From 8c62b232273c58cf9cd6a939ad61b05a9725ebce Mon Sep 17 00:00:00 2001 From: bryan newbold Date: Sun, 13 Jul 2008 20:56:44 -0400 Subject: start of SR --- physics/special relativity | 53 ++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 53 insertions(+) create mode 100644 physics/special relativity (limited to 'physics') diff --git a/physics/special relativity b/physics/special relativity new file mode 100644 index 0000000..41bf4b8 --- /dev/null +++ b/physics/special relativity @@ -0,0 +1,53 @@ +=========================== +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_* + +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. -- cgit v1.2.1