Space is the boundless three-dimensional extent in which objects and
events have relative position and direction. Physical space is
often conceived in three linear dimensions, although modern physicists
usually consider it, with time, to be part of a boundless
four-dimensional 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
Socrates in his reflections on what the Greeks called khôra
(i.e. "space"), or in the
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.
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.
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
Critique of Pure Reason as being a subjective "pure a priori form of
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. According to Albert Einstein's theory of
general relativity, space around gravitational fields deviates from
Euclidean space. Experimental tests of general relativity have
confirmed that non-Euclidean geometries provide a better model for the
shape of space.
1 Philosophy of space
1.1 Leibniz and Newton
1.3 Non-Euclidean geometry
1.4 Gauss and Poincaré
3.1 Classical mechanics
4 Spatial measurement
5 Geographical space
6 In psychology
7 See also
9 External links
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 philosopher-mathematician, and Isaac
Newton, the English physicist-mathematician, set out two opposing
theories of what space is. Rather than being an entity that
independently exists over and above other matter, Leibniz held that
space is no more than the collection of spatial relations between
objects in the world: "space is that which results from places taken
together". Unoccupied regions are those that could have objects in
them, and thus spatial relations with other places. For Leibniz, then,
space was an idealised abstraction from the relations between
individual entities or their possible locations and therefore could
not be continuous but must be discrete.
Space could be thought of
in a similar way to the relations between family members. Although
people in the family are related to one another, the relations do not
exist independently of the people. Leibniz argued that space could
not exist independently of objects in the world because that implies a
difference between two universes exactly alike except for the location
of the material world in each universe. But since there would be no
observational way of telling these universes apart then, according to
the identity of 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.
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. 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. 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. 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.
Main article: Non-Euclidean geometry
Spherical geometry is similar to elliptical geometry. On a sphere (the
surface of a ball) there are no parallel lines.
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 L1 and a point P
not on L1, there is exactly one straight line L2 on the plane that
passes through the point P and is parallel to the straight line L1.
Until the 19th century, few doubted the truth of the postulate;
instead debate centered over whether it was necessary as an axiom, or
whether it was a theory that could be derived from the other
axioms. Around 1830 though, the Hungarian
János Bolyai and the
Nikolai Ivanovich Lobachevsky
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
circumference-to-diameter that is less than pi.
Type of geometry
Number of parallels
Sum of angles in a triangle
Ratio of circumference to diameter of circle
Measure of curvature
Gauss and Poincaré
Carl Friedrich Gauss
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.
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. 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. 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
Euclidean geometry is simpler than non-Euclidean
geometry, he assumed the former would always be used to describe the
'true' geometry of the world.
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.
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. 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
Main article: Three-dimensional space
Not to be confused with
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.
Many of the laws of physics, such as the various inverse square laws,
depend on dimension three.
In physics, our three-dimensional space is viewed as embedded in
four-dimensional spacetime, called
Minkowski space (see special
relativity). The idea behind space-time is that time is
hyperbolic-orthogonal to each of the three spatial dimensions.
Main article: Classical mechanics
Part of a series of articles about
displaystyle vec F =m vec a
Second law of motion
Frame of reference
Inertial frame of reference
Inertia / Moment of inertia
Newton's laws of motion
Appell's equation of motion
Koopman–von Neumann mechanics
Equations of motion
Euler's laws of motion
Inertial / Non-inertial reference frame
Mechanics of planar particle motion
Newton's law of universal gravitation
Newton's laws of motion
Simple harmonic motion
Rotating reference frame
Angular acceleration / displacement / frequency /
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.
Main article: Theory of 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 space-time
along space-time intervals are—which justifies the name.
In addition, time and space dimensions should not be viewed as exactly
equivalent in Minkowski space-time. One can freely move in space but
not in time. Thus, time and space coordinates are treated differently
both in special 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 space-time 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 space-time,
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.
reported the first such direct observation of gravitational waves on
14 September 2015.
Main article: Shape of the universe
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 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
Main article: 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.
See also: Spatial analysis
Geography is the branch of science concerned with identifying and
describing the 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 to create an estimate for unobserved
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
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
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.
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
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.
Absolute space and time
Shape of the universe
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
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 and Ebison, Classical Mechanics, p. 1
^ Carnap, R., An Introduction to the Philosophy of Science
^ Leibniz, Fifth letter to Samuel Clarke
^ Vailati, E., Leibniz & Clarke: A Study of Their Correspondence,
^ Sklar, L., Philosophy of Physics, p. 20
^ Sklar, L., Philosophy of Physics, p. 21
^ Sklar, L., Philosophy of Physics, p. 22
^ "Newton's bucket". st-and.ac.uk.
^ Carnap, R., An Introduction to the Philosophy of Science, p. 177-178
^ Lucas, John Randolph. Space,
Time and Causality. p. 149.
^ Carnap, R., An Introduction to the Philosophy of Science, p. 126
^ Carnap, R., An Introduction to the Philosophy of Science, p. 134-136
^ Jammer, Max (1954). Concepts of Space. The History of Theories of
Space in Physics. p. 165. Cambridge:
Harvard University Press.
^ 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
^ Greene, Brian (2003). The Fabric of the Cosmos. New York: Random
House. ISBN 0-375-72720-5.
^ 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. 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
^ "Cosmic Detectives". The European
Space Agency (ESA). 2013-04-02.
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