Shapiro Delay of Neutrinos and Gravitational Waves
From the near-simultaneous observations of neutrinos and photons from SN 1987A, we know that the Shapiro delay for high-energy neutrinos is the same as that for photons to within 10% (consistent with recent estimates of the neutrino mass which imply that those neutrinos were moving at very close to the speed of light). Since gravitational waves have not been directly detected, we don't have any data on the Shapiro delay for gravitational waves. In general relativity and other metric theories of gravity, the Shapiro delay for gravitational waves is expected to be the same as that for light (and neutrinos). However in theories such as Teves and other modified GR theories which reproduce Milgrom's law and avoid the need for dark matter, the Shapiro delay for gravitational waves is much smaller than that for neutrinos or photons.
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