**Space** is a three-dimensional continuum containing positions and directions.^{ [1] } In classical physics, physical space is often conceived in three linear dimensions. Modern physicists usually consider it, with time, to be part of a boundless four-dimensional continuum known as * spacetime *.^{ [2] } 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.

- Philosophy of space
- Galileo
- René Descartes
- Leibniz and Newton
- Kant
- Non-Euclidean geometry
- Gauss and Poincaré
- Einstein
- Mathematics
- Physics
- Relativity
- Cosmology
- Spatial measurement
- Geographical space
- In psychology
- In the social sciences
- See also
- References
- External links

In the 19th and 20th centuries mathematicians began to examine geometries that are non-Euclidean, in which space is conceived as * curved *, rather than * flat *, as in the Euclidean space. According to Albert Einstein's theory of general relativity, space around gravitational fields deviates from Euclidean space.^{ [3] } Experimental tests of general relativity have confirmed that non-Euclidean geometries provide a better model for the shape of space.

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 al-Makan*) of the 11th-century Arab polymath Alhazen.^{ [4] } 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.^{ [5] } 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".

Galilean and Cartesian theories about space, matter, and motion are at the foundation of the Scientific Revolution, which is understood to have culminated with the publication of Newton's * Principia Mathematica * in 1687.^{ [6] } Newton's theories about space and time helped him explain the movement of objects. While his theory of space is considered the most influential in physics, it emerged from his predecessors' ideas about the same.^{ [7] }

As one of the pioneers of modern science, Galileo revised the established Aristotelian and Ptolemaic ideas about a geocentric cosmos. He backed the Copernican theory that the universe was heliocentric, with a stationary Sun at the center and the planets—including the Earth—revolving around the Sun. If the Earth moved, the Aristotelian belief that its natural tendency was to remain at rest was in question. Galileo wanted to prove instead that the Sun moved around its axis, that motion was as natural to an object as the state of rest. In other words, for Galileo, celestial bodies, including the Earth, were naturally inclined to move in circles. This view displaced another Aristotelian idea—that all objects gravitated towards their designated natural place-of-belonging.^{ [8] }

Descartes set out to replace the Aristotelian worldview with a theory about space and motion as determined by natural laws. In other words, he sought a metaphysical foundation or a mechanical explanation for his theories about matter and motion. Cartesian space was Euclidean in structure—infinite, uniform and flat.^{ [9] } It was defined as that which contained matter; conversely, matter by definition had a spatial extension so that there was no such thing as empty space.^{ [6] }

The Cartesian notion of space is closely linked to his theories about the nature of the body, mind and matter. He is famously known for his "cogito ergo sum" (I think therefore I am), or the idea that we can only be certain of the fact that we can doubt, and therefore think and therefore exist. His theories belong to the rationalist tradition, which attributes knowledge about the world to our ability to think rather than to our experiences, as the empiricists believe.^{ [10] } He posited a clear distinction between the body and mind, which is referred to as the Cartesian dualism.

Following Galileo and Descartes, during the seventeenth century the philosophy of space and time revolved around the ideas of Gottfried Leibniz, a German philosopher–mathematician, and Isaac Newton, who 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".^{ [11] } 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.^{ [12] } 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.^{ [13] } 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.^{ [14] }

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 non-inertial 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 non-inertial motion generates forces, it must be absolute.^{ [15] } 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.^{ [16] } Instead, Newton argued, it must be a result of non-inertial motion relative to space itself. For several centuries the bucket argument was considered decisive in showing that space must exist independently of matter.

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 *.^{ [17] } 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.^{ [18] }

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

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 |

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 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.^{ [20] }

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.^{ [21] } 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-world. 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.^{ [22] } 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.^{ [23] } 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.^{ [24] }

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 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.^{ [25] } 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 non-Euclidean geometry is usually used to describe spacetime.

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.

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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 three-dimensional space is viewed as embedded in a four-dimensional spacetime, called Minkowski space (see special relativity). The idea behind spacetime is that time is hyperbolic-orthogonal to each of the three spatial dimensions.

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Before Albert 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 space along spacetime intervals are—which justifies the name.

In addition, time and space dimensions should not be viewed as exactly equivalent in Minkowski space. 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.^{ [26] }

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.^{ [27] }^{ [28] }

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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^{ [29] } 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.

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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 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.

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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 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 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.

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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 space-related 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 three-dimensional space in humans is thought to be learned during infancy using unconscious inference, and is closely related to hand-eye coordination. The visual ability to perceive the world in three dimensions is called depth perception.

Space has been studied in the social sciences from the perspectives of Marxism, feminism, postmodernism, postcolonialism, urban theory and critical geography. These theories account for the effect of the history of colonialism, transatlantic slavery and globalization on our understanding and experience of space and place. The topic has garnered attention since the 1980s, after the publication of Henri Lefebvre's *The Production of Space .* In this book, Lefebvre applies Marxist ideas about the production of commodities and accumulation of capital to discuss space as a social product. His focus is on the multiple and overlapping social processes that produce space.^{ [30] }

In his book *The Condition of Postmodernity,* David Harvey describes what he terms the "time-space compression." This is the effect of technological advances and capitalism on our perception of time, space and distance.^{ [31] } Changes in the modes of production and consumption of capital affect and are affected by developments in transportation and technology. These advances create relationships across time and space, new markets and groups of wealthy elites in urban centers, all of which annihilate distances and affect our perception of linearity and distance.^{ [32] }

In his book *Thirdspace,* Edward Soja describes space and spatiality as an integral and neglected aspect of what he calls the "trialectics of being," the three modes that determine how we inhabit, experience and understand the world. He argues that critical theories in the Humanities and Social Sciences study the historical and social dimensions of our lived experience, neglecting the spatial dimension.^{ [33] } He builds on Henri Lefebvre's work to address the dualistic way in which humans understand space—as either material/physical or as represented/imagined. Lefebvre's "lived space"^{ [34] } and Soja's "thirdspace" are terms that account for the complex ways in which humans understand and navigate place, which "firstspace" and "Secondspace" (Soja's terms for material and imagined spaces respectively) do not fully encompass.

Postcolonial theorist Homi Bhabha's concept of Third Space is different from Soja's Thirdspace, even though both terms offer a way to think outside the terms of a binary logic. Bhabha's Third Space is the space in which hybrid cultural forms and identities exist. In his theories, the term hybrid describes new cultural forms that emerge through the interaction between colonizer and colonized.^{ [35] }

**General relativity**, also known as the **general theory of relativity** and **Einstein's theory of gravity**, is the geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of gravitation in modern physics. General relativity generalises special relativity and refines Newton's law of universal gravitation, providing a unified description of gravity as a geometric property of space and time or four-dimensional spacetime. In particular, the *curvature of spacetime* is directly related to the energy and momentum of whatever matter and radiation are present. The relation is specified by the Einstein field equations, a system of second order partial differential equations.

In classical physics and special relativity, an **inertial frame of reference** is a frame of reference not undergoing any acceleration. It is a frame in which an isolated physical object—an object with zero net force acting on it—is perceived to move with a constant velocity or, equivalently, it is a frame of reference in which Newton's first law of motion holds. All inertial frames are in a state of constant, rectilinear motion with respect to one another; in other words, an accelerometer moving with any of them would detect zero acceleration.

In physics, **spacetime** is any mathematical model that fuses the three dimensions of space and the one dimension of time into a single four-dimensional continuum. Spacetime diagrams are useful in visualizing and understanding relativistic effects such as how different observers perceive *where* and *when* events occur.

The **theory of relativity** usually encompasses two interrelated physics theories by Albert Einstein: special relativity and general relativity, proposed and published in 1905 and 1915, respectively. Special relativity applies to all physical phenomena in the absence of gravity. General relativity explains the law of gravitation and its relation to the forces of nature. It applies to the cosmological and astrophysical realm, including astronomy.

In physics, **gravity** (from Latin * gravitas* 'weight') is a fundamental interaction which causes mutual attraction between all things that have mass. Gravity is, by far, the weakest of the four fundamental interactions, approximately 10^{38} times weaker than the strong interaction, 10^{36} times weaker than the electromagnetic force and 10^{29} times weaker than the weak interaction. As a result, it has no significant influence at the level of subatomic particles. However, gravity is the most significant interaction between objects at the macroscopic scale, and it determines the motion of planets, stars, galaxies, and even light.

In philosophy, **philosophy of physics** deals with conceptual and interpretational issues in modern physics, many of which overlap with research done by certain kinds of theoretical physicists. Philosophy of physics can be broadly divided into three areas:

**Mathematical physics** refers to the development of mathematical methods for application to problems in physics. The *Journal of Mathematical Physics* defines the field as "the application of mathematics to problems in physics and the development of mathematical methods suitable for such applications and for the formulation of physical theories". An alternative definition would also include those mathematics that are inspired by physics, known as physical mathematics.

In theoretical physics, particularly in discussions of gravitation theories, **Mach's principle** is the name given by Albert Einstein to an imprecise hypothesis often credited to the physicist and philosopher Ernst Mach. The hypothesis attempted to explain how rotating objects, such as gyroscopes and spinning celestial bodies, maintain a frame of reference.

**Philosophy of space and time** is the branch of philosophy concerned with the issues surrounding the ontology and epistemology 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 central aspect of early analytic philosophy. The subject focuses on a number of basic issues, including whether time and space exist independently of the mind, whether they exist independently of one another, what accounts for time's apparently unidirectional flow, whether times other than the present moment exist, and questions about the nature of identity.

In theoretical physics, **geometrodynamics** is an attempt to describe spacetime and associated phenomena completely in terms of geometry. Technically, its goal is to unify the fundamental forces and reformulate general relativity as a configuration space of three-metrics, modulo three-dimensional diffeomorphisms. The origin of this idea can be found in an English mathematician William Kingdon Clifford's works. This theory was enthusiastically promoted by John Wheeler in the 1960s, and work on it continues in the 21st century.

**Absolute space and time** is a concept in physics and philosophy about the properties of the universe. In physics, absolute space and time may be a preferred frame.

**General relativity** is a theory of gravitation developed by Albert Einstein between 1907 and 1915. The theory of general relativity says that the observed gravitational effect between masses results from their warping of spacetime.

In physics, Albert Einstein derived the theory of special relativity in 1905 from principle now called the **postulates of special relativity**. Einstein's formulation is said to only require two postulates, though his derivation implies a few more assumptions.

General relativity is a theory of gravitation that was developed by Albert Einstein between 1907 and 1915, with contributions by many others after 1915. According to general relativity, the observed gravitational attraction between masses results from the warping of space and time by those masses.

In physics, theories of gravitation postulate mechanisms of interaction governing the movements of bodies with mass. There have been numerous theories of gravitation since ancient times. The first extant sources discussing such theories are found in ancient Greek philosophy. This work was furthered through the Middle Ages by Indian, Islamic, and European scientists, before gaining great strides during the Renaissance and Scientific Revolution—culminating in the formulation of Newton's law of gravity. This was superseded by Albert Einstein's theory of relativity in the early 20th century.

The **expansion of the universe** is the increase in distance between gravitationally unbound parts of the observable universe with time. It is an intrinsic expansion; the universe does not expand "into" anything and does not require space to exist "outside" it. To any observer in the universe, it appears that all but the nearest galaxies recede at speeds that are proportional to their distance from the observer, on average. While objects cannot move faster than light, this limitation only applies with respect to local reference frames and does not limit the recession rates of cosmologically distant objects.

The **mathematics of general relativity** is complex. In Newton's theories of motion, an object's length and the rate at which time passes remain constant while the object accelerates, meaning that many problems in Newtonian mechanics may be solved by algebra alone. In relativity, however, an object's length and the rate at which time passes both change appreciably as the object's speed approaches the speed of light, meaning that more variables and more complicated mathematics are required to calculate the object's motion. As a result, relativity requires the use of concepts such as vectors, tensors, pseudotensors and curvilinear coordinates.

The theory of special relativity was initially developed in 1905 by Albert Einstein. However, other interpretations of special relativity have been developed, some on the basis of different foundational axioms. While some are mathematically equivalent to Einstein's theory, others aim to revise or extend it.

Physics is a scientific discipline that seeks to construct and experimentally test theories of the physical universe. These theories vary in their scope and can be organized into several distinct branches, which are outlined in this article.

In physics, a **non-relativistic spacetime** is any mathematical model that fuses *n*–dimensional space and *m*–dimensional time into a single continuum other than the (3+1) model used in relativity theory.

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*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 al-Haytham'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 El-Bizri, "In Defence of the Sovereignty of Philosophy: al-Baghdadi's Critique of Ibn al-Haytham'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. - 1 2 Huggett, Nick, ed. (1999).
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*Descartes: a very short introduction*. Oxford: Oxford University Press. ISBN 978-0-19-154036-3. OCLC 428970574. - ↑ Leibniz, Fifth letter to Samuel Clarke. By H.G. Alexander (1956).
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*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".
*st-and.ac.uk*. Archived from the original on 17 March 2008. Retrieved 20 July 2008. - ↑ Carnap, R.
*An Introduction to the Philosophy of Science*. pp. 177–178. - ↑ Lucas, John Randolph (1984).
*Space, Time and Causality*. Clarendon Press. p. 149. ISBN 978-0-19-875057-4. - ↑ Carnap, R.
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*An Introduction to the Philosophy of Science*. pp. 134–136. - ↑ 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 0-7167-6034-7 - ↑ Castelvecchi, Davide; Witze, Alexandra (11 February 2016). "Einstein's gravitational waves found at last".
*Nature News*. Archived from the original on 16 February 2016. 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. S2CID 124959784.- "Observation of Gravitational Waves from a Binary Black Hole Merger" (PDF).
*LIGO Scientific Collaboration*.

- "Observation of Gravitational Waves from a Binary Black Hole Merger" (PDF).
- ↑ "Cosmic Detectives". The European Space Agency (ESA). 2 April 2013. Archived from the original on 5 April 2013. Retrieved 26 April 2013.
- ↑ Stanek, Lukasz (2011).
*Henri Lefebvre on Space: Architecture, Urban Research, and the Production of Theory*. Univ of Minnesota Press. pp. ix. - ↑ "Time-Space Compression – Geography – Oxford Bibliographies – obo". Archived from the original on 20 September 2018. Retrieved 28 August 2018.
- ↑ Harvey, David (2001).
*Spaces of Capital: Towards a Critical Geography*. Edinburgh University Press. pp. 244–246. - ↑ W., Soja, Edward (1996).
*Thirdspace: journeys to Los Angeles and other real-and-imagined places*. Cambridge, Mass.: Blackwell. ISBN 978-1-55786-674-5. OCLC 33863376.`{{cite book}}`

: CS1 maint: multiple names: authors list (link) - ↑ Lefebvre, Henri (1991).
*The production of space*. Oxford, OX, UK: Blackwell. ISBN 978-0-631-14048-1. OCLC 22624721. - ↑ Ashcroft Bill; Griffiths, Gareth; Tiffin, Helen (2013).
*Postcolonial studies: the key concepts*(Third ed.). London. ISBN 978-0-415-66190-4. OCLC 824119565.`{{cite book}}`

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