Our previous post on 07/02/2012 ended with the question:
Why is the idea/hypothesis of gravitational waves (GW) in General Relativity so special? Why is, unlike in all other predictions, the second part of the question: “what if we don’t?”, absent, despite the stream of negative experimental results during the last 50 years? We are trying to give the answer here.
First of all, GW are associated with the name of Einstein. The most common statement is: “observation of GW will be a triumph of Einstein’s GR”. How the above statement evolves from “whether Einstein’s theory really predicted the existence of gravitational radiation” is a different story and we will return to this later.
In 1999, Einstein was named the person of the century by Time magazine , and any skepticism about existence of GW will be obviously perceived as criticism of Einstein and his GR. GW are not special in this respect, using Einstein’s name as some sort of argument is not uncommon, e.g. “If Einstein were alive today, he would probably be a string theorist, engaged in a remarkable, but still very controversial, theory that claims to explain absolutely everything around us” (see “String fellows”  ). In today’s fashion it is a plausible assumption because it is not falsifiable (no one can ask Einstein’s opinion). Einstein, of course, never talked about strings, but we suspect that if he were alive he would not join string fellows. To affirm our conclusion, we just cite Einstein’s opinion about extra dimensions : “It is anomalous to replace the four-dimensional continuum by a five-dimensional one and then subsequently to tie up artificially one of these five dimensions in order to account for the fact that it does not manifest itself.”
Let us mention only two the most common textbook statements in support of GW existence (yes, there is no detection of GW but there are many textbooks). We will call them “myths” for the following reason. Looking at the dictionary for definition of “myth”, we read – “a traditional or legendary story, usually concerning some being or hero or event, with or without a determinable basis of fact or a natural explanation”, or “an unproved or false collective belief that is used to justify a social institution”. It seems like such a definition is not applicable to science, but we found that in the modern world people more often tempt to believe in some speculative “scientific” “discoveries” rather than checking the sources, e.g. original papers, especially that most of them are now available on Internet just from one click (or from double-click).
The first myth is the most popular among journalists and is repeated again and again in popular articles, public talks and in introductions to some scientific articles.
Myth 1: In 1916 Einstein gave the proof of existence of GW in GR.
Very often the reference is not given (in 1916 Einstein published five papers including his famous  ) and it is not clear which paper is meant, probably, under assumption that either all readers are familiar with this paper or can easily find it, or most likely have to accept this as well-known and unquestionable fact.
If the proof was given in  , then why was the question raised 20 years later (in 1936) by Einstein himself ”Do gravitational waves exist?” (the lost paper, for details see the book by Kennefick )?
In paper  Einstein wrote: “They [the values of the metric tensor found in previous calculations] led me to the simple approximative solution given above. However, one has to keep in mind that the choice of coordinates which has been made here has no equivalence in the general case, as the gamma and the gamma prime have tensorial character only with respect to linear orthogonal substitutions, but not under general substitutions”. So, linear approximation of GR is not generally covariant. Einstein spent 10 years to find the equations which are invariant under general coordinate transformations, contrary to special relativity and Maxwell theory which are invariant only under Lorentz transformations. In 1937 (see the end of the first section where linear approximation is discussed again) after Eq. (13a) there is the statement: “если весь метод приближенных уравнений оправдан” (if the whole method of approximate equations is justified). Is it? We do not have on hands the original paper in English  and translated it back from Russian from . The complete collection (four volumes) of Einstein’s scientific papers were translated into Russian and published in 1966 and, to our surprise, it remains the only one such a collection in the world!
The second popular textbook statement:
Myth 2: GW in Einstein’s GR are analogous to electromagnetic waves (EMW) in the Maxwell theory.
The use of this analogy reached a complete absurd. One such an example (Ch. 1, an overview, doctoral (!?) school , pp. 1-2): “… James Clerk Maxwell … was able (in 1873) to predict the existence … of the electromagnetic waves. Nevertheless, some distinguished physicists, such as Lord Kelvin, had serious doubts about the existence of such waves … However, in 1887, eight years after Maxwell’s death, electromagnetic waves were both generated and detected by Heinrich Hertz…”, and next “In the same way, in general relativity”(?!), which is “Einstein’s field equations (1915)… Albert Einstein, in 1916, … predicted the existence of … the gravitational waves … Similarly to what happened when electromagnetic waves were first predicted, some distinguished physicists had serious doubts about their existence. Arthur Eddington …”.
Is it really “In the same way”? Hardly, something is missing: are GW “generated and detected” and by whom? Actually, electromagnetic waves have been observed well before Hertz: people see light from the dawn of mankind. This is not the case for gravitational waves.
In 1916 Einstein demonstrated the existence of a wave solution for linear approximation which is indeed related to the Maxwell theory. It is one of Lorentz invariant models which are generalizations of the Maxwell theory (spin one) to higher spins. It was constructed by Fierz and Pauli for spin two  and later for any whole and fractional spins. We are not aware about any observation of particles with spin 2 (“graviton”) or higher (as well as 3/2 “gravitino”).
Without “gravitational” Hertz, or Hertzes (who “generated and detected”), the only analogy (and probably the necessary condition for observation) is the existence of skeptics (Lord Kelvin – Sir Eddington). Lord Kelvin died in 1907, i.e. long after Hertz was able to eliminate his “serious doubts”. Sir Eddington was not so lucky, he died in 1944 with serious doubts and many other sceptics disappeared after him still waiting for “gravitational Hertzes”. To keep the described analogy, new skeptics are needed (no skeptics – no analogy – no “generated and detected”).
In Foreword to Feynman’s lectures on Gravitation (, p. XXV) we read: “As late as 1957 … it was still possible to have a serious discussion about whether Einstein’s theory really predicted the existence of gravitational radiation” (This is recollection of the authors of the foreword about Chapel Hill Conference). From this statement it follows that soon after 1957 it became impossible to have serous discussion about existence of GW or such discussions became non-serious. Why? What happened? Were GW “generated and detected”? No, an experiment not even started but textbooks and serious predictions about time of observation started to appear. The first textbook (to the best of our knowledge) with GW in the title is due to Weber (1961) where we read (, p. 87): “… in recent years … it has been possible for a number of physicists to conclude that general relativity really does predict the existence of gravitational waves”, and the experimental work started (see second footnote on p. 137). We are still waiting for detection of GW, but what about changes in the number of physicists for whom it became possible to conclude that GR predicts GW?
On the same 1957 Conference that often presented as some pivotal point for GW hypothesis and the beginning of decline of scepticism (we return to this later), Feynman gave a presentation (the sessions on the quantization of gravity) that was followed by discussion (see  and more accessible book , pp. 134-135). Leon Rosenfeld made the following remark: “It seems to me that the question of the existence and absorption of waves is crucial for the question whether there is any meaning in quantizing gravitation. In electrodynamics the whole idea of quantization comes from the radiation field”. Bondi: “this vexed question of the existence of gravitational waves does become more important for this reason”. Feynman agreed that arguments in favour of quantization depend on the existence of waves. Perhaps, vice versa, the success of the quantization program gives a clue about existence of waves.
1970’s – 1980’s: it was shown that GR is not renormalizable, quantization is not possible (see, e.g. ). Quantization was performed using the standard method that was employed before in linear (Maxwell) or not so highly non-linear as GR theories (Yang-Mills), i.e. starting, as the first approximation, from linearized GR – exactly as in 1916 Einstein’s paper, and the negative result is consistent with Einstein’s concern about justification of linear approximation: “if the whole method of approximate equations is justified”. Linearization of GR does not lead to physical results.
This is related to the warning of Carmeli in his textbook (1982) “Classical fields. General relativity and gauge theory” : “It is well known that in other nonlinear theories, such as hydrodynamics, one also refers to linearization methods, and our experience shows that solutions of the linearized equations may bear little or no relation to solutions of rigorous equations. In particular, solutions of the linearized equations exist which by no means approximate the rigorous solution. It is the nonlinearity of the theory [GR] that makes it so distinguishable … One should therefore in no way consider the linearized theory as being a substitute to the full theory.” And try to quantize starting from linear approximation.
This statement of Carmeli (he was the student of Rosen, Einstein’s assistant) repeats Einstein’s thoughts on the role of non-linearity of GR. In 1936 Einstein wrote to his friend Max Born: “Together with a young collaborator, I arrived at the interesting result that gravitational waves do not exist, though they had been assumed a certainty to the first approximation. This shows that the non-linear general relativistic field equations can tell us more or, rather, limit us more than we have believed up to now” .
The non-linearity of Einstein’s field equations remains unchanged, they continues to be fundamentally different from spin 2 model (linear approximation), and quantization of GR starting from this linear approximation is not possible, and there is no detection of graviton and GW.
“Physicists … perhaps are too conservative in believing that physics (theoretical) should always be made and interpreted the same way, e.g. by wanting to do with GRG the same as in Electrodynamics. Perhaps, the revolution implied by GR is that it is precisely another way of concerning the physical world” (Andre Mercier, , p. 243).
Analyzing Einstein’s views on GW, Kennefick wrote (, p. 97): “Did the retraction of his nonexistence proof mean that Einstein was cured of skepticism? Perhaps not, or at any rate, not completely”.
Let us return to the fate of skepticism. Why in 1957 “it was still possible to have a serious discussion about whether Einstein’s theory really predicted the existence of gravitational radiation”, but in 1961 “it has been possible for a number of physicists to conclude that general relativity really does predict the existence of gravitational waves” and “After some point during the early 1960s, the debate ceased to be relevant because a sufficient consensus had formed against the sceptical position”. The last quotation is taken from the book of Kennefick , p. 276, which title, “Traveling at the speed of thought”, is an ironic phrase of the skeptic – Arthur Eddington. This book gives quite extended account of disappearance of skepticism and associated with it events.
According to the author of , p. 115, after the World War II: “Physics especially experienced a remarkable surge in the number of researchers, particularly in the United States. America became the epicenter of research in theoretical physics …” GR and skepticism about GW were originated in Europe, but more important fact – the financial support of this field, including support for the 1957 Conference, began, and the biggest contribution originally came from the United State Air Force (see , p. 116).
The Air Force, we guess, is not a philanthropic organization that could be interested in an answer to the purely scientific question “Do gravitational waves exist?”. (There is a Russian proverb: “Кто платит, тот заказывает музыку”; its English analogue is: “He who pays the piper calls the tune”.) Grants are given to non-sceptics, non-skeptics can have graduate students, hire posdocs, start experiments, etc., etc., etc. In academy one can be skeptical but new hiring of skeptics is out of question (the standard phrase – “to secure external funding” – more often appears in advertisements for academic positions, so such positions are not for skeptics). This is a plausible scenario. But to check it, the history of hiring in the GR-related positions in those years has to be analyzed, as well as the list of proposals that got financial support and unsuccessful topics. Similar, but more recent and better documented situation, was described in Peter Woit’s book “Not even wrong” , when he wrote concerning hiring string theoreticians.
After the Air Force (after changes in U.S. policies , p. 116), National Science Foundation becomes the main source and it continues to give generous support to this field, especially for GW search. Our, not very hard, attempt to find out whether the Air Force continues to support GR research leads us to only the grant from U.S. Army Aviation and Missile Command: “…generating and controlling significant gravitational forces via this new theory, making a 70 ton tank appear to weight much less, cutting edge technology, enormous value for DOD weapons and weapon systems” (see , p. 66), but we were not able to find any report or information about this project, only lots of conspiracy theories about results and fate of Dr. Ning Li and her AC Gravity LLD. We even started to suspect that this document could be a very elaborate hoax. We cannot solve this mystery (we are not paying taxes in U.S.). However, one phrase from document seems to point that this is genuine: “If unsuccessful, this avenue can be eliminated from future efforts, and would put to the rest controversy surrounding these theories” ($448,970 U.S. Government Dollars are given and time was set 25 Apr 2001 – 25 Sep 2002).
Controversy (skepticism) about existence of GW is over and nothing can put to the rest this idea. Some statements in  even sound as a warning to skeptics (we believe that this is just an observation of the author concerning state of affair in the field, not a deliberate attempt to scare the potential or underground sceptics), e.g., , p. 275: “There seems to be some evidence that Cooperstock … lost a certain amount of standing on this topic as a result of his open defiance of the emerging orthodoxy” and he can publish only in Foundations of Physics, the journal that encourages the publication of “speculations not tied to hard…” (the current editor is the Nobel prize winner in Physics t’Hooft), contrary to Physical Review (where , p. 230 “Rosenblum and Cooperstock’s last publications in Physical Review D on this controversy are dated from 1984 and 1986, respectively” – after this point no papers in PRD, i.e. “controversy is effectively over” because, unlike editorial preface to Foundations of Physics, Physical Review D does not encourage submission of “speculations not tied to hard…” and “accept for publication those manuscripts that significantly advance physics and have been found to be scientifically sound, important to the field,…”, i.e. publish only non-speculative, novel, cutting-edge results on GW, strings, cosmology, supersymmetry, etc. (see the Editorial policy of PRD ). Skepticism will damage your professional standing! (skepticism in science becomes non-professional!) and such results can be published only in non-leading journals.
According to  p. 276: “Eventually a critical mass of consensus, enough to close off further debate, formed…, dissent was no longer viewed as healthy or desirable, … disagreement would only retard the progress of a field”. Such consensus, despite absence of any experimental confirmations and disappearance of skepticism, is our main concern about health of this field – this uniform front is good for parades in the front of public but not for a real action. We agree with that , p. 254 “since the true goal of physics theory is the description of the real world, it is particularly appropriate, with regard to gravitational theory, to nurture a spirit of skepticism. Surely this is a healthy ingredient for the growth of any science”, but these are words of Cooperstock and , p. 255 “Cooperstock’s capital had already been depleted” and there is no granting agencies that can possibly bail out sceptics (to restore their capital).
The author of  observes, p. 275: “It seems that the aim of the all of the conferences, workshops, papers, reviews, appeals to experiment, and so on, is not to enforce or encourage agreement as such, but rather to eliminate or reduce the space for disagreement.” The reduction of space for disagreement can be accomplished using different methods and the most effective instrument for reduction of space for disagreement has to be added – generous financial support of a particular view.
Looks like (is it a law?) that any model or prediction after 30-40 years without experiment becomes a conventional wisdom (it can take longer if financial support is not available). After this point, discussion cannot be serious (even considered as making disservice for the field) and results of experiments become irrelevant (for how long?). When will someone repeats after Chretien, the former Prime Minister of Canada: “enough is enough”?
“In the study of gravitational waves the chase seems to have become a route, since no positive experimental results at all are available to justify the copious writtings on the subject” – these are words of Bonnor  and they perfectly describe current stage of the chase but these words were spoken already in 1963!!
What is going on (and on, and on) after non-skeptics have prevailed? GW in 21st century.
To be continued…
 Time magazine http://www.time.com/time/magazine/article/0,9171,993017,00.html
 String fellows http://www.guardian.co.uk/science/2005/jan/20/science.research/print
 A. Einstein, Science, 74 (1922), 438-439.
 A. Einstein, Annalen der Physik, 49 (1916) 769-822.
 A. Einstein, Sitzungsber. preuss. Akad. Wiss., 1 (1916) 688-696.
 D. Kennefick, Traveling at the Speed of Thoughts, Einstein and the Quest for Gravitational Waves, Princeton University Press, 2007.
 A. Einstein and N. Rosen, Journal of Franklin Institute, 223 (1937) 43-54.
 A. Einstein, The Complete Collection of Scientific Papers, Nauka, Moskva, 1965, vol. 2, p. 438 (in Russian).
 Gravitational waves, Eds. I.Ciufolini, V. Gorini, U. Moscella and P. Fre, 2001, IOP Press, Bristol and Philadelphia.
 M. Fierz and W. Pauli, Proceedings of Royal Society, London, 173 (1939) 211.
 R.P. Feynman, Lectures on Gravitation, Westview Press,
 J. Weber, General Relativity and Gravitational Waves, Interscience Publishers, Inc., New York, 1961.
 M.H. Goroff and A. Sagnotti, Nuclear Physics B, 266 (1986) 709-736.
 M. Carmeli, Classical Fields, General Relativity and Gauge Theory, World Scientific, New Jersey, 2001.
 P. Woit, Not even wrong, the failure of string theory and the search for unity in physical law, Basic Books, New York, 2006.
 Department of Defense, Annual Report on Cooperative Agreements and Other Transactions Entered into During FY2001 Under 10 USC 2371: www.acq.osd.mil/dpap/Docs/FY01RPT.doc .
 Physical Review D, Editorial policy http://prd.aps.org/info/polprocd.html .
 F.I. Cooperstock and D.W. Hobill, General Relativity and Gravitation, 14 (1982) 361-378.
 W.B. Bonnor, British Journal of Applied Physics, 14 (1963) 555-562.