Interferometric detection of gravitational waves: how can a wild roam through mindless mathematical laws really be a trek towards the goal of unification?
aa r X i v : . [ phy s i c s . pop - ph ] M a r Interferometric detection of gravitationalwaves: how can a wild roam throughmindless mathematical laws really be atrek towards the goal of unification? C. Corda, R. Katebi and N. O. Schmidt
September 20, 2018 Research Institute for Astronomy and Astrophysics of Maragha (RIAAM),P.O. Box 55134-441, Maragha, Iran and Dipartimento di Fisica, ScuolaSuperiore di Studi Universitari e Ricerca "Santa Rita", Via Severino Delogu, 6- 00144 Roma Eur, Italy Department of Physics and Astronomy, Ohio University, Athens, Ohio 45701,USA Department of Mathematics, Boise State University, 1910 University Drive,Boise, ID 83725, USAEssay written for the FQXi Essay Contest 2016: Wandering Towardsa Goal
Abstract
The event GW150914 was the first historical detection of gravitationalwaves (GWs). The emergence of this ground-breaking discovery camenot only from incredibly innovative experimental work, but also from acentennial of theoretical analyses. Many such analyses were performedby pioneering scientists who had wandered through a wild territory ofmathematical laws. We explore such wandering and explain how it mayimpact the grand goal of unification in physics.
In November of 1915 Albert Einstein sent his historical paper on the generaltheory of relativity [1] to the Prussian Academy of Science. Two subsequent pa-pers by the same Einstein, in 1916 [2] and in 1918 [3], predict that any massiveobject moving through space-time will generate GWs. Thereafter, in Septem-ber of 2015 the Laser Interferometer Gravitational-Wave Observatory (LIGO)detected the first GW signal from a binary black hole merger; this remarkable,1istorical event is known as GW150914 [4] and is in alignment with the goal ofestablishing a unified field theory of physics. The event GW150914 representeda cornerstone for science and for gravitational physics in particular. In fact, thisremarkable event equipped scientists with the means to give definitive proof ofthe existence of GWs, the existence of black holes having mass greater than 25solar masses, and the existence of binary systems of black holes which coalescein a time less than the age of the universe [4]. The one century period betweenthese two historical events encompasses a great interplay of experimental andtheoretical advancements. Who on Earth would have guessed that pioneeringscientists, who have wandered through a wild territory of mindless mathemat-ical laws, would ultimately help pave-the-way to the creation of LIGO and thedetection of GW150914?In order to take science to the next level, we must first establish and experimentally-verify a unified field theory of physics so it can be further applied to disciplinessuch as chemistry, biology, engineering, computing, and medicine, etc. Thus, inorder to develop and assess candidates for such a grand unified theory, we mustbe able to probe systems of massive objects throughout the universe. To learnhow such systems operate and interact, we must be able to detect and analyzethe GWs that they generate in the first place; this motivates the hunt for GWs.Detecting GWs is a mighty challenge because it requires highly-sophisticatedtechnology that is capable of making extremely precise measurements. Conse-quently, in order to advance science and establish a unified field theory, scientistsworking in this field need such tools to detect and analyze GWs. Therefore, thecreation of LIGO and the GW150914 detection are colossal, powerful steps for-ward in the trek that aims to achieve unification. A great hope is indeed thefuture detection of primordial GWs, which could show that gravity might alsobe brought into the unification and will be, in turn, a next great step toward es-tablishing the root of a unified field theory that may be verified in the laboratory[5]. Before we explore aspects of the mindless wandering which ultimately ledto the ground-breaking detection of GW150914 by LIGO, let us briefly touchon some pertinent background material: what is a GW and which types ofastrophysical objects generate GWs that scientists can detect? Let us consideran analogy. Suppose that you’re standing along the shore of a vast lake that isflat calm. If you reach down and move your hand through the water, then youraction will cause a disturbance, or ripple effect, as the generated water wavesensue the trajectory of your hand and propagate outward in the lake. AlbertEinstein’s general theory of relativity predicts a similar effect: if an object withmass is moving through space-time, then this action will cause a disturbance asthe generated GWs ensue the trajectory of the object and propagate outward inthe universe. Thus, according to the general theory of relativity, any acceleratingobject with mass should generate GWs. But small ripples in space-time woulddissipate relatively quickly, just as small ripples in the lake would fade outbefore they could be seen by a second observer standing along the shore ata sufficiently far distance. Therefore, in order to detect GWs on Earth thatare generated from distant sources throughout the universe, scientists search2or enormously massive objects, such as neutron stars or black holes, that arecapable of generating GWs that propagate all the way to Earth.In 1974 Russel A. Hulse and Joseph H. Taylor discovered the Hulse-Taylorbinary (or PSR 1913+16) using the Arecibo radio telescope [6]. The Hulse-Taylor binary is a compact star system consisting of two neutron stars (one ofwhich is a pulsar - i.e. a neutron star emitting electromagnetic radiation) thatorbit around a common center of mass. The Hulse-Taylor binary was the firstbinary star system to be observed and is regarded as the first indirect proofof the existence of GWs as predicted by the general theory of relativity. Eventhough the first efforts at direct GW detection started long before the Hulse-Taylor binary (see the recent paper by the Nobel Laureate G. F. Smoot andcollaborators on the history of GW research [7]), this astronomical revelationgenerated intense excitement in the physics community while further motivatingefforts to create new technology for direct GW detection. In fact, this historicalfinding was so significant that it earned Hulse and Taylor the 1993 Nobel Prizein Physics [8].On one hand, the event GW150914 and the subsequent event GW151226,which is the second direct detection of GWs from a 22 solar-mass binary blackhole coalescence [9] are considered to be one of the greatest triumphs of exper-imental physics because they represent the most precise experimental measure-ments in the whole history of science. In fact, they involve measuring distanceson the order of − meters. This is a distance shorter than the proton’s radius!In a recent interview during a trip in Italy, the famous theoretical physicist KipThorne, who is one of the LIGO’s Founding Fathers and is, in turn, a candidatefor the Nobel Prize in Physics for the direct detection of GWs, claimed, with avery remarkable modesty that [10] (translated from the Italian language) “ Thenext Nobel Prize for Physics? It must be assigned to the gravitational waves, butI do not deserve it. The real heroes of this event (the detection of gravitationalwaves) are the experimental physicists who resolved all the practical problemsof a very complex experiment making possible this discovery. I am not amongthem.”.
On the other hand, the goal of this Essay is to stress that the event GW150914and the subsequent event GW151226 arise not only from extremely precise ex-perimental work, as it has been emphasized by Thorne, but also from a centen-nial of theoretical analyses which have been performed through lots of mindlessmathematical laws.Einstein predicted the existence of GWs in his theoretical, historical paper[2] and improved his analysis two years later [3], claiming that this second paperpermitted him to correct a trivial mistake in his previous work [2]. In any case,Einstein’s position on the existence or non-existence of GWs changed varioustimes. In 1936 Einstein wrote to Max Born [11]: “
Together with a young col-laborator (Nathan Rosen), I arrived at the interesting result that gravitationalwaves do not exist, though they had been assumed a certainty to the first approx-imation. This shows that the non-linear general relativistic field equations cantell us more or, rather, limit us more than we have believed up to now ”. Einsteinsubmitted this research titled “
Do Gravitational Waves Exist? ” to the Physical3eview with Rosen as the co-author [12]. Although the original version of thismanuscript no longer exists, one can infer from the letter of Einstein to Born[11, 12] that Einstein and Rosen answered "No" in response to the questionof the title. Despite Einstein’s great eminence and fame, the Physical Reviewreturned the paper to Einstein with a critical review and the kind request thatthe journal’s Editor, who was the physicist John Torrence Tate Sr., “ would beglad to have [Einstein’s] reaction to the various comments and criticisms thereferee has made ” [12]. When Einstein received the returned paper with thecritical review he became infuriated and decided to ultimately withdraw thepaper from the Physical Review with a very irritated letter (Einstein was so fu-rious that he wrote the letter in Germany instead of in English!). Details of thiscurious story can be found in [12]. In any case, Einstein, who decided to publishthe paper with the Journal of the Franklin Institute in Philadelphia [13], againreversed his opinion on the existence of GWs in 1937. In fact, Einstein’s newcollaborator, Infeld, discovered a mistake in the paper of Einstein and Rosenduring a discussion with the relativist Howard Percy Robertson [12, 14], whois famous for his works in cosmology (he was co-author of the widely knownRobertson-Walker metric). Infeld reported his discussion with Robertson toEinstein. This time Einstein not only agreed with the arguments of Infeld andRobertson, but also added that he had coincidentally and independently foundanother mistake in the paper that he wrote together with Rosen [12, 14]. Atthat time the paper was in the phase of proofs for the Journal of the FranklinInstitute. Thus, despite that the journal had already accepted the paper in itsoriginal form, Einstein was forced to explain that fundamental changes in thepaper were required because the consequences of the equations derived in themanuscript were incorrect [12]. Then, the paper of Einstein and Rosen was pub-lished with radically altered conclusions [13]. Differently from Einstein, Rosendid not change his opinion on the non-existence of GWs [12]. In fact, he wasnot happy with the paper [13] and published a paper in a Soviet journal byclaiming the non-existence of GWs [15]. In the following year, Einstein reversedhis opinion one more time. In fact, in 1938 Einstein wrote a paper together withInfeld and the mathematician and physicist Banesh Hoffmann [16]. This was a(fruitless) attempt to find a theory which could unify gravity and electromag-netism, where one of the assumptions of the paper was that GWs should notexist [16]. Thus, in general, Einstein’s attitude on the existence or non-existenceof GWs was of substantial uncertainty. This was stressed by the same Einsteinin a lecture that he delivered to the University of Princeton exactly one dayafter he corrected his paper [13]. In fact, he concluded the lecture by saying “
Ifyou ask me whether there are gravitational waves or not, I must answer that Ido not know. But it is a highly interesting problem ” [12, 14].A key event in GW research occurred in the 1950s, when the famous astro-physicist Hermann Bondi, with his collaborators Felix Arnold Edward Piraniand Ivor Robinson, published the fundamental paper [17]. In that work, theyshowed that Rosen’s arguments in [15], which claimed that GWs do not exist,were incorrect. Furthermore, they also correctly predicted the effect that wouldeventually be used in the future by LIGO to detect the real GWs of GW1509144nd GW151226. The most remarkable contribution on this issue was by Pirani,who also wrote the important papers [18 - 20].Thus, for the theme of this Essay, we note that for more than 40 years - i.e.from Einstein’s prevision in [2,3] to the work of Pirani and Bondi [17 - 20] - theprimary goal of GW detection was not yet well-defined. Instead, we’ve had agigantic and intriguing, but also wild and controversial, debate regarding theexistence or non-existence of GWs through a hefty amount of theoretical workover a vast territory of mindless mathematical laws. In this case, identifyingthe real goal to be approached (the detection of GWs) was a greatly disputedissue. In order to ultimately realize the significance of GW detection and de-velop the mathematical formalism to describe the GW phenomena, numerouspioneering scientists invested an enormous amount of time and energy to wan-der through this mindless territory by asking questions, considering hypothesesand conducting thought experiments. We indeed cited only the most importantcontributions to the debate on GWs, which also involved the work of Eddington[21], Beck [22], Baldwin and Jeffery [23]. Despite Einstein’s claim that, even ad-mitting the concrete existence of GWs, their detection will always be impossiblebecause of the very weak coupling between matter and GWs [3], Pirani and col-laborators [17 - 20] predicted a GW effect that could be observed. They indeedproposed the geodesic deviation equation as a tool for designing a practical GWdetector. In other words, if a GW propagates in a region of space-time wheretwo free-falling test masses are present, the GW effect will drive the masses tooscillate.Recently, one of us, C. Corda, generalized the work in [17 - 20] to the frame-work of extended theories of gravity [24 - 26], also together with collaborators[27]. In fact, the motion of the test masses due to a GW in extended theoriesof gravity is different with respect to the motion of test masses due to a GW inthe general theory of relativity [24 - 27]. This is because in the standard generaltheory of relativity one finds only two different, independent GW polarizations,while in extended theories of gravity the independent GW polarizations are atleast three [24 - 27]. The results in [24 - 27] could become very important inthe framework of the nascent GW astronomy in order to ultimately discrimi-nate between the general theory of relativity and extended theories of gravity,with important consequences concerning the final unification of theories. Anextension of the general theory of relativity could indeed be necessary in orderto achieve such a prestigious goal - see [24] for details.The greatest problem in GW interferometric detectors is that the “signal”,which is the motion of the test masses, is very weak. In fact, let us consider aGW which originates from an astrophysical source and propagates in a region ofspace-time where two test masses stay separated by a distance on the order of afew kilometers. The GW drives such test masses to oscillate with an oscillationamplitude of order of − meters. In order to achieve this extremely difficultmeasure, GW physicists use the so-called intereferometers. These are extremelyprecise “yardsticks” that use the properties of light in order to realize this al-most impossible measure. Thus, on one hand, the main task for experimentalphysicists is to figure out how to reduce the potential noise interference that5akes such tiny measurements so difficult to perform in practice. The mostimportant source of noise for interferometric GW detectors is the seismic noise,but many additional sources of noise are present; see [28] for details. On theother hand, reducing the potential impact of various sources of noise has notbeen sufficient in order to guarantee the GW detection. We have seen that anenormous amount of computations and mathematical laws were necessary onlyto identify the goal of GW detection. During the development of interferometricGW detectors, which starts from the original intuitions of the Soviet physicistsMikhail Evgen’evich Gertsenshtein and Vladislav Ivanovich in the early 1960s[29] and continues until the LIGO discovery [4], an immense number of simula-tions and data analyses have been indeed performed by using various mindlessmathematical laws. An important and very useful tool has indeed been numeri-cal relativity, which is the branch of the general theory of relativity that createsalgorithms and uses numerical methods to analyze and potentially solve prob-lems. To achieve the detection of the event GW150914, many researchers haveworked hard to obtain numerical solutions to the problem of a binary black holesystem, which enables them to get increasingly accurate computational resultsthat describe the GWs emitted by such a system [4]. In fact, scientists firstgenerated the wave forms by simulating binary black holes, black hole - neutronstars and neutron star - neutron star mergers by employing numerical relativ-ity and powerful super computers in order to have many template waveformsfor checking the possible detections [30 - 32]. Thus, the work of experimentalphysicists must be complementary to the work of theorists.Concerning the previously cited possibility of ultimately discriminating be-tween the general theory of relativity and extended theories of gravity, onlya perfect knowledge of the motion of the test masses, which are the beam-splitter and the mirrors of the interferometer, will permit one to determineif the general theory of relativity is the definitive theory of gravity. At thepresent time, the sensitivity of the current ground-based GW interferometersis not high enough to determine the motion of the test masses with an abso-lute precision. A network including interferometers with different orientationsis indeed required and we’re hoping that future advancements in ground-basedprojects and space-based projects will have a sufficiently high sensitivity. Suchadvancements would enable physicists to determine, with absolute precision, thedirection of GW propagation and the motion of the various involved mirrors. Inother words, in the nascent GW astronomy we hope not only to obtain new, pre-cise, astrophysical information, but we also hope to be able to obtain a perfectknowledge of the motion of the test masses. Such advances in GW technologywould equip us with the means and results to ultimately confirm the generaltheory of relativity or, alternatively, to ultimately clarify that the general theoryof relativity must be extended. This ambitious result, we observe, will only beobtained through a correct mixture of technological innovation, collaboration,debate, and wild roams through mindless mathematical laws with adherence tothe scientific method. This achievement will surely be a great step forward inthe trek towards the grand unification of physics.6 cknowledgements
Christian Corda has been supported financially by the Research Institute forAstronomy and Astrophysics of Maragha (RIAAM), Iran.
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