Editing Absolute space and time (section)

==Mathematical definitions==

''Space'', as understood in [[Newtonian mechanics]], is [[three-dimensional space|three-dimensional]] and [[Euclidean space|Euclidean]], with a fixed [[orientation (vector space)|orientation]]. It is denoted ''E''<sup>3</sup>. If some point ''O'' in ''E''<sup>3</sup> is fixed and defined as an [[origin (mathematics)|origin]], the ''position'' of any point ''P'' in ''E''<sup>3</sup> is uniquely determined by its [[radius vector]] <math>\mathbf{r} = \vec{OP}</math> (the origin of this vector coincides with the point ''O'' and its end coincides with the point ''P''). The three-dimensional [[linear vector space]] ''R''<sup>3</sup> is a [[set (mathematics)|set]] of all radius vectors. The space ''R''<sup>3</sup> is endowed with a [[scalar product]] ⟨ , ⟩.

''Time'' is a [[scalar (mathematics)|scalar]] which is the same in all space ''E''<sup>3</sup> and is denoted as ''t''. The [[ordered set]] { ''t'' } is called a time axis.

''Motion'' (also ''path'' or ''[[trajectory]]'') is a [[function (mathematics)|function]] ''r'' : Δ → ''R''<sup>3</sup> that [[map (mathematics)|maps]] a point in the [[interval (mathematics)|interval]] Δ from the time axis to a [[position (vector)|position]] (radius vector) in ''R''<sup>3</sup>.

The above four concepts are the "well-known" objects mentioned by [[Isaac Newton]] in his [[Philosophiæ Naturalis Principia Mathematica|Principia]]:
:''I do not define time, space, place and motion, as being well known to all.''<ref>[[Isaac Newton|Newton]] 1687 ''[[Philosophiae Naturalis Principia Mathematica]]'', Londini, Jussu Societatis Regiae ac Typis J. Streater,  or  '''''[[The Mathematical Principles of Natural Philosophy]]''''', [[London]], English translation by [[Andrew Motte]] 1700s. From part of the Scholium, reprinted on page 737 of ''On the Shoulders of Giants'':The Great Works of Physics and Astronomy (works by [[Copernicus]], [[Johannes Kepler|Kepler]], [[Galileo]], [[Isaac Newton|Newton]], and [[Albert Einstein|Einstein]]). [[Stephen Hawking]], ed. 2002 {{ISBN|0-7624-1348-4}}</ref>