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Diffstat (limited to 'physics/special relativity')
| -rw-r--r-- | physics/special relativity | 15 |
1 files changed, 9 insertions, 6 deletions
diff --git a/physics/special relativity b/physics/special relativity index 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</k/physics/generalrelativity/>`_* +*See also `physics/general relativity</k/physics/generalrelativity/>`__* 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 |