The new science of gravitational physics had an interesting crisis in its initial years.
The resolution of that crisis is enlightening about relativity.
Eddington found a problem with Einstein's basis in a coordinate system artifact for gravitational waves 'leading [him] ' to jest that they "propagate at the speed of thought." '
The crisis was eventually resolved by assuming Einstein's proposed gravitational waves could be detected. That conclusion resulted in efforts like LIGO.
University of Colorado definition:
Gravitational physicists explore the implications of the general theory of relativity, in which gravitation is a consequence of the curvature of space and time. This curvature thus controls the motion of inertial objects. Modern research in gravitational physics includes studying applications of numerical relativity, black hole dynamics, sources of gravitational radiation, critical phenomena in gravitational collapse, the initial value problem of general relativity, and relativistic astrophysics.
excerpt of Wikipedia's description of its beginnings:
In 1905, Henri Poincaré proposed gravitational waves, emanating from a body and propagating at the speed of light, as being required by the Lorentz transformations and suggested that, in analogy to an accelerating electrical charge producing electromagnetic waves, accelerated masses in a relativistic field theory of gravity should produce gravitational waves. When Einstein published his general theory of relativity in 1915, he was skeptical of Poincaré's idea since the theory implied there were no "gravitational dipoles". Nonetheless, he still pursued the idea and based on various approximations came to the conclusion there must, in fact, be three types of gravitational waves (dubbed longitudinal-longitudinal, transverse-longitudinal, and transverse-transverse by Hermann Weyl).
However, the nature of Einstein's approximations led many (including Einstein himself) to doubt the result.
In 1922, Arthur Eddington showed that two of Einstein's types of waves were artifacts of the coordinate system he used, and could be made to propagate at any speed by choosing appropriate coordinates, leading Eddington to jest that they "propagate at the speed of thought". This also cast doubt on the physicality of the third (transverse-transverse) type that Eddington showed always propagate at the speed of light regardless of coordinate system.
In 1936, Einstein and Nathan Rosen submitted a paper to Physical Review in which they claimed gravitational waves could not exist in the full general theory of relativity because any such solution of the field equations would have a singularity. The journal sent their manuscript to be reviewed by Howard P. Robertson, who anonymously reported that the singularities in question were simply the harmless coordinate singularities of the employed cylindrical coordinates.
Einstein, who was unfamiliar with the concept of peer review, angrily withdrew the manuscript, never to publish in Physical Review again.
Nonetheless, his assistant Leopold Infeld, who had been in contact with Robertson, convinced Einstein that the criticism was correct, and the paper was rewritten with the opposite conclusion and published elsewhere.
In 1956, Felix Pirani remedied the confusion caused by the use of various coordinate systems by rephrasing the gravitational waves in terms of the manifestly observable Riemann curvature tensor. At the time this work was mostly ignored because the community was focused on a different question: whether gravitational waves could transmit energy. This matter was settled by a thought experiment proposed by Richard Feynman during the first "GR" conference at Chapel Hill in 1957. In short, his argument known as the "sticky bead argument" notes that if one takes a rod with beads then the effect of a passing gravitational wave would be to move the beads along the rod; friction would then produce heat, implying that the passing wave had done work. Shortly after, Hermann Bondi, a former gravitational wave skeptic, published a detailed version of the "sticky bead argument".
From the beginning in 1922, gravitational waves were in doubt. Einstein himself tried to publish a paper denying them but withdrew that paper after being convinced his conclusion was wrong.
The account is not clear whether Einstein or Infeld wrote the final paper bringing gravitational waves back to relativity.
'In 1956, Felix Pirani remedied the confusion' but his solution was not accepted until Feynman's famous 'sticky bead argument' in 1957 convinced those in this gravitational physics discipline these gravitational waves could be detected.
In 1969, Weber claimed to have detected the first gravitational waves, [but] by the late 1970s general consensus was that Weber's results were spurious.
Prototypes for LIGO were developed in the 1970s.
LIGO and gravitational waves have been covered elsewhere by Thunderbolts Project.
I find the sticky bead argument awkward but certainly It was necessary in 1957 to maintain the importance of relativity and an agreement was reached.
I find it funny: ' in the Chapel Hill conference, Richard Feynman — who had insisted on registering under a pseudonym to express his disdain for the contemporary state of gravitational physics.'
There was a big problem to resolve in 1957. Wow!
Wikipedia has a topic 'sticky bead argument' with details.
If the Feynman experiment had used two electrically charged bodies no one would question the force between the two electric fields would result in the motion of one body affecting the position of the other. That is because physicists know the electric fields can exert a force.
The Feynman scenario required a huge mass to bring a strong gravitational field.
In classical physics, moving the large mass changes the force of gravity for mutual attraction between the 2 bodies. While the person is moving one mass the other mass will get a change in the tiny force of gravity toward the moving mass.
There is no wave with Newton's gravity because gravity is instantaneous.
In 1957 Feynman had to address the different context for gravity in relativity; a mass does not exert a mutual force of attraction with another mass. A mass has a gravitational field and that field results in the curvature of the observer's spacetime. The inherent problem with relativity is there is no force of gravity affecting motion.
With Newton this force is determined by both masses and their distance.
In relativity there are only gravitational fields affecting spacetime curvature.
The conclusion from Feynman's 'sticky bead argument' is the gravitational field must impart energy (i.e., the missing force) to affect the other body. In the 1957 context of relativity Feynman could not use the force of gravity to impart its energy. This energy (not a force) would be transmitted by gravitational waves in some manner like electromagnetic waves, with no details. These waves would use the fabric of spacetime as the propagation medium. Because light being electromagnetic radiation as waves is limited to c in a vacuum the velocity of gravitational waves is also assumed to be at c.
These gravitational waves though lacking thorough detail were assumed to be detectable.
In a way, their detection by LIGO is crucially required to confirm the conclusion reached in 1957.
Gravitational waves arose because relativity removed the force of gravity but used only the gravitational field.
From Galileo and Newton a gravitational field is from a mass in a sphere of uniform density. This field exerts a force for free fall acceleration which occurs on a smaller mass in this field (of the larger mass) when there are no other forces affecting the smaller mass.
However relativity employed spacetime curvature from the gravitational field but not as a force or even a free fall. The observer's mass is not available to determine a mutual force.
In relativity the force of gravity requires propagation from the primary accomplished by gravitational waves with no defined second mass.
Gravitational waves need the spacetime fabric as their medium for propagation.
These waves exist only in spacetime because in classical physics gravity is an instantaneous force between masses. This force defined by Newton diminishes with the inverse square of distance.
There are no waves for electric and magnetic forces. The electric field force also diminishes with the inverse square of distance.
The discipline called gravitational physics began with some physicists having 'disdain' but an agreement was eventually reached.
Gravitational waves remain accepted by gravitational physicists despite the rough start with some questioning the concept's validity. Relativity remains undeniable dogma for many.
LIGO has been unable to provide the confirmation required of its efforts.
Only one event in the 43 since LIGO began in 2015 has a possible independent observation but a news story in Germany's press indicated the gamma ray burst was detected first and then LIGO had an event to match. All the rest are just detections with nothing to indicate a real event. There has been no observed inspiral event with two known objects to record its data to verify LIGO's system.