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Home , Eugene Wigner

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the just mentioned disciplines changed radically and I will focus on Wigner's contribution to this change.

Fromchemistry to Let me remind you ofthe status of chemistryatthe time. The crit­ ical role of nitrogen fixation for the Central Powers' ability to pursueWorldWar I was well known. Fritz Haberwas awarded the chemistry in 1918 for this achievement. At the time and physics did not seem like practical careers. The fathers of John v. Neumann and .. Photo: Wigner at the also directed their blackboardwith Teller. sons towardchemical engineering. Yet, all three moved from chem- istry that seemed to them an empirical craft, toward a physics based on that was already penetrated by subtle mathematics. An alternative way to Remembering Eugene see this is that chemistry changed from being an empirical craftto a discipline increasingly intertwined with . Wigner made considerable contributions to this process. His Wigner and pondering excellent chemical engineering training in Berlin prepared him for his role of designing the production facility in the . The taskwas to upgrade traditional chemical hislegacy 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 pioneer ofnuclear 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 called his attention to . 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 of his well over 300 publications in all branches substantially added to this orientation.All this culminated in a of physics, in chemistry and in pure mathematics. My first reac­ program ofapplying the theoryof group representations to atom­ tion was to withdraw from this attempt of doing him justice in a ic spectroscopy. The papers that he wrotein 1927-9, some ofthem single talk. On some reflection I thought of a way out. jointlywith Neumann,are seminalin thefield: At that time most disliked , a sentiment The early years expressed in the widely used "Gruppenpest". This parlance was Wigner's 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 of the Copenhagen School and from 1925 on analysis to be the natural mathematics for all ofphysics, with pri­ were amongthe main architects of (QM). By ority accorded to the differential equations of Newtonian 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 on some ofthe subtler aspects of QM. One of the reasons that QM was among Wigner's mentors in chemistry. is stillnot accepted with com­ Wigner make reliable Their joint work on molecular reaction chemistry is one of the plete ease is that its most standard papers in the . After obtaining his engineering appropriate way to mathe­ degree Wigner returned to 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 providedby group 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 theoryof group 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 of physics, 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 of the non-Newtonian entry ports for inglypurposeful appointments. During this period the 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 and appeared This is an edited version ofa talk delivered at the European Physical Soci­ in many editions. 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. It is 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. on molecular spectra, solid Wigner was and remained ambivalent as to this issue, but we state, and can filter out two inconsistent lines within his argument and the infinite unitary repre­ examine the condition underwhich theycouldbe reconciledwith sentations of the Lorentz each other. group. His contribution to , particularlyin Quantum mechanics the context of nuclear Wigner sees that the superior qualities of QM are unaffected by physics was awarded the the flaws ofits foundations. Heconcludes on a cheerfulnote:"The Nobel Prize in 1963. My lack of competence in nuclear physics miracle ofappropriateness ofthelanguage of mathematics for the and the vast number of papers keeps me from highlighting his formulation of the laws of physics is a wonderful gift which we principal achievements along these lines. However, it is not hard 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 our pleasure, even though to ourbaffle­ chemistry made up of a hierarchy of levels: structure of atoms, ment, to wide branches oflearning:' molecules, crystals and nuclei and to some extent elementarypar­ This is a"cheerful note" in the sense that it comforts the pioneer ticles. A precise and reliable mathematical description was given who was desperate to establish a new bridgehead even if he had interms ofgroup theory. This vast collection ofpapers constitutes toviolate"commonsense". Therewasa time span ofalmosta cen­ the bulk ofWigner's legacy. Yet there is something else. QM has tury and a half between 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 of view of distant rigor are well established, I believe that the rules for associating descendents the most interesting lesson of historyis 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 and Reflec­ 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 of humor. 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. It is 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 of the methodology of SRT is superior to prominent use of"unreasonable" in the title of this paper? that of QM. Although SRT strains our common sense notion of Unreasonable theory absolute time, Einstein taught us how to do without this notion A theory will be deemed"unreasonable" if it conflicts with com­ for uncommon experiences. mon sense imbedded in established tradition. Under such By contrast,we haven't yet learned to recognize the provincial­ conditions onewill place a newtheory"on probation" .Therewere ism we have to keep under control to be comfortable with QM. many theories that were emended or have fallen by the wayside According to a well-reasoned recent study, this discipline is no less and are happily forgotten. It is more interesting that occasionally paradoxical than ever.(See F.Laloe, Am. J.Phys, 69, 2001, P 655.) "unreasonable" theories are stubbornlyirrepressible. Thinkofthe When Wigner was first introduced to QM, paradoxes were unreasonably moving earth of Copernicus. rampant; yet the theorywas utterly convincing; hence Wigner's After the new theory is sufficiently confirmed, it appeared that acceptance of"unreasonable" methods.When he wrote this paper it is "common sense" that has to be harmonized with it, rather thirty years later, he had a secret hope that a sharpened method than vice versa.Nothing is so hard as modifying entrenched tra­ might lead to the resolution of paradoxes. I believe this secret dition and it is remarkable that mathematical physics excels in hope may have been behind the mysterious motto of the paper: handling such situations. The heuristic foundation is then reclas­ "...and itis probable that there is somesecretherewhich remains sified as temporary scaffolding that only hides the beauty of the to be discovered:' - C. S. Peirce. fa~ade.We can make use of the contrasting role of the scaffolding only if we recognize science as a two-stage process. In the heuris­ Experienceand mathematics tic stage the prime concern is to extend the frontier even at the What else could be the "secret", but a rational explanation ofthe price of contradiction and paradox. In the stage of consolidation, "unreasonable" correspondence between experience and europhysics news MARCH/APRIL 2003 S9 FEATURES mathematics.The apparent conflict between the two attitudes can century are indeed marked by a tone of resignation. However be reconciled by realizing that the scientific enterprise is a com­ looking back at the overall picture we see rather a vast explosion posite of apparently opposite moves. The first heuristic ofknowledge. There was a retrenchment ofexpectations; but this penetration into a new area ofknowledge calls for the free creative is overshadowed by opening up new evolutionary avenues of imagination of the discoverer, maybe defying . exploration. common sense The second stage ofconsolida­ A centurylater we have every reason to beton tion calls for the elimination ofsuch conflicts. the evolutionary option. It is evident that the To sum up, the architects of QM are to be area of knowledge is being extended rather credited with the creation of a flawless theory than narrowed. Instead ofdeploring the break­ of atoms, molecules and the condensed state down overcome onlyby revolution, we should ofmatter, butthe so-called"breakdown ofclas­ understand the rules of the new evolution sical physics" is a poor substitute for the actual opened up by using new mathematics and separation ofthe classical theory into perenni­ wider scope of the concept ofmotion. al and obsolete parts. The failure to remove The first significant advance beyond Newton the latter manifests itself as a "paradox" that was directed at the expansion of the mathe­ was improperly attributed to a flaw of QM, matical base. The work of continental whereas actually it is a flaw in the 20th century mathematicians active over a century and a interpretation ofclassical physics. Whereas this halfconverged into a highlysuccessful analysis interpretation may have been problematic at ofthe continuum.They considered Newtonian the beginning of the 20th century, after anoth­ mechanics as a natural proving ground for the er century there should be no difficulty to new mathematics. This was an expression of handle the matter, assuming willingness to preference over the dynamics ofDescartes but break with dogmatic thinking. The problem a rejection of Newton's Euclidean addiction; it to bekept in mind is that Newton scholars have led to an innovative analytical mechanics. The given well-deserved attention to the complica­ ... Photo:TheHungarianQuartet. physics community accepted the innovation tions involved in the axiomatics for the and called its Hamiltonian version canonical mechanics of the Principia and to the paths mechanics. This terminology implied, correct­ thatconnectNewtonwithhis precursors. By contrast, little atten­ ly, that a specific mathematical formalism might have a closer tion is given to Newton as the founder of all of mathematical affinityto a theoryofphysics than alternative choices, even ifone physics and to the imperfections the successors have only par­ happens to be more familiar. Unfortunately, the term canonicalis tially corrected in building late classical physics. overstated; it is preferable to call the formalism optimal for New­ I have recently addressed this question of consolidation in tonian mechanics, but not to foreclose another choice for dealing Tisza: The reasonable effectiveness ofmathematics in the natural with heat,light, electricityand magnetism, andfor . sciences,Experimental Metaphysics, R. S. Cohen, et al. (eds.), The The first one to break out of the canonical straight jacket was Kluwer Publ. CO.,1997, pp. 213-238. The title is an obvious take­ Faraday; he initiated an alternative approach, as all the listed non­ off on Wigner's paper and my aim was to recognize behind its mechanical phenomena can be also associated with the chemical playful ambivalence Wigner as the champion of reason who was structure of the atom. Maxwell's translation ofFaraday's qualita­ bidinghis time. Although mypaperis rather lengthy, the underly­ tive theory of the electromagnetic field into a mathematical ing ideas are relatively simple and I will sum up the main points. formalism became an accepted branch of classical physics. This The basic axiom of Newtonian mathematical physics is stated innovation was accepted by Einstein who stressed that the diver­ in the Preface to the first edition ofthe Principia:rational mechan­ sification of classical physics has to be met by consistency ics ought to address ""with the same precision as conditions. The requirement that Newtonian mechanics and geometry handles the size and shape of idealized objects. It is Maxwellian electrodynamics be mutually consistent calls for the interesting, however, that the core of Newton's method is also in scrutiny of the concept of simultaneity and leads to the founda­ line with Einstein's preference for "theories of principle". The tion ofspecial relativity. association of "motion" with "mathematics" was a stroke of genius; but to appreciate its full impact, we must distinguish ... to Einstein between the short-term and the long-term uses ofthis idea. Einstein emphasized that his method of transcending classical physics is logically flawless and he hoped that QM could be han­ From Newton... dled similarly. I suggest that this is a sensible program. Faraday's By producing the mechanics of the Principia Newton demon­ chemical departure goes much beyond the electromagnetic field stratedthat in the short-term there is a simple instance ofmotion, andmarks a bifurcation in the evolution ofclassical physics into a namelyrigid translation that can be formalized in terms ofavail­ mechanical and a chemical branch that calls for the formulation able mathematics. Newton expected that his work would be of another consistency relation. effective also in the long-term. (The Third Rule of Reasoning in Whereas in case ofSRT the sensitive conceptwas absolute time, Philosophy, in Book III ofthe Principia. As an empiricist Newton in the case of QM there is a different particle concept implicit in added the Fourth Rule according to which this extrapolation is Newtonian mechanics and in Faraday's chemical departure. Fara­ subject to experimental verification.) day's chemical atom was different from the mechanical atom It is a fact that the Third Rule exercised great attractionbothfor implicit inNewtonian mechanics. The mechanical atom is defined Einstein and Bohr. When Newtonian mechanics failed to account by its position and velocity; it has no intrinsic structure. Two for the stability of the Rutherford atom, Einstein felt as if the observations refer to the same particle ifthe observations refer to groundwere pulled from under him.Was this the end ofthe New­ points on the same orbit as for the evening star and the morning tonian epistemology? The epistemological discussions of the star. By contrast, the chemical atom has intrinsic structure and

60 europhysics news MARCH/APRIL 2003 FEATURES different sample of the same structure form a class of indistin­ Widespread interpretation preferred reduction of chemistry to guishable particles, regardless ofposition. mechanics. Real particles have both mechanical and chemical properties This expectation collapsed when Newtonian mechanics failed and it is the that ensures their mutual con­ to account for the stabilityofthe nuclear atom.Whatactually hap­ sistency. The Heisenberg principle pened was a consistent joint use of the disciplines and the restricts the scope ofthe mechanical particle concept ofOM is in closer harmony with chemistrythan measurement; the overall power of with mechanics. measurabilityis increased due to the This a n s w e r s I am glad to see that Hungarian education tends to unify basic emergence of the chemical branch. chemical experience, such as the Periodic Table, quantum states, This becomes apparent in the con- Einstei n's concern chemical bonds with fundamental atomic physics. (George Marx, text of the extraordinary junction Physics Education, September-November 1976, Institute of in1859 when Bunsen and Kirchhoff Physics, UK.) joined chemical analysis with spec­ that God does troscopic measurements. The Remembering E.Wigner discovery that all the stars are made not play dice with I wish to conclude on a personal note. I did not belong to Wigner's of the same elements we find on circle of intimate Hungarian friends, but our paths crossed since earth was easily the largest exten- US. the beginning ofmylife in physics. I was a mathematics student in sion ofknowledge ever attained in a Budapest and Gottingen, where I attended 's first ever single step. course on quantum mechanics. I was impressedthathigher math­ At exactly this time the concept of ematics found application to subtle empirical problems molecular mean free path was established which led to the kinet­ and-somewhat hesitantly-considered changing from mathe­ ic gas theory. The bifurcation of physics into mechanical and matics to mathematicalphysics. This was thebackgroundwhen on chemical branches was firmly in place. Accordingly, it is mislead­ vacation in Budapest I got an unexpected invitation for tea from ing to speak of the breakdown of classical physics; we have to Eugene Wigner. By that time, 1929, he was already a foremost the­ differentiate between the two branches. The fact that the applica­ orist; the difference in ourstatuswas staggering. The invitation was tion of Newtonian mechanics fails to explain the observed an indication of the kindness and stability ofa discrete set ofstates ofthe nuclear atom, indicates the helpfulness of Eugene, for which he failure ofmechanical classical physics on the atomic level. By con­ was well known. This invitation trast, the Bunsen- Kirchhofflandmarkindicates a great expansion ... when helped me overcome my timidity in of the scope of the chemical branch. It led through Planck to making my important decision. quantum theory and on to OM. o n vac a t ion inTo return to the present,beyond my Although the bare facts ofthe discovery of spectrum analysis limited personal contacts I was also are well known, not enough is made ofthe epistemological revo­ engrossed with Wigner's style of lution involved that marks a vast enrichment of the methods of Budapest I got insisting on the integrity ofmathe­ acquiring knowledge. matics, no less than its empirical I claim that such an epistemological principle is implicit in the an unexpected adequacy. I hope that this affinity Bunsen-Kirchhoff spectrum analysis. In this procedure light ensures my credentials to interpret beams replaced the chemical reagents of traditional qualitative invitation for tea. an aspect of his work that he left analysis. Light beams travel unimpeded though space and there­ ambiguous. Traditional principles fore the junction of chemical and optical methods vastly expand refuted by experiment must be what these methods could achieve on their own. This is connect­ abandoned. This does not call for a ed with an entirely new conception of measurement. It is very revolutionary break with the past. At this late stage tradition is different from the Newtonian prediction that is vulnerable to any likely to be only slightly out offocus, the flaw of tradition is to be randomness. The light beam emerging from the grat­ removed by careful analysis. The required methods were not ing consists of a random stream of yet leads to an available at the turn of the 20 th century and the empirically all accurate inference ofthe energy. This answers Einstein's but perfect OM seemed paradoxical from the perspective of an concern that God does not play dice with us. He certainly does obsolete tradition. We ought to remove the paradoxes of OM not and to great advantage for us. bychanging this theory, butbyremoving the obsolete partofclas­ All this suggests that the chemical branch of classical physics sical physics. From my familiarity with Wigner's work, I feel that should be given an increasing role in the formulation of the link his understated alternative ofpursuing C. S.Peirce's "secret" comes between classical and quantum physics. This would call for giving closer to his real views than the apparently flippant endorsement chemical principles a greater role within the context of modern ofthe freewheeling use ofparadoxes to supportsubjective beliefs. physics. If my analysis of the situation would in any way contribute to a critical review of ancient preconceptions, I am confident that ... toWigner Eugene would endorse my role as his mouthpiece. Indeed, among the great scientific achievements of the 20th cen­ tury was the confluence ofmechanics andchemistry, separatedby Acknowledgements a millennial tradition. In the words of J.ofWigner: "we can be I wish to thank for discussions, particularly on proud of the unification of physics and chemistry that happened the background in which the paper in question came about. in our century." (See The Unity afScience 111,1988,p 5, reprinted Wigner thanks him for the reference to Peirce, butAbner tells me in Fizikai Szemle, 92,1992, p. 436 ). This momentous event did not that the selection ofthe motto was Wigner's. It was important to receive the appreciation it deserved. I suggest that this is because him. I also thank George Marx for informing me about current an ambiguity clouded the meaning of the term "unification". A trends in Hungarian education. europhysics news MARCH/APRIL 2003 61