HOME
The Info List - Space


--- Advertisement ---



Space
Space
is the boundless three-dimensional extent in which objects and events have relative position and direction.[1] Physical space is often conceived in three linear dimensions, although modern physicists usually consider it, with time, to be part of a boundless 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 Plato, or Socrates
Socrates
in his reflections on what the Greeks called khôra (i.e. "space"), or in the Physics
Physics
of Aristotle
Aristotle
( Book
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.[2] Many of these classical philosophical questions were discussed in the Renaissance
Renaissance
and then reformulated in the 17th century, particularly during the early development of classical mechanics. In Isaac Newton's view, space was absolute—in the sense that it existed permanently and independently of whether there was any matter in the space.[3] Other natural philosophers, notably Gottfried Leibniz, thought instead that space was in fact a collection of relations between objects, given by their distance and direction from one another. In the 18th century, the philosopher and theologian George Berkeley
George Berkeley
attempted to refute the "visibility of spatial depth" in his Essay Towards a New Theory of Vision. Later, the metaphysician Immanuel Kant
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 intuition". 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.[4] Experimental tests of general relativity have confirmed that non-Euclidean geometries provide a better model for the shape of space.

Contents

1 Philosophy of space

1.1 Leibniz and Newton 1.2 Kant 1.3 Non-Euclidean geometry 1.4 Gauss and Poincaré 1.5 Einstein

2 Mathematics 3 Physics

3.1 Classical mechanics 3.2 Relativity 3.3 Cosmology

4 Spatial measurement 5 Geographical space 6 In psychology 7 See also 8 References 9 External links

Philosophy of space Leibniz and Newton

Gottfried Leibniz

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".[5] Unoccupied regions are those that could have objects in them, and thus spatial relations with other places. For Leibniz, then, space was an idealised abstraction from the relations between individual entities or their possible locations and therefore could not be continuous but must be discrete.[6] Space
Space
could be thought of in a similar way to the relations between family members. Although people in the family are related to one another, the relations do not exist independently of the people.[7] Leibniz argued that space could not exist independently of objects in the world because that implies a difference between two universes exactly alike except for the location of the material world in each universe. But since there would be no observational way of telling these universes apart then, according to the identity of indiscernibles, there would be no real difference between them. According to the principle of sufficient reason, any theory of space that implied that there could be these two possible universes must therefore be wrong.[8]

Isaac Newton

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.[9] He used the example of water in a spinning bucket to demonstrate his argument. Water
Water
in a bucket is hung from a rope and set to spin, starts with a flat surface. After a while, as the bucket continues to spin, the surface of the water becomes concave. If the bucket's spinning is stopped then the surface of the water remains concave as it continues to spin. The concave surface is therefore apparently not the result of relative motion between the bucket and the water.[10] Instead, Newton argued, it must be a result of 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

Immanuel Kant

In the eighteenth century the German philosopher Immanuel Kant developed a theory of knowledge in which knowledge about space can be both a priori and synthetic.[11] According to Kant, knowledge about space is synthetic, in that statements about space are not simply true by virtue of the meaning of the words in the statement. In his work, Kant rejected the view that space must be either a substance or relation. Instead he came to the conclusion that space and time are not discovered by humans to be objective features of the world, but imposed by us as part of a framework for organizing experience.[12] Non-Euclidean geometry Main article: Non-Euclidean geometry

Spherical 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.[13] Around 1830 though, the Hungarian János Bolyai
János Bolyai
and the Russian 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
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

Hyperbolic Infinite < 180° > π < 0

Euclidean 1 180° π 0

Elliptical 0 > 180° < π > 0

Gauss and Poincaré

Carl Friedrich Gauss

Henri 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, a German mathematician, was the first to consider an empirical investigation of the geometrical structure of space. He thought of making a test of the sum of the angles of an enormous stellar triangle, and there are reports that he actually carried out a test, on a small scale, by triangulating mountain tops in Germany.[14] Henri Poincaré, a French mathematician and physicist of the late 19th century, introduced an important insight in which he attempted to demonstrate the futility of any attempt to discover which geometry applies to space by experiment.[15] He considered the predicament that would face scientists if they were confined to the surface of an imaginary large sphere with particular properties, known as a 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.[16] In fact, the scientists cannot in principle determine whether they inhabit a plane or sphere and, Poincaré argued, the same is true for the debate over whether real space is Euclidean or not. For him, which geometry was used to describe space was a matter of convention.[17] Since Euclidean geometry
Euclidean geometry
is simpler than non-Euclidean geometry, he assumed the former would always be used to describe the 'true' geometry of the world.[18] Einstein

Albert Einstein

In 1905, Albert Einstein
Albert Einstein
published his special theory of relativity, which led to the concept that space and time can be viewed as a single construct known as spacetime. In this theory, the speed of light in a vacuum is the same for all observers—which has the result that two events that appear simultaneous to one particular observer will not be simultaneous to another observer if the observers are moving with respect to one another. Moreover, an observer will measure a moving clock to tick more slowly than one that is stationary with respect to them; and objects are measured to be shortened in the direction that they are moving with respect to the observer. Subsequently, Einstein
Einstein
worked on a general theory of relativity, which is a theory of how gravity interacts with spacetime. Instead of viewing gravity as a force field acting in spacetime, Einstein suggested that it modifies the geometric structure of spacetime itself.[19] According to the general theory, time goes more slowly at places with lower gravitational potentials and rays of light bend in the presence of a gravitational field. Scientists have studied the behaviour of binary pulsars, confirming the predictions of Einstein's theories, and non- Euclidean geometry
Euclidean geometry
is usually used to describe spacetime. Mathematics Main article: Three-dimensional space Not to be confused with Space
Space
(mathematics). In modern mathematics spaces are defined as sets with some added structure. They are frequently described as different types of manifolds, which are spaces that locally approximate to Euclidean space, and where the properties are defined largely on local connectedness of points that lie on the manifold. There are however, many diverse mathematical objects that are called spaces. For example, vector spaces such as function spaces may have infinite numbers of independent dimensions and a notion of distance very different from Euclidean space, and topological spaces replace the concept of distance with a more abstract idea of nearness. Physics Many of the laws of physics, such as the various inverse square laws, depend on dimension three.[20] In physics, our three-dimensional space is viewed as embedded in four-dimensional spacetime, called Minkowski space
Minkowski space
(see special relativity). The idea behind space-time is that time is hyperbolic-orthogonal to each of the three spatial dimensions. Classical mechanics Main article: Classical mechanics

Part of a series of articles about

Classical mechanics

F →

= m

a →

displaystyle vec F =m vec a

Second
Second
law of motion

History Timeline

Branches

Applied Celestial Continuum Dynamics Kinematics Kinetics Statics Statistical

Fundamentals

Acceleration Angular momentum Couple D'Alembert's principle Energy

kinetic potential

Force Frame of reference Inertial frame of reference Impulse Inertia / Moment of inertia Mass

Mechanical power Mechanical work

Moment Momentum Space Speed Time Torque Velocity Virtual work

Formulations

Newton's laws of motion

Analytical mechanics

Lagrangian mechanics Hamiltonian mechanics Routhian mechanics Hamilton–Jacobi equation Appell's equation of motion Udwadia–Kalaba equation Koopman–von Neumann mechanics

Core topics

Damping (ratio) Displacement Equations of motion Euler's laws of motion Fictitious force Friction Harmonic oscillator

Inertial / Non-inertial reference frame Mechanics of planar particle motion

Motion (linear) Newton's law of universal gravitation Newton's laws of motion Relative velocity Rigid body

dynamics Euler's equations

Simple harmonic motion Vibration

Rotation

Circular motion Rotating reference frame Centripetal force Centrifugal force

reactive

Coriolis force Pendulum Tangential speed Rotational speed

Angular acceleration / displacement / frequency / velocity

Scientists

Galileo Huygens Newton Kepler Horrocks Halley Euler d'Alembert Clairaut Lagrange Laplace Hamilton Poisson Daniel Bernoulli Johann Bernoulli Cauchy

v t e

Space
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. Relativity 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.[21] 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
Hulse–Taylor binary
system, for example) experiments attempting to directly measure these waves are ongoing at the LIGO
LIGO
and Virgo collaborations. LIGO
LIGO
scientists reported the first such direct observation of gravitational waves on 14 September 2015.[22][23] Cosmology 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[24] and has been expanding ever since. The overall shape of space is not known, but space is known to be expanding very rapidly due to the cosmic inflation. Spatial measurement 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. Geographical space See also: Spatial analysis Geography
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
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 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
Spatial planning
is a method of regulating the use of space at land-level, with decisions made at regional, national and international levels. Space
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
Ownership
of space is not restricted to land. Ownership
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
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), 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. See also

Physics
Physics
portal

Book: Space

Absolute space and time Aether theories Cosmology General relativity Personal space Shape of the universe Space
Space
exploration Spatial-temporal reasoning Spatial analysis

References

^ " Space
Space
Physics
Physics
and Metaphysics". Encyclopædia Britannica.  ^ Refer to Plato's Timaeus in the Loeb Classical Library, Harvard University, and to his reflections on khora. See also Aristotle's Physics, Book
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, p. 115 ^ 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
Time
and Causality. p. 149. ISBN 0-19-875057-9.  ^ 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
Space
in Physics. p. 165. Cambridge: Harvard University
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
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
Nature
News. Retrieved 12 January 2018.  ^ Abbott, Benjamin P.; et al. ( LIGO
LIGO
Scientific Collaboration and Virgo Collaboration) (2016). " Observation
Observation
of Gravitational Waves from a Binary Black Hole Merger". Phys. Rev. Lett. 116 (6): 061102. arXiv:1602.03837 . Bibcode:2016PhRvL.116f1102A. doi:10.1103/PhysRevLett.116.061102. PMID 26918975. Lay summary (PDF).  ^ "Cosmic Detectives". The European Space
Space
Agency (ESA). 2013-04-02. Retrieved 2013-04-26. 

External links

Wikiquote has quotations related to: Space

Look up space in Wiktionary, the free dictionary.

v t e

Elements of nature

Universe

Space Time Energy Matter Change

Earth

Earth
Earth
science History (geological) Structure Geology Plate tectonics Oceans Gaia hypothesis Future

Weather

Meteorology Atmosphere (Earth) Climate Clouds Sunlight Tides Wind

Natural environment

Ecology Ecosystem Field Radiation Wilderness Wildfires

Life

Origin (abiogenesis) Evolutionary history Biosphere Hierarchy Biology (astrobiology)

Organism Eukaryota

flora

plants

fauna

animals

fungi protista

Prokaryotes

archaea bacteria

Viruses

Category:Nature Portal:Science

Authority control

.