Space is the boundless, three-dimensional extent in which objects In physics, a physical body or physical object is a collection of masses, taken to be one. For example, a cricket ball can be considered an object but the ball also consists of many particles (pieces of matter) and events occur and have relative position and direction.^[1] Physical space is often conceived in three linear The word linear comes from the Latin word linearis, which means created by lines. In mathematics, a linear map or function f is a function which satisfies the following two properties: dimensions In mathematics and physics, the dimension of a space or object is informally defined as the minimum number of coordinates needed to specify each point within it. Thus a line has a dimension of one because only one coordinate is needed to specify a point on it. A surface such as a plane or the surface of a cylinder or sphere has a dimension of two, although modern physicists Physics is a natural science that involves the study of matter and its motion through space-time, as well as all applicable concepts, such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves usually consider it, with time Time is a physical process and non-spatial dimension in which reality is macroscopically transformed in continuity from the past through the present and on to the future. Time has been defined as a one-dimensional quantity used to sequence events, to quantify the durations of events and the intervals between them, and to quantify and measure the, to be part of the boundless four-dimensional continuum known as spacetime In physics, spacetime is any mathematical model that combines space and time into a single continuum. Spacetime is usually interpreted with space being three-dimensional and time playing the role of a fourth dimension that is of a different sort from the spatial dimensions. According to certain Euclidean space perceptions, the universe has three. In mathematics Mathematics is the study of quantity, structure, space, and change. Mathematicians seek out patterns, formulate new conjectures, and establish truth by rigorous deduction from appropriately chosen axioms and definitions one examines 'spaces' with different numbers of dimensions and with different underlying structures. The concept of space is considered to be of fundamental importance to an understanding of the physical universe The Universe is commonly defined as the totality of everything that exists, including all physical matter and energy, the planets, stars, galaxies, and the contents of intergalactic space, although this usage may differ with the context . The term Universe may be used in slightly different contextual senses, denoting such concepts as the cosmos, although disagreement continues between philosophers Philosophy is the study of general and fundamental problems concerning matters such as existence, knowledge, values, reason, mind, and language. It is distinguished from other ways of addressing fundamental questions by its critical, generally systematic approach and its reliance on rational argument. The word "philosophy" comes from the over whether it is itself an entity, a relationship between entities, or part of a conceptual framework A conceptual framework is used in research to outline possible courses of action or to present a preferred approach to an idea or thought. For example, the philosopher Isaiah Berlin used the 'hedgehogs' versus 'foxes' approach; a 'hedgehog' might approach the world in terms of a single organizing principle; a 'fox' might pursue multiple.

Many of the philosophical questions arose in the 17th century, during the early development of classical mechanics In the fields of physics, classical mechanics is one of the two major sub-fields of study in the science of mechanics, which is concerned with the set of physical laws governing and mathematically describing the motions of bodies and aggregates of bodies geometrically distributed within a certain boundary under the action of a system of forces. In Isaac Newton's Sir Isaac Newton FRS was an English physicist, mathematician, astronomer, natural philosopher, alchemist, and theologian who is considered by many scholars and members of the general public to be one of the most influential people in human history. His 1687 publication of the Philosophiæ Naturalis Principia Mathematica (usually called the view, space was absolute - in the sense that it existed permanently and independently of whether there were any matter in the space.^[2] Other natural philosophers Natural philosophy or the philosophy of nature , is a term applied to the study of nature and the physical universe that was dominant before the development of modern science. It is considered to be the precursor of natural sciences such as physics, notably Gottfried Leibniz Gottfried Wilhelm Leibniz (German pronunciation: [ˈɡɔtfʁiːt ˈvɪlhɛlm fɔn ˈlaɪpnɪts]; born 1 July 1646 in Leipzig [OS: 21 June] – died in Hannover 14 November 1716) was a German mathematician and philosopher. Leibniz wrote primarily in Latin and French, thought instead that space was a collection of relations between objects, given by their distance Distance is a numerical description of how far apart objects are. In physics or everyday discussion, distance may refer to a physical length, or an estimation based on other criteria . In mathematics, a distance function or metric is a generalization of the concept of physical distance. A metric is a function that behaves according to a specific and direction Direction is the information contained in the relative position of one point with respect to another point without the distance information. Directions may be either relative to some indicated reference , or absolute according to some previously agreed upon frame of reference (New York City lies due west of Madrid). Direction is often indicated from one another. In the 18th century, Immanuel Kant Immanuel Kant (22 April 1724 – 12 February 1804) was an 18th-century German philosopher from the Prussian city of Königsberg. Kant was the last influential philosopher of modern Europe in the classic sequence of the theory of knowledge during the Enlightenment beginning with thinkers John Locke, George Berkeley, and David Hume described space and time as elements of a systematic framework that humans use to structure their experience.

In the 19th and 20th centuries mathematicians began to examine non-Euclidean geometries A non-Euclidean geometry is the study of shapes and constructions that do not map directly to any n-dimensional Euclidean system, characterized by a non-vanishing Riemann curvature tensor. Examples of non-Euclidean geometries include the hyperbolic and elliptic geometry, which are contrasted with a Euclidean geometry. The essential difference, in which space can be said to be curved, rather than flat. According to Albert Einstein's Albert Einstein (pronounced /ˈælbərt ˈaɪnstaɪn/; German: [ˈalbɐt ˈaɪnʃtaɪn] ; 14 March 1879 – 18 April 1955) was a theoretical physicist, philosopher and author who is widely regarded as one of the most influential and best known scientists and intellectuals of all time. A German-Swiss Nobel laureate, he is often regarded as the theory of general relativity General relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1915. It is the current description of gravitation in modern physics. It unifies special relativity and Newton's law of universal gravitation, and describes gravity as a geometric property of space and time, or spacetime, space around gravitational fields A gravitational field is a model used within physics to explain how gravity exists in the universe. In its original concept, gravity was a force between point masses. Following Newton, Laplace attempted to model gravity as some kind of radiation field or fluid, and since the 19th century explanations for gravity have usually been sought in terms deviates from Euclidean space.^[3] Experimental tests of general relativity At its introduction in 1915, the general theory of relativity did not have a solid empirical foundation. It was known that it correctly accounted for the "anomalous" precession of the perihelion of Mercury and on philosophical grounds it was considered satisfying that it was able to unify Newton's law of universal gravitation with have confirmed that non-Euclidean space provides a better model for the shape of space.

Philosophy of space

Leibniz and Newton

In 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, epistemology, and character of space and time. While such ideas have been central to philosophy from its inception, the philosophy of space and time was both an inspiration for and a central aspect of early analytic philosophy. The subject emerged as a central issue in epistemology Epistemology or theory of knowledge is the branch of philosophy concerned with the nature and scope (limitations) of knowledge. It addresses the questions: and metaphysics Metaphysics is a branch of philosophy that is not easily defined. It is concerned with explaining the fundamental nature of being and the world. Someone who studies metaphysics would be called either a metaphysicist or a metaphysician. At its heart, Gottfried Leibniz Gottfried Wilhelm Leibniz (German pronunciation: [ˈɡɔtfʁiːt ˈvɪlhɛlm fɔn ˈlaɪpnɪts]; born 1 July 1646 in Leipzig [OS: 21 June] – died in Hannover 14 November 1716) was a German mathematician and philosopher. Leibniz wrote primarily in Latin and French, the German philosopher-mathematician, and Isaac Newton Sir Isaac Newton FRS was an English physicist, mathematician, astronomer, natural philosopher, alchemist, and theologian who is considered by many scholars and members of the general public to be one of the most influential people in human history. His 1687 publication of the Philosophiæ Naturalis Principia Mathematica (usually called the, 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".^[4] 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 is a conceptual process by which higher, more abstract concepts are derived from the usage and classification of literal, "real," or "concrete" concepts from the relations between individual entities or their possible locations and therefore could not be continuous In probability theory, a probability distribution is called continuous if its cumulative distribution function is continuous[citation needed]. This is equivalent to saying that for random variables X with the distribution in question, Pr[X = a] = 0 for all real numbers a, i.e.: the probability that X attains the value a is zero, for any number a but must be discrete Discrete probability distributions arise in the mathematical description of probabilistic and statistical problems in which the values that might be observed are restricted to being within a pre-defined list of possible values. This list has either a finite number of members, or at most is countable.^[5] 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.^[6] 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 which states that two or more objects or entities are identical , if they have all their properties in common. That is, entities x and y are identical if any predicate possessed by x is also possessed by y and vice versa. A related principle is the indiscernibility of identicals, discussed, there would be no real difference between them. According to the principle of sufficient reason The principle of sufficient reason states that anything that happens does so for a definite reason. In virtue of which no fact can be real or no statement true unless it has sufficient reason why it should not be otherwise. It is usually attributed to Gottfried Leibniz, although the first person to use it was Anaximander of Miletus, any theory of space that implied that there could be these two possible universes, must therefore be wrong.^[7]

Newton took space to be more than relations between material objects and based his position on observation Observation is either an activity of a living being , consisting of receiving knowledge of the outside world through the senses, or the recording of data using scientific instruments. The term may also refer to any data collected during this activity and experimentation Experiment is the step in the scientific method that arbitrates between competing models or hypotheses. Experimentation is also used to test existing theories or new hypotheses in order to support them or disprove them. An experiment or test can be carried out using the scientific method to answer a question or investigate a problem. First an. For a relationist Karl Mannheim pioneered the idea of Relationism, in the development of his theories on the Sociology of Knowledge. More particular applications of the term have arisen since his time there can be no real difference between inertial motion In physics, an inertial frame of reference is a frame of reference which describes time homogeneously and space homogeneously, isotropically, and in a time independent manner. This allows motion and interactions to be described without the presence of fictitious forces. Special relativity states that there are actually infinitely many such frames,, in which the object travels with constant velocity In physics, velocity is the rate of change of position. It is a vector physical quantity; both magnitude and direction are required to define it. The scalar absolute value of velocity is speed, a quantity that is measured in meters per second (m/s or ms−1) when using the SI (metric) system, and non-inertial motion A non-inertial reference frame is a reference frame that is not an inertial reference frame. As such, the laws of physics in such a frame do not take on their most simple form, as required by the special principle of relativity. To explain the motion of bodies entirely within the viewpoint of non-inertial reference frames, fictitious forces must, 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 In physics, a force is any influence that causes a free body to undergo an acceleration. Force can also be described by intuitive concepts such as a push or pull that can cause an object with mass to change its velocity , i.e., to accelerate, or which can cause a flexible object to deform. A force has both magnitude and direction, making it a, it must be absolute.^[8] He used the example of water in a spinning bucket to demonstrate his argument. Water Water is a chemical substance with the chemical formula H2O. Its molecule contains one oxygen and two hydrogen atoms connected by covalent bonds. Water is a liquid at ambient conditions, but it often co-exists on Earth with its solid state, ice, and gaseous state, water vapor or steam in a bucket A bucket, also called a pail, is a watertight, vertical cylinder or truncated cone, with an open top and a flat bottom, usually attached to a semicircular carrying handle called the bail. A bucket is distinguished from other containers by being unlidded. Their main purpose is the carrying of water, but they may also have other purposes. Elaborate 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^[9]. Instead, Newton argued, it must be a result of non-inertial motion relative to space itself. For several centuries the bucket argument was 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 an 18th-century German philosopher from the Prussian city of Königsberg. Kant was the last influential philosopher of modern Europe in the classic sequence of the theory of knowledge during the Enlightenment beginning with thinkers John Locke, George Berkeley, and David Hume developed a theory of knowledge Knowledge is defined by the Oxford English Dictionary as expertise, and skills acquired by a person through experience or education; the theoretical or practical understanding of a subject; (ii) what is known in a particular field or in total; facts and information; or (iii) awareness or familiarity gained by experience of a fact or situation in which knowledge about space can be both a priori The terms a priori and a posteriori ("subsequent to") are used in philosophy (epistemology) to distinguish two types of knowledge, justifications or arguments. A priori knowledge or justification is independent of experience (for example 'All bachelors are unmarried'); a posteriori knowledge or justification is dependent on experience or and synthetic The analytic-synthetic distinction, , is a conceptual distinction, used primarily in philosophy to distinguish propositions into two types: analytic propositions and synthetic propositions. Analytic propositions are those which are true simply by virtue of their meaning while synthetic propositions are not; however, philosophers have used the.^[10] 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 are part of an unavoidable systematic framework for organizing our experiences.^[11]

Non-Euclidean geometry

Euclid's Elements contained five postulates that form the basis for Euclidean geometry. One of these, the parallel postulate has been the subject of debate among mathematicians for many centuries. It states that on any plane on which there is a straight line L₁ and a point P not on L₁, there is only 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.^[12] Around 1830 though, the Hungarian János Bolyai and the Russian Nikolai Ivanovich Lobachevsky separately published treatises on a type of geometry that does not include the parallel postulate, called hyperbolic geometry. In this geometry, an infinite number of parallel lines pass through the point P. Consequently the sum of angles in a triangle is less than 180^o 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^o 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, the 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 he actually carried out a test, on a small scale, by triangulating mountain tops in Germany.^[13]

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.^[14] 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.^[15] 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.^[16] Since Euclidean geometry is simpler than non-Euclidean geometry, he assumed the former would always be used to describe the 'true' geometry of the world.^[17]

Einstein

In 1905, Albert Einstein published a paper on a special theory of relativity, in which he proposed that space and time be combined into 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.

Over the following ten years 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.^[18] According to the general theory, time goes more slowly at places with lower gravitational potentials and rays of light bend in the presence of a gravitational field. Scientists have studied the behaviour of binary pulsars, confirming the predictions of Einstein's theories and Non-Euclidean geometry is usually used to describe spacetime.

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, function spaces in general have no close relation to Euclidean space.

Physics

Classical mechanics

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.

Astronomy

Astronomy is the science involved with the observation, explanation and measuring of objects in outer space.

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.^[19]

Experiments are ongoing to attempt to directly measure gravitational waves. This is essentially solutions to the equations of general relativity, which describe moving ripples of spacetime. Indirect evidence for this has been found in the motions of the Hulse-Taylor binary system.

Cosmology

Relativity theory leads to the cosmological question of what shape the universe is, and where space came from. It appears that space was created in the Big Bang 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. Alan Guth whom is known for his Inflationary theory, presented the first ideas in a seminar at Stanford Linear Accelerator Center on January 23, 1980.

Spatial measurement

The measurement of physical space has long been important. Although earlier societies had developed measuring systems, the International System of Units, (SI), is now the most common system of units used in the measuring of space, and is almost universally used within science.

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.

Geography

Geography is the branch of science concerned with identifying and describing the Earth, utilizing spatial awareness to try and 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 phenomena.

Geographical space is often considered as land, and can have a relation to ownership usage (in which space is seen as property or territory). While some cultures assert the rights of the individual in terms of ownership, other cultures will identify with a communal approach to land ownership, while still other cultures such as Australian Aboriginals, rather than asserting ownership rights to land, invert the relationship and consider that they are in fact owned by the land. Spatial planning is a method of regulating the use of space at land-level, with decisions made at regional, national and international levels. Space can also impact on human and cultural behavior, being an important factor in architecture, where it will impact on the design of buildings and structures, and on farming.

Ownership of space is not restricted to land. Ownership of airspace and of waters is decided internationally. Other forms of ownership have been recently asserted to other spaces — for example to the radio bands of the electromagnetic spectrum or to cyberspace.

Public space is a term used to define areas of land as collectively owned by the community, and managed in their name by delegated bodies; such spaces are open to all. While private property is the land culturally owned by an individual or company, for their own use and pleasure.

Abstract space is a term used in geography to refer to a hypothetical space characterized by complete homogeneity. When modeling activity or behavior, it is a conceptual tool used to limit extraneous variables such as terrain.

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.

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).

See also

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

References

1. ^ Britannica Online Encyclopedia: Space
2. ^ French and Ebison, Classical Mechanics, p. 1
3. ^ Carnap, R. An introduction to the Philosophy of Science
4. ^ Leibniz, Fifth letter to Samuel Clarke
5. ^ Vailati, E, Leibniz & Clarke: A Study of Their Correspondence p. 115
6. ^ Sklar, L, Philosophy of Physics, p. 20
7. ^ Sklar, L, Philosophy of Physics, p. 21
8. ^ Sklar, L, Philosophy of Physics, p. 22
9. ^ Newton's bucket
10. ^ Carnap, R, An introduction to the philosophy of science, p. 177-178
11. ^ Lucas, John Randolph. Space, Time and Causality. p. 149.
12. ^ Carnap, R, An introduction to the philosophy of science, p. 126
13. ^ Carnap, R, An introduction to the philosophy of science, p. 134-136
14. ^ Jammer, M, Concepts of Space, p. 165
15. ^ 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
16. ^ Carnap, R, An introduction to the philosophy of science, p. 148
17. ^ Sklar, L, Philosophy of Physics, p. 57
18. ^ Sklar, L, Philsosophy of Physics, p. 43
19. ^ chapters 8 and 9- John A. Wheeler "A Journey Into Gravity and Spacetime" Scientific American ISBN 0-7167-6034-7

Categories: Spacetime | Topology | Environments | Nothing

See Also:

What Links Here:

Recently Viewed Pages:

• Home
• 401k: Answers
• Finances: Blogs
• Securitization: Encyclopedia
• Financial Risk: Encyclopedia
• Finances: Dictionary
• Deposit Account: Encyclopedia
• Money: Encyclopedia
• Investment: Encyclopedia
• Mutual Funds: Encyclopedia

Most Popular Pages:

• Equilibrant: Answers
• Bao Nhan Dan: Blogs
• Home
• Resultant of Forces: Answers
• Nhan Dan: Images
• Fbop: News
• Magnitude: Answers
• Nhan Dan: Blogs
• Resultant Speed: Answers
• Search Terms

Related 'Space' Searches: