Space
Space is the boundless threedimensional extent in which objects and events have relative position and direction.^{[1]} Physical space is often conceived in three linear dimensions, although modern physicists usually consider it, with time, to be part of a boundless fourdimensional continuum known as spacetime. The concept of space is considered to be of fundamental importance to an understanding of the physical universe. However, disagreement continues between philosophers over whether it is itself an entity, a relationship between entities, or part of a conceptual framework.
Debates concerning the nature, essence and the mode of existence of space date back to antiquity; namely, to treatises like the Timaeus of Plato, or Socrates in his reflections on what the Greeks called khôra (i.e. "space"), or in the Physics of Aristotle (Book IV, Delta) in the definition of topos (i.e. place), or in the later "geometrical conception of place" as "space qua extension" in the Discourse on Place (Qawl fi alMakan) of the 11thcentury Arab polymath Alhazen.^{[2]} 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 mechanics. In Isaac Newton's view, space was absolute—in the sense that it existed permanently and independently of whether there was any matter in the space.^{[3]} Other natural philosophers, notably Gottfried Leibniz, thought instead that space was in fact a collection of relations between objects, given by their distance and direction from one another. In the 18th century, the philosopher and theologian George Berkeley attempted to refute the "visibility of spatial depth" in his Essay Towards a New Theory of Vision. Later, the metaphysician Immanuel Kant said that the concepts of space and time are not empirical ones derived from experiences of the outside world—they are elements of an already given systematic framework that humans possess and use to structure all experiences. Kant referred to the experience of "space" in his Critique of Pure Reason as being a subjective "pure a priori form of intuition".
In the 19th and 20th centuries mathematicians began to examine geometries that are nonEuclidean, in which space is conceived as curved, rather than flat. According to Albert Einstein's theory of general relativity, space around gravitational fields deviates from Euclidean space.^{[4]} Experimental tests of general relativity have confirmed that nonEuclidean geometries provide a better model for the shape of space.
Contents
Philosophy of space
Leibniz and Newton
In the seventeenth century, the philosophy of space and time emerged as a central issue in epistemology and metaphysics. At its heart, Gottfried Leibniz, the German philosophermathematician, and Isaac Newton, the English physicistmathematician, 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".^{[5]} Unoccupied regions are those that could have objects in them, and thus spatial relations with other places. For Leibniz, then, space was an idealised abstraction from the relations between individual entities or their possible locations and therefore could not be continuous but must be discrete.^{[6]} 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.^{[7]} 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 indiscernibles, there would be no real difference between them. According to the principle of sufficient reason, any theory of space that implied that there could be these two possible universes must therefore be wrong.^{[8]}
Newton took space to be more than relations between material objects and based his position on observation and experimentation. For a relationist there can be no real difference between inertial motion, in which the object travels with constant velocity, and noninertial motion, in which the velocity changes with time, since all spatial measurements are relative to other objects and their motions. But Newton argued that since noninertial motion generates forces, it must be absolute.^{[9]} He used the example of water in a spinning bucket to demonstrate his argument. Water in a bucket 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.^{[10]} Instead, Newton argued, it must be a result of noninertial motion relative to space itself. For several centuries the bucket argument was considered decisive in showing that space must exist independently of matter.
Kant
In the eighteenth century the German philosopher Immanuel Kant developed a theory of knowledge in which knowledge about space can be both a priori and synthetic.^{[11]} 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 imposed by us as part of a framework for organizing experience.^{[12]}
NonEuclidean geometry
Euclid's Elements contained five postulates that form the basis for Euclidean geometry. One of these, the parallel postulate, has been the subject of debate among mathematicians for many centuries. It states that on any plane on which there is a straight line L_{1} and a point P not on L_{1}, there is exactly 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.^{[13]} Around 1830 though, the Hungarian János Bolyai and the Russian Nikolai Ivanovich Lobachevsky separately published treatises on a type of geometry that does not include the parallel postulate, called hyperbolic geometry. 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° and the ratio of a circle's circumference to its diameter is greater than pi. In the 1850s, Bernhard Riemann developed an equivalent theory of elliptical geometry, in which no parallel lines pass through P. In this geometry, triangles have more than 180° and circles have a ratio of circumferencetodiameter 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°  > π  < 0 
Euclidean  1  180°  π  0 
Elliptical  0  > 180°  < π  > 0 
Gauss and Poincaré
Although there was a prevailing Kantian consensus at the time, once nonEuclidean geometries had been formalised, some began to wonder whether or not physical space is curved. Carl Friedrich Gauss, 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 that he actually carried out a test, on a small scale, by triangulating mountain tops in Germany.^{[14]}
Henri Poincaré, 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.^{[15]} 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 sphereworld. In this world, the temperature 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.^{[16]} 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 convention.^{[17]} Since Euclidean geometry is simpler than nonEuclidean geometry, he assumed the former would always be used to describe the 'true' geometry of the world.^{[18]}
Einstein
In 1905, Albert Einstein published his special theory of relativity, which led to the concept that space and time can be viewed as a single construct known as spacetime. In this theory, the speed of light in a vacuum is the same for all observers—which has the result 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 slowly than one that is stationary with respect to them; and objects are measured to be shortened in the direction that they are moving with respect to the observer.
Subsequently, 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 field acting in spacetime, Einstein suggested that it modifies the geometric structure of spacetime itself.^{[19]} According to the general theory, time goes more slowly 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 pulsars, confirming the predictions of Einstein's theories, and nonEuclidean geometry is usually used to describe spacetime.
Mathematics
In modern mathematics spaces are defined as sets with some added structure. They are frequently described as different types of manifolds, 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 spaces such as function spaces may have infinite numbers of independent dimensions and a notion of distance very different from Euclidean space, and topological spaces replace the concept of distance with a more abstract idea of nearness.
Physics
Part of a series of articles about 
Classical mechanics 

Core topics

Space is one of the few fundamental quantities in physics, 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 time and mass), space can be explored via measurement and experiment.
Today, our threedimensional space is viewed as embedded in a fourdimensional spacetime, called Minkowski space (see special relativity). The idea behind spacetime is that time is hyperbolicorthogonal to each of the three spatial dimensions.
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–spacetime. It turns out that distances in space or in time separately are not invariant with respect to Lorentz coordinate transformations, but distances in Minkowski spacetime along spacetime intervals are—which justifies the name.
In addition, time and space dimensions should not be viewed as exactly equivalent in Minkowski spacetime. One can freely move in space but not in time. Thus, time and space coordinates are treated differently both in special relativity (where time is sometimes considered an imaginary coordinate) and in general relativity (where different signs are assigned to time and space components of spacetime metric).
Furthermore, in Einstein's general theory of relativity, it is postulated that spacetime is geometrically distorted curved near to gravitationally significant masses.^{[20]}
One consequence of this postulate, which follows from the equations of general relativity, is the prediction of moving ripples of spacetime, called gravitational waves. While indirect evidence for these waves has been found (in the motions of the Hulse–Taylor binary system, for example) experiments attempting to directly measure these waves are ongoing at the LIGO and Virgo collaborations. LIGO scientists reported the first such direct observation of gravitational waves on 14 September 2015.^{[21]}^{[22]}
Cosmology
Relativity theory leads to the cosmological question of what shape the universe is, and where space came from. It appears that space was created in the Big Bang, 13.8 billion years ago^{[23]} 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 inflation.
Spatial measurement
The measurement of physical space has long been important. Although earlier societies had developed measuring systems, the International System of Units, (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 meter, is defined as the distance traveled by light in a vacuum during a time interval of exactly 1/299,792,458 of a second. This definition coupled with present definition of the second is based on the special theory of relativity in which the speed of light plays the role of a fundamental constant of nature.
Geographical space
Geography is the branch of science concerned with identifying and describing places on Earth, utilizing spatial awareness to try to understand why things exist in specific locations. Cartography is the mapping of spaces to allow better navigation, for visualization purposes and to act as a locational device. Geostatistics apply statistical concepts to collected spatial data of Earth to create an estimate for unobserved phenomena.
Geographical space is often considered as land, and can have a relation to ownership usage (in which space is seen as property 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 planning is a method of regulating the use of space at landlevel, with decisions made at regional, national and international levels. Space can also impact on human and cultural behavior, being an important factor in architecture, where it will impact on the design of buildings and structures, and on farming.
Ownership of space is not restricted to land. Ownership of airspace and of waters is decided internationally. Other forms of ownership have been recently asserted to other spaces—for example to the radio bands of the electromagnetic spectrum or to cyberspace.
Public space 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 property is the land culturally owned by an individual or company, for their own use and pleasure.
Abstract space is a term used in geography 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 psychology. 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 space.
Other, more specialized topics studied include amodal perception and object permanence. The perception of surroundings is important due to its necessary relevance to survival, especially with regards to hunting and self preservation as well as simply one's idea of personal space.
Several spacerelated phobias have been identified, including agoraphobia (the fear of open spaces), astrophobia (the fear of celestial space) and claustrophobia (the fear of enclosed spaces).
The understanding of threedimensional space in humans is thought to be learned during infancy using unconscious inference, and is closely related to handeye coordination. The visual ability to perceive the world in three dimensions is called depth perception.
See also
References
 ^ "Space – Physics and Metaphysics". Encyclopædia Britannica.
 ^ Refer to Plato's Timaeus in the Loeb Classical Library, Harvard University, and to his reflections on khora. See also Aristotle's Physics, Book IV, Chapter 5, on the definition of topos. Concerning Ibn alHaytham's 11th century conception of "geometrical place" as "spatial extension", which is akin to Descartes' and Leibniz's 17th century notions of extensio and analysis situs, and his own mathematical refutation of Aristotle's definition of topos in natural philosophy, refer to: Nader ElBizri, "In Defence of the Sovereignty of Philosophy: alBaghdadi's Critique of Ibn alHaytham's Geometrisation of Place", Arabic Sciences and Philosophy (Cambridge University Press), Vol. 17 (2007), pp. 57–80.
 ^ French, A. J.; Ebison, M. G. (1986). Introduction to Classical Mechanics. Dordrecht: Springer, p. 1.
 ^ Carnap, R. (1995). An Introduction to the Philosophy of Science. New York: Dove. (Original edition: Philosophical Foundations of Physics. New York: Basic books, 1966).
 ^ Leibniz, Fifth letter to Samuel Clarke. By H. G. Alexander (1956). The LeibnizClarke Correspondence. Manchester: Manchester University Press, pp. 5596.
 ^ Vailati, E. (1997). Leibniz & Clarke: A Study of Their Correspondence. New York: Oxford University Press, p. 115.
 ^ Sklar, L. (1992). Philosophy of Physics. Boulder: Westview Press, p. 20.
 ^ Sklar, L. Philosophy of Physics. p. 21.
 ^ Sklar, L. Philosophy of Physics. p. 22.
 ^ "Newton's bucket". stand.ac.uk.
 ^ Carnap, R. An Introduction to the Philosophy of Science. pp. 177178.
 ^ Lucas, John Randolph. Space, Time and Causality. p. 149. ISBN 0198750579.
 ^ Carnap, R. An Introduction to the Philosophy of Science. p. 126.
 ^ Carnap, R. An Introduction to the Philosophy of Science. pp. 134136.
 ^ Jammer, Max (1954). Concepts of Space. The History of Theories of Space in Physics. Cambridge: Harvard University Press, p. 165.
 ^ A medium with a variable index of refraction could also be used to bend the path of light and again deceive the scientists if they attempt to use light to map out their geometry.
 ^ Carnap, R. An Introduction to the Philosophy of Science. p. 148.
 ^ Sklar, L. Philosophy of Physics. p. 57.
 ^ Sklar, L. Philosophy of Physics. p. 43.
 ^ Wheeler, John A. A Journey Into Gravity and Spacetime. Chapters 8 and 9, Scientific American, ISBN 0716760347
 ^ Castelvecchi, Davide; Witze, Alexandra (11 February 2016). "Einstein's gravitational waves found at last". Nature News. Retrieved 12 January 2018.
 ^ Abbott, Benjamin P.; et al. (LIGO Scientific Collaboration and Virgo Collaboration) (2016). "Observation of Gravitational Waves from a Binary Black Hole Merger". Phys. Rev. Lett. 116 (6): 061102. arXiv:1602.03837 . Bibcode:2016PhRvL.116f1102A. doi:10.1103/PhysRevLett.116.061102. PMID 26918975. Lay summary (PDF).
 ^ "Cosmic Detectives". The European Space Agency (ESA). 20130402. Retrieved 20130426.
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