# Space

used to indicate positions in space.]]

**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 Plato, or Socrates in his reflections on what the Greeks called*khôra*(i.e. "space"), or in the*Physics*of Aristotle (Book IV, Delta) in the definition of*topos*(i.e. place), or in the later "geometrical conception of place" as "space*qua*extension" in the*Discourse on Place*(*Qawl fi al-Makan*) of the 11th-century Arab polymath Alhazen.Refer to Plato's*Timaeus*in the Loeb Classical Library, Harvard University, and to his reflections on*khora*. See also Aristotle's*Physics*, Book IV, Chapter 5, on the definition of*topos*. Concerning Ibn al-Haytham's 11th century conception of "geometrical place" as "spatial extension", which is akin to Descartes' and Leibniz's 17th century notions of*extensio*and*analysis situs*, and his own mathematical refutation of Aristotle's definition of*topos*in natural philosophy, refer to: Nader El-Bizri, "In Defence of the Sovereignty of Philosophy: al-Baghdadi's Critique of Ibn al-Haytham's Geometrisation of Place",*Arabic Sciences and Philosophy*( Cambridge University Press), Vol. 17 (2007), pp. 57-80. 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.French and Ebison, Classical Mechanics, p. 1 Other natural philosophers, notably Gottfried Leibniz, thought instead that space was in fact a collection of relations between objects, given by their distance and direction from one another. In the 18th century, the philosopher and theologian George Berkeley attempted to refute the "visibility of spatial depth" in his*Essay Towards a New Theory of Vision*. Later, the metaphysician Immanuel Kant said that the concepts of space and time are not empirical ones derived from experiences of the outside world—they are elements of an already given systematic framework that humans possess and use to structure all experiences. Kant referred to the experience of "space" in his*Critique of Pure Reason*as being a subjective "pure*a priori*form of intuition". 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.Carnap, R. An introduction to the Philosophy of Science Experimental tests of general relativity have confirmed that non-Euclidean geometries provide a better model for the shape of space.## 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".Leibniz, Fifth letter to Samuel Clarke 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.Vailati, E, Leibniz & Clarke: A Study of Their Correspondence p. 115 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.Sklar, L, Philosophy of Physics, p. 20 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.Sklar, L, Philosophy of Physics, p. 21 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.Sklar, L, Philosophy of Physics, p. 22 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.### 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*.Carnap, R, An introduction to the philosophy of science, p. 177-178 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

### 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, 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.Carnap, R, An introduction to the philosophy of science, p. 134-136 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.Jammer, M, Concepts of Space, p. 165 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.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 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.Carnap, R, An introduction to the philosophy of science, p. 148 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.Sklar, L, Philosophy of Physics, p. 57### Einstein

In 1905, Albert Einstein published his special theory of relativity, which led to the concept that space and time can be viewed as a single construct known as*spacetime*. In this theory, the speed of light in 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 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.Sklar, L, Philosophy of Physics, p. 43 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, 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. 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.### 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.### 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.chapters 8 and 9- John A. Wheeler "A Journey Into Gravity and Spacetime" Scientific American 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.### 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, 13.8 billion years ago{{cite web |title = Cosmic Detectives |url=http://www.esa.int/Our_Activities/Space_Science/Cosmic_detectives |publisher = The European Space Agency (ESA) |date = 2013-04-02 |accessdate = 2013-04-26}} 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

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.