APOD: Advanced LIGO: Gravitational Wave... (2016 Feb 07)

[Sunnysky]

It is quite doubtful about LIGO's claim of having detected gravity wave. If you imagine a tube of 1 light-year radius and 1.4 billion light years long you will have about 17.6 million solar starts inside the tube. For 100-200Hz gravity wave, the wave length would be 1500-3000km which are still much smaller compared with the solar radius of 0.7 million km. So, statistics shows there must be dispersion effect on different wavelength waves; the longer wavelength wave will travel faster than the shorter wavelength one and the shorter wavelength wave will suffer more amplitude damping. Now the challenge is, then, how can LIGO get the gravity waveform exactly the same as the theoretical calculations for two black holes merging without considering any dispersion effects?

[Markus Schwarz]

It is quite doubtful about LIGO's claim of having detected gravity wave. If you imagine a tube of 1 light-year radius and 1.4 billion light years long you will have about 17.6 million solar starts inside the tube. For 100-200Hz gravity wave, the wave length would be 1500-3000km which are still much smaller compared with the solar radius of 0.7 million km. So, statistics shows there must be dispersion effect on different wavelength waves; the longer wavelength wave will travel faster than the shorter wavelength one and the shorter wavelength wave will suffer more amplitude damping. Now the challenge is, then, how can LIGO get the gravity waveform exactly the same as the theoretical calculations for two black holes merging without considering any dispersion effects?

I don't understand your argument. Where do you get the 17.6 million stars per "tube" from?
From the linearised field equations of general relativity in empty space (valid for the propagation of gravitational waves) one obtains that the phase and group velocity of gravitational waves equals the speed of light and that there is no dispersion. I don't understand what statistics should have to do with it.

[neufer]

It is quite doubtful about LIGO's claim of having detected gravity wave. If you imagine a tube of 1 light-year radius and 1.4 billion light years long you will have about 17.6 million solar starts inside the tube. For 100-200Hz gravity wave, the wave length would be 1500-3000km which are still much smaller compared with the solar radius of 0.7 million km. So, statistics shows there must be dispersion effect on different wavelength waves; the longer wavelength wave will travel faster than the shorter wavelength one and the shorter wavelength wave will suffer more amplitude damping. Now the challenge is, then, how can LIGO get the gravity waveform exactly the same as the theoretical calculations for two black holes merging without considering any dispersion effects?

I don't understand your argument. Where do you get the 17.6 million stars per "tube" from?

Diffraction effects would indicate that the relevant "tube" should be not much wider than ~0.2 of a light-year radius on average. This corresponds to about only a few percent of the intervening matter Sunnysky suggests.

Dispersion effects involve coherent scattering due to absorption & re-radiation and thus depends upon the square of the gravitational constant. Hence it must, of necessity, be a very small effect.

From the linearised field equations of general relativity in empty space (valid for the propagation of gravitational waves) one obtains that the phase and group velocity of gravitational waves equals the speed of light and that there is no dispersion.

There is no dispersion in a vacuum...but if there was a long string of equally spaced Weber bars (say one every 100 km ) between us and the source then that might have a noticeable effect.