At a Forbes blog, Sabine Hossenfelder uncritically promotes a combative Danish newspaper inwards her article
ATdotDE together with discovered my ain LIGO gravitational wave. I am absolutely sure that the probability that such clear signal-like events hap past times run a jeopardy is negligible. Also, the gravitational waves are the exclusively conceivable signal that tin laissez passer on the sack brand the delay betwixt the 2 detectors this small. Any seismic or similar procedure would almost for certain atomic number 82 to a much longer delay, basically because the vibrations would spread through the globe past times the speed of audio etc.
Andrew Jackson et al. is proverb that "something is wrong" because "the relaxation dissonance from LIGO-LA together with LIGO-WA detectors are correlated together with possess got the same delay" but this correlation betwixt these 2 "noises" shouldn't exist.
Except that this disputation is wrong. The residuals aren't just noise. They're the divergence betwixt the best gibe together with the actual observation. But the best gibe isn't the same affair equally the actual gravitational wave.
In particular, equally I possess got emphasized from the real beginning, the 2 detectors – LIGO-LA together with LIGO-WA – are directed inwards somewhat unlike directions, together with thus they basically observe unlike polarizations of the gravitational wave. Because that gravitational moving ridge is rather full general – it is neither circularly polarized, nor linearly polarized – the 2 detectors that basically mensurate the linearly polarized components inwards 2 unlike directions must yield somewhat unlike signals.
If the incoming gravitational moving ridge were linearly polarized, the 2 signals could travel proportional to each other amongst no extra stage delay, equally on the animations above. If the incoming gravitational moving ridge were circularly polarized, the 2 detectors' signals would await similar delayed past times a stage together with inwards principle, i should enjoin that the 2 functions are virtually equally independent equally the sine together with cosine (times a modulating function). In reality, the actual incoming gravitational moving ridge is something inwards between. It is rather good approximated past times a linearly polarized wave, but it is non quite linearly polarized, together with thus the 2 signals aren't proportional to each other.
Just an example: Imagine that you lot possess got some uncomplicated moving ridge modulated past times a Gaussian that is "circularly polarized" together with it's reflected past times the complex exponential\[
\exp(i\omega t - ct^2).
\] Well, if you lot mensurate this moving ridge inwards the 2 detectors, assuming that they're rotated past times 45 degrees for the sake of simplicity, they volition hit the existent together with imaginary parts of the component above, respectively. Those 2 functions – i.e. the Washington together with Louisiana signals – volition be\[
e^{-ct^2} \cos\omega t, \quad e^{-ct^2} \sin\omega t
\] together with these 2 functions aren't proportional to each other, non fifty-fifty if you lot shift them past times an arbitrary fourth dimension delay. It's like shooting fish in a barrel to run across why: the foremost component is fifty-fifty about its "center of mass" spell the instant i is strange about its "center of mass". Any nontrivial linear combinations of these 2 functions volition travel signal-like! That's truthful fifty-fifty if you lot shift them past times a fourth dimension delay to "make them await proportional to each other". Some fourth dimension shift may around together with temporarily "mimic the stage delay", which is \(\pi/2\) inwards my example, but the fixed fourth dimension delay can't supersede the stage delay just because the frequency of the gravitational moving ridge is changing amongst fourth dimension or is modulated (i.e. because the moving ridge isn't monochromatic together with periodic). The replacement is exclusively around proficient if the modulating frequency of the signal together with the charge per unit of measurement of the frequency alter are much slower than the peak frequencies of the signal. To set it mathematically:\[
\forall (A,B)\in \RR^2 \backslash \{(0,0)\}, \,\,\forall \Delta t\in \RR:\\
H5N1 e^{-ct^2} \cos\omega t + B e^{-c(t-\Delta t)^2} \sin [\omega (t-\Delta t)] \neq 0
\] I possess got absolutely no doubtfulness that the signal is existent together with comes from a dark hole merger. But I am non together with thus sure whether LIGO members genuinely empathise that the 2 LIGO detectors' signals aren't supposed to travel proportional to each other because the incoming gravitational moving ridge isn't linearly polarized – together with for a circularly polarized wave, the non-parallel detectors discovery the phase-shifted parts of the incoming signals, similar the existent together with imaginary component of a complex wave, together with the actual polarization is "somewhat elliptic together with general", together with thus everything that tin laissez passer on the sack travel nonzero is nonzero.
I possess got been e'er worried that LIGO – together with possibly every unmarried soul who has ever written a newspaper predicting the waves inwards 2 non-parallel detectors – makes this petty fault because they talked virtually things similar the "inverted signal" which seems to assume that the LIGO-LA signal should travel equal to the LIGO-WA signal times a positive number, or a negative number. But none of these choices is truthful inwards the real-world, generic case. Instead, they discovery 2 parts of an elliptically, to a greater extent than frequently than non polarized gravitational wave.
So it's completely obvious that the signals aren't supposed to travel proportional to each other together with if you lot just compute the optimal linear combination of the 2 signals that should travel noise-like, it but won't travel noiselike but volition incorporate a component of the signal inwards the same menses of fourth dimension – basically the linear polarization of the signal amongst honour to a unlike axis than i that maximizes the signal's strength.
Dear LIGO folks, travel sure that you lot possess got discovered the gravitational waves from a dark hole merger but if I possess got pointed out something that you lot genuinely did inwards a sloppy mode past times neglecting the general, non-linear polarization of the incoming wave, I urge you lot to redo the theoretical predictions together with comparisons amongst the experiments, practise it earlier your gurus are named the physics Nobel prize inwards Fall 2017, together with give cheers me inwards the Nobel prize lecture.
Thank you lot real much, Ladies together with Gentlemen.
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