Editing Space (section)

=== Leibniz and Newton ===
[[File:Gottfried Wilhelm Leibniz, Bernhard Christoph Francke.jpg|[[Gottfried Leibniz]]|upright|thumb]]
Following Galileo and Descartes, during the seventeenth century the [[philosophy of space and time]] revolved around the ideas of [[Gottfried Leibniz]], a German philosopher–mathematician, and [[Isaac Newton]], 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".<ref>Leibniz, Fifth letter to Samuel Clarke. By H.G. Alexander (1956). ''The Leibniz-Clarke Correspondence''. Manchester: Manchester University Press, pp. 55–96.</ref> 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 probability distribution|continuous]] but must be [[discrete probability distribution|discrete]].<ref>Vailati, E. (1997). ''Leibniz & Clarke: A Study of Their Correspondence''. New York: Oxford University Press, p. 115.</ref>
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.<ref>Sklar, L. (1992). ''Philosophy of Physics''. Boulder: Westview Press, p. 20.</ref>
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.<ref>Sklar, L. ''Philosophy of Physics''. p. 21.</ref>

[[Image:GodfreyKneller-IsaacNewton-1689.jpg|[[Isaac Newton]]|upright|thumb]]
Newton took space to be more than relations between material objects and based his position on [[observation]] and experimentation. For a [[Relational theory|relationist]] there can be no real difference between [[inertial frame of reference|inertial motion]], in which the object travels with constant [[velocity]], and [[non-inertial reference frame|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]]s, it must be absolute.<ref>Sklar, L. ''Philosophy of Physics''. p. 22.</ref> He used the example of [[Bucket argument|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.<ref>{{cite web|url=http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Newton_bucket.html|title=Newton's bucket|work=st-and.ac.uk|access-date=20 July 2008|archive-url=https://web.archive.org/web/20080317062957/http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Newton_bucket.html|archive-date=17 March 2008|url-status=live}}</ref> 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.