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diff --git a/physics/special relativity.page b/physics/special relativity.page deleted file mode 100644 index 2f5b9af..0000000 --- a/physics/special relativity.page +++ /dev/null @@ -1,62 +0,0 @@ ---- -format: rst -categories: physics -toc: no -... - -=========================== -Special Relativity -=========================== - -.. warning:: This is a rough work in progress!! Likely to be factual errors, - poor grammar, etc. - -.. note:: Most of this content is based on a 2002 Caltech course taught by - Kip Thorn [PH237]_ - -*See also `physics/general relativity</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 -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 | -+----------------+--------------------+ - -Separations -------------- - -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 -is Lorentz-invariant; the scalar value of separation between two events does -not depend on the inertial frame chosen. - -Note the negative sign in front of the time dimension. The are three types of -separations: **space-like** when :m:`$(\Delta s)^2 > 0$`, **null-** or -**light-like** when :m:`$(\Delta s)^2 = 0$`, and **time-like** when -:m:`$(\Delta s)^2 < 0$`. When dealing with time-like separations, ignore the -implication of an imaginary number. The difference in time :m:`$\Delta \Tau$` -is always real: :m:`($\Delta \Tau)^2= -(\Delta s)^2$`. - - -References ----------------- - -.. [PH237] `Gravitational Waves`:title: (aka ph237), a course taught by Kip Thorne at Caltech in 2002. See http://elmer.tapir.caltech.edu/ph237/ for notes and lecture videos. |