Does gravity propagate instantaneously, or at a finite speed?

Settled in 2017 by LIGO/Virgo & Fermi-GBM collaborations (GW170817).

Kapitza's problem #60 asks students to propose experimental methods for measuring the speed of gravitational propagation and to discuss the practical limitations of such experiments -- a question with no feasible answer using 1960s technology. General relativity predicts gravity should propagate at exactly the speed of light, but this went essentially untested directly until the 2015 first detection of gravitational waves. The 2017 GW170817 neutron-star-merger event, observed simultaneously in gravitational waves and gamma rays after traveling roughly 130 million light-years, arrived within about 1.7 seconds of each other, placing an extraordinarily tight bound ($|c_{\text{gravity}}/c_{\text{light}}-1|$ less than about 5x10^-16) confirming gravity and light propagate at the same speed to remarkable precision.

A question Kapitza could only ask students to speculate about experimentally in 1966 was answered half a century later by literally timing a signal that crossed 130 million light-years, arriving within seconds of its light counterpart.

Explanations that circulated

• Gravity's speed cannot be measured independently of light's speed, so the question is untestable (the ~1.7-second arrival-time gap between gravitational waves and gamma rays from the same neutron-star-merger event, across a ~130-million-light-year journey, directly bounded any difference between the two speeds to better than 1 part in 10^15)
• Newtonian gravity's apparent instantaneity in orbital mechanics means gravity actually propagates infinitely fast (general relativity predicts gravity propagates at exactly c, and orbital mechanics only appears instantaneous because of subtle velocity-dependent cancellations in the field equations, not because propagation is truly infinite)

References

• Gravitational Waves and Gamma-Rays from a Binary Neutron Star Merger: GW170817 and GRB 170817A, LIGO Scientific Collaboration, Virgo Collaboration, Fermi GBM, INTEGRAL, Astrophysical Journal Letters, 2017