@0celo7 Well, you can forget about the derivative (it just gives constants), and just have to show that $x^n\exp(-\lvert x \rvert)$ is bounded for all $n$.Since it is standard lore that exponentials decay faster than anypolynomial, the proof should not be hard to construct
@0celo7 I want to say he's just suppressing the matrix because it is trace-free so one component of the separation vector completely determines the other component...but then I'm not sure where the squaring of the trig functions comes from since there's no need to rotate anything if he's already in the TT-gauge coordinates
the $l_0$ and part of the $\sin\varepsilon$ and $\cos\varphi$ etc. should come from the fact that the initial separation vector is something like $2 l_0(\sin\varepsilon \cos\varphi, \sin\varepsilon \sin\varphi$
@ACuriousMind ye, few days ago, waiting for the results now, but all went well (most probably :D), and found a position to work for my supervisor full time this summer, so kinda held up with that for now
@0celo7 it's an amazing chapter but he just says super profound statements in passing like they're casual conversation starters and we're left trying to figure out what's going on
@0celo7 it's possible but I thought the only projection involved was orthogonal to the direction of the wave propagation which in this case just means kill the z-component of the separation vector?
@Phonon yeah, his bit on getting a handjob from his wife made me almost pass out from laughter
because he defines $\xi$ as the relative separation between the two masses which only makes sense if it's along the spring; $n$ on the other hand has components both along and normal to the spring
his picture is actually confusing me because in the picture it looks like $\xi$ is a small deviation of each point of the detector in some direction perpendicular to $z$ based on his weird wavy thing he draws around the detector
but that isn't the relative separation between the two masses
then yeah we would have to project onto the rod which would be a rotation by $\vartheta$ in the $y-z$ plane and a rotation by $\varphi$ in the $x-y$ plane
I wasn't always reading about physics or math, though I did read and learn about a lot of other things during the last year which I am now breaking from temporarily.