In a previous blog, I wasn't sure whether either Einstein's or Eddington's calculation, which differ by a mere factor of $2$, of the energy loss due to the damping of the rotational speed of a dumbbell due to the emission of gravity waves. After a lengthy calculation which avoids the use of the gravitational pseudo-tensor, Eddington in his book The Mathematical Theory of General Relativity comes to the conclusion that neither his calculation, nor Einstein's applies to the merger of two black-holes or anything like them.
The "chirp" referred to in the title concerns the rapid increase in frequency that the LIGO team has observed, or at least implied, when two black hole merger. I can't fathom how this results from interference patterns on a screen due to a delay in one of the light signals in the arms of a Michelson interferometer, but I will take them at their word and show how the calculation of the change in period of the orbiting binary mixes dipole and quadrupole radiation.
It is commonly accepted that the decrease in the binary pulsar 1913+16 is due to the emission of gravitational radiation. Yet, due to the finite propagation time of gravity, there will be created in any periodic orbit a tangential force which tends to increase the orbital period. So which is it? Does the period decrease due to the loss of mass-energy through gravitational radiation or to an increase in period due to the finite time that it takes an orbiting planet to feel the force of attraction.
After having commented on Maxwell's criticism of Lorenz's use of retarded potentials, I began to have second thoughts. Maxwell considered his theory of the electromagnetic field to be "big guns", and certainly didn't want anyone usurping him of his discovery in identifying the speed of light as the speed of the propagation of electromagnetic waves.
This question was raised by Carlip, in his attack against van Flandern's contention which reaffirmed Laplace's conclusion that gravity propagates a least a hundred million times greater than the speed of light, and answered by him in the affirmative, I will show that Carlip's analysis more than being insignificant, in the words of McDonald, is completely confused.
Maxwell's equations do admirally well in the description of radiation caused by oscillating charges in an antenna. A changing magnetic field produces an electric field, and a changing electric field is capable of producing a magnetic field. In order that there be undamped propagation of electromagnetic waves, both the electric and magnetic fields must be inversely proportional to the radial coordinate.
Let me start by saying I was wrong about the lack of a relationship between the quadrupole force and curvature. I used the symmetric force between two current elements when I should have used the directed force produced by one current element on the other. Curvature, force, and mean square deviations are all related and allow for a 'thermodynamic statistical description of curvature.
Do gravitational waves carry energy? ...No, they do not! Why should they? By definition, a gravitational wave is a 'weak' distortion of spacetime, that is, Minkowski (empty) space time. If something which is nothing can undergo distortion, then neither energy nor momentum is conserved. By its very nature, it constitutes a perpetual motion machine of the same kind, like powering a submarine from the thermal heat capacity of the water surrounding it.
A professor from Caltech and member of the LIGO team says it all:
Daily we read the remarkable breakthroughs that LIGO has accomplished in creating a whole new field of gravitational spectroscopy. Without even the hint of a smidgen of uncertainty, the sources of gravitational waves have been identified as either black hole or neutron star binaries. The final single compact object produces a "ringdown" oscillation of a black hole. The point mass formalism breaks down at merger requiring numerical integration of general relativity.