From 7ad3b8aef5ad4492e94d350c0ce32d89797b3cab Mon Sep 17 00:00:00 2001 From: bryan newbold Date: Sun, 1 Feb 2009 08:34:55 -0500 Subject: cleanup, fixed some math --- physics/general relativity | 3 ++- physics/gravitational waves | 6 ++++-- physics/special relativity | 15 +++++++++------ 3 files changed, 15 insertions(+), 9 deletions(-) (limited to 'physics') diff --git a/physics/general relativity b/physics/general relativity index 7521db5..7fc29eb 100644 --- a/physics/general relativity +++ b/physics/general relativity @@ -8,8 +8,9 @@ General Relativity .. note:: Most of this content is based on a 2002 Caltech course taught by Kip Thorn [PH237]_ -*See also math/tensors _* +*See also math/tensors __* +(no content) References ---------------- diff --git a/physics/gravitational waves b/physics/gravitational waves index ab7174e..5aa1744 100644 --- a/physics/gravitational waves +++ b/physics/gravitational waves @@ -38,9 +38,11 @@ Fifth term: current quadrupole Energy ---------------- -Quick calculation: for a source with mass M, size L, period P, the quadrupole moment $M_2 \approx M L^2$, h \approx 1/c^2 (Newtonian potential energy) ???? +Quick calculation: for a source with mass M, size L, period P, the quadrupole +moment :m:$M_2 \approx M L^2$, :m:$h \approx 1/c^2 (Newtonian potential +energy) ???? -h on the order of$10^{-22}$+h on the order of :m:$10^{-22}$ Propagation ----------------- diff --git a/physics/special relativity b/physics/special relativity index 41bf4b8..37fd3e9 100644 --- a/physics/special relativity +++ b/physics/special relativity @@ -8,7 +8,7 @@ Special Relativity .. note:: Most of this content is based on a 2002 Caltech course taught by Kip Thorn [PH237]_ -*See also physics/general relativity_* +*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 @@ -17,22 +17,25 @@ 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 | +| $x^0$: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 +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 -- cgit v1.2.1