A Golden Age of General Relativity? Some remarks on the history of general relativity. Hubert Goenner Institute for Theoretical Physics University G ottingen Friedrich-Hund-Platz 1 37077 G ottingen 1 Introduction In 1986, Jean Eisenstaedt has published a well received paper: The low wa- ter mark of general relativity: 1925-1955 on activities concerning Einsteins general relativity [1], [3]. The first date coincides with the year of the break through to quantum mechanics by Werner Heisenberg, accompanied by Max Born and Pascual Jordan, with Schr odinger following them in 1926 via a different route. It also signifies the year from which on Einsteins interest shifted from general relativity to his unsuccessful unified field theory. The second date possibly is not intended to point to Einsteins death year but to coincide with the Jubilee-Conference in Bern, in 1955. For D. Kennefick who called Eisenstaedts period an interregnum in research in general rel- ativity, the advent of quantum mechanics and the paucity of experiments in gravitation were sufficient reasons for an explanation ([4], p. 105). It was only consequent that Clifford C. Will, at the end of the 1980s, wrote of a Renaissance of General Relativity: by the late 1950s general relativity had become a sterile, formalistic subject, cut off from the mainstream of physics. [..] Yet by 1970, general relativity had become one of the most active and exciting branches of physics. ([8], p. 7). Other authors set the date for the demise of general relativity even a decade earlier: In the 1940s the subject of general relativity was virtually dead - or at best dormant. Peter [Bergmann] set up the first active research group in GR in the USA. Singlehandedly he resurrected the field. Several years later other schools of GR developed around J. Wheeler, H. Bondi, L. Infeld and P. Jordan, but it is clear that Peter was the first to understand the importance of resurrecting GR from its dormancy and placing it as an important part of fundamental It is unclear whether Bergmanns book of 1942 on general relativity was on the mind of the authors [9], or rather not. arXiv:1607.03319v1 [physics.hist-ph] 12 Jul 2016 physics and then actively pursuing this goal [10]. Also, Robert Dicke was considered to have played a role: He soon became a leading figure in what is known as renaissance of general relativity [11]. Another claim differs from these statements assuming a period of reduced activity in the field of general relativity and its applications: Kip Thorne wrote of the golden age of general relativity as the period roughly from 1960 to 1975 during which the study of general relativity, which had previ- ously been regarded as something of a curiosity, entered the mainstream of theoretical physics ([5], p. 74). Ten years earlier, he had given an even more precise period, i.e., from 1963 to 1974 [6]. It is obvious that, after World War II, research on general relativity and other relativistic theories of gravitation broadened enormously both in the number of workers and the spread of universities which housed relativists; cf. e.g., table 1 in ([7], p. 614). My aim here is to show that a label like renaissance of general relativity rests on weak empirical ground while the golden age of general relativity is an exaggerated description of a period of rapidly growing activity. For historiography, both labels should be used with In order to assess such historiographic catchwords, a more precise defini- tion of Golden Age must be given. With regard to this concept we might ask whether it is to describe: - A period of great, publicly visible activity in general relativity? - A period which brought greattheoreticaladvances for general relativity? - A period which brought great advances inexperimentationandobservation applicable to test general relativity? Similar questions may be raised with regard to the period of marginaliza- tion within the field of physics[12], also coarsened to signify the dark ages of general relativity [13], both alternative interpretations for the low water - Is the assumed low-level status of general relativity within the physics com- munity from 1925 to the 1950s well grounded in the conceptual development of the theory? - If such a period existed, to what degree was it due to reasonsexternalto science proper? - Do we have to distinguish different developments in different countries? For the establishment of both claims beyond personal interests, we may ask - the authors quoted above have used anyquantitativeindicator? - a naive comparison of the periods 1925-1955 and 1955-1975 is meaningful In the following we will discuss and try to answer some of these questions. We shall distinguish betweencommunications(public awareness of the field, teaching, conferences) andachievements(conceptual progress, publication of research, institutions). 2 Manpower, funds, and activity-indicators Before we can evaluate the development within the field of general relativity, we must look at physics as embedded in the larger area of society. As we know, physics was notably influenced by the impact of World War II, and by the ensuing Cold War. It is common knowledge that World War II, e.g., due to the development of radar, rockets, or of the atomic bomb, by many was branded as the physicists war [17]. Keywords for some effects correlated with politics are the increase in manpower in physics [including general relativity] and the new private and military funding of physics [including general relativity]. 2.1 Manpower and financing Since September 1956, the US Air-force intensely supported research in gravi- tation through the General Physics Laboratory of the Aeronautical Research Laboratories (ARL) at Wright-Patterson Air Force Base, Dayton, Ohio ([15], p. 375). This financial source was brought to an end in 1969 by the Mansfield Amendment [16]. To my knowledge, the supported projects were not classified. In Europe, since 1958, the North Atlantic Treaty Organization (NATO) also supported science by both individual grants, by its conference series and the subsequent book publications. Although, in the past, only a trickle has flown into grants for gravity research, the program continues until this day [18]. At the same time, roughly, funds from industrial companies went into research in gravitation. Exemplary is the Research Institute for Advanced Studies (RIAS), Baltimore, founded in 1955 by George Bunker of the Glenn L. Martin Company. The RIAS changed its name and turned its mission away from basic research in 1973. Another example is the manufacturer Texas Instruments. The university of Texas at Dallas began in 1961 as a research arm of Texas Instruments, and with it soon the Southwest Center for Advanced Studies (SCAS). In 1969 the founders bequeathed SCAS to the state of Texas. As is known, SCAS became a nucleus for gravitational physics, brought into flower mostly by European scientists holding a perma- nent job there (I. Robinson and W. Rindler from England/Vienna), and by some from Pascual Jordans Hamburg Relativity-Seminar with shorter en- gagements like those of J. Ehlers (1964-1965) or C. Bichteler (1966-1968, in the mathematics department); the last two moved on to the University of Texas in Austin. Another point to be made is the difference inmanpowerof physicists [relativists] working during the low water- and the renaissance -periods. Since the launch of Sputnik, in 1957, a shortage of physicists in the USA was claimed, and an advantage on the manpower front assumed for the Soviet Union ([19], p. 148). Countermeasures in the educational system were taken. In the report of the Physics Survey Committee of the National Academy of Sciences of the USA we read: [..] between 1964 and 1970, the number of PhD physicists increased by 60 percent, the number of PhD astronomers by 62 percent, and the number of PhDs in astrophysics and relativity 300 percent (from 65 to 257 individuals) ([20], p. 840-841). Also, around 1970 the number of physicists in the subfield astrophysics and relativity amounted to only 1.5 % of the total of physicists with a PhD in the USA. This number is mentioned here in order to put into perspective the claim that, between the 1950s and 1970, general relativity was one of the most active [..] branches of physics. Around 1970, there were three times more astronomers n o t working in relativity. Although these figures refer to the USA, we may assume that a similar if less pronounced situation existed in (NATO-) Europe. We note that a quantitative comparison of the periods pre- and post-1955 could clearly only be made per head of scientists working Both, Ehlers (from 1966 to 1971) and Bichteler (1969 to retirement) This should not be misunderstood as refering to PhDs produced; physicistsholding PhDs are meant. on relativistic gravitation. A corresponding study has not yet been done. Naturally, manpower and funding are closely correlated. This is shown clearly by Fig. 1, relating Federal R & D expenditures and bachelors student pro- duction in the physical sciences, mathematics and engineering in the United The number of bachelor students almost doubled between 1957 and 1973 with the expenditures increasing by a factor 2 1/2 ! This remains unparal- leled in the period 1925 to 1955; it is explained by reasonsexternalto the field of gravitation. An indication that, at least in West-Germany, research in gravitation developedsmoothlyduring the three decades from 1960 to 1990, is the number of PhDs produced there in the field of general relativity. It amounts to equally 13-14 for each decade. Thus, to a great extent what was named the Golden age of relativity in the United States, may have been nothing but a feature of a general trend in physics after the Sputnik-shock. 2.2 Activity indicators As activity-indicators, we could take the number of national and interna- tional conferences organized, the number of groups/single persons working in relativityrelative to some reference group, the number of books and papers published, the number of journals regularly printing papers on general rela- tivity, or centers with a graduate program in general relativity. We also note that the necessary funds for international conferences including the travel costs had not been available before the 1950s. 2.2.1 Publications Not one of the indicators suggested above was checked by those claiming a Golden Age of General Relativity. Looking at the bibliographies by Combridge at Kings College [23] and in Synges book on general relativity [24], the average yearly output of papers amounted to'14/year, and from 1925 to 1955 to roughly 12/year, whereas between 1955 and 1965 the rate of published papers rose to ca. 15/year. Papers on general relativity published in the prestigious French journal Comptes Rendus grew from a yearly total of 10 in 1957 to a maximum of 23 in 1959 and stayed at about this yearly rate until 1964. Although not representative, these inspections do not point to remarkable variations in publications listed between 1915 and 1960, in particular not between 1925 and 1935, or in the first half of the 1960s. Of course, all such indicators do have their weaknesses [22]. J. Eisenstaedt , in his first article of 1986, gave the yearly number of papers in relativity for the five years 1932-1936 to be around sixty. This figure goes well with Combridges statistics. He also gives the number of 30 articles on general relativity published in 1955 (from Physics Abstracts). This is in stark contrast to the stable growth rate in the number of physics publicationsin all fields of physicsbetween 1920 and 1960, an exponential growth, doubling the number of papers in approximately 15 years [25]. Of course, exponential growth need not be present in special fields of physics as shown by a study on weak interactions [26]. In another study three periods of growth in scientific publications (all fields) are given: compared with less than 1% growth before, to 2 to 3% up to the period between the two world wars and 8 to 9% to 2012 [27]. Somerepresentativeempirical material for the time after 1945, may be obtained from the core collection of the web of science. From 1945 up to today, there was a continuous growth of publications in general relativity with the steepest increase between 1960 to golden age? He did not say whether papers on special relativity are in- or excluded. His data were taken from Physics Abstracts and Physikalische Berichte. We have searched for the topics general relativity and Einsteins theory. From the latter list all references not related to general relativity have been removed. The 5-fold increase in the decade after 1990 possibly is due to a changed data base used by the web of science (more journals included in the database?). If the past Golden Age is identified with the steepest growth of publications on general relativity, then the period of 1960 to 1970 is the correct one. . 2.2.2 International Conferences As to conferencesbeforeworld war II, there existed very few such events. Among them were the Volta Conferences in Italy by the Royal Academy of Science in Rome. The first such conference in 1927 was the Como Confer- ence, held at Lake Como in 1927 about the uncertainty principle by Niels Bohr and Werner Heisenberg. A well known older series of Conferences were the Solvay Conferences in Brussels. We note those conferences relevant for relativity and gravitation: - 1911 La th eorie du rayonnement et les quanta; The theory of radiation and quanta (Einstein present); - 1958 La structure et l evolution de lunivers (The structure and evolution of the universe); - 1964 The Structure and Evolution of Galaxies; - 1973 Astrophysics and Gravitation. Before the 1940s, international conferences could be financed only by sci- entific academies and wealthy entrepreneurs (like Ernest Solvay). Due to the increase in state funds for science and education, from the mid of the 1950s, national and international conferences on gravitation and cosmology, partially as continuing series, began to sprout and became a regular feature of activity in the field of gravitation. An (incomplete) list of the best known such conferences is given in Appendix 1. If taken as an indicator for activ- ity, the organization of conferences on gravitation fulfills the claim that the period starting around 1960 to 1975 brought both the weaving of a net of relativists and the awareness for the field in the physics community. However, due to the lack of funds and the lower amount of working power in physics, such an increase in conferences could not have happened during 1925 up to the decade after World War II. In this context, the low water mark of general relativity seems to be a projection from the present into 3 Advances in research about general relativ- Since the 1920s, during Einsteins lifetime and thereafter, a number of im- portant results were obtained. For briefness, we present a choice of them - after 1920 - chronologically in four lists. The first collects results fromthe time before world war II: 1923/24 Exact solutions describing an expanding uni- versewith space sections of constant curvature (Friedman); 1925 -1933 The universe as an exploding primordial atom itre) with a beginning later derisively named the big bang; 1929Hubble-law. 1936/1937 Gravitational lensing; theory by A. Einstein. Ap- plication to galaxy clusters by F. Zwicky. 1938 Equations of motions for point particles in linear approximation.Unlike in Maxwells theory, the equations of motion in the gravitational field cannot be postulated indepen- dently of the field equations (Einstein-Infeld-Hoffmann). 1939 Gravitational collapse (Oppenheimer, Snyder, Volkoff ) Tolman- Oppenheimer-Volkoff-limit (TOV).This triggered a development leading eventually to the concepts of white dwarfs, neutron stars both as stellar remnants, and of black holes (treated as solutions of the vacuum field equations). In thenext list, results obtainedafter world war IIuntil the mid 1950s are assembled: 1946/48 The theory of Cosmic Background Radiation. (Dicke, Gamov, Alpher & Herman)It is one of the pillars of present cosmology. 1949 G odel-cosmos (K. G odel)This is a locally rotating ex- act solution of Einsteins equations with dust matter. Universal space sections do not exist, but closed timelike worldlines. 1954/58 Petrov-Pirani classification. (Petrov 1954, Pi- rani 1958)An application is the peeling theorem describing the asymptotic behavior of the Weyl tensor in a lightlike direction. 1956/58 Event horizon (Rindler, Finkelstein)W. Rindler formulated the concept within cosmology (event- and particle horizons). Finkelstein applied it to a collapsing star and showed that an event horizon develops. G odel, Petrov, and Penrose are mathematicians, Dicke, Gamov, Alpher, Herman, and Finkelstein physicists. Thethird listcontains progressduring the 1960sachieved in general rela- tivity. It falls into the categories: mathematical physics without empirical backing, new mathematical methods, and the application of general relativity to astrophysics. 1960/62 Spinors: Newman-Penrose formalism.A tech- nique for formulating general relativity with spinors in place of tensors introduced by R. Penrose and E. T. Newmann. The for- malism is helpful for the characterization of outgoing gravita- tional radiation in asymptotically Minkowskian space time. 1962 Exact solutions as an initial-value problem (Arnowitt- Deser-Misner, ADM)Einsteins field equations are decom- posed into hyperbolic time-evolution equations and elliptic con- straint equations. The formalism is also important for numerical calculations. 1963 Kerr-metric (Roy Kerr)(Exact solution describing the field outside of a star rotating about a fixed axis. As no interior Its first observation occured in 1964 (Penzias & Wilson); that this radiation has a black-body spectrum corresponding to a temperature of approximately 2.725 K was con- vincingly measured much later. solution (with matter) is known, the Kerr- metric is interpreted as a black hole with 2 parameters: mass and angular momentum. 1965 Kerr-metric with electric charge (Newman)(A ro- tating black hole with 3 parameters: mass, angular momentum, electric charge. It is a solution of the Einstein-Maxwell (vacuum) equations.) 1964 Popularization of the name Black Hole (Wheeler) 1966-1970 Singularity theorems (Penrose, Hawking) Thefourth listcollects some of the important developments of the 1970s. Note that most of them concern purely theoretical statements and conjectures with no empirical basis. 1960 - 2000 Uniqueness theorems for stationary Black Holes (Israel, Carter, Mazur)A black hole has no hair (J. Bekenstein). 1969 Cosmic-censorship-hypothesis (Penrose)Singularities are always hidden behind event horizons; otherwise, the theory would become unpredictable. 1970/71 Post-Newtonian approximation (Nordveth, Will) It is the modern form of the EIH-method and is used to describe observable effects and to discern alternative gravitational theo- 1970/73 Gravitation as Poinc