From f61026119df4700f69eb73e95620bc5928ca0fcb Mon Sep 17 00:00:00 2001 From: User Date: Tue, 13 Oct 2009 02:52:09 +0000 Subject: Grand rename for gitit transfer --- physics/special relativity.page | 56 +++++++++++++++++++++++++++++++++++++++++ 1 file changed, 56 insertions(+) create mode 100644 physics/special relativity.page (limited to 'physics/special relativity.page') diff --git a/physics/special relativity.page b/physics/special relativity.page new file mode 100644 index 0000000..37fd3e9 --- /dev/null +++ b/physics/special relativity.page @@ -0,0 +1,56 @@ +=========================== +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