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. 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.
Isaac Newton viewed space as absolute, existing permanently and independently of whether there was any matter in it. In contrast, other
natural philosophers, notably
Gottfried Leibniz, thought 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".
Galileo Galilean and
Cartesian theories about space, matter, and motion are at the foundation of the
Scientific Revolution, which is understood to have culminated with the publication of
Newton's
Principia Mathematica in 1687. Newton's theories about space and time helped him explain the movement of objects. While his theory of space is considered the most influential in physics, it emerged from his predecessors' ideas about the same. As one of the pioneers of
modern science, Galileo revised the established
Aristotelian and
Ptolemaic ideas about a
geocentric cosmos. He backed the
Copernican theory that the universe was
heliocentric, with a stationary Sun at the center and the planets—including the Earth—revolving around the Sun. If the Earth moved, the Aristotelian belief that its natural tendency was to remain at rest was in question. Galileo wanted to prove instead that the Sun moved around its axis, that motion was as natural to an object as the state of rest. In other words, for Galileo, celestial bodies, including the Earth, were naturally inclined to move in circles. This view displaced another Aristotelian idea—that all objects gravitated towards their designated natural place-of-belonging.
René Descartes Descartes set out to replace the Aristotelian worldview with a theory about space and motion as determined by
natural laws. In other words, he sought a
metaphysical foundation or a
mechanical explanation for his theories about matter and motion.
Cartesian space was
Euclidean in structure—infinite, uniform and flat. It was defined as that which contained matter; conversely, matter by definition had a spatial extension so that there was no such thing as empty space. He posited a clear distinction between the body and mind, which is referred to as the
Cartesian dualism.
Leibniz and Newton |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". 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. |upright|thumb 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.
Kant In the eighteenth century the German philosopher
Immanuel Kant published his theory of space as "a property of our mind" by which "we represent to ourselves objects as outside us, and all as in space" in the
Critique of Pure Reason On his view the nature of spatial predicates are "relations that only attach to the form of intuition alone, and thus to the subjective constitution of our mind, without which these predicates could not be attached to anything at all." This develops his theory of
knowledge in which knowledge about space itself can be both
a priori and
synthetic. According to Kant, knowledge about space is
synthetic because any proposition about space cannot be true
merely in virtue of the meaning of the terms contained in the proposition. In the counter-example, the proposition "all unmarried men are bachelors"
is true by virtue of each term's meaning. Further, space is
a priori because it is the form of our receptive abilities to receive information about the external world. For example, someone without sight can still perceive spatial attributes via touch, hearing, and smell. Knowledge of space itself is
a priori because it belongs to the subjective constitution of our mind as the form or manner of our intuition of external objects.
Non-Euclidean 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 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° 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.
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.
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
convention. 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.
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
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. 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. Non-Euclidean geometry is usually used to describe spacetime. == Mathematics ==