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authorbnewbold <bnewbold@ziggy.(none)>2010-01-24 05:23:28 -0500
committerbnewbold <bnewbold@ziggy.(none)>2010-01-24 05:23:28 -0500
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parent214bc7f402377bdafea60be508c7194e596ef238 (diff)
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+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
+-------------- -------- ---------
+Index notation Variable Type
+-------------- -------- ---------
+ $x^0$ $t$ Time
+ $x^1$ $x$ Spatial
+ $x^2$ $y$ Spatial
+ $x^3$ $z$ Spatial
+-------------- -------- ---------
+The separation $(\Delta s)^2$ between two events in space time, in a given
+Lorentzian/inertial frame, is defined
+$$ (\Delta s)^2 \equiv -(\Delta t)^2 + (\Delta x)^2 + (\Delta y)^2 + (\Delta z)^2 $$
+$$ (\Delta s)^2 \equiv -(\Delta x^0)^2 + \sum_{i,j} \delta_{ij} \Delta x^i \Delta x^j$$
+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: ($\Delta \Tau)^2= -(\Delta s)^2$.
+[PH237]: **Gravitational Waves** (aka ph237), a course taught by Kip Thorne at Caltech in 2002. See for notes and lecture videos.