lecture one of ph237

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+=======================
+Gravitational Waves
+=======================
+
+:Author: bnewbold@mit.edu
+
+.. 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 gages.
+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 propogation.
+
+Two polarizations: cross and plus, corresponding to spin of particles aligning wiht or against propagation?  (Ref: eugene vickner? reviews of modern physics)
+
+Waves' multipole order $\geq$ spin of quantum = 2 for graviton ((??))
+
+Waves don't propogate like E, because mass monopoles don't oscillate like charges.
+
+:latex:`$ h \req \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 qudrupole 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 quadupole moment $M_2 \req M L^2$, h \req 1/c^2 (newtonian potential energy) ????
+
+h on the order of $10^{-22}$
+
+Propogation
+-----------------
+
+When wavelength much less than curvature of universe (background), then gravitational waves propagate like light waves: undergo red shifts, gravitational lensing, inflationary redshift, etc. 
+
+Spectrum
+----------------
+
+High Frequency: Above 1 Hz, LIGO (10 Hz to 1kHz), resonant bars
+    Small black holes (2 to 1k suns), neutron stars, supernovae
+
+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
+-----------------
+
+$\Delta L = h L \lreq 4 \times 10^{-16} \text{cm}$
+
+LIGO (10 Hz to 1kHz)
+    Also GEO, VIRGO, TAMA (?), AIGO
+
+LISA (10^-4 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.