FEATURES the just mentioned disciplines changed radically and I will focus onWigner's contribution to this change. From chemistry to physics Let me remindyou ofthe status ofchemistryatthe time. The crit­ ical role ofnitrogen fixation for the Central Powers' ability to pursueWorldWar I was well known. Fritz Haberwas awarded the chemistry Nobel Prize in 1918 for this achievement. At the time mathematics and physics did not seem like practical careers. The fathers ofJohn v. Neumann and .. Photo: Wigner at the Edward Teller also directed their blackboard with Teller. sonstowardchemical engineering. Yet, all three moved from chem- istry that seemed to them an empirical craft, toward a physics based on mechanics that was already penetrated by subtle mathematics. An alternative way to Remembering Eugene see this is that chemistry changed from being anempirical craftto a discipline increasingly intertwinedwith mathematical physics. Wigner made considerable contributions to this process. His Wigner and pondering excellent chemical engineering training in Berlin preparedhim for his role ofdesigning the plutonium production facility in the Manhattan Project. The taskwas to upgrade traditional chemical his legacy engineering techniques to include nuclear phenomena, say, the novel cooling problems. This cooperative effort with chemical Laszlo Tisza, Department ofPhysics, Massachusetts Institute of engineers turned Wigner into a pioneerofnuclear engineering. Technology, Cambridge, MA, 02139, USA Wigner's background helped shape his contribution to funda­ mental QM years before this event. His early experience in x-ray crystallography called his attention to symmetry. This resonated TA Jhen I looked into the 1992, November issue of Fizikai with his liking for mathematics stimulated by a favorite high VV Szemle in which Wigner was celebrated on his 90th birth­ school teacher Dr. Laszlo Ratz. His friend Johnny von Neumann day, I saw the list ofhis well over 300 publications in all branches substantially added to this orientation.All this culminated in a ofphysics, in chemistry and in pure mathematics. My first reac­ program ofapplying the theoryofgroup representations to atom­ tion was to withdraw from this attempt ofdoing him justice in a ic spectroscopy. The papers thathe wrotein 1927-9, some ofthem single talk. On some reflection I thought ofa way out. jointlywith Neumann,are seminalin thefield: At that time most physicists disliked group theory, a sentiment The early years expressed in the widely used"Gruppenpest". This parlance was Wigner's life coincidedwith the 20th century. Hewas almost ofthe not a whimsical expression of distaste, but had a philosophical same"quantum age" as Heisenberg and Pauli, however, these two background. Most classical physicists expected infinitesimal were in the center ofthe Copenhagen School and from 1925 on analysis to be the natural mathematics for all ofphysics, with pri­ were amongthe main architects ofquantum mechanics (QM). By ority accorded to the differential equations ofNewtonian contrast 1925 was the year when Wigner graduated as chemical mechanics. It was a widely engineer in Berlin. He must have felt way behind these pioneers, held tacit assumption that yet, he soon became one of the leaders of the new discipline. this must be the way mathe­ Moreover we shall see that his being rooted in chemistry sheds matics enters microphysics. ... how could light on some ofthe subtler aspects ofQM. One ofthe reasons that QM Michael Polanyi was among Wigner's mentors in chemistry. is stillnotaccepted with com­ Their joint work on molecular reaction chemistry is one ofthe plete ease is that its most Wigner make reliable standard papers in the field. After obtaining his engineering appropriate way to mathe­ degree Wigner returned to Budapest to work in the tanning fac­ matics is different. Such a new contributions to so tory where his father was director. He felt frustrated, but Polanyi way is providedbygroup the­ came to the rescue with an invitation to Berlin to an assistantship ory. Although the important many subdisciplines in x-ray crystallography. Wigner resumed attendance at the rotation group is continuous, physics colloquium and felt great attraction to QM. The factory the theoryofgroup represen­ of physics? had been a dead-end, but the chemical training and his sensitiza­ tations deals with a discrete tion to mathematics in school were positive influences, since QM substructure. It was Johnny was basically a novel confluence ofphysics, mathematics and von Neumann who alerted chemistry. Wigner to this highly esotericlinkbetween discrete and continu­ Wigner drifted towards physics through a sequence ofincreas­ ous mathematics and one ofthe non-Newtonian entryports for inglypurposeful appointments. Duringthis periodthe relation of mathematics into QM. This effort culminated in the book Group Theory & Application to the QM ofAtomic Spectra, 1931. This workin Germanwas translated into English in 1959 andappeared This is an edited version ofa talk delivered at the European Physical Soci­ in manyeditions. ety meeting EPS-12 in Budapest, August 26-30, 2002 58 europhyslcs news MARCH!APRIL 2003 Article available at http://www.europhysicsnews.org or http://dx.doi.org/10.1051/epn:2003205 FEATURES The Nobel Prize or rational reconstruction all paradoxes must be resolved and Although Wigner's book entrenched prejudices abandoned: the cathedral stands even as was confined to atomic the scaffolding is removed. Itis an entirely novel insight ofscien­ spectroscopy, he authored tific methodology that the logical standards in the two stages are group-theory papers also very different. onmolecular spectra, solid Wigner was and remained ambivalent as to this issue, but we state, nuclear physics and can filter out two inconsistent lines within his argument and the infinite unitary repre­ examine the condition underwhich theycouldbereconciledwith sentations of the Lorentz each other. group. His contribution to symmetries, particularlyin Quantum mechanics the context of nuclear Wigner sees that the superior qualities ofQM are unaffected by physics was awarded the the flaws ofits foundations. Heconcludes on a cheerfulnote:"The Nobel Prize in 1963. My lack ofcompetence in nuclear physics miracle ofappropriateness ofthelanguage ofmathematics for the and the vast number ofpapers keeps me from highlighting his formulation ofthe laws ofphysics is a wonderful gift which we principal achievements along these lines. However, it is nothard neither understand nor deserve. We should be grateful for it and to hint how could Wigner make reliable contributions to so hope that itwill remain in future research and that it will extend, many subdisciplines of physics? His oeuvre was centered on for better or for worse, to ourpleasure, even though to ourbaffle­ chemistry made up ofa hierarchy oflevels: structure of atoms, ment, to wide branches oflearning:' molecules, crystals and nuclei and to some extent elementarypar­ This is a"cheerful note" inthe sense thatitcomforts the pioneer ticles. A precise and reliable mathematical description was given who was desperate to establish a new bridgehead even ifhe had interms ofgroup theory. This vast collection ofpapers constitutes toviolate"commonsense". There was a timespanofalmosta cen­ the bulk ofWigner's legacy. Yet there is something else. QM has tury and a halfbetween the masterpieces of Copernicus and mysterious paradoxical aspects and there is no unanimity even Newton. The transitionalfigures ofthis period achieved their role as to the definition ofthe difficulties, let alone as to their removal. only because they were able to operate in a logical twilight zone Whereas the rules ofexperimental precision and mathematical of contradictory notions. From the point ofview ofdistant rigor are well established, I believe that the rules for associating descendents the most interesting lesson ofhistoryis the struggle mathematics with experience are sufficiently ambiguous to give from the twilight zone into clarity by overcoming inherited rise to paradoxes. This seldom-featured ambiguity is the butt of dogma,the generator ofparadox. This struggle can beturnedinto Wigner's ironical musings in The Unreasonable Effectiveness of a paradigm that was to be replayed Mathematics in the Natural Sciences. (Comm. in Pure and Appl. in a few instances. Math.13, No.l, 1960; reprintedinWigner, Symmetries andReflec­ The outstanding example of the tions, Indiana University Press, Bloomington & London, 1967, P ... the most 20th centuryisEinstein'sspecialrela­ 222.) tivity (SRT). The significant This is an often reproduced and widely read paper; it has great interesting lesson difference from the Lorentz-Poin­ charm with an understated sense ofhumor. It is utterly free of care theory is Einstein's insight that technical jargon, but has a complex message, the first part of Newtonian absolute time has only which is that"mathematics is effective in the natural sciences". of history is the asymptotic validity. This followed This message is undisputed but it is not new. Itis more question­ from the postulated consistency of able why this effectiveness should be"unreasonable"? In the struggle from the Newtonian mechanics and biography byAndrew Szanton to which Wigner generously con­ Maxwellian electrodynamics. tributed, a word count would seem to reveal the importance he twilight zone Einstein recognized that the assigned to what is "reasonable". What should we make ofthe methodology ofSRT is superior to prominent use of"unreasonable"