SPACE AND TIME 62 YEARS AFTER THE BERNE CONFERENCE1 Claus Kiefer Institute for Theoretical Physics, University of Cologne Abstract In 1955, an international conference took place in Berne at which the state of relativity theory and its possible generalizations were presented and critically discussed. I review the most important contributions to that con- ference and put them into the perspective of today’s knowledge about the nature of space and time. arXiv:1812.10679v3 [gr-qc] 31 Aug 2020 1To appear in: Thinking About Space and Time, edited by C. Beisbart, T. Sauer, and C. Wuthrich¨ (Birkhauser,¨ Basel, 2020). 1 Historical Context From July 11 to July 16, 1955, a conference took place in Berne celebrating the fiftieth anniversary of the special theory of relativity. This was perhaps the first international conference devoted to an overview of relativity theory, its ramifica- tions, and applications. The main goal of that conference was neither historical nor was it restricted to special relativity; in fact, most of the topics deal with general relativity and its generalizations, both in classical and quantum directions, along with cosmology and with mathematical structures. The list of participants con- tains an impressive number of famous figures together with a selection of young scientists.2 The Proceedings of that conference were published in 1956 and con- tain most of the presented talks together with a record of the discussions (Mercier and Kervaire 1956). In my contribution, I will heavily rely on these Proceedings, the title page of which is displayed in Fig. 1. The Berne Conference was later known as the GR0 Conference, where the numbering refers to the series of conferences organized by The International So- ciety on General Relativity and Gravitation (GRG).3 This society was founded at the GR6 conference, which took place in Copenhagen in 1971, and grew out of the International Committee on General Relativity and Gravitation, which was responsible for the earlier conferences. Several of the GRG Presidents were, in fact, participants of the Berne Conference, among them Christian Møller, Nathan Rosen, Peter Bergmann, and Yvonne Choquet-Bruhat. The conference was organized by the Seminar for Theoretical Physics of the University of Bern, located at the Institute for Exact Sciences at Sidlerstrasse 5. The President of the Organization Committee was Wolfgang Pauli (Zurich),¨ the Scientific Secretary Andre´ Mercier from Berne. The lectures themselves took place in the lecture hall of the Natural History Museum. Figure 2 shows the build- ing at Sidlerstrasse at the time of the conference. It was there that Einstein deliv- ered his lectures as a privatdozent in Berne. These were the lectures on molecular theory of heat (Molekulare Theorie der Warme¨ ) in the summer term 1908 (with three attendants, which were his friends), and on the theory of radiation in the winter term 1908/09 (with four attendants, even including a student), see Folsing¨ (1994, p. 274). Between 1959 and 1963, the new building shown in Fig. 3 was erected, de- signed by the architect couple Hans and Gret Reinhard. It clearly demonstrates the new spirit of the day.4 In his foreword to the Proceedings, the secretary Andre´ Mercier made the 2One of the younger participants, Walter Gilbert, was awarded the 1980 Nobel Prize in chem- istry. 3See isgrg.org 4See unibe.ch/university/portrait/history/ 1 Figure 1: Title page from the Proceedings of the Bern Conference 1955. c Birkhauser¨ Verlag, Basel. Photo by the author. following interesting remarks on the theory of relativity: The theory of relativity marks all in all one term: it is the achievement of a physics of cartesian spirit that gives an account of the phenomena by figures and by motions . One hears today the saying that we live in the atomic era. Should we not also speak of the relativistic era?5 This, of course, alludes to the fact that the theory of relativity was not very popular in the 1950s, apparently overshadowed by quantum theory and its appli- cations to atomic and nuclear physics. 5This is my translation from the original French which reads: “La Theorie´ de la Relativite´ mar- que en somme un terme: elle est l’achevement` d’une physique d’esprit cartesien´ rendant compte des phenom´ enes` par figures et par mouvements. On entend dire aujourd’hui que nous vivons a` l’ere` atomique. Ne pourrait-on aussi bien parler de l’ere` relativiste?” (Mercier and Kervaire (1956), p. 19) 2 Figure 2: Contemporary look of the building at Sidlerstrasse 5. c Universitat¨ Bern. Figure 3: Present look of the building at Sidlerstrasse 5. c Universitat¨ Bern. Of interest is also the welcome speech of a local politician, a certain Dr. V. Moine, Directeur de l’instruction publique du Canton de Berne. He reflects the philosophical spirit of the conference’s location: This city, enclosed like a jewel by the crown of the river Aare, with its military and political past which made it the head of the old Switzer- land, practical and empirical as a farmer’s wife, has always valued the positive and immediate higher than the theoretical. Its symmetric streets, its order, the equilibrium which is brought out by its buildings, the traditional caution of its laws make it more a city of Aristotle than of Platon. 6 (The building shown in Fig. 3 perhaps also gives testimony of this Aristotelian attitude.) This practical spirit is also seen in the organization of the conference. 6This is my translation from the original French which reads: “Cette ville, enserree´ comme un joyau dans la couronne de l’Aar, au passe´ militaire et politique qui fit d’elle la teteˆ de la vieille Su- isse, pratique et empirique comme une paysanne, a toujours plus appreci´ e´ le positif et l’immediat´ que le theorique.´ Ses rues symetriques,´ son ordonnance, l’equilibre qui se degage´ de ses edifices,´ la prudence traditionelle de ses lois en font plus une cite´ d’ARISTOTE que de PLATON....” (Mercier and Kervaire (1956), p. 25) 3 Three languages (English, French, German) are used interchangeably, and in the discussions they are often mixed in an interesting way; an example is the discus- sion after Bergmann’s talk with its melange´ of the three languages (Mercier and Kervaire (1956), pp. 95/96). Albert Einstein had been invited to this conference, but he died on April 18, 1955, three months before the Berne Conference. Anyway, he had not envisaged to attend the meeting. In his reply to a letter of invitation by Louis Kollros,7 Einstein had written: We two are no spring chickens anymore! As for me, I cannot think about a participation. 8 It is left entirely to our imagination to figure out what would have happened if Einstein had been able to attend the Berne meeting. 2 Classical General Relativity and Beyond The year 1955 marked the 40th anniversary of Einstein’s general theory of rel- ativity. Since it was difficult in those years to test the theory empirically be- yond the classic tests (redshift, light deflection, perihelion motion), much atten- tion was focused on theoretical and mathematical developments. This concerned, in particular, the structure of the Einstein field equations, notably the initial value problem and the problem of motion. As for the former, two of the main figures, Andre´ Lichnerowicz and Yvonne Choquet-Bruhat (at that time Foures-Bruhat)` were present at the meeting. As for the latter, Leopold Infeld was the main figure who was present. The well-posedness of the initial value problem (Cauchy problem) is of great importance. Only if there exist initial data, that is, data on a three-dimensional hypersurface that determine the evolution according to the Einstein equations uniquely, can one use the theory to predict physical processes, for example, the emission of gravitational waves from coalescing compact objects. Today, well- posedness is generally granted as established, see, for example, Isenberg (2014). It is a key ingredient in numerical relativity. By the time of the Berne Conference, a first theorem on the initial value prob- lem had already been proven by Choquet-Bruhat in 1952. A more general theorem was proven in a 1969 paper of Choquet-Bruhat and Robert Geroch, see Isenberg 7Louis Kollros (1878–1959) was a Swiss mathematician; from 1909 to 1948 he was professor at ETH Zurich.¨ 8This is my translation from the original German which reads: “Wir sind beide keine Junglinge¨ mehr! Was mich betrifft, so kann ich nicht an eine Beteiligung denken. ” (Mercier and Kervaire (1956), p. 271) 4 (2014) and Chrusciel´ and Friedrich (2004) for a detailed discussion and refer- ences.9 The theorem proven by Choquet-Bruhat and Geroch can be stated as follows (see Isenberg (2014), p. 307): Theorem: For any smooth set of initial data (hab;Kcd), where hab is the three- metric and Kcd is the extrinsic curvature (second fundamental form), on a speci- fied three-manifold which satisfies the vacuum constraint equations, there exists a unique (up to diffeomorphism) maximal globally hyperbolic development. Further developments are discussed in the above cited references. One con- cerns the extension to the non-vacuum case: the theorem also holds, for example, for the physically relevant case of the Einstein–Maxwell theory. On the mathe- matical side, it has been shown that the required degree of regularity can be weak- ened. Other developments concern the stability of Minkowski spacetime under long-time evolution, the stability of de Sitter space, and investigations on the cos- mic censorship conjecture. The latter conjecture – in its weak form stating that the singularities arising from gravitational collapse cannot influence future null infin- ity – was formulated by Roger Penrose in 1969. Most of these later investigations made heavy use of the global methods (Penrose–Carter diagrammes) developed in the 1960s, which were unavailable at the time of the Bern Conference.