Why isn't there an Impedance with gravitational waves?
http://www.scientificamerican.com/video/gravitational-waves-are-the-ringing-of-spacetime/
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1$\begingroup$ Are you talking about acoustic impedance? $\endgroup$– DanuCommented Feb 22, 2016 at 21:05
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3$\begingroup$ What would impede spacetime? $\endgroup$– Kyle KanosCommented Feb 22, 2016 at 21:29
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$\begingroup$ Optical impedance is called the index of refraction; we also have acoustic impedance which is the density times the speed of sound in that material; and of course, electrical impedance. Now that we a method for finding gravity waves, gravitational surveys may eventually find gravitational impedance ... perhaps dark energy or dark matter. A research project for a cosmologist. $\endgroup$– Peter DiehrCommented Feb 22, 2016 at 23:40
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$\begingroup$ Couldn't severely warped spacetime itself act as impedance? In other words in the vicinity of a black hole's event horizon? $\endgroup$– docscienceCommented Feb 23, 2016 at 0:04
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4$\begingroup$ "Spacetime has a characteristic impedance ∼ $c^3/G$ (Blair, 1991)" - Advanced Gravitational Wave Detectors $\endgroup$– Alfred CentauriCommented Feb 23, 2016 at 0:06
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2 Answers
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Spacetime is a very stiff elastic medium which is capable of propagating gravitational waves. The impedance of spacetime is $$ Z_s = \frac{c^3}G = 4 \times 10^{35} \rm\,kg/s. $$This impedance appears in two books on gravitational waves. The most recent is titled "Advanced Gravitational Wave Detectors" edited by Blair, Howell, et al (page 52). The gravitational wave designated GW150914 had measured intensity of about 20 mw/m$^2$ at 200 Hz. If this was a 200 Hz sound wave, it would be very loud. However, the large impedance of spacetime meant that the displacment of spacetime ($\Delta L/L$) was only about 1 part in $10^{21}$.
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1$\begingroup$ Is there any proof that Space is a stiff elastic medium? $\endgroup$ Commented Dec 21, 2016 at 22:01
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3$\begingroup$ @BillAlsept Is the discovery of gravitational waves enough proof for you? $\endgroup$ Commented Nov 25, 2017 at 23:01
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$\begingroup$ @probably_someone no, and light waves do not prove there is a medium for light either $\endgroup$ Commented Nov 26, 2017 at 0:29
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1$\begingroup$ @BillAlsept What would it actually mean to prove that space "is" a stiff elastic medium? What kind of measurement would be necessary? $\endgroup$ Commented Nov 26, 2017 at 18:35
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$\begingroup$ @BillAlsept but the electromagnetic impedance of space is well known and intimately tied to the EM wave equations as well. $\endgroup$– geshelCommented May 15, 2021 at 18:05
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The $10^{35}$ kg/s value is valid at the Planck length. Wave impedance is scale dependent, has to be to do work. Invariant impedances (quantum Hall, centrifugal,...) are topological, communicate only phase. Gwave impedances at scales accessible to us differ from those at the Planck length. This is discussed in a recent presentation to a workshop on storage rings and gravitational wave detectors/sources, organized by LHC folks looking at what to do a decade or two from now.
