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 diff --git a/physics/special-relativity.page b/physics/special-relativity.pagenew file mode 100644index 0000000..bb5f564--- /dev/null+++ b/physics/special-relativity.page@@ -0,0 +1,60 @@+---+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]_++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 +-------------- -------- ---------+ $x^0$ $t$ Time + $x^1$ $x$ Spatial + $x^2$ $y$ Spatial + $x^3$ $z$ Spatial +-------------- -------- ---------++Separations+-------------++The separation $(\Delta s)^2$ between two events in space time, in a given+Lorentzian/inertial frame, is defined+as:++$$(\Delta s)^2 \equiv -(\Delta t)^2 + (\Delta x)^2 + (\Delta y)^2 + (\Delta z)^2$$++or++$$(\Delta s)^2 \equiv -(\Delta x^0)^2 + \sum_{i,j} \delta_{ij} \Delta x^i \Delta x^j$$++where $\delta_{ij}$ is the Kronecker delta (unity or 1 when +$i=j$; 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 $(\Delta s)^2 > 0$, **null-** or +**light-like** when $(\Delta s)^2 = 0$, and **time-like** when +$(\Delta s)^2 < 0$. When dealing with time-like separations, ignore the+implication of an imaginary number. The difference in time $\Delta \Tau$ +is always real: ($\Delta \Tau)^2= -(\Delta s)^2$.+++References+----------------++[PH237]: **Gravitational Waves** (aka ph237), a course taught by Kip Thorne at Caltech in 2002. See http://elmer.tapir.caltech.edu/ph237/ for notes and lecture videos.