From dba922cd0c8f5ce7252f33268189259706fc9e75 Mon Sep 17 00:00:00 2001
From: bnewbold
Date: Sun, 24 Jan 2010 05:23:28 0500
Subject: partial fixes

physics/general relativity.page  24 
physics/gravitational waves.page  117 
physics/gravitationalwaves.page  117 +++++++++++++++++++++++++++++++++++++++
physics/special relativity.page  62 
physics/specialrelativity.page  60 ++++++++++++++++++++
physics/units.page  14 ++
6 files changed, 184 insertions(+), 210 deletions()
delete mode 100644 physics/general relativity.page
delete mode 100644 physics/gravitational waves.page
create mode 100644 physics/gravitationalwaves.page
delete mode 100644 physics/special relativity.page
create mode 100644 physics/specialrelativity.page
(limited to 'physics')
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 `__*

(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
deleted file mode 100644
index 66f6c04..0000000
 a/physics/gravitational waves.page
+++ /dev/null
@@ 1,117 +0,0 @@

format: rst
categories: physics
toc: no
...

=======================
Gravitational Waves
=======================

.. 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]_

Raw Info

Rank 4 Riemann tensors, will cover different gauge.
Waves are double integrals of curvature tensor...



Gravitons as Quantum Particles

Invariance angles: (Spin of quantum particle) = :latex:`$2 pi$` / (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

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 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
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) ????

h on the order of :m:`$10^{22}$`

Propagation


When wavelength much less than curvature of universe (background), then gravitational waves propagate like light waves: undergo red shifts, gravitational lensing, inflationary red shift, etc.

Sources


Inspirals of bodies into supermassive black holes
 Eg, white dwarfs, neutron stars, small black holes.
 Supermassive black holes are expected near the centers of galaxies.
 Low frequencies (LISA); waveforms could hold data about spacetime curvature
 local to the black hole.
 Waveforms could be very difficult to predict.

Binary black hole mergers
 Broadband signals depending on masses.

Neutron Star/Black hole mergers
 Stellar mass objects existing in the main bodies of galaxies.
 Higher frequencies (LIGO and AdvLIGO).

Neutron Star/Neutron Star mergers
 Have actual examples in our galaxy of these events; but final inspiral rate
 is so low that we have must listen in other galaxies. Merger waves will
 probably be lost in higher frequency noise, so can't probe local
 gravitational curvature.
 May observe "tails" of waves: scattering off of high curvature around the
 binary.

Pulsars (spinning neutron stars)
 Known to exist in our galaxy.

Spectrum


High Frequency: Above 1 Hz, LIGO (10 Hz to 1kHz), resonant bars
 Small black holes (2 to 1k suns), neutron stars, supernovas

Low frequency: 1Hz and lower, LISA (10^4 Hz to 0.1 Hz), Doppler tracking of spacecraft
 Massive black holes (300 to 30 million suns), binary stars

Very Low Frequency: 10^8 Hz, Pulsar timing (our clocks shifted by gwaves, average of distance pulsars are not over long periods)

Extreme Low Frequency: 10^16 Hz, Cosmic Microwave Background anisotropy

Detectors


:m:`$\Delta L = h L ~ \leq 4 \times 10^{16} \text{cm}$`

LIGO (10 Hz to 1kHz)
 Also GEO, VIRGO, TAMA (?), AIGO

LISA (10e4 Hz to 0.1 Hz)

Resonant Bars
~~~~~~~~~~~~~~~
First by Webber.
Currently in Louisiana State University (Allegro), University of West Australia (Niobe), CERN (Explorer), University of Padova (Auriga), and University of Rome (Nautilus)

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/gravitationalwaves.page b/physics/gravitationalwaves.page
new file mode 100644
index 0000000..c853e2b
 /dev/null
+++ b/physics/gravitationalwaves.page
@@ 0,0 +1,117 @@
+
+format: rst
+categories: physics
+toc: no
+...
+
+=======================
+Gravitational Waves
+=======================
+
+.. 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]_
+
+Raw Info
+
+Rank 4 Riemann tensors, will cover different gauge.
+Waves are double integrals of curvature tensor...
+
+
+
+Gravitons as Quantum Particles
+
+Invariance angles: (Spin of quantum particle) = $2 pi$ / (invariance angle)
+
+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 $\geq$ spin of quantum = 2 for graviton ((??))
+
+Waves don't propagate like E, because mass monopoles don't oscillate like charges.
+
+$ 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 $M_2 \approx M L^2$, $h \approx 1/c^2 (Newtonian potential energy) ????
+
+h on the order of $10^{22}$
+
+Propagation
+
+
+When wavelength much less than curvature of universe (background), then gravitational waves propagate like light waves: undergo red shifts, gravitational lensing, inflationary red shift, etc.
+
+Sources
+
+
+Inspirals of bodies into supermassive black holes
+ Eg, white dwarfs, neutron stars, small black holes.
+ Supermassive black holes are expected near the centers of galaxies.
+ Low frequencies (LISA); waveforms could hold data about spacetime curvature
+ local to the black hole.
+ Waveforms could be very difficult to predict.
+
+Binary black hole mergers
+ Broadband signals depending on masses.
+
+Neutron Star/Black hole mergers
+ Stellar mass objects existing in the main bodies of galaxies.
+ Higher frequencies (LIGO and AdvLIGO).
+
+Neutron Star/Neutron Star mergers
+ Have actual examples in our galaxy of these events; but final inspiral rate
+ is so low that we have must listen in other galaxies. Merger waves will
+ probably be lost in higher frequency noise, so can't probe local
+ gravitational curvature.
+ May observe "tails" of waves: scattering off of high curvature around the
+ binary.
+
+Pulsars (spinning neutron stars)
+ Known to exist in our galaxy.
+
+Spectrum
+
+
+High Frequency: Above 1 Hz, LIGO (10 Hz to 1kHz), resonant bars
+ Small black holes (2 to 1k suns), neutron stars, supernovas
+
+Low frequency: 1Hz and lower, LISA (10^4 Hz to 0.1 Hz), Doppler tracking of spacecraft
+ Massive black holes (300 to 30 million suns), binary stars
+
+Very Low Frequency: 10^8 Hz, Pulsar timing (our clocks shifted by gwaves, average of distance pulsars are not over long periods)
+
+Extreme Low Frequency: 10^16 Hz, Cosmic Microwave Background anisotropy
+
+Detectors
+
+
+$\Delta L = h L ~ \leq 4 \times 10^{16} \text{cm}$
+
+LIGO (10 Hz to 1kHz)
+ Also GEO, VIRGO, TAMA (?), AIGO
+
+LISA (10e4 Hz to 0.1 Hz)
+
+Resonant Bars
+~~~~~~~~~~~~~~~
+First by Webber.
+Currently in Louisiana State University (Allegro), University of West Australia (Niobe), CERN (Explorer), University of Padova (Auriga), and University of Rome (Nautilus)
+
+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/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`__*

As opposed to general relativity, special relativity takes place in a *flat*
Minkowski space time: a 4space 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 Lorentzinvariant; 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: **spacelike** when :m:`$(\Delta s)^2 > 0$`, **null** or
**lightlike** when :m:`$(\Delta s)^2 = 0$`, and **timelike** when
:m:`$(\Delta s)^2 < 0$`. When dealing with timelike 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/specialrelativity.page b/physics/specialrelativity.page
new file mode 100644
index 0000000..bb5f564
 /dev/null
+++ b/physics/specialrelativity.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 4space 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 Lorentzinvariant; 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: **spacelike** when $(\Delta s)^2 > 0$, **null** or
+**lightlike** when $(\Delta s)^2 = 0$, and **timelike** when
+$(\Delta s)^2 < 0$. When dealing with timelike 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 rescale) 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
electronvolts: 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:`$$(\alpha,\beta,\gamma)=\left(\begin{array}{ccc} 2 & 1 & 0\\ 0 & 1 & 1\\ 1 & 1 & 1\end{array}\right)\left(\begin{array}{c} a\\ b\\ c\end{array}\right)=(2a+b,b+c,abc)$$`
+$$(\alpha,\beta,\gamma)=\left(\begin{array}{ccc} 2 & 1 & 0\\ 0 & 1 & 1\\ 1 & 1 & 1\end{array}\right)\left(\begin{array}{c} a\\ b\\ c\end{array}\right)=(2a+b,b+c,abc)$$
or in reverse:
:m:`$$(a,b,c)=\left(\begin{array}{ccc} 0 & 1 & 1\\ 1 & 2 & 2\\ 1 & 1 & 2\end{array}\right)\left(\begin{array}{c} \alpha\\ \beta\\ \gamma\end{array}\right)=(\beta+\gamma,\alpha+2\beta+\gamma,\alpha\beta2\gamma)$$`
+$$(a,b,c)=\left(\begin{array}{ccc} 0 & 1 & 1\\ 1 & 2 & 2\\ 1 & 1 & 2\end{array}\right)\left(\begin{array}{c} \alpha\\ \beta\\ \gamma\end{array}\right)=(\beta+\gamma,\alpha+2\beta+\gamma,\alpha\beta2\gamma)$$
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
masslengthtime units we get three quantities which define the "Plank Scale",
which may provide estimation of the domain where quantum gravity effects become

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