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]
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.
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
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
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
Albert Einstein In 1905,
Part of a series of articles about Classical mechanics F → = m a → displaystyle vec F =m vec a
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
Book: Space Absolute space and time
Aether theories
Cosmology
General relativity
Personal space
Shape of the universe
References ^ "
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