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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
commitdba922cd0c8f5ce7252f33268189259706fc9e75 (patch)
tree67554e74d34a0d798cc628a04567e863fd6887fe
parent214bc7f402377bdafea60be508c7194e596ef238 (diff)
downloadknowledge-dba922cd0c8f5ce7252f33268189259706fc9e75.tar.gz
knowledge-dba922cd0c8f5ce7252f33268189259706fc9e75.zip
partial fixes
-rw-r--r--physics/general relativity.page24
-rw-r--r--physics/gravitational-waves.page (renamed from physics/gravitational waves.page)26
-rw-r--r--physics/special relativity.page62
-rw-r--r--physics/special-relativity.page60
-rw-r--r--physics/units.page14
5 files changed, 80 insertions, 106 deletions
diff --git a/physics/general relativity.page b/physics/general relativity.page
deleted file mode 100644
index f4a45af..0000000
--- a/physics/general relativity.page
+++ /dev/null
@@ -1,24 +0,0 @@
----
-format: rst
-categories: physics
-toc: no
-...
-
-===========================
-General 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 `math/tensors </math/tensors>`__*
-
-(no content)
-
-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.
diff --git a/physics/gravitational waves.page b/physics/gravitational-waves.page
index 66f6c04..c853e2b 100644
--- a/physics/gravitational waves.page
+++ b/physics/gravitational-waves.page
@@ -22,33 +22,33 @@ Waves are double integrals of curvature tensor...
Gravitons as Quantum Particles
---------------------------------
-Invariance angles: (Spin of quantum particle) = :latex:`$2 pi$` / (invariance angle)
+Invariance angles: (Spin of quantum particle) = $2 pi$ / (invariance angle)
-Graviton has :latex:`$\pi$` invariance angle, so it is spin 2; photons have unique :latex:`$\arrow{E}$` vector, so invariance angle is :latex:`$2\pi$`, spin 1
+Graviton has $\pi$ invariance angle, so it is spin 2; photons have unique $\arrow{E}$ vector, so invariance angle is $2\pi$, spin 1
Also describes spin by the group of Lorentz transformations which effect propagation.
Two polarizations: cross and plus, corresponding to spin of particles aligning with or against propagation? (Ref: Eugene Vickner? reviews of modern physics)
-Waves' multipole order :latex:`$\geq$` spin of quantum = 2 for graviton ((??))
+Waves' multipole order $\geq$ spin of quantum = 2 for graviton ((??))
Waves don't propagate like E, because mass monopoles don't oscillate like charges.
-:latex:`$ h \approx \frac{G}{c^2} \frac{M_0}{r} + \frac{G}{c^3} \frac{M'_1}{r} + \frac{G}{c^4} \frac{M''_2}{r} + \frac{G}{c^4} \frac{S'_1}{r} + \frac{G}{c^5} \frac{S''_1}{r}$`
-First term: mass can't oscillate
-Second term: momentum can't oscillate
-Third term: mass quadrupole moment dominates
-Fourth term: angular momentum can't oscillate
+$ h \approx \frac{G}{c^2} \frac{M_0}{r} + \frac{G}{c^3} \frac{M'_1}{r} + \frac{G}{c^4} \frac{M''_2}{r} + \frac{G}{c^4} \frac{S'_1}{r} + \frac{G}{c^5} \frac{S''_1}{r}$
+
+First term: mass can't oscillate,
+Second term: momentum can't oscillate,
+Third term: mass quadrupole moment dominates,
+Fourth term: angular momentum can't oscillate,
Fifth term: current quadrupole
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) ????
+moment $M_2 \approx M L^2$, $h \approx 1/c^2 (Newtonian potential energy) ????
-h on the order of :m:`$10^{-22}$`
+h on the order of $10^{-22}$
Propagation
-----------------
@@ -99,7 +99,7 @@ Extreme Low Frequency: 10^-16 Hz, Cosmic Microwave Background anisotropy
Detectors
-----------------
-:m:`$\Delta L = h L ~ \leq 4 \times 10^{-16} \text{cm}$`
+$\Delta L = h L ~ \leq 4 \times 10^{-16} \text{cm}$
LIGO (10 Hz to 1kHz)
Also GEO, VIRGO, TAMA (?), AIGO
@@ -114,4 +114,4 @@ Currently in Louisiana State University (Allegro), University of West Australia
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.
+[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.
diff --git a/physics/special relativity.page b/physics/special relativity.page
deleted file mode 100644
index 2f5b9af..0000000
--- a/physics/special relativity.page
+++ /dev/null
@@ -1,62 +0,0 @@
----
-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]_
-
-*See also `physics/general relativity</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
-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.
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.
diff --git a/physics/units.page b/physics/units.page
index 385136c..bfc78bc 100644
--- a/physics/units.page
+++ b/physics/units.page
@@ -3,11 +3,11 @@ format: rst
categories: physics
toc: no
...
+
======================
Units
======================
-.. contents::
SI Units
--------------------
@@ -26,7 +26,7 @@ Natural Units
Natural units are a system of units which replace (or re-scale) the usual mass,
length, and time bases with quantities which have "natural" (physical)
constants associated with them. The two constants usually chosen are the speed
-of light (c) and Plank's constant (:m:`$\hbar$`); the gravitational constant
+of light (c) and Plank's constant ($\hbar$); the gravitational constant
(G) is a possibility for the third constant/unit, but energy (in
electron-volts: eV) is often used instead because it gives more useful
relations and because there is no accepted theory of quantum gravity to unite
@@ -36,18 +36,18 @@ Working with natural units simplifies physical relations and equations because
many conversion factors drop out.
Given the relations between cgs units (gm, cm, sec) and natural units (c,
-:m:`$\hbar$` , eV), we can find the natural units of an arbitrary quantity
-:m:`$[Q]=[gm]^{a}[cm]^{b}[sec]^{c}=[c]^{\alpha}[\hbar]^{\beta}[eV]^{\gamma}$`:
+$\hbar$ , eV), we can find the natural units of an arbitrary quantity
+$[Q]=[gm]^{a}[cm]^{b}[sec]^{c}=[c]^{\alpha}[\hbar]^{\beta}[eV]^{\gamma}$:
-:m:`$$(\alpha,\beta,\gamma)=\left(\begin{array}{ccc} -2 & 1 & 0\\ 0 & 1 & 1\\ 1 & -1 & -1\end{array}\right)\left(\begin{array}{c} a\\ b\\ c\end{array}\right)=(-2a+b,b+c,a-b-c)$$`
+$$(\alpha,\beta,\gamma)=\left(\begin{array}{ccc} -2 & 1 & 0\\ 0 & 1 & 1\\ 1 & -1 & -1\end{array}\right)\left(\begin{array}{c} a\\ b\\ c\end{array}\right)=(-2a+b,b+c,a-b-c)$$
or in reverse:
-:m:`$$(a,b,c)=\left(\begin{array}{ccc} 0 & 1 & 1\\ 1 & 2 & 2\\ -1 & -1 & -2\end{array}\right)\left(\begin{array}{c} \alpha\\ \beta\\ \gamma\end{array}\right)=(\beta+\gamma,\alpha+2\beta+\gamma,-\alpha-\beta-2\gamma)$$`
+$$(a,b,c)=\left(\begin{array}{ccc} 0 & 1 & 1\\ 1 & 2 & 2\\ -1 & -1 & -2\end{array}\right)\left(\begin{array}{c} \alpha\\ \beta\\ \gamma\end{array}\right)=(\beta+\gamma,\alpha+2\beta+\gamma,-\alpha-\beta-2\gamma)$$
Plank Units
----------------
-Plank units (defined by Plank soon after defining his constant :m:`$\hbar$`) are a version of _`Natural Units` using the gravitational constant G as the the
+Plank units (defined by Plank soon after defining his constant $\hbar$) are a version of _`Natural Units` using the gravitational constant G as the the
third unit (instead of the common measure of energy). When converted back into
mass-length-time units we get three quantities which define the "Plank Scale",
which may provide estimation of the domain where quantum gravity effects become