From b3eca34d2f1c01e979e56ab91f9ef60d7775dd47 Mon Sep 17 00:00:00 2001 From: bryan newbold Date: Tue, 17 Jun 2008 09:43:18 -0400 Subject: lecture one of ph237 --- physics/gravitational waves | 81 +++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 81 insertions(+) create mode 100644 physics/gravitational waves (limited to 'physics') diff --git a/physics/gravitational waves b/physics/gravitational waves new file mode 100644 index 0000000..db2e667 --- /dev/null +++ b/physics/gravitational waves @@ -0,0 +1,81 @@ +======================= +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. -- cgit v1.2.1