Black holes and gravitational waves – Part III

gwA representation of gravitational waves

To conclude black holes and gravitational waves trilogy, I propose A.Loinger’s considerations about gravitational waves:


The case of gravitational waves is more subtle (in comparison with black holes – E.N). Until Einstein’s death, the great majority of physicists, Einstein included, had well grounded doubts about a real physical existence of gravitational waves (In golden and small einstenian volume The Meaning of Relativity the locution “gravitational wave” never appears, as well as the locution “black hole”). See for example what Moller wrote in his 1972 treatise The Theory of Relativity. It is due to Fock a serious attempt to theoretically prove the physical existence of the gravitational waves (see his good 1964 book The Theory of Space, Time and Gravitation) but his method presents a conceptual gap, as I’ve shown in last mentioned work (2bis).

Starting around the seventies it came to light a growing flood of works on gravity waves, mainly written by authors that overlooked the problem of their “corporeality” or they touched it briefly. They’re very erudite mathematical essays, that take advantage of all resources of modern analysis and modern differential geometry, like after all is the case for many notes about black holes (3).

I think that the issue should be set as follows: in years long gone, Tullio Levi-Civita first demonstrated that the equation of the characteristics relating to Einstein’s field equations formally coincides with the equation of the characteristics related to d’Alembert’s waves equations and Maxwell equations ( 4). It is thus clear that the einsteinian field equations admit wave-type solutions, and with curvature tensor different from zero. However one can demonstrate, with arguments of various kinds, that such wavy characters are nothing more than formal properties of given general coordinates systems [see (2) and [2bis]]. I conclude by noting that Levi-Civita (4), with good reasons, interpreted said characteristics equation as differential equation for the motion of electromagnetic wave fronts.

(2) A. LOINGER, (8 Oct. 1998).

(2bis) A. LOINGER, 9904207 (20 Apr. 1999);

(3) One of the most famous enthusiasts for such subjects confided to me that, for him, Einstein rejected black hole notion because he didn’t know the most modern development of differential geometry.  I’ll just observe that in reality today’s differential geometry concepts date back to the thirties, and are mainly due to Hermann Weyl. It seems to me that to accuse Einstein of backwardness in matters of Relativity is roughly equivalent to affirm that Dante’s verses are not up to modern songwriters verses.

(4) T. LEVI-CIVITA, Rend. Acc. Lincei, 11 (s.6a) (1930) 3 e 113.


What to say then about the discovery of gravitational waves? Unfortunately I haven’t got the knowledge or the competence of a physicist, so I can only write my personal considerations after the concepts exposed so far.

I think that a part of science has taken a deviation that at this point is hardly recoverable. This habit of making the theory prevail over practice, that we’ve seen it was born with Maxwell, is risky for scientific progress: as long as phenomenons can be observed and replicated in laboratory the deviation is small ed easy justifiable, let’s think (to remain on topic) to the displacement current that didn’t prevent electrodynamics development.

When one starts to talk about events that happen billions light years away instead the question becomes different and the risk of making fantasy gallops and justify it with mathematics grows exponentially. To make things worse the deviation worsens exponentially with the passing of generations of researchers because they stack unverifiable concepts on old never experimentally validated concepts: I think it’s no coincidence that the solid Einstein’s Theory after a few decades has led to nuclear fission, while those built on its shoulders only to a flourishing speculation about blacks holes, unverifiable on all levels and with impossible practical consequences.

I think that to assume the existence of something indirectly is against the very principle of science, which should have as its basis the scientific method. It would be like pointing a telescope at the African Savannah and try to figure out if behind a curtain hides an elephant or a hippo, relying solely on indirect observations such the presence of a pool of water: in fact, it does not carry enough information for me to say with certainty whether behind the curtain there is a hippopotamus wallowing or an elephant drinking.

Therefore I’m not led to believe in black holes existence, because they’ve never been observed but only theorized. All observations are indirect (gravitational lensing, measurements of the accretion disk etc ..). I’m not saying that at the heart of those phenomena there is nothing, just I don’t believe it’s a black hole. There are other possibilities, like black stars for example (see post I). They behave like a black hole but without unprovable phenomena like event horizon, holes in space-time, information paradox etc.

About gravitational waves, the question changes: as we can observe in graphic below


the wave was detected by two interferometers: the Livingston LIGO in the state of Louisiana and the one in Hanford, Washington. The waves after appropriate corrections (7ms shifting and inversion) are very similar, then it is a double detection.
Therefore I would be led to believe the scientific community with one doubt: gravitational waves are inconceivably microscopic in size, as they’re about 1000 times smaller than the diameter of a proton. LIGO accuracy must be huge, so it takes very little to trigger its sensors. Could it have been a subtle seismic phenomenon that affected American continent? Something so subtle to not to be detectable by seismographs but enough to trigger the two interferometers? Or a series of coincidences that led to detecting similar waves ? I’m aware that it would be a practically impossible coincidence, however I think it it would have been better if the interferometers VIRGO (Italian) and GEO600 (German) also had picked up the wave, but unfortunately at the time of the detection they weren’t active.

To conclude, I’m not against this announcement but before fully celebrating I prefer to wait further updates from scientific community: now that scientists know how to detect such waves, it shouldn’t be difficult to catch others, thus excluding the risk of a blunder.



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