= Minkowski spacetime
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{title2=$\mathbb R^{1,3}$}
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<Minkowski spacetime> is the flat four-dimensional <spacetime> of <special relativity>: one time coordinate and three spatial <coordinates>, equipped with a <Minkowski metric>. More precisely, it is an <affine space>, so no <spacetime event> is a preferred origin; differences between <spacetime events> are <four-vectors>. <Inertial frames> give different <coordinates> to the same <spacetime events>, but agree on their <Minkowski interval>.
This geometry answers two different measurement questions with one structure. Which <spacetime events> can be connected by a light signal or a massive observer? The <light cone> classifies them. How much time does a moving clock record? Its <world line> and the <Minkowski metric> determine its <proper time>. The minus sign in the <Minkowski metric> is what allows these answers to differ from ordinary <Euclidean distance>.
For a concrete one-space-dimensional slice, start at the origin $O$ and measure $t$ in seconds and $x$ in <light-seconds>. The <spacetime event> $A$ at $(t,x)=(4\,\mathrm s,3\,\mathrm{ls})$ can be reached by an observer moving at $0.75c$, whereas $B=(2\,\mathrm s,3\,\mathrm{ls})$ would require $1.5c$ to be reached directly from $O$. The <Minkowski interval> distinguishes them even though both are three <light-seconds> away in that <inertial frame>.
Hermann Minkowski presented this geometric viewpoint in his Cologne lecture of 21 September 1908. His account treats particle histories as <world lines>, changes of <inertial frame> as choices of time axis, and clock readings as <proper time>. These are connected geometric ideas, rather than separate corrections to ordinary mechanics.https://www.gutenberg.org/files/66944/old/66944-h/66944-h.htm[Minkowski, Space and Time, §§I–III; Saha's translation in the 1920 collection]{ref}
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