth's atmosphere ....
 is the science involved with the observation, explanation and measuring of objects in outer spaceOuter space

Outer space, also simply called space, refers to the relatively empty regions of the universe outside the atmospheres of...
.

Relativity

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

In physics, spacetime is a mathematical model that combines three-dimensional space and one-dimensional time into a single c...
. It turns out that distances in spaceSpacetime

In physics, spacetime is a mathematical model that combines three-dimensional space and one-dimensional time into a single c...
 or in timeSpacetime

In physics, spacetime is a mathematical model that combines three-dimensional space and one-dimensional time into a single c...
 separately are not invariant with respect to Lorentz coordinate transformations, but distances in Minkowski space-time along space-time intervalsSpacetime

In physics, spacetime is a mathematical model that combines three-dimensional space and one-dimensional time into a single c...
 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 Summary

The special theory of relativity was proposed in 1905 by Albert Einstein in his article "On the Electrodynamics of Moving Bo...
 (where time is sometimes considered an imaginaryImaginary number Summary

In mathematics, an imaginary number is a complex number whose square is a negative real number or zero....
 coordinate) and in general relativityGeneral relativity

General relativity is the geometrical theory of gravitation published by Albert Einstein in 1915....
 (where different signs are assigned to time and space components of spacetimeSpacetime

In physics, spacetime is a mathematical model that combines three-dimensional space and one-dimensional time into a single c...
 metricMetric tensor

In mathematics, the metric tensor is a symmetric tensor field of rank 2 that is used to measure distance in a space....
).

Furthermore, from Einstein's general theory of relativity, it has been shown that space-time is geometrically distorted- curved -near to gravitationally significant masses.

Experiments are ongoing to attempt to directly measure gravitational waveGravitational wave

In physics, a gravitational wave is a fluctuation in the curvature of spacetime which propagates as a wave, traveling outwar...
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.