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authorbryan newbold <bnewbold@snark.mit.edu>2009-02-01 08:34:55 -0500
committerbryan newbold <bnewbold@snark.mit.edu>2009-02-01 08:34:55 -0500
commit7ad3b8aef5ad4492e94d350c0ce32d89797b3cab (patch)
tree9a18754b8025daa381ad592a632f95532b3a129b /physics
parent7218768aba3a43f1a62867f35f05cb85a30d7ed2 (diff)
downloadknowledge-7ad3b8aef5ad4492e94d350c0ce32d89797b3cab.tar.gz
knowledge-7ad3b8aef5ad4492e94d350c0ce32d89797b3cab.zip
cleanup, fixed some math
Diffstat (limited to 'physics')
-rw-r--r--physics/general relativity3
-rw-r--r--physics/gravitational waves6
-rw-r--r--physics/special relativity15
3 files changed, 15 insertions, 9 deletions
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 </k/math/tensors>`_*
+*See also `math/tensors </k/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</k/physics/generalrelativity/>`_*
+*See also `physics/general relativity</k/physics/generalrelativity/>`__*
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