From f61026119df4700f69eb73e95620bc5928ca0fcb Mon Sep 17 00:00:00 2001
From: User
Date: Tue, 13 Oct 2009 02:52:09 +0000
Subject: Grand rename for gitit transfer

physics/LIGO  48 
physics/LIGO.page  48 +++++++++++++++++
physics/general relativity  18 
physics/general relativity.page  18 +++++++
physics/gravitational waves  111 
physics/gravitational waves.page  111 +++++++++++++++++++++++++++++++++++++++
physics/quantum/fermigas  51 
physics/quantum/fermigas.page  51 ++++++++++++++++++
physics/special relativity  56 
physics/special relativity.page  56 ++++++++++++++++++++
physics/units  53 
physics/units.page  53 +++++++++++++++++++
12 files changed, 337 insertions(+), 337 deletions()
delete mode 100644 physics/LIGO
create mode 100644 physics/LIGO.page
delete mode 100644 physics/general relativity
create mode 100644 physics/general relativity.page
delete mode 100644 physics/gravitational waves
create mode 100644 physics/gravitational waves.page
delete mode 100644 physics/quantum/fermigas
create mode 100644 physics/quantum/fermigas.page
delete mode 100644 physics/special relativity
create mode 100644 physics/special relativity.page
delete mode 100644 physics/units
create mode 100644 physics/units.page
(limited to 'physics')
diff git a/physics/LIGO b/physics/LIGO
deleted file mode 100644
index ce682b4..0000000
 a/physics/LIGO
+++ /dev/null
@@ 1,48 +0,0 @@
=======================================================================
LIGO: Laser Interferometer Gravitational Observatory
=======================================================================

.. 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]_

Noise Sources
~~~~~~~~~~~~~~~~~~~~~~

For initial LIGO, seismic noise dominates below about 60Hz, suspension thermal
noise between 60 and 180Hz, and radiation pressure shot noise above 180Hz.

Sensitivity
~~~~~~~~~~~~~~~~~~~~~

Advanced LIGO will use 40kg sapphire test masses with sensitivity of about 10e19 meters: 1/10000 of an atomic nucleus, 10e13 of a wavelength, and half of the entire mirror's wave function.

LISA
~~~~~~~~~~~~~

5e6 km separations between three spacecraft, 1 (astronomical unit, ~1.5e8 from the sun. 1 watt lasers.
The heterodyne detection is of the beat frequencies at each spacecraft of the
two incoming beams. Doppler shifts of spacecraft must be taken into account,
due not only to sun radiation pressure etc, but varying gravitational fields
from planetary orbits.

The test masses inside LISA should be free falling and have relative
separations stable to 10e9 cm (10e5 wavelength of light).

LISA's sensitivity is in the milihertz regime.

.. note: (insert LISA noise curve?)

Data Analysis
~~~~~~~~~~~~~~~~~~~~

Using matched filtering (eg, take cross correlation between two waveforms,
integrating their product), frequency sensitivity will be around the inverse
of the number of cycles of waveform (for LIGO, around 20,000 cycles, for LISA
around 200,000 cycles).

This technique requires known, theoretically derived waveforms (within
phase/amplitude). There are other methods when we don't have good guesses
about the waveform we are looking for...

diff git a/physics/LIGO.page b/physics/LIGO.page
new file mode 100644
index 0000000..ce682b4
 /dev/null
+++ b/physics/LIGO.page
@@ 0,0 +1,48 @@
+=======================================================================
+LIGO: Laser Interferometer Gravitational Observatory
+=======================================================================
+
+.. 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]_
+
+Noise Sources
+~~~~~~~~~~~~~~~~~~~~~~
+
+For initial LIGO, seismic noise dominates below about 60Hz, suspension thermal
+noise between 60 and 180Hz, and radiation pressure shot noise above 180Hz.
+
+Sensitivity
+~~~~~~~~~~~~~~~~~~~~~
+
+Advanced LIGO will use 40kg sapphire test masses with sensitivity of about 10e19 meters: 1/10000 of an atomic nucleus, 10e13 of a wavelength, and half of the entire mirror's wave function.
+
+LISA
+~~~~~~~~~~~~~
+
+5e6 km separations between three spacecraft, 1 (astronomical unit, ~1.5e8 from the sun. 1 watt lasers.
+The heterodyne detection is of the beat frequencies at each spacecraft of the
+two incoming beams. Doppler shifts of spacecraft must be taken into account,
+due not only to sun radiation pressure etc, but varying gravitational fields
+from planetary orbits.
+
+The test masses inside LISA should be free falling and have relative
+separations stable to 10e9 cm (10e5 wavelength of light).
+
+LISA's sensitivity is in the milihertz regime.
+
+.. note: (insert LISA noise curve?)
+
+Data Analysis
+~~~~~~~~~~~~~~~~~~~~
+
+Using matched filtering (eg, take cross correlation between two waveforms,
+integrating their product), frequency sensitivity will be around the inverse
+of the number of cycles of waveform (for LIGO, around 20,000 cycles, for LISA
+around 200,000 cycles).
+
+This technique requires known, theoretically derived waveforms (within
+phase/amplitude). There are other methods when we don't have good guesses
+about the waveform we are looking for...
+
diff git a/physics/general relativity b/physics/general relativity
deleted file mode 100644
index 7fc29eb..0000000
 a/physics/general relativity
+++ /dev/null
@@ 1,18 +0,0 @@
===========================
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/general relativity.page b/physics/general relativity.page
new file mode 100644
index 0000000..7fc29eb
 /dev/null
+++ b/physics/general relativity.page
@@ 0,0 +1,18 @@
+===========================
+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 b/physics/gravitational waves
deleted file mode 100644
index 5aa1744..0000000
 a/physics/gravitational waves
+++ /dev/null
@@ 1,111 +0,0 @@
=======================
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/gravitational waves.page b/physics/gravitational waves.page
new file mode 100644
index 0000000..5aa1744
 /dev/null
+++ b/physics/gravitational waves.page
@@ 0,0 +1,111 @@
+=======================
+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/quantum/fermigas b/physics/quantum/fermigas
deleted file mode 100644
index 0114b43..0000000
 a/physics/quantum/fermigas
+++ /dev/null
@@ 1,51 +0,0 @@
===============
Fermi Gas
===============

Derivation of the Fermi Energy

Consider a crystal lattice with an electron gas as a 3 dimensional infinite
square well with dimensions :m:`$l_{x}, l_{y}, l_z$`. The wavefunctions of
individual fermions (pretending they are noninteracting) can be seperated
as :m:`$\psi(x,y)=\psi_{x}(x)\psi_{y}(y)\psi_{z}(z)$`. The solutions will be
the usual ones to the Schrodinger equation:

:m:`$$\frac{\hbar^2}{2m}\frac{d^2 \psi_x}{dx}=E_x \psi_x$$`

with the usual wave numbers :m:`$k_x=\frac{\sqrt{2mE_x}}{\hbar}$`, and quantum
numbers satisfying the boundry conditions :m:`$k_x l_x = n_x \pi$`. The full
wavefunction for each particle will be:

:m:`$$\psi_{n_{x}n_{y}n_{z}}(x,y,z)=\sqrt{\frac{4}{l_{x}l_{y}}}\sin\left(\frac{n_{x}\pi}{l_{x}}x\right)\sin\left(\frac{n_{y}\pi}{l_{y}}y\right)\sin\left(\frac{n_{z}\pi}{l_{z}}z\right)$$`

and the associated energies (with :m:`$E = E_x + E_y + E_z$`):

:m:`$$E_{n_{x}n_{y}n_z}=\frac{\hbar^{2}\pi^{2}}{2m}\left(\frac{n_{x}^{2}}{l_{x}^{2}}+\frac{n_{y}^{2}}{l_{y}^{2}}+\frac{n_{z}^{2}}{l_{z}^{2}}\right)=\frac{\hbar^2\vec{k}^2}{2m}$$`

where :m:`$\vec{k}^2$` is the magnitude of the particle's kvector in kspace.
This kspace can be imagined as a grid of blocks, each representing a possible
particle state (with a double degeneracy for spin). Positions on this grid have
coordinates :m:`$(k_{x},k_{y},k_z)$` corresponding to the positive integer
quantum numbers. These blocks will be filled
from the lowest energy upwards: for large numbers of occupying particles,
the filling pattern can be approximated as an expanding spherical shell with
radius :m:`$\vec{k_F}^2$`.

Note that we're "over counting" the number of occupied states because the
"sides" of the quarter sphere in kspace (where one of the associated quantum
numbers is zero) do not represent valid states. These surfaces can be ignored
for very large N because the surface area to volume ratio is so low, but the
correction can be important. There will then be a second correction due to
removing the states along the individual axes twice (once for each
sidesurface), u.s.w.

The surface of this shell is called the Fermi surface and represents the most
excited states in the gas. The radius can be derived by calculating the total
volume enclosed: each block has volume :m:`$\frac{\pi^3}{l_x l_y
l_z}=\frac{\pi^3}{V}$` and there are N/2 blocks occupied by N fermions, so:

:m:`$$\frac{1}{8}(\frac{4\pi}{3} k_{F}^{3})&=&\frac{Nq}{2}(\frac{\pi^{3}}{V})\\k_{F}&=&\sqrt{\frac{3Nq\pi^2}{V}}^3=\sqrt{3\pi^2\rho}^3$$`

:m:`$\rho$` is the "free fermion density". The corresponding energy is:

:m:`$$E_{F}=\frac{\hbar^{2}}{2m}k_{F}^{2}=\frac{\hbar^{2}}{2m}(3\rho \pi)^{2/3}$$`
diff git a/physics/quantum/fermigas.page b/physics/quantum/fermigas.page
new file mode 100644
index 0000000..0114b43
 /dev/null
+++ b/physics/quantum/fermigas.page
@@ 0,0 +1,51 @@
+===============
+Fermi Gas
+===============
+
+Derivation of the Fermi Energy
+
+Consider a crystal lattice with an electron gas as a 3 dimensional infinite
+square well with dimensions :m:`$l_{x}, l_{y}, l_z$`. The wavefunctions of
+individual fermions (pretending they are noninteracting) can be seperated
+as :m:`$\psi(x,y)=\psi_{x}(x)\psi_{y}(y)\psi_{z}(z)$`. The solutions will be
+the usual ones to the Schrodinger equation:
+
+:m:`$$\frac{\hbar^2}{2m}\frac{d^2 \psi_x}{dx}=E_x \psi_x$$`
+
+with the usual wave numbers :m:`$k_x=\frac{\sqrt{2mE_x}}{\hbar}$`, and quantum
+numbers satisfying the boundry conditions :m:`$k_x l_x = n_x \pi$`. The full
+wavefunction for each particle will be:
+
+:m:`$$\psi_{n_{x}n_{y}n_{z}}(x,y,z)=\sqrt{\frac{4}{l_{x}l_{y}}}\sin\left(\frac{n_{x}\pi}{l_{x}}x\right)\sin\left(\frac{n_{y}\pi}{l_{y}}y\right)\sin\left(\frac{n_{z}\pi}{l_{z}}z\right)$$`
+
+and the associated energies (with :m:`$E = E_x + E_y + E_z$`):
+
+:m:`$$E_{n_{x}n_{y}n_z}=\frac{\hbar^{2}\pi^{2}}{2m}\left(\frac{n_{x}^{2}}{l_{x}^{2}}+\frac{n_{y}^{2}}{l_{y}^{2}}+\frac{n_{z}^{2}}{l_{z}^{2}}\right)=\frac{\hbar^2\vec{k}^2}{2m}$$`
+
+where :m:`$\vec{k}^2$` is the magnitude of the particle's kvector in kspace.
+This kspace can be imagined as a grid of blocks, each representing a possible
+particle state (with a double degeneracy for spin). Positions on this grid have
+coordinates :m:`$(k_{x},k_{y},k_z)$` corresponding to the positive integer
+quantum numbers. These blocks will be filled
+from the lowest energy upwards: for large numbers of occupying particles,
+the filling pattern can be approximated as an expanding spherical shell with
+radius :m:`$\vec{k_F}^2$`.
+
+Note that we're "over counting" the number of occupied states because the
+"sides" of the quarter sphere in kspace (where one of the associated quantum
+numbers is zero) do not represent valid states. These surfaces can be ignored
+for very large N because the surface area to volume ratio is so low, but the
+correction can be important. There will then be a second correction due to
+removing the states along the individual axes twice (once for each
+sidesurface), u.s.w.
+
+The surface of this shell is called the Fermi surface and represents the most
+excited states in the gas. The radius can be derived by calculating the total
+volume enclosed: each block has volume :m:`$\frac{\pi^3}{l_x l_y
+l_z}=\frac{\pi^3}{V}$` and there are N/2 blocks occupied by N fermions, so:
+
+:m:`$$\frac{1}{8}(\frac{4\pi}{3} k_{F}^{3})&=&\frac{Nq}{2}(\frac{\pi^{3}}{V})\\k_{F}&=&\sqrt{\frac{3Nq\pi^2}{V}}^3=\sqrt{3\pi^2\rho}^3$$`
+
+:m:`$\rho$` is the "free fermion density". The corresponding energy is:
+
+:m:`$$E_{F}=\frac{\hbar^{2}}{2m}k_{F}^{2}=\frac{\hbar^{2}}{2m}(3\rho \pi)^{2/3}$$`
diff git a/physics/special relativity b/physics/special relativity
deleted file mode 100644
index 37fd3e9..0000000
 a/physics/special relativity
+++ /dev/null
@@ 1,56 +0,0 @@
===========================
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/special relativity.page b/physics/special relativity.page
new file mode 100644
index 0000000..37fd3e9
 /dev/null
+++ b/physics/special relativity.page
@@ 0,0 +1,56 @@
+===========================
+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/units b/physics/units
deleted file mode 100644
index b1968f4..0000000
 a/physics/units
+++ /dev/null
@@ 1,53 +0,0 @@
======================
Units
======================

.. contents::

SI Units

The SI system uses meterskilogramsseconds. It also defines the Coulomb as
a unit for measuring electric charge, which introduces redundant conversions
between masslengthtime units and the electric charge.

cgs Units

The cgs system uses centimetersgramsseconds, and also defines electric charge
in terms of the fundamental quantities of mass, length, and time. The unit of
charge is "esu" or electrostatic unit.

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
(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
these three constants. See _`Plank Units` for more on using G as a unit.

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:`$[Q]=[gm]^{a}[cm]^{b}[sec]^{c}=[c]^{\alpha}[\hbar]^{\beta}[eV]^{\gamma}$`:

:m:`$$(\alpha,\beta,\gamma)=\left(\begin{array}{ccc} 2 & 1 & 0\\ 0 & 1 & 1\\ 1 & 1 & 1\end{array}\right)\left(\begin{array}{c} a\\ b\\ c\end{array}\right)=(2a+b,b+c,abc)$$`

or in reverse:

:m:`$$(a,b,c)=\left(\begin{array}{ccc} 0 & 1 & 1\\ 1 & 2 & 2\\ 1 & 1 & 2\end{array}\right)\left(\begin{array}{c} \alpha\\ \beta\\ \gamma\end{array}\right)=(\beta+\gamma,\alpha+2\beta+\gamma,\alpha\beta2\gamma)$$`

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
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
important (similar to how the speed of light and Plank's constant provide
estimation of when special relativistic and quantum mechanical effects become
important).


diff git a/physics/units.page b/physics/units.page
new file mode 100644
index 0000000..b1968f4
 /dev/null
+++ b/physics/units.page
@@ 0,0 +1,53 @@
+======================
+Units
+======================
+
+.. contents::
+
+SI Units
+
+The SI system uses meterskilogramsseconds. It also defines the Coulomb as
+a unit for measuring electric charge, which introduces redundant conversions
+between masslengthtime units and the electric charge.
+
+cgs Units
+
+The cgs system uses centimetersgramsseconds, and also defines electric charge
+in terms of the fundamental quantities of mass, length, and time. The unit of
+charge is "esu" or electrostatic unit.
+
+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
+(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
+these three constants. See _`Plank Units` for more on using G as a unit.
+
+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:`$[Q]=[gm]^{a}[cm]^{b}[sec]^{c}=[c]^{\alpha}[\hbar]^{\beta}[eV]^{\gamma}$`:
+
+:m:`$$(\alpha,\beta,\gamma)=\left(\begin{array}{ccc} 2 & 1 & 0\\ 0 & 1 & 1\\ 1 & 1 & 1\end{array}\right)\left(\begin{array}{c} a\\ b\\ c\end{array}\right)=(2a+b,b+c,abc)$$`
+
+or in reverse:
+
+:m:`$$(a,b,c)=\left(\begin{array}{ccc} 0 & 1 & 1\\ 1 & 2 & 2\\ 1 & 1 & 2\end{array}\right)\left(\begin{array}{c} \alpha\\ \beta\\ \gamma\end{array}\right)=(\beta+\gamma,\alpha+2\beta+\gamma,\alpha\beta2\gamma)$$`
+
+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
+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
+important (similar to how the speed of light and Plank's constant provide
+estimation of when special relativistic and quantum mechanical effects become
+important).
+
+

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