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 diff --git a/physics/special relativity b/physics/special relativityindex 41bf4b8..37fd3e9 100644--- a/physics/special relativity+++ b/physics/special relativity@@ -8,7 +8,7 @@ Special Relativity .. note:: Most of this content is based on a 2002 Caltech course taught by Kip Thorn [PH237]_ -*See also physics/general relativity_*+*See also physics/general relativity__* As opposed to general relativity, special relativity takes place in a *flat* Minkowski space time: a 4-space with three spatial dimensions and one time@@ -17,22 +17,25 @@ dimension. +----------------+--------------------+ | Index notation | Variable | Type | +----------------+--------------------+-| $x^\0:m: | $t$:m: | Time |-| $x^\1:m: | $x$:m: | Spatial |-| $x^\2:m: | $y$:m: | Spatial |-| $x^\3:m: | $z$:m: | Spatial |+| $x^0$:m: | $t$:m: | Time |+| $x^1$:m: | $x$:m: | Spatial |+| $x^2$:m: | $y$:m: | Spatial |+| $x^3$:m: | $z$:m: | Spatial | +----------------+--------------------+ Separations ------------- -The separation $(\Delta s)^2:m: between two events in space time, in a given+The separation $(\Delta s)^2$:m: between two events in space time, in a given Lorentzian/inertial frame, is defined as: :m:$$(\Delta s)^2 \equiv -(\Delta t)^2 + (\Delta x)^2 + (\Delta y)^2 + (\Delta z)^2$$+ or+ :m:$$(\Delta s)^2 \equiv -(\Delta x^0)^2 + \sum_{i,j} \delta_{ij} \Delta x^i \Delta x^j$$+ where :m:$\delta_{ij}$ is the Kronecker delta (unity or 1 when :m:$i=j\$; zero otherwise), and the indices i and j are over the spatial dimensions 1,2,3 (corresponding to x,y,z). It can be shown that this separation