Space is the boundless
three-dimensional
Three-dimensional space (also: 3D space, 3-space or, rarely, tri-dimensional space) is a geometric setting in which three values (called ''parameters'') are required to determine the position of an element (i.e., point). This is the informal ...
extent in which
objects
Object may refer to:
General meanings
* Object (philosophy), a thing, being, or concept
** Object (abstract), an object which does not exist at any particular time or place
** Physical object, an identifiable collection of matter
* Goal, an ...
and events have relative
position
Position often refers to:
* Position (geometry), the spatial location (rather than orientation) of an entity
* Position, a job or occupation
Position may also refer to:
Games and recreation
* Position (poker), location relative to the dealer
* ...
and
direction. In
classical physics
Classical physics is a group of physics theories that predate modern, more complete, or more widely applicable theories. If a currently accepted theory is considered to be modern, and its introduction represented a major paradigm shift, then the ...
, physical space is often conceived in three
linear
Linearity is the property of a mathematical relationship (''function'') that can be graphically represented as a straight line. Linearity is closely related to '' proportionality''. Examples in physics include rectilinear motion, the linear r ...
dimension
In physics and mathematics, the dimension of a Space (mathematics), mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any Point (geometry), point within it. Thus, a Line (geometry), lin ...
s, although
modern physicist
Modern physics is a branch of physics that developed in the early 20th century and onward or branches greatly influenced by early 20th century physics. Notable branches of modern physics include quantum mechanics, special relativity and general ...
s usually consider it, with
time
Time is the continued sequence of existence and events that occurs in an apparently irreversible succession from the past, through the present, into the future. It is a component quantity of various measurements used to sequence events, to ...
, to be part of a boundless
four-dimensional
A four-dimensional space (4D) is a mathematical extension of the concept of three-dimensional or 3D space. Three-dimensional space is the simplest possible abstraction of the observation that one only needs three numbers, called ''dimensions'', ...
continuum
Continuum may refer to:
* Continuum (measurement), theories or models that explain gradual transitions from one condition to another without abrupt changes
Mathematics
* Continuum (set theory), the real line or the corresponding cardinal number ...
known as
spacetime
In physics, spacetime is a mathematical model that combines the three dimensions of space and one dimension of time into a single four-dimensional manifold. Spacetime diagrams can be used to visualize relativistic effects, such as why differen ...
. The concept of space is considered to be of fundamental importance to an understanding of the physical
universe
The universe is all of space and time and their contents, including planets, stars, galaxies, and all other forms of matter and energy. The Big Bang theory is the prevailing cosmological description of the development of the universe. Acc ...
. However, disagreement continues between
philosophers
A philosopher is a person who practices or investigates philosophy. The term ''philosopher'' comes from the grc, φιλόσοφος, , translit=philosophos, meaning 'lover of wisdom'. The coining of the term has been attributed to the Greek th ...
over whether it is itself an entity, a relationship between entities, or part of a
conceptual framework
A conceptual framework is an analytical tool with several variations and contexts. It can be applied in different categories of work where an overall picture is needed. It is used to make conceptual distinctions and organize ideas. Strong conceptu ...
.
Debates concerning the nature, essence and the mode of existence of space date back to antiquity; namely, to treatises like the ''
Timaeus Timaeus (or Timaios) is a Greek name. It may refer to:
* ''Timaeus'' (dialogue), a Socratic dialogue by Plato
*Timaeus of Locri, 5th-century BC Pythagorean philosopher, appearing in Plato's dialogue
*Timaeus (historian) (c. 345 BC-c. 250 BC), Greek ...
'' of
Plato
Plato ( ; grc-gre, Πλάτων ; 428/427 or 424/423 – 348/347 BC) was a Greek philosopher born in Athens during the Classical period in Ancient Greece. He founded the Platonist school of thought and the Academy, the first institution ...
, or
Socrates
Socrates (; ; –399 BC) was a Greek philosopher from Athens who is credited as the founder of Western philosophy and among the first moral philosophers of the ethical tradition of thought. An enigmatic figure, Socrates authored no te ...
in his reflections on what the Greeks called ''
khôra
''Khôra'' (also ''chora''; grc, χώρα) was the territory of the Ancient Greek ''polis'' outside the city proper. The term has been used in philosophy by Plato to designate a receptacle (as a "third kind" 'triton genos'' ''Timaeus'' 48e4), a s ...
'' (i.e. "space"), or in the ''
Physics
Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which r ...
'' of
Aristotle
Aristotle (; grc-gre, Ἀριστοτέλης ''Aristotélēs'', ; 384–322 BC) was a Greek philosopher and polymath during the Classical period in Ancient Greece. Taught by Plato, he was the founder of the Peripatetic school of phil ...
(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
A polymath ( el, πολυμαθής, , "having learned much"; la, homo universalis, "universal human") is an individual whose knowledge spans a substantial number of subjects, known to draw on complex bodies of knowledge to solve specific pro ...
Alhazen
Ḥasan Ibn al-Haytham, Latinized as Alhazen (; full name ; ), was a medieval mathematician, astronomer, and physicist of the Islamic Golden Age from present-day Iraq.For the description of his main fields, see e.g. ("He is one of the prin ...
. Many of these classical philosophical questions were discussed in the
Renaissance
The Renaissance ( , ) , from , with the same meanings. is a period in European history marking the transition from the Middle Ages to modernity and covering the 15th and 16th centuries, characterized by an effort to revive and surpass ideas ...
and then reformulated in the 17th century, particularly during the early development of
classical mechanics
Classical mechanics is a physical theory describing the motion of macroscopic objects, from projectiles to parts of machinery, and astronomical objects, such as spacecraft, planets, stars, and galaxies. For objects governed by classical ...
. In
Isaac Newton
Sir Isaac Newton (25 December 1642 – 20 March 1726/27) was an English mathematician, physicist, astronomer, alchemist, theologian, and author (described in his time as a "natural philosopher"), widely recognised as one of the grea ...
's view, space was absolute—in the sense that it existed permanently and independently of whether there was any matter in the space. Other
natural philosopher
Natural philosophy or philosophy of nature (from Latin ''philosophia naturalis'') is the philosophical study of physics
Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior throu ...
s, notably
Gottfried Leibniz
Gottfried Wilhelm (von) Leibniz . ( – 14 November 1716) was a German polymath active as a mathematician, philosopher, scientist and diplomat. He is one of the most prominent figures in both the history of philosophy and the history of mathem ...
, thought instead that space was in fact a collection of relations between objects, given by their
distance
Distance is a numerical or occasionally qualitative measurement of how far apart objects or points are. In physics or everyday usage, distance may refer to a physical length or an estimation based on other criteria (e.g. "two counties over"). ...
and
direction from one another. In the 18th century, the philosopher and theologian
George Berkeley
George Berkeley (; 12 March 168514 January 1753) – known as Bishop Berkeley (Bishop of Cloyne of the Anglican Church of Ireland) – was an Anglo-Irish philosopher whose primary achievement was the advancement of a theory he called "immate ...
attempted to refute the "visibility of spatial depth" in his ''Essay Towards a New Theory of Vision''. Later, the
metaphysic
Metaphysics is the branch of philosophy that studies the fundamental nature of reality, the first principles of being, identity and change, space and time, causality, necessity, and possibility. It includes questions about the nature of conscio ...
ian
Immanuel Kant
Immanuel Kant (, , ; 22 April 1724 – 12 February 1804) was a German philosopher and one of the central Enlightenment thinkers. Born in Königsberg, Kant's comprehensive and systematic works in epistemology, metaphysics, ethics, and ...
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
("from the earlier") and ("from the later") are Latin phrases used in philosophy to distinguish types of knowledge, justification, or argument by their reliance on empirical evidence or experience. knowledge is independent from current ex ...
'' form of intuition".
In the 19th and 20th centuries mathematicians began to examine geometries that are
non-Euclidean
In mathematics, non-Euclidean geometry consists of two geometries based on axioms closely related to those that specify Euclidean geometry. As Euclidean geometry lies at the intersection of metric geometry and affine geometry, non-Euclidean geo ...
, in which space is conceived as ''curved'', rather than ''flat''. According to
Albert Einstein
Albert Einstein ( ; ; 14 March 1879 – 18 April 1955) was a German-born theoretical physicist, widely acknowledged to be one of the greatest and most influential physicists of all time. Einstein is best known for developing the theory ...
's theory of
general relativity
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 ...
, space around
gravitational field
In physics, a gravitational field is a model used to explain the influences that a massive body extends into the space around itself, producing a force on another massive body. Thus, a gravitational field is used to explain gravitational phenome ...
s deviates from Euclidean space. Experimental
tests of general relativity
Tests of general relativity serve to establish observational evidence for the theory of general relativity. The first three tests, proposed by Albert Einstein in 1915, concerned the "anomalous" precession of the perihelion of Mercury, the bending ...
have confirmed that non-Euclidean geometries provide a better model for the shape of space.
Philosophy of space
Galileo
Galilean
Generically, a Galilean (; he, גלילי; grc, Γαλιλαίων; la, Galilaeos) is an inhabitant of Galilee, a region of Israel surrounding the Sea of Galilee (Kinneret). The New Testament notes that the Apostle Peter's accent gave him a ...
and
Cartesian Cartesian means of or relating to the French philosopher René Descartes—from his Latinized name ''Cartesius''. It may refer to:
Mathematics
*Cartesian closed category, a closed category in category theory
*Cartesian coordinate system, modern ...
theories about space, matter, and motion are at the foundation of the
Scientific Revolution
The Scientific Revolution was a series of events that marked the emergence of modern science during the early modern period, when developments in mathematics, physics, astronomy, biology (including human anatomy) and chemistry transfo ...
, which is understood to have culminated with the publication of
Newton
Newton most commonly refers to:
* Isaac Newton (1642–1726/1727), English scientist
* Newton (unit), SI unit of force named after Isaac Newton
Newton may also refer to:
Arts and entertainment
* ''Newton'' (film), a 2017 Indian film
* Newton ( ...
's ''
Principia'' in 1687.
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.
As one of the pioneers of
modern science
The history of science covers the development of science from ancient history, ancient times to the present. It encompasses all three major branches of science: natural science, natural, social science, social, and formal science, formal.
Sc ...
, Galileo revised the established
Aristotelian and
Ptolemaic Ptolemaic is the adjective formed from the name Ptolemy, and may refer to:
Pertaining to the Ptolemaic dynasty
* Ptolemaic dynasty, the Macedonian Greek dynasty that ruled Egypt founded in 305 BC by Ptolemy I Soter
* Ptolemaic Kingdom
Pertaining ...
ideas about a
geocentric
In astronomy, the geocentric model (also known as geocentrism, often exemplified specifically by the Ptolemaic system) is a superseded description of the Universe with Earth at the center. Under most geocentric models, the Sun, Moon, stars, an ...
cosmos. He backed the
Copernican theory that the universe was
heliocentric
Heliocentrism (also known as the Heliocentric model) is the astronomical model in which the Earth and planets revolve around the Sun at the center of the universe. Historically, heliocentrism was opposed to geocentrism, which placed the Earth at ...
, 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.
René Descartes
Descartes set out to replace the Aristotelian worldview with a theory about space and motion as determined by
natural law
Natural law ( la, ius naturale, ''lex naturalis'') is a system of law based on a close observation of human nature, and based on values intrinsic to human nature that can be deduced and applied independently of positive law (the express enacte ...
s. In other words, he sought a
metaphysical
Metaphysics is the branch of philosophy that studies the fundamental nature of reality, the first principles of being, identity and change, space and time, causality, necessity, and possibility. It includes questions about the nature of conscio ...
foundation or a
mechanical
Mechanical may refer to:
Machine
* Machine (mechanical), a system of mechanisms that shape the actuator input to achieve a specific application of output forces and movement
* Mechanical calculator, a device used to perform the basic operations of ...
explanation for his theories about matter and motion.
Cartesian space
A Cartesian coordinate system (, ) in a plane is a coordinate system that specifies each point uniquely by a pair of numerical coordinates, which are the signed distances to the point from two fixed perpendicular oriented lines, measured in ...
was
Euclidean in structure—infinite, uniform and flat. 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.
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
In philosophy, empiricism is an epistemological theory that holds that knowledge or justification comes only or primarily from sensory experience. It is one of several views within epistemology, along with rationalism and skepticism. Empiri ...
believe. He posited a clear distinction between the body and mind, which is referred to as the
Cartesian dualism Cartesian means of or relating to the French philosopher René Descartes—from his Latinized name ''Cartesius''. It may refer to:
Mathematics
*Cartesian closed category, a closed category in category theory
* Cartesian coordinate system, moder ...
.
Leibniz and Newton
Following Galileo and Descartes, during the seventeenth century the
philosophy of space and time
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 wa ...
revolved around the ideas of
Gottfried Leibniz
Gottfried Wilhelm (von) Leibniz . ( – 14 November 1716) was a German polymath active as a mathematician, philosopher, scientist and diplomat. He is one of the most prominent figures in both the history of philosophy and the history of mathem ...
, a German philosopher–mathematician, and
Isaac Newton
Sir Isaac Newton (25 December 1642 – 20 March 1726/27) was an English mathematician, physicist, astronomer, alchemist, theologian, and author (described in his time as a "natural philosopher"), widely recognised as one of the grea ...
, 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". 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
Abstraction in its main sense is a conceptual process wherein general rules and concepts are derived from the usage and classification of specific examples, literal ("real" or "concrete") signifiers, first principles, or other methods.
"An abstr ...
from the relations between individual entities or their possible locations and therefore could not be
continuous
Continuity or continuous may refer to:
Mathematics
* Continuity (mathematics), the opposing concept to discreteness; common examples include
** Continuous probability distribution or random variable in probability and statistics
** Continuous ...
but must be
discrete
Discrete may refer to:
*Discrete particle or quantum in physics, for example in quantum theory
* Discrete device, an electronic component with just one circuit element, either passive or active, other than an integrated circuit
*Discrete group, a ...
.
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 indiscernibles
The identity of indiscernibles is an ontological principle that states that there cannot be separate objects or entities that have all their properties in common. That is, entities ''x'' and ''y'' are identical if every predicate possessed by ''x'' ...
, there would be no real difference between them. According to the
principle of sufficient reason
The principle of sufficient reason states that everything must have a reason or a cause. The principle was articulated and made prominent by Gottfried Wilhelm Leibniz, with many antecedents, and was further used and developed by Arthur Schopenhau ...
, 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
observation
Observation is the active acquisition of information from a primary source. In living beings, observation employs the senses. In science, observation can also involve the perception and recording of data via the use of scientific instruments. The ...
and experimentation. For a
relationist there can be no real difference between
inertial motion, in which the object travels with constant
velocity
Velocity is the directional speed of an object in motion as an indication of its rate of change in position as observed from a particular frame of reference and as measured by a particular standard of time (e.g. northbound). Velocity is a ...
, 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
force
In physics, a force is an influence that can change the motion of an object. A force can cause an object with mass to change its velocity (e.g. moving from a state of rest), i.e., to accelerate. Force can also be described intuitively as a p ...
s, it must be absolute. He used the example of
water in a spinning bucket to demonstrate his argument. Water in a
bucket
A bucket is typically a watertight, vertical Cylinder (geometry), cylinder or Truncation (geometry), truncated Cone (geometry), cone or square, with an open top and a flat bottom, attached to a semicircular carrying handle (grip), handle called ...
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 considered decisive in showing that space must exist independently of matter.
Kant
In the eighteenth century the German philosopher
Immanuel Kant
Immanuel Kant (, , ; 22 April 1724 – 12 February 1804) was a German philosopher and one of the central Enlightenment thinkers. Born in Königsberg, Kant's comprehensive and systematic works in epistemology, metaphysics, ethics, and ...
developed a theory of
knowledge
Knowledge can be defined as awareness of facts or as practical skills, and may also refer to familiarity with objects or situations. Knowledge of facts, also called propositional knowledge, is often defined as true belief that is distinc ...
in which knowledge about space can be both ''a priori'' and ''
synthetic Synthetic things are composed of multiple parts, often with the implication that they are artificial. In particular, 'synthetic' may refer to:
Science
* Synthetic chemical or compound, produced by the process of chemical synthesis
* Synthetic o ...
''. 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.
Non-Euclidean geometry
Euclid's ''Elements'' contained five postulates that form the basis for Euclidean geometry. One of these, the
parallel postulate
In 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. It states that, in two-dimensional geometry:
''If a line segment ...
, has been the subject of debate among mathematicians for many centuries. It states that on any
plane
Plane(s) most often refers to:
* Aero- or airplane, a powered, fixed-wing aircraft
* Plane (geometry), a flat, 2-dimensional surface
Plane or planes may also refer to:
Biology
* Plane (tree) or ''Platanus'', wetland native plant
* Planes (gen ...
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. Around 1830 though, the Hungarian
János Bolyai
János Bolyai (; 15 December 1802 – 27 January 1860) or Johann Bolyai, was a Hungarian mathematician, who developed absolute geometry—a geometry that includes both Euclidean geometry and hyperbolic geometry. The discovery of a consisten ...
and the Russian
Nikolai Ivanovich Lobachevsky
Nikolai Ivanovich Lobachevsky ( rus, Никола́й Ива́нович Лобаче́вский, p=nʲikɐˈlaj ɪˈvanəvʲɪtɕ ləbɐˈtɕɛfskʲɪj, a=Ru-Nikolai_Ivanovich_Lobachevsky.ogg; – ) was a Russian mathematician and geometer, kn ...
separately published treatises on a type of geometry that does not include the parallel postulate, called
hyperbolic geometry
In mathematics, hyperbolic geometry (also called Lobachevskian geometry or Bolyai– Lobachevskian geometry) is a non-Euclidean geometry. The parallel postulate of Euclidean geometry is replaced with:
:For any given line ''R'' and point ''P'' ...
. In this geometry, an
infinite
Infinite may refer to:
Mathematics
*Infinite set, a set that is not a finite set
*Infinity, an abstract concept describing something without any limit
Music
* Infinite (group), a South Korean boy band
*''Infinite'' (EP), debut EP of American m ...
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
A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre. Equivalently, it is the curve traced out by a point that moves in a plane so that its distance from a given point is const ...
's
circumference
In geometry, the circumference (from Latin ''circumferens'', meaning "carrying around") is the perimeter of a circle or ellipse. That is, the circumference would be the arc length of the circle, as if it were opened up and straightened out to ...
to its
diameter
In geometry, a diameter of a circle is any straight line segment that passes through the center of the circle and whose endpoints lie on the circle. It can also be defined as the longest chord of the circle. Both definitions are also valid for ...
is greater than
pi. In the 1850s,
Bernhard Riemann
Georg Friedrich Bernhard Riemann (; 17 September 1826 – 20 July 1866) was a German mathematician who made contributions to analysis, number theory, and differential geometry. In the field of real analysis, he is mostly known for the first rig ...
developed an equivalent theory of
elliptical geometry
Elliptic geometry is an example of a geometry in which Euclid's parallel postulate does not hold. Instead, as in spherical geometry, there are no parallel lines since any two lines must intersect. However, unlike in spherical geometry, two lines a ...
, in which no parallel lines pass through ''P''. In this geometry, triangles have more than 180° and circles have a ratio of circumference-to-diameter that is less than
pi.
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 Gauss
Johann Carl Friedrich Gauss (; german: Gauß ; la, Carolus Fridericus Gauss; 30 April 177723 February 1855) was a German mathematician and physicist who made significant contributions to many fields in mathematics and science. Sometimes refer ...
, 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.
Henri Poincaré
Jules Henri Poincaré ( S: stress final syllable ; 29 April 1854 – 17 July 1912) was a French mathematician, theoretical physicist, engineer, and philosopher of science. He is often described as a polymath, and in mathematics as "The ...
, 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-world
The idea of a sphere-world was constructed by Henri Poincaré who, while pursuing his argument for conventionalism (see philosophy of space and time), offered a thought experiment about a sphere with strange properties.
The concept
Poincaré as ...
. 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. 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. Since
Euclidean geometry
Euclidean geometry is a mathematical system attributed to ancient Greek mathematics, Greek mathematician Euclid, which he described in his textbook on geometry: the ''Euclid's Elements, Elements''. Euclid's approach consists in assuming a small ...
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 Einstein
Albert Einstein ( ; ; 14 March 1879 – 18 April 1955) was a German-born theoretical physicist, widely acknowledged to be one of the greatest and most influential physicists of all time. Einstein is best known for developing the theory ...
published his
special theory of relativity
In physics, the special theory of relativity, or special relativity for short, is a scientific theory regarding the relationship between Spacetime, space and time. In Albert Einstein's original treatment, the theory is based on two Postulates of ...
, which led to the concept that space and time can be viewed as a single construct known as ''
spacetime
In physics, spacetime is a mathematical model that combines the three dimensions of space and one dimension of time into a single four-dimensional manifold. Spacetime diagrams can be used to visualize relativistic effects, such as why differen ...
''. In this theory, the
speed of light
The speed of light in vacuum, commonly denoted , is a universal physical constant that is important in many areas of physics. The speed of light is exactly equal to ). According to the special theory of relativity, is the upper limit ...
in a
vacuum
A vacuum is a space devoid of matter. The word is derived from the Latin adjective ''vacuus'' for "vacant" or "void". An approximation to such vacuum is a region with a gaseous pressure much less than atmospheric pressure. Physicists often dis ...
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
General relativity, also known as the general theory of relativity and Einstein's theory of gravity, is the differential geometry, geometric scientific theory, theory of gravitation published by Albert Einstein in 1915 and is the current descr ...
, which is a theory of how
gravity
In physics, gravity () is a fundamental interaction which causes mutual attraction between all things with mass or energy. Gravity is, by far, the weakest of the four fundamental interactions, approximately 1038 times weaker than the stro ...
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. 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 pulsar
A binary pulsar is a pulsar with a binary companion, often a white dwarf or neutron star. (In at least one case, the double pulsar PSR J0737-3039, the companion neutron star is another pulsar as well.) Binary pulsars are one of the few objects w ...
s, confirming the predictions of Einstein's theories, and non-Euclidean geometry is usually used to describe spacetime.
Mathematics
In modern mathematics
spaces Spaces may refer to:
* Google Spaces (app), a cross-platform application for group messaging and sharing
* Windows Live Spaces, the next generation of MSN Spaces
* Spaces (software), a virtual desktop manager implemented in Mac OS X Leopard
* Spac ...
are defined as
sets with some added structure. They are frequently described as different types of
manifold
In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point. More precisely, an n-dimensional manifold, or ''n-manifold'' for short, is a topological space with the property that each point has a n ...
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 space
In mathematics and physics, a vector space (also called a linear space) is a set whose elements, often called ''vectors'', may be added together and multiplied ("scaled") by numbers called '' scalars''. Scalars are often real numbers, but can ...
s such as
function space
In mathematics, a function space is a set of functions between two fixed sets. Often, the domain and/or codomain will have additional structure which is inherited by the function space. For example, the set of functions from any set into a vect ...
s may have infinite numbers of independent dimensions and a notion of distance very different from Euclidean space, and
topological space
In mathematics, a topological space is, roughly speaking, a geometrical space in which closeness is defined but cannot necessarily be measured by a numeric distance. More specifically, a topological space is a set whose elements are called points ...
s replace the concept of distance with a more abstract idea of nearness.
Physics
Space is one of the few
fundamental quantities in
physics
Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which r ...
, 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
Mass is an intrinsic property of a body. It was traditionally believed to be related to the quantity of matter in a physical body, until the discovery of the atom and particle physics. It was found that different atoms and different elementar ...
), space can be explored via
measurement
Measurement is the quantification of attributes of an object or event, which can be used to compare with other objects or events.
In other words, measurement is a process of determining how large or small a physical quantity is as compared ...
and experiment.
Today, our
three-dimensional space
Three-dimensional space (also: 3D space, 3-space or, rarely, tri-dimensional space) is a geometric setting in which three values (called ''parameters'') are required to determine the position (geometry), position of an element (i.e., Point (m ...
is viewed as embedded in a four-dimensional
spacetime
In physics, spacetime is a mathematical model that combines the three dimensions of space and one dimension of time into a single four-dimensional manifold. Spacetime diagrams can be used to visualize relativistic effects, such as why differen ...
, called
Minkowski space
In mathematical physics, Minkowski space (or Minkowski spacetime) () is a combination of three-dimensional Euclidean space and time into a four-dimensional manifold where the spacetime interval between any two events is independent of the inerti ...
(see
special relativity
In physics, the special theory of relativity, or special relativity for short, is a scientific theory regarding the relationship between space and time. In Albert Einstein's original treatment, the theory is based on two postulates:
# The laws o ...
). The idea behind spacetime is that time is
hyperbolic-orthogonal
In geometry, the relation of hyperbolic orthogonality between two lines separated by the asymptotes of a hyperbola is a concept used in special relativity to define simultaneous events. Two events will be simultaneous when they are on a line hyperb ...
to each of the three spatial dimensions.
Relativity
Before
Albert Einstein
Albert Einstein ( ; ; 14 March 1879 – 18 April 1955) was a German-born theoretical physicist, widely acknowledged to be one of the greatest and most influential physicists of all time. Einstein is best known for developing the theory ...
'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
In physics, spacetime is a mathematical model that combines the three dimensions of space and one dimension of time into a single four-dimensional manifold. Spacetime diagrams can be used to visualize relativistic effects, such as why differen ...
. It turns out that distances in
space
Space is the boundless three-dimensional extent in which objects and events have relative position and direction. In classical physics, physical space is often conceived in three linear dimensions, although modern physicists usually consider ...
or in
time
Time is the continued sequence of existence and events that occurs in an apparently irreversible succession from the past, through the present, into the future. It is a component quantity of various measurements used to sequence events, to ...
separately are not invariant with respect to Lorentz coordinate transformations, but distances in Minkowski space along
spacetime interval
In physics, spacetime is a mathematical model that combines the three dimensions of space and one dimension of time into a single four-dimensional manifold. Spacetime diagrams can be used to visualize relativistic effects, such as why differen ...
s 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
In physics, the special theory of relativity, or special relativity for short, is a scientific theory regarding the relationship between space and time. In Albert Einstein's original treatment, the theory is based on two postulates:
# The laws o ...
(where time is sometimes considered an
imaginary coordinate) and in
general relativity
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 ...
(where different signs are assigned to time and space components of
spacetime
In physics, spacetime is a mathematical model that combines the three dimensions of space and one dimension of time into a single four-dimensional manifold. Spacetime diagrams can be used to visualize relativistic effects, such as why differen ...
metric
Metric or metrical may refer to:
* Metric system, an internationally adopted decimal system of measurement
* An adjective indicating relation to measurement in general, or a noun describing a specific type of measurement
Mathematics
In mathema ...
).
Furthermore, in
Einstein's general theory of relativity
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. ...
, it is postulated that spacetime is geometrically distorted – ''curved'' – near to gravitationally significant masses.
One consequence of this postulate, which follows from the equations of general relativity, is the prediction of moving ripples of spacetime, called
gravitational wave
Gravitational waves are waves of the intensity of gravity generated by the accelerated masses of an orbital binary system that propagate as waves outward from their source at the speed of light. They were first proposed by Oliver Heaviside in 1 ...
s. While indirect evidence for these waves has been found (in the motions of the
Hulse–Taylor binary
The Hulse–Taylor binary is a binary star system composed of a neutron star and a pulsar (known as PSR B1913+16, PSR J1915+1606 or PSR 1913+16) which orbit around their common center of mass. It is the first binary pulsar ever discovere ...
system, for example) experiments attempting to directly measure these waves are ongoing at the
LIGO
The Laser Interferometer Gravitational-Wave Observatory (LIGO) is a large-scale physics experiment and observatory designed to detect cosmic gravitational waves and to develop gravitational-wave observations as an astronomical tool. Two large ...
and
Virgo
Virgo may refer to:
*Virgo (astrology), the sixth astrological sign of the zodiac
*Virgo (constellation), a constellation
*Virgo Cluster, a cluster of galaxies in the constellation Virgo
*Virgo Stellar Stream, remains of a dwarf galaxy
*Virgo Supe ...
collaborations. LIGO scientists reported the
first such direct observation of gravitational waves on 14 September 2015.
[
*]
Cosmology
Relativity theory leads to the
cosmological
Cosmology () is a branch of physics and metaphysics dealing with the nature of the universe. The term ''cosmology'' was first used in English in 1656 in Thomas Blount's ''Glossographia'', and in 1731 taken up in Latin by German philosopher ...
question of what shape the universe is, and where space came from. It appears that space was created in the
Big Bang
The Big Bang event is a physical theory that describes how the universe expanded from an initial state of high density and temperature. Various cosmological models of the Big Bang explain the evolution of the observable universe from the ...
, 13.8 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 inflation
In physical cosmology, cosmic inflation, cosmological inflation, or just inflation, is a theory of exponential expansion of space in the early universe. The inflationary epoch lasted from seconds after the conjectured Big Bang singularity ...
.
Spatial measurement
The measurement of ''physical space'' has long been important. Although earlier societies had developed measuring systems, the SI, 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 speed of light, 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 physics, the special theory of relativity, or special relativity for short, is a scientific theory regarding the relationship between Spacetime, space and time. In Albert Einstein's original treatment, the theory is based on two Postulates of ...
in which the
speed of light
The speed of light in vacuum, commonly denoted , is a universal physical constant that is important in many areas of physics. The speed of light is exactly equal to ). According to the special theory of relativity, is the upper limit ...
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 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 International waters, 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 space-related phobias have been identified, including agoraphobia (the fear of open spaces), wikt:astrophobia, 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 visual perception#Unconscious inference, unconscious inference, and is closely related to hand-eye coordination. The visual ability to perceive the world in three dimensions is called depth perception.
In the social sciences
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.
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. 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.
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. 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" 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.
Postcolonialism, Postcolonial theorist Homi K. Bhabha, Homi Bhabha's concept of Third Space Theory, Third Space is different from Soja's Thirdspace, even though both terms offer a way to think outside the terms of a Binary opposition, binary logic. Bhabha's Third Space is the space in which hybrid cultural forms and identities exist. In his theories, the term Hybridity, hybrid describes new cultural forms that emerge through the interaction between colonizer and colonized.
See also
* State space (physics)
* Absolute space and time
* Aether theories
* Cosmology
* General relativity
* Philosophy of space and time
* Proxemics
* Shape of the universe
* Social space
* Space exploration
* Spatial analysis
* Spatial–temporal reasoning
References
External links
{{Authority control
Space,
Geometry
Nature
Spacetime
Topology