What are Gravitational Waves Anyway?

We all know what sound waves are. A mechanical wave, which a sound wave is, vibrates in the medium by causing compression and rarefactions, as in the diagram below.

propagation of sound

Compression causes the particles of the medium to bunch up, while rarefaction causes them to separate. If gravitational waves are "the ripples in the fabric of space time" then they must be considered mechanical waves.Since rarefactions and compressions occur in the direction of propagation the ripples in space time must be longitudinal waves. 

Longitudinal waves, unlike transverse waves, cannot be polarized. Light is a good example of a transverse wave, which is a dipole wave, where the polarizations occur in directions normal to the direction of propagation. Polarization can go from being linear to circular.

The important difference between longitudinal and transverse waves is that the latter does not need a medium to propagate in. It is as if the electric and magnetic fields, directed normally to the direction of propagation, ride piggy-back on one another. This means that not only can light propagate in a medium, like air or a solid material, but also can propagate in the vacuum of space. 

Are gravitational waves the intergalactic sound waves of the universe, which in ancient times we referred to as the "music of the heavens"? If they are then how do you explain the tensorial polarization of the waves? Then it wouldn't be possible to derive the spectra that LIGO has in the chirping and merging of two black holes by a non-general relativistic approach which uses the gravitational analogs of the electric and magnetic fields. Gravitation acceleration has been derived by Hilbron as the time derivative of the gravitational analog of the vector potential. That it reproduces known (supposedly, observed results) the gravitational waves must be a kind of electromagnetic wave. And it is supported by the fact (?) that gravitational waves also travel at the speed of light.

For if gravitational waves were longitudinal waves, their propagation would use up energy in making ripples in space-time, and it would be hard to rationalize the signal obtained by LIGO of the "merger of two black holes some 1.3 billion light years away." They would have dissipated away their energy a long time ago. The fact that the merger of a pair of neutron stars in August 2017, observed by LIGO, was so exactly confirmed by electromagnetic astronomers, rather than a confirmation makes it suspicious that gravitational waves are a form of electromagnetic waves, that is electromagnetic waves affected by gravity. But then, why do they need the fabric of space-time to propagate on, whereas electromagnetic waves do not?

Gravitational wave luminosity is of the same nature as electrodynamic, black body radiation, except for a difference in orders of magnitude. What cancels out the lower third-order term that would match thermal black body radiation to a tee? It is often said that conservation of mass and momentum prevent lower that quadrupole radiation from appearing. But where does that enter the expression for gravitational luminosity except to raise aberration to fifth order in the relative velocity?

We have no way of determining the velocity of a moving car from the inside without reference to observations made on the outside. Not true with acceleration, where we can distinguish between acceleration and deceleration by forces acting on our bodies. Michelson and Morley showed---using a Michelson interferometer--that motion through the ether was imperceptible.

What if uniform acceleration were  imperceptible and gravity belonged to such a frame? We are supposedly living in a steadily expanding universe according to Hubble. However, consider the Milky Way itself which is a large spiral galaxy that is part of a cluster of galaxies known as the Local Group. If the Milky Way could be thought of as a uniformly rotating disc at  an angular speed, $\sqrt{G\varrho}$, where $\varrho$ is some average density. This is the inverse of Newton's free fall time. The Milky Way rotates as a pinwheel at $270$ km/sec, and takes $200$ million light years to complete one rotation. This would give an angular speed of $\omega\approx 10^{-15}$ sec$^{-1}$. 

milky way

The uniformly rotating disc could thus be thought of as a hyperbolic plane, and planet earth would be one of the Poincarites that inhabit such a two-dimensional world. It is a well-known property of the hyperbolic plane that we would be unable to determine our position in the plane because if we proceeded in any direction our rulers and clocks would increase or decrease along with us so that it would be impossible to distinguish our position with say an observer on the rim of the disc. Recall that Einstein believed that the watch of an observer on the rim would go slower than the inertial observer located at the center of the disc. This, however, is impossible in a hyperbolic world. There are no privileged positions on the disc. 

Perhaps the simplest way to understand the effect of gravity is to transform the Poincare disc model to the upper half-plane. An isometry will take the disc to the upper half-plane which can be likened to an unevenly heated region where the $x$-axis represents "infinite" cold [cf. A New Perspective in Relativity, Ch. 2]. The strength of gravitation attraction could then be measured in terms of temperature of the unevenly heated half-plane---an entirely scalar operation.

Gravity in such a world would appear to us  static just like the ether in the Michelson-Morley experiment. The only way it could be brought alive is by the way is to shine light from the outside which would see as a refraction due a medium with an index of refraction different than one. So light can measure the effects that gravitational fields have on it.

Albeit all this is speculative, but no less speculative than gravitational waves which need a medium to propagate in like mechanical waves, yet are polarized, albeit a putative tensorial polarization. Just by the fact that they can be derived from a gravitational analog of electrodynamics makes that tensorial character precarious as well as the fact that they arise from a linearization of Einstein's equation for weak fields.

And pinpointing the source of gravitational waves is no less precarious. If light cannot escape the event horizon of a black hole neither should gravity. How can there exist a binary black holes if there separation is greater than their event horizons? The last phase before merger consists of ringing, implying a rapid change in frequency, and radiation. But is this frequency that of the beam in the interferometer or that appearing in Kepler's III to describe the evolution of the merger. And how is this compatible with Kepler's laws for don't forget that Kepler's laws are compatible with an inverse square law, and not an inverse cubic that would result, say, in Cotes' spirals.

Newton foresaw such a possible by adding on the cubic to his inverse square law. That would modify the angular dependency while keeping the radial part constant. In fact, it preceded the former: Proposition 9 dealt with motion along an equal angular spiral under the action of a central force which must be cubic. Proposition 11 dealt with motion to a focus in an ellipse where the force law was inverse square.