From dba922cd0c8f5ce7252f33268189259706fc9e75 Mon Sep 17 00:00:00 2001 From: bnewbold Date: Sun, 24 Jan 2010 05:23:28 -0500 Subject: partial fixes --- physics/special-relativity.page | 60 +++++++++++++++++++++++++++++++++++++++++ 1 file changed, 60 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..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. -- cgit v1.2.3