6 Volume 3, Issue 1, Spring 2008 ESI NEWS

Jorge Schaeffer (1927-), Alfred Marcel Schnei-der (1925-), Hans Schneider (1927-), BiyaminSchwarz (1919-2000), Josef Silberstein (1920-),Frank Spitzer (1926-1992), Theodor David Ster-ling (1923-), Erwin Trebitsch (1920-), Hans Fe-lix Weinberger (1928-) und John (Hans) Wermer(1927-).

The following names belong to young Aus-trians born after 1920 who were expelledfrom their home country and got theiracademic training as physicists in GreatBritain or the United States:

Fred Peter Adler (1925-), Erika Rivka Bauminger(1927-), Arthur Biermann (1925-), Frank JoachimBlatt (1924-), Henry Victor Bohm (1929-), Fred-eric de Hoffmann (1924-1989), Harold PaulFurth (1930-), Thomas Gold (1920-2004), RobertGomer (1924-), Kurt Gottfried (1929-), Leopold E.Halpern (1925-2007), Erich Martin Hardt (1919-),Charles Maria Herfeld (1925-), Arvid Herzenberg(1925-), Charles M. Herzfeld (1925-), Walter F.Hitschfeld (1922-), Frederic Gerald Holton (1922-), Robert Karplus (1927-), Walter Kohn (1924-),Noemie Koller (1933-), Alfred Leitner (1921-), Pe-ter Lindenfeld (1921-), Ernest M. Loebl (1923-),

Georg M. Low (1926-1984), William Zeev Low(1922-), Harry Lustig (1925-), Hans Michael Mark(1929-), Peter Arnold Moldauer (1923-1985),Peter Wolfgang Neurath (1923-), Paul MichaelPfalzner (1923-), Dan Porat (1922-), Kurt Reibel(1926-), Frederic Reif (1927-), Wolfgang Rindler(1924-), Fritz Rohrlich (1921-), Norbert Rosen-zweig (1925-), Baruch Rosner (1931-), John Ross(1926-), Edwin E. Salpeter (1924-), Erwin RobertSchmerling (1928-), Siegfried Fred Singer (1924-), Joseph Sucher (1930-), Robert Stratton (1928-), Gerald Erich Tauber (1922-), George MaximeTemmer (1922-1997), Kurt Toman (1921-), AryeLeo Weinreb (1921-), Werner Paul Wolf (1930-),Paul Zilsel (1923-2006).

These two lists of mathematicians andphysicists impressively demonstrate theloss of intellectual potential Austria suf-fered in the aftermath of the year 1938.

References1Hans Safrian, Hans Witek.Und keiner war dabei.

Dokumente des alltaglichen Antisemitismus.Wien: Pi-cus Verlag 2008. Enlarged edition of a groundbreak-ing work first published in 1988.

2Gerhard Sonnert and Gerald Holton. What Hap-pened to the Children Who Fled Nazi Persecution.

New York: Palgrave Macmillan 2006. German edi-tion: Was geschah mit den Kindern? Erfolg undTrauma jungerer Fluchtlinge, die von den Nation-alsozialisten vertrieben wurden. Wien: LIT Verlag2008.

3Jean Medawar and David Pyke. Hitlers Gift:The True Story of the Scientists Expelled by the NaziRegime. New York: Arcade Publishing 2001.

4Walter Kohn. In: Karl Sigmund. Kuhler Abschiedvon Europa. Wien 1938 und der Exodus der Math-ematik. Ausstellungskatalog. Osterreichische Mathe-matische Gesellschaft (Hg.), Wien 2001, p. 128.

5Herbert Posch, Doris Ingrisch, Gert Dressel.Anschlu und Ausschluss 1938. Vertriebene undverbliebene Studierende der Universitat Wien. Wien:LIT Verlag 2008.

6Wolfgang L. Reiter. The Year 1938 and its Con-sequences for the Sciences in Austria. In: The Cul-tural Exodus from Austria. Second revised and en-larged edition. Friedrich Stadler, Peter Weibel, Eds.Wien und New York: Springer-Verlag 1995, pp. 188-205.

7Saul Friedlander. Nazi Germany and the Jews.Vol. I. The Years of Prosecution, 1933-1939. NewYork: Harper-Collins 1997, pp. 241-248.

8Wolfgang L. Reiter. Die Vertreibung derjudischen Intelligenz: Verdopplung eines Ver-lustes 1938/1945. Internationale MathematischeNachrichten, Nr. 187, August 2001, pp. 1-20.

9Wolfgang L. Reiter, Naturwissenschaften undRemigration. In: Sandra Wiesinger-Stock, ErikaWeinzierl, Konstantin Kaiser (Hg.), Vom Weggehen.Zum Exil von Kunst und Wissenschaft. Wien: Mandel-baum Verlag 2006, pp. 177-218.

Hermann Minkowski andthe Scandal of SpacetimeScott Walter

When Hermann Min-kowskis first paper onrelativity theory1 ap-peared in April 1908,it was met with an im-mediate, largely criti-cal response. His paperpurported to extend thereach of the principle of relativity to theelectrodynamics of moving media, but oneof the founders of relativity theory, theyoung Albert Einstein, along with his co-author Jakob Laub, found Minkowskistheory to be wanting on physical and for-mal grounds alike. The lesson in physicsdelivered by his two former studentsdid not merit a rejoinder, but their sum-mary dismissal of his sophisticated four-dimensional formalism for physics appearsto have given Minkowski pause.

The necessity of such a formalism forphysics was stressed by Minkowski in alecture entitled Raum und Zeit, deliveredat the annual meeting of the German As-sociation for Natural Scientists and Physi-cians in Cologne, on 21 September 1908.

Minkowski argued famously in Colognethat certain circumstances required scien-tists to discard the view of physical spaceas a Euclidean three-space, in favour ofa four-dimensional world with a geometrycharacterized by the invariance of a certainquadratic form. Delivered in grand style,Minkowskis lecture appears to have strucka chord, generating a reaction that was phe-nomenal in terms of sheer publication num-bers and disciplinary breadth.

Historians have naturally sought to ex-plain this burst of interest in relativity the-ory. According to one current of thought,Minkowski added nothing of substanceto Einsteins theory of relativity, but ex-pressed relativist ideas more forcefully andmemorably than Einstein.2 . It has alsobeen suggested that Minkowski supplieda mathematical imprimatur to relativitytheory, thereby reassuring those who haddoubted its internal coherence.3 A thirdexplanation claims that Minkowskis ex-plicit appeal to pre-established harmonybetween pure mathematics and physicsresonated with Wilhelmine scientists andphilosophers, just when such Leibnizianideas were undergoing a revival in philo-sophical circles.4

The lack of historical consensus on thereasons for the sharp post-1908 upswing

in the fortunes of special relativity reflects,to a certain extent, the varied, conflictingaccounts provided by the historical actorsthemselves.5 A focus on the disciplinaryreception of Minkowskis theory, however,shows a common concern over the ade-quacy of Euclidean geometry for the foun-dations of physics. Much of the excitementgenerated by Minkowskis Cologne lectureamong scientists and philosophers arosefrom an idea that was scandalous when an-nounced on September 21, 1908, but whichwas soon assimilated, first by theorists andthen by the scientific community at large:Euclidean geometry was no longer ade-quate to the task of describing physical re-ality, and had to be replaced by the geome-try of a four-dimensional space Minkowskinamed the world (Welt).

The scandalous nature of spacetime isbrought into focus first by examining thesituation of physical geometry at the timeof Minkowskis first lecture on relativity in1907, and then by following the evolutionof his definition of the world in his writ-ings on relativity. For the sake of concision,these preliminary observations are omittedhere, in favour of a few examples of thereaction sustained by Minkowskis radicalworld view on the part of a few of his mostcapable readers in physics.6

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ESI NEWS Volume 3, Issue 1, Spring 2008 7

The published ver-sion of Raum undZeit sparked an explo-sion of publications inrelativity theory, withthe number of paperson relativity triplingbetween 1908 (32 pa-pers) and 1910 (95 papers).7 This sud-den upswing in the interest is clearly acomplex historical phenomenon requiringcareful study, for the theory of relativ-ity carried different meaning for differentobservers.8 While Minkowskis spacetimetheory is conceptually and formally dis-tinct from Einsteins special relativity the-ory and the Lorentz-Poincare relativity the-ory, the history of its reception is similarlypolysemous. For example, a disciplinaryanalysis of the reception of MinkowskisCologne lecture reveals a overwhelminglypositive response on the part of mathe-maticians, and a decidedly mixed reactionon the part of physicists.9 A close ex-amination of the physicists response toMinkowskis lecture shows that what theyobjected to above all in Minkowskis viewwas the idea that Euclidean space was nolonger adequate for understanding physicalphenomena. The range of response amongphysicists to Minkowskis attack on Eu-clidean space, we will see here, went fairlysmoothly from cognitive shock and out-right denial, on one end, to unreserved en-thusiasm and collaborative extension onthe other end.

Among the physicists shocked byMinkowskis spacetime theory wasDanzigs Max Wien, an experimentalphysicist. In a letter to the Munich theo-retical physicist Arnold Sommerfeld, MaxWien described his experience readingMinkowskis Cologne lecture as provok-ing a slight brain-shiver, now space andtime appear conglomerated together in agray, miserable chaos.10 His cousin WillyWien, director of the Wurzburg Physi-cal Institute and co-editor of Annalen derPhysik, was shocked, too, but it wasnt theloss of Euclidean space that bothered himso much as Minkowskis claim that cir-cumstances forced spacetime geometry onphysicists. The entire Minkowskian sys-tem, Wien said in a 1909 lecture, evokesthe conviction that the facts would haveto join it as a fully internal consequence.Wien would have none of this, as he feltthat the touchstone of physics was experi-ment, not abstract mathematical deduction.For the physicist, Wien concluded hislecture, Nature alone must make the finaldecision.11

On the opposite end of the spectrumof response to Minkowskis attack on Eu-clidean space, Max Born and Arnold Som-merfeld saw in Minkowski spacetime thefuture of theoretical physics. Both men hadclose ties to Minkowski, and upon the lat-ters untimely death on 12 January 1909,each took up the cause of promoting aspacetime approach to physics. In a cru-cial contribution to Minkowskis program,Sommerfeld transformed Minkowskis un-orthodox matrix calculus into a four-dimensional vector algebra and analy-sis,12 based on the notational conven-tions he had introduced in 1904 as edi-tor of the physics volumes of Felix Kleinsmonumental Encyclopedia of Mathemati-cal Sciences Including Applications. Som-merfelds streamlined spacetime formal-ism was taken over and extended by MaxLaue, then working in Sommerfelds insti-tute in Munich, for use in the first Ger-man textbook on relativity theory.13 Lauestextbook was hugely successful, and ef-fectively established the Sommerfeld-Laueformalism as the standard for research inrelativity physics.

Sommerfeld insisted upon the sim-plification afforded to calculation by theadoption of a spacetime approach, andleft aside Minkowskis philosophical in-terpretation of spacetime, with one excep-tion. In the introduction to his 1910 re-formulation of Minkowskis matrix calcu-lus, Sommerfeld echoed Minkowskis be-lief that absolute space should vanish fromphysics, to be replaced by the absoluteworld of Minkowski spacetime.14 Thisexchange of absolutes, Euclidean 3-spacefor Minkowski spacetime, was clearly de-signed to calm physicists shocked byMinkowskis high-handed dismissal of Eu-clidean space as the frame adequate for un-derstanding physical phenomena.

Between the extremes represented bythe responses of Max Wien and ArnoldSommerfeld emerged the mainstream re-sponse to Minkowskis interpretation. Thelatter is well represented by remarks ex-pressed by Max Laue in his influential rel-ativity textbook, mentioned above. Laueconsidered Minkowski spacetime as analmost indispensable resource for pre-cise mathematical operations in relativ-ity.15 He expressed reservations, however,about Minkowskis philosophy, in thatthe geometrical interpretation (or anal-ogy) of the Lorentz transformation calledupon a space of four dimensions. Onecould avail oneself of the new four-dimensional formalism, Laue assured hisreaders, even if one was not blessed

with Minkowskis spacetime-intuition, andwithout committing oneself to the ex-istence of Minkowskis four-dimensionalworld.

By disengaging Minkowskis space-time ontology from the Sommerfeld-Lauespacetime calculus, Laue cleared the wayfor the acceptance by physicists of his ten-sor calculus, and of spacetime geometryin general. A detailed study of the re-ception of Minkowskis ideas on relativityhas yet to be realized, but anecdotal evi-dence points to a change in attitudes to-ward Minkowskis spacetime view in the1950s. For example, in the sixth edition ofLaues textbook, celebrating the fiftieth an-niversary of relativity theory, and markingthe end of Einsteins life, its author stillfelt the need to warn physicists away fromMinkowskis scandalous claim in Colognethat space and time form a unity. As if indefiance of Laue, this particular view ofMinkowskis (Von Stund an . . . ) wassoon cited (in the original German) onthe title page of a rival textbook on spe-cial relativity.16 In Laues opinion, how-ever, Minkowskis most famous phrase re-mained an exaggeration.17

Minkowskis carefully-crafted Colognelecture shocked scientists sensibilities, insharp contrast to all previous writingson relativity, including his own. The au-thor of Raum and Zeit famously char-acterized his intuitions (Anschauungen) ofspace and time as grounded in experi-mental physics, and radical in nature. Pre-dictably, his lecture created a scandal forphysicists in its day, but unlike most scan-dals, it did not fade away with the nextprovocation. Instead, Minkowski focusedattention on how mathematics structuresour understanding of the physical universe,in a way no other writer had done sinceRiemann, or has managed to do since,paving the way for acceptance of evenmore visually-unintuitive theories to comein the early twentieth century, includinggeneral relativity and quantum mechanics.Minkowskis provocation of physicists inCologne, his rejection of existing referentsof time, space, and geometry, and his ap-peal to subjective intuition to describe ex-ternal reality may certainly be detachedfrom Minkowski geometry, as Laue andothers wished, but not if we want to under-stand the explosion of interest in relativitytheory in 1909.

Notes1Hermann Minkowski, Die Grundgleichungen

fur die electromagnetischen Vorgange in bewegtenKorpern. Nachrichten von der KoniglichenGesellschaft der Wissenschaften zu Gottingen, pp. 53

http://www.esi.ac.at/ Erwin Schrodinger Institute of Mathematical Physics

8 Volume 3, Issue 1, Spring 2008 ESI NEWS

111, 1908.2Gerald Holton, The metaphor of space-time

events in science. Eranos Jahrbuch, 34: 33 78,1965.Tetu Hirosige, Theory of relativity and the ether.Japanese Studies in the History of Science, 7: 37 53, 1968.

3Jozsef Illy, Revolutions in a revolution. Studiesin History and Philosophy of Science, 12: 173 210,1981.

4Lewis Pyenson, The Young Einstein: The Adventof Relativity. Adam Hilger, Bristol, 1985.

5Richard Staley, On the histories of relativity:propagation and elaboration of relativity theory inparticipant histories in Germany, 19051911. Isis,89:263299, 1998.

6For an expanded version of this narrative see:Scott Walter, Minkowskis modern world. In Ves-selin Petkov, editor, Minkowski Spacetime: A HundredYears Later. Springer, Berlin, in press.

7Scott Walter, Minkowski, mathematicians, andthe mathematical theory of relativity. In HubertGoenner, Jurgen Renn, Tilman Sauer, and Jim Ritter,editors, The Expanding Worlds of General Relativity,volume 7 of Einstein Studies, pp. 45 86. Birkhauser,Boston/Basel, 1999.

8Klaus Hentschel, Interpretationen und Fehlinter-pretationen der speziellen und der allgemeinen Rel-ativitatstheorie durch Zeitgenossen Albert Einsteins.Birkhauser, Basel, 1990.

9Scott Walter, Minkowski, mathematicians, andthe mathematical theory of relativity. In HubertGoenner, Jurgen Renn, Tilman Sauer, and Jim Ritter,editors, The Expanding Worlds of General Relativity,volume 7 of Einstein Studies, pp. 45 86. Birkhauser,Boston/Basel, 1999.

10Ulrich Benz, Arnold Sommerfeld: Lehrerund Forscher an der Schwelle zum Atomzeitalter,18681951. Wissenschaftliche Verlagsgesellschaft,Stuttgart, 1975, p. 71

11Scott Walter, The non-Euclidean style ofMinkowskian relativity. In Jeremy Gray, editor, The

Symbolic Universe: Geometry and Physics, 18901930, pp. 91 127. Oxford University Press, Oxford,1999.

12Arnold Sommerfeld, Zur Relativitatstheorie,I: Vierdimensionale Vektoralgebra. Annalen derPhysik, 32: 749 776, 1910,Arnold Sommerfeld, Zur Relativitatstheorie, II:

Vierdimensionale Vektoranalysis. Annalen derPhysik, 33:649689, 1910.

13Max von Laue, Das Relativitatsprinzip. Vieweg,Braunschweig, 1911.

14Arnold Sommerfeld, Zur Relativitatstheorie,I: Vierdimensionale Vektoralgebra. Annalen derPhysik, 32:749776, 1910, p. 749

15Max von Laue, Das Relativitatsprinzip. Vieweg,Braunschweig, 1911, p. 46

16John Lighton Synge, Relativity: The Special The-ory. North-Holland, Amsterdam, 1956.

17Max von Laue, Die Relativitatstheorie: diespezielle Relativitatstheorie. Vieweg, Braunschweig,6th edition, 1955, p. 60

Hyperbolic DynamicalSystems at the ESI in 2008Domokos Szasz

Depending on theirfundamental be-haviours, dynamicalsystems can be clas-sified as stable orunstable. Basic ex-amples of stable sys-tems are the math-ematical pendulum or the solar systemwith periodic or quasi-periodic motions(cf. KAM-theory). Unstable behaviour isstrongly connected to non-vanishing ofLyapunov exponents, to sensitivity to ini-tial conditions, and to stochastic or chaoticbehaviour. Basic examples of unstable sys-tems are particle systems (e. g. those ofhard balls) giving rise to statistical me-chanics, or hydrodynamic equations givingrise to turbulence.

Technically speaking, for the mapwhich describes the transition of the systemfrom time zero to time one, hyperbolicitymeans that the spectrum of the linearizedmap has no eigenvalue on the unit circle.Hyperbolicity is most easily detected if thiscondition also holds for all iterates of themap, i.e., for the transitions of the systemfrom time zero to time n for every n 1.

In 1996, Philippe Choquard, Carlan-gelo Liverani, Harald Posch and myself or-ganized the semester Hyperbolic Systemswith Singularities at the ESI. Though bil-liard systems, hard ball systems, etc. wereamong our top interests, the name of thesemester was different and chosen with thefollowing idea back in our minds. We in-

tended to go beyond billiard-like systems,we wanted to understand them primarily asexamples of hyperbolic systems with sin-gularities. The hope was that this widerframework would help to better under-stand billiard-like systems. The semesterwas most successful, with many excitingresults in the seminars, discussions and insubsequent preprints.

Let me point out here only one result,Lai Sang Youngs tower construction, fortwo reasons. Firstly, the title of her paper probably accidentally was StatisticalProperties of Hyperbolic Systems with Sin-gularities thus containing the same termi-nus technicus as the name of the semester.(Her paper was ESI preprint No. 445 andappeared in 1998 in Annals of Mathemat-ics). The second reason is that the inmy view most sensational result of thatpaper, the exponential decay of correla-tions for planar finite horizon Sinai bil-liards, was proved exactly by using the ad-vantage of considering billiards from thisbroader perspective, as hyperbolic systemswith singularities. In this way, part of hertools and ideas were borrowed from meth-ods worked out for the Henon map, for uni-modal maps of the interval, etc. Since thenbilliard methods are getting better and bet-ter embedded into the theory of hyperbolicdynamical systems. It is worth pointing outthat before Youngs work, for the sameclass of billiards, stretched exponential de-cay had already been known (Bunimovich-Sinai, 1981, Bunimovich-Chernov-Sinai,1991) and this weaker property was stillsufficient to establish the CLT (central limittheorem), for instance. However, for thederivation of finer stochastic properties (e.g. the local version of CLT, Szasz-Varju,

2004) this weaker property was not suffi-cient and for obtaining them it seems tohave been necessary to go down to thetower construction itself.

This time the name of the programme isnot very original: Hyperbolic Systems withSingularities, organized by Harald Posch,Lai Sang Young and myself. The fact thatphysicists have been among the organiz-ers (Harald Posch both times and PhilippeChoquard in 1996) reflects the fact that thetopic is central to both mathematics andphysics. Furthermore the composition of amixed audience has the absolute advantagethat both mathematical and physical theo-ries can gain a lot from the interaction ofthe communities involved.

The duration of the programme israther short: six weeks altogether. By us-ing the abbreviationWn, n = 1, 2, ..., 6 forthe 6 weeks of the programme, the struc-ture of the semester is the following. W2- W5 are the central parts of the program.During W2 and W5 there will be two work-shops. W2 (June 2-6) will be focused onnonequilibrium systems and was organizedessentially by Harald Posch with the assis-tance of the co-organizers. The talks andthe discussions will concentrate on fourmajor topics:

Hamiltonian systems: low-dimensional particle systems

Hamiltonian systems: anharmonicchains and coupled maps

Stochastic systems Open quantum systems

In the last decade these problems have beenin the focus of attention equally of mathe-maticians and physicists. To mention justone fundamental problem, to which the

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