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diff --git a/physics/gravitational-waves.page b/physics/gravitational-waves.page index c853e2b..4466e37 100644 --- a/physics/gravitational-waves.page +++ b/physics/gravitational-waves.page @@ -1,30 +1,24 @@ --- -format: rst -categories: physics toc: no +title: Gravitational Waves ... -======================= -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]_ +.. 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 +Graviton has $\pi$ invariance angle, so it is spin 2; photons have unique $\vec{E}$ vector, so invariance angle is $2\pi$, spin 1 Also describes spin by the group of Lorentz transformations which effect propagation. @@ -34,13 +28,13 @@ 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}$ +$$ h \approx \frac{G}{c^2} \frac{M_0}{r} + \frac{G}{c^3} \frac{M'_1}{r} + \frac{G}{c^4} \frac{M''_2}{r} + \frac{G}{c^4} \frac{S'_1}{r} + \frac{G}{c^5} \frac{S''_1}{r} $$ -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 + - 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 ---------------- @@ -99,7 +93,7 @@ Extreme Low Frequency: 10^-16 Hz, Cosmic Microwave Background anisotropy Detectors ----------------- -$\Delta L = h L ~ \leq 4 \times 10^{-16} \text{cm}$ +$$\Delta L = h L ~ \leq 4 \times 10^{-16} \text{cm}$$ LIGO (10 Hz to 1kHz) Also GEO, VIRGO, TAMA (?), AIGO @@ -115,3 +109,4 @@ 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. + |