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In Memoriam

Ludwig Boltzmann:A Life of Passion

Wolfgang L. Re iter*

Ludwig Boltzmann (18441906) died just over a century ago. In commemoration of his death, Isketch his pioneering contributions to thermodynamics and statistical mechanics within the con-

text of his often tr oubled life.

Key words: Henriette von Aigentler; Svante Arrhenius; Elsa Boltzmann; Ida Boltz-mann; Ludwig Boltzmann; Anton Bruckner; Albert Einstein; Emperor Ferdinand I;Emperor Franz Joseph I; Dieter Flamm; Josiah Willard Gibbs; Theodor Gomperz;Heinrich G omperz;H ermann von H elmholtz;H einrich Hertz; Gustav Kirchhoff; JosefLoschmidt; Ernst Mach; Franz Mertens; Stefan Meyer; Walther Nernst; Wilhelm Ost-wald; Max Planck; Rainer Maria Rilke;Josef Stefan;Johann Strauss the younger;E rnstZermelo; University of Vienna; University of Graz; University of Munich; Universityof Leipzig;University of Berlin;Duino;atomic hypothesis;Boltzmann equation;Boltz-mann factor; entropy; thermodynamics; statistical mechanics.

Introduction

Ludwig Boltzmann (18441906, figure 1) died just over a century ago. He belongs to aselect group of great scientists whose concepts and work remain at the center of signif-icant work in theoretical physics today.This is part icularly rema rkab le,because the mostfertile period of Boltzmanns work was during the last quarter of the 19th century.

As a member of the Commission for the Investigation of Radioactive Substances ofthe Vienna Academy of Sciences, Boltzmann must have felt deep satisfaction tha t theatomic picture of matte r he championed gained firm experimental support th rough thediscoveries of X rays, radioactivity, and t he electron at the end of the 19th century. Fur-ther, Albert Einstein (18791955) stood on Bo ltzmanns shoulders in 1905 when he

Phys. perspect. 9 (2007) 3573741422-6944/07/03035718DOI 10.1007/s00016-007-0339-1

* Wolfgang L. Reiter cofounded and is Vice President of the Erwin Schrdinger InternationalInstitute for Mathematical Physics.H e studied physics,mathematics,a nd philosophy and receivedhis Ph.D. degree in nuclear physics from the Institut fr Rad iumforschung und Kern physik o fthe U niversity of Vienna in 1974. Un til 2002 he was Directo r of the Nat ural Sciences Un it ofthe Austrian Federal Ministry for Edu cation, Science, and Culture, and Lecturer at the Uni-versity of Vienna. His research inter ests are in the history of physics and t he emigration o f sci-entists from Austria.


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Wolfgang L. Reiter Phys. perspect.358

proposed his revolutionary light-quanta hypothesis, his method for determining thedimensions of molecules, and h is theory of Brownian motion.1 Boltzmann thus lived onthe watershed between 19th and 20th-century physics.2 Rooted in the Newtonian tra-dition with its mechanical models, he stands between James Clerk Maxwell(18311879), whom he admired enormously, and the young Einstein, whom he would

have embraced as his true heir had he been aware of Einsteins groundbreakingachievements of 1905.

Boltzmanns firm belief in the existence of atoms was deeply rooted in his confi-dence in the Newtonian mechanical worldview. To understand the macroscopic prop-erties of matter, in particular those of gases, Boltzmann took a decisive step of greatsimplicity, applying statistical arguments to de termine t he p ropert ies of states in ther-mal equilibrium and their dynamical evolution. The Boltzmann equat ion and its richmathematical structure are still hot top ics today in statistical physics, and t he o rigin of

Fig. 1. Ludwig Boltzmann (18441906) as Professor of Mathematics at the University of Vienna in1875. Credit: Courtesy of the sterreichische Z entralbibliothek fr Ph ysik.


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Vol. 9 (2007) Ludwig Boltzmann 359

its asymmetry in t ime can only be understood proper ly when its initial conditions areviewed on a cosmological time scale.3

Early Life and Education

Ludwig Boltzmann was born just outside the city walls of Vienna at what was thenLandstrasse 286 on Februa ry 20, 1844 that very night marking the passage fromShrove Tuesday to Ash Wednesday. Ever the wry rationalist, he later commented thathe was born between happ iness and dep ression. His life was indeed marked by alter-nating periods of euphor ia and depre ssion, and embraced a love of music and an inter-est in public affairs. He was born at a cultural and political watershed in Austria: JohannStrauss the younger (18251899) gave his first public performance at the Dommayer

Caf near the Schnbrunn palace in Vienna in 1844, and t he failed revolution of 1848in Austria (and in other European countries) ushered in a period of Habsburg abso-lutism after Emperor Ferdinand I (17931875) was succeeded by Emperor FranzJoseph I (18301916).

Boltzmann was educated mainly by monks at the Akademisches Gymnasium inLinz, a p rovincial city in U pper Austria where his father Lud wig was a civil servant inthe state financial administration. He re his son took piano lessons from Anton Bruck-ner (18241896) and developed his lifelong interest in music. His fathers prematuredeath in 1859 must have deeply wounded his youthful psyche. Nonetheless, he passedhis final Gymnasium examinations, the Matura, with distinction in 1863 and thenmatriculated at the U niversity of Vienna to study mathema tics and physics. Its Instituteof Physics was located in the III District of Vienna and even in the same quart er, atLandstrasse 104 (now Erdbergstrasse 15), where he had been born.

Boltzmann received his Ph.D. degree three years later, in December 1866, which atthat time did not require a written thesis. Already that October he had become assis-tant to h is teacher Josef Stefan (18351893, figure 2), who decisively shaped his stu-dents scientific outlook and introduced him to his own field of research, gas theory.4

Together with H ermann von H elmholtz (18211894), Stefan was the second early sup-porter of Maxwells theory of electromagnetism on the continent. No wonder thatBoltzmanns first publication of 1865 dealt with an application of Maxwells theory.5

His second publication one year later was on the relationship of the second law of ther-modynamics to the principles of mechanics and set the tone for his lifelong work inkinetic theory and statistical mechanics.6 At Stefans institute he met Josef Loschmidt(18211895, figure 3), since 1868 Professor extraordinary (ausserordentlicher Profes-sor) and four years later full (ordentlicher) Pro fessor of Physics and a dedicated atom-

ist.7 Loschmidt, a generation older than Boltzmann, became his fatherly friend andexerted a lasting influence on him.*

* While the number of molecules per unit volume of a gas at standard temperature and pressureis generally known as Avogadros number, Boltzmann, on th e occasion of the u nveiling ofLoschmidts bust at the U niversity of Vienna in 1899, proposed t hat th is number b e calledLoschmidt's n umber, a term that is sometimes still used in German-speaking countries.


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In 1868, at the age of twenty-four, Boltzmann (figure 4) took the next step in his aca-demic career, becoming Lecturer (Privatdozent) of Mathematical Physics at the Uni-versity of Vienna. Much later he r ecalled th is period in his life with great nostalgia.

[The Institute of Physics at] E rdberg ha s remained for all my life a symbol of hon-est and inspired experimental work. When I [later] succeeded in injecting a bit o f life

into the Institute of [Physics at] Graz I used t o call it, jokingly, Little Erdberg. By thisI did not mean that t he available space was scarce, because it was quite ample, prob-ably twice as much a s in Stefans Institute [of Physics]; but I had no t succeeded inequalling the spirit of Erdbe rg as yet. Even in Munich, when young PhDs came totell me that they did not know what to work on, I used to think: How different wewere in Erdberg! Today there is beautiful experimental apparatus and people arelooking for ideas on how to use it. We always had plenty of ideas and were only pre-occupied with the lack of equipment.8

Fig. 2. Josef Stefan (18351893), Boltzmann s teacher at the U niversity of Vienna. Credit:Courtesy ofthe sterreichische Zentralbibliothek fr Physik.


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In one of his as usual rather lengthy papers that he published in 1868 (this one is 44pages long),9 Boltzmann worked out a generalization of Maxwells velocity-distribu-tion law under the assumption tha t external forces (for example, gravity) were presentand ar rived at an expression that is now called the Boltzmann factor eE/kT,where E isthe t otal energy, T is the absolute temperature, and k is the Boltzmann constant anexpression that is ubiquitous today in science and technology.

Graz, Vienna, Graz

In 1869 the twenty-five-year-old Boltzmann was appointed Professor of MathematicalPhysics at the Un iversity of Graz, a position he held for four years, until 1873. This wasBoltzmanns first period in Graz and was marked by two fundamen tal scientific break-throughs that he published in 1872 in his paper, Further Studies on the Thermal Equi-librium of Gas Molecules, 10 namely, his H-theorem (H being the negative of the

Fig. 3. Josef Loschmidt (18211895), Boltzmann s mentor a s a studen t at the U niversity of Vienna.Credit: Courtesy of the sterreichische Z entralbibliothek fr Ph ysik.


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entropy S) and his eponymous transport equation. Boltzmann took hisH-theorem toprove that the entropy S of the un iverse always increases; it was greeted by fierceobjections, first in 1876 by his teacher and friend Loschmidt, who pointed out t hat itembodied a reversibility pa radox,11 and two decades later, in 1896, by the Germanmathematician E rnst Zermelo (18711953), who called attention to the so-calledrecurrence paradox.12 Both objections forced Boltzmann to reexamine and elabo-

rate his basic assumptions;13 the first objection soon led him to h is pioneering statisti-cal interpretation of the second law of thermodynamics.

Boltzmann was one of the new breed of theore tical physicists, although no clear-cutdivision existed at the time between theoretical and experimental physicists. In fact,while Boltzmanns theoretical work is universally known, his extensive experimentalwork is not. Despite his poor eyesight, Boltzmann was a talented experimentalist andenjoyed showing sophisticated mechanical experiments of his own design in his lec-tures.14 Furthe r, his early and strong interest in Maxwells electrodynamics led him to

Fig. 4. Ludwig Boltzmann (18441906) as Privatdozentat the University of Vienna, ca. 1868. Credit:Courtesy of the sterreichische Zentralbibliothek fr Physik.


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investigate the dielectric constants of solids and gases and to experimentally confirmMaxwells re lation, n2 = (where n is the index of refraction, the dielectric constant,and the permeability) in 18731874,15 while working in Helmholtzs laboratory inBerlin and in his own laboratories in Graz and Vienna. He t hus provided the firstexperimental evidence for the validity of Maxwells theory of light much earlier thanHe inrich H ertz (18571894) did in h is classic experiment s in 18871888.

In 1873 Boltzmann met Henriette von A igentler (18541938), the first female stu-dent at the University of Graz, and soon became engaged to her. That same year heaccepted the position of Professor of Mathema tics at the U niversity of Vienna, whichwas a major step upward in his career within the Austro-Hungarian academic hierar-chy. (The letters that he and his fiance exchanged between Vienna and Graz havebeen pub lished by Boltzmanns grandson, Dieter F lamm.16) Three years later, in 1876,

Boltzmann returned to the University of Graz as Professor of Physics, married H enri-ette, and bought and refurbished an old farmhouse in Oberkroisbach on the outskirtsof Graz, where he kept a cow to provide fresh milk for their children (figure 5).

Boltzmanns second period in Graz, which lasted from 1876 until 1890, was markedby further groundbreak ing scientific contributions. In 1877 Boltzmann published hisstatistical interpr etation o f the second law of thermodynamics, which E instein termedthe Boltzmann principle:The entropy S of a macrostate ( as determined by its pressure,tempera ture, and other variables) is proportional to the logarithm of the number Wofmicrostates (as det ermined by the positions and velocities of all of the a toms), that is,S = klogW.17 The constant of proportionality k, known universally as the Boltzmannconstant , was first evaluated by Max Planck (18581947) in 1900.18 The formula S =klogW is engraved on Boltzmanns tombstone in the Central Cemetery (Z entralfried-hof) in Vienna.19

In 1884 Boltzmann proved a conjecture of Stefans, that t he tota l energy emitted bya black body is proportional to the fourth power of its absolute temperatur e, whichprovided further support for Maxwells electromagnetic theory. Stefan had recognizedthe import ance of Maxwells theory and had introduced his first and most gifted stu-dent to it. As Carlo Cercignani has noted, that same year Boltzmann

also wrote a fundamental paper,20 generally unknown to the majority of physicists,who by reading only second-hand reports are led to the er roneous belief that Boltz-mann dealt only with ideal gases; this paper clearly indicates that he consideredmutually interacting molecules as well, with non -negligible potential energy, andthus it is he and not Josiah Willard G ibbs (18391903) who should be consideredas the founder of equilibrium statistical mechanics and of the method of ensem-bles.21

Three years later, in 1887, Boltzmann built upon an earlier work of 1884 and formulat-ed t he ergodic hypothesis.22

By this time Boltzmann was a scientific celebrity who at tracted foreign students to

Gr az, such as the future Nobel Laureate s Svante A rrhenius (18591927) and Walther

Nernst (18641941), to study with the acknowledged E uropean master of ther mody-

namics, statistical mechanics, and kinetic theory. Her e, then, was a man flushed with

professional success, enjoying a happy family life with his wife, his children, and a dog


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at his farmhouse in Obe rkroisbach. Yet, dark clouds began to gather over this rosyGraz idyll. Several events conspired to undermine Boltzmanns ment al stability and

precipitate his long slide into depression. His beloved mot her died in 1885. Three

years later, he was elected R ector of the U niversity of Graz and soon thereafter was

confronted by a mon th of aggressive prote sts by German nationalist students. Next,

without informing the Austrian authorities officially, Boltzmann accepted the p resti-

gious Berlin chair of theoretical physics that had been vacated by the death of Gus-

tav Kirchhoff (18241887), but he subsequently reneged, offering somewhat uncon-

Fig. 5. Ludwig Boltzmann (18441906) with his family in G raz in 1886.Left to right: daughter Henri-ette (18801945), wife H enriette von A igentler ( 18541938), daughter Ida Katharina (18841910), sonLudwig Hugo (18781889), son Arth ur Lud wig (18811952). Credit: Courtesy of the sterreichischeZentra lbibliothek fr Physik.


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vincing reasons his myopia, the lack of a comprehensive written plan for a lecturecourse he was to give in theoret ical physics, and the absence of a significant group of

mathematical physicists in Berlin. Probably the m ost damaging blow to him, howev-

er, was the death of his eleven-year-old son Ludwig from misdiagnosed appendicitis

in 1889.

Munich,Vienna, Leipzig,Vienna

Boltzmanns neurasthenia (as it was then called) could no longer be ignored.23 Hisdecisions were progressively marked by restlessness and a sort of escapism probablytriggered by his feeling of increasing isolation in G raz. He revived his interest in mov-ing to Berlin and announced h is desire to leave Graz, hoping that such a change in his

life would calm his mental instability and insecurity.Then, again abandoning his idea ofmoving to Berlin, he accepted the chair of theoretical physics at the Un iversity ofMunich in 1890, after spending eighteen years in Graz. His restlessness subsided inMunich, but he was haunted by homesickness for his native Austria.Three years later,Stefan died and the Viennese physicists immediately agreed to try to persuade Boltz-mann to return to his alma materas Stefans successor. Boltzmann hesitated for twolong years, but finally accepted the chair of theoret ical physics at the Un iversity ofVienna in 1894. His decision to r eturn to Vienna may well have been influenced sig-nificantly by his worsening myopia and t he generous retirement package offered by theUniversity of Vienna as compared to that offered by the U niversity of Munich.

Boltzmanns decision to accept the chair of theoretical physics in Vienna turned outto be a mistake. Munich was a hotbed of physical research, while his hometown Vien-na was much less so. Moreover, Vienna soon harbored a philosophical climate that was

strongly dominated by the phenomenological empiricism of Ernst Mach (18381916),which was violently hostile to Boltzmanns atomism, the core of his lifework. Machmoved to Vienna in 1895, the year after Boltzmanns return, to become Professor ofPhilosophy with Special Emphasis on the History and Theory of the Inductive Sci-ences.* Subsequently, both Boltzmann and Mach now performed on the same stageand competed for attention at the University of Vienna and at the Imperial Academyof Sciences. However, despite their fundamental scientific opposition and deep philo-sophical and epistemological differences (Machs dialectic rationalism, 24 Boltz-manns materialism), they were on cordial personal terms and had the highestesteem for each other. Moreover, along with the classical philologist Theodor Gomperz(18321912) and his son, the philosopher He inrich G omperz (18731942), Boltzmannsupported Machs call to Vienna.25 There is no justification whatever for the enduring

myth, which still circulates among physicists and o thers,26 that Machs rejection ofBoltzmanns atomism led to Boltzmanns tragic end.

Boltzmann remained in Vienna only six years before moving to the University ofLeipzig as Professor of Theoretical Physics in 1900, a decision he initially embraced

* Ordentlicher Professor der Philosoph ie, insbesondere fr Geschichte und Th eorie der induk tiven

Wissenschaften.


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owing to the less-than-satisfactory circumstances that had developed in his institute inVienna.Thus, he complained that he was a mere schoolmaster in Vienna; that his stu-dents, who were mainly candidates for teaching positions in secondary schools (Gym-nasia), lacked inter est in physics; and that the lively scientific atmosphere he had expe-rienced in Munich was strikingly absent in Vienna. The physical chemist Wilhelm Ost-wald (18531932), the most energetic energeticist of the per iod and close adheren t toMachs philosophy, paved t he way for Boltzmanns call to Leipzig, which Boltzmannprized as an outstanding instance of scientific enmity being compatible with personalfriendship. Nevertheless, Boltzmanns move to Leipzig was a disaster: During the sum-mer prior to leaving Vienna, he had a nervous breakdown, for which he had to be hos-pitalized in a sanator ium, and even though he was welcomed with open arms by theLeipzig faculty after his release, his depression was so severe that he made t he first

attemp t on his own life in Leipzig. In contrast to his usual outspokenness, he nevertalked to anyone later about the two years he spent in Leipzig. In Vienna, his chair hadremained vacant, probably because he already had begun to negotiate his returnbefore leaving for Leipzig.

Ever since his aborted move to Ber lin in 1888, Boltzmann had become increasinglytrapped in self-conflict regarding his recurrent wish to change universities. He movedback to Vienna in 1902, but as a condition of his appointmen t had to promise in writ-ing never to leave Austria again: Emperor Franz Joseph I, who was not a part icularlydedicated supporter of the sciences, was not amused by the per egrinations of hisfamous but unreliable subject. Furthe r disruption followed: Because of the urgent needfor more space for the Institute o f Physics, now at Trkenstrasse 3 in the IX D istrict,the U niversity of Vienna appropr iated the apa rtment in it where the Bo ltzmann fami-ly was living.This was Boltzmanns official university residence, and t o compensate h im

for its loss the Ministry for E ducation (Ministerium fr Cultus und Un terricht) gave hima sum o f money with which he bought a villa at Ha izingergasse 26 in the XVIII District(Whring), which is still owned by his descendants.

Boltzmann (figure 6) now lectured on theoretical physics at the University of

Vienna and finished the second volume of his L ectures on the Principles of Mechan-

ics.27 In 1904, on t he occasion o f his 60th birthday, he was presented with a splendid

Festschriftthat was edited by his assistant Stefan Meyer (18721949) and comprised

117 contributions from the international community of physicists.28 Despite this uni-

versal acclaim, however, Boltzmanns wife sent an alarming message to their daugh-

ter Ida (18841910), who had remained in Leipzig to finish school:Daddy gets worse

every day. He has lost his faith in our future. I had imagined a better life here in Vien-

na. 29 Boltzmann suffered from heavy attacks of asthma and headaches, and he was

nearly blind from his myopia. He also had unde rtaken an additional heavy burdenafter Mach suffered a stroke in 1901: He took over Machs lecture course on the phi-

losophy and methodology of science in 1903.* He began it with great success, but

after a few lectures was unable to continue.30 This further undermined his self-confi-

dence.

* Philosophie der Natur und M ethodologie der Naturwissenschaften.


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Boltzmanns Last Years, 19051906

Although Boltzmanns writings on t he philosophy of science and epistemology belongto h is lesser-known and little-discussed legacy, he made important contributions to thisfield, presenting a t heory of scientific change that was inspired by Cha rles Darwins

theory of evolution. Further, despite his increasing physical and mental disabilities, hecrossed the A tlantic twice, in 1904 and 1905. (He had done so once before when he hadlectured at C lark U niversity in Worcester, Massachusetts, in 1899.) In 1904 he gave aninvited lecture in St. Louis, Missouri, in connection with the World Fair,31 and in 1905he lectured at the University of California in Berkeley and at Stanford University.Boltzmann (figure 7) memorialized his trip to California in a typically humorous essay,Journey of a German Professor to Eldorado, 32 which was published in his PopularWritings and remains a delightful piece of prose.

Fig. 6. Ludwig Boltzmann (18441906) as Pro fessor of Theoret ical Physics at th e U niversity of Viennaat Ch ristmastime 1902. Credit: Court esy of the sterreichische Zen tralbibliothek fr Physik.


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That was Boltzmanns last burst of intellectua l activity; it was followed by a deepdepression and hospitalization. He gave his last course on theoretical physics at theUn iversity of Vienna in the winter semester of 19051906; subsequently, he was unableto fulfil his teaching duties in the summer semester of 1906 owing to his physical and

mental suffering. His menta l condition was officially diagnosed as a serious form ofneurasthen ia, a vaguely defined term denoting a general weakness of the nervous sys-tem associated with a broad spectrum of mental disorders ranging from anxiety tosleeplessness.33 In light of his symptoms, however, it is likely that Boltzmann was suf-fering from a much more serious mental illness: manic depression.

Ludwig Boltzmann too k his own life at one of the most scenic spots on the Adriat-ic coast, in Du ino, near Trieste, a little village that is overlooked by an old castle in thepossession of the noble family della Torre e Tasso where the Austrian poet Rainer

Fig. 7. Charicatur e by Karl Pr zibram (18781973) of Lud wig Boltzmann (18441906) as visiting pro-fessor in California in 1905. Credit: Courtesy of the sterreichische Z entralbibliothek fr Physik.


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Maria Rilke (18751926), as poet in residence, began to compose his famous DuinoElegies six years later. The Viennese newspaper Die Zeitreported the tragic news onFriday, September 7, 1906: He hanged himself with a short cord from the crossbar ofa window casement. His daughter was the first to discover t he suicide.*

The Boltzmanns had planned to return to Vienna on Thursday, September 6. Theday before, Boltzmanns wife Henriette and their youngest daughter E lsa (18911965)went for a swim, expecting Boltzmann to join them, but he never did. He had relapsedinto that black state of mind that had tormen ted him for years. Despite the relaxedatmosphere during this late-summer family holiday by the sea, which he had longpromised to spend with his beloved wife,he was restless and deeply depressed. Increas-ingly shortsighted, anxious about his ability to carry out his teaching duties at the Un i-versity of Vienna for the forthcoming semester, and beset by the manic depression tha t

had led earlier to more than one hospitalization, Boltzmann commited suicide on Sep-tember 5, 1906, in his room in the Ho tel Ples,** which today is part of the internation-al United World College of the A driatic-Collegio del Mondo Un ito dellAdriatico. Hisdaughter E lsa had been sent back to the hote l by her mothe r to check up on her fatherand thus was the first person to discover the tragedy, a gruesome and shocking experi-ence that she never talked about for the re st of her life.

Boltzmann passed from this world without leaving a suicide note, but the preface tohis lectures on mechanics, which Boltzmann signed in the Austrian resort town ofAbbazia (today Opatija, Croatia) on August 3, 1897, opens with a motto that he care-fully chose to sum up his view of science and of life:

* Aus Triest kom mt uns die Meldung:H ofrat Prof. Dr. L udwig Boltzm ann, der zum Somm er-aufenthalt mit seiner Tochter in Duino weilte, wurde gestern als Leiche in seinem Z imm er aufge-

funden. Er hatte sich mit einem k urzen Strick am Fensterkreuz erhngt. Seine Tochter war die

erste,die den Selbstmord entdeckte. See Wiener Neuigkeiten.Selbstmord des Prof.Boltzmann,Die Zeit, No.1420 (September 7, 1906), p.1.

** Several locations have been advanced for where B oltzmann committed suicide. Boltzmannscolleague in Vienna, the mathematician Franz Mertens (18401927), claimed that it was in thechurch of Duino, but t his claim can be excluded, because the church was never reconsecrated;see Walter Hflechner,Lud wig Boltzm ann:L eben und Briefe (Graz:Akademische Druck- u.Verlagsanstalt, 1994),p. I 289.That Boltzmann comm itted suicide in his hot el room is supportedby a short obituary,Die Ausfhrung des Selbstmords, in the VienneseNeue Freie Presse ,No.15102 (September 7, 1906),p.3, but the h otel is not named in it.The name of the hotel,th e Hot elPles,is given in a short no te in the Slovenian newspaper,Edinost, No. 247 (September 7, 1906),p. 2. This was published by Mart in Brecelj in the Slovenian daily, Primorski Dnevnik, N o. 83(April 9, 2006), p. 12, under the title,Pred sto leti je v D evinu um rl vliki avstrijski fizik L ud-wig Edward Boltzm ann [A hund red years ago the great Austrian physicist Ludwig Edua rd Boltz-mann died in D uino]. Further confirmation of the hotels name and of its address, Duino 50/54,is found in the parish register, L iber Defunctorum (Book of the Dead ), of the Catholic ParishChurch of Duino together with the cause of his death. Under the heading,Morbus seu CausaMortis (Illness or cause of death), we read: Suicidium alienatione mentali se suspenso perpe-travit(He committed suicide in a state of mental alienation by hanging himself).I am indebtedto Mart in Brecelj for this information and t o Fabio Pagan, International Centre for Theoreti-cal Physics,Trieste,Italy,for providing the relevant documents.A plaque in memory of LudwigBoltzmann was mounted on the H otel Ples in D uino on September 4, 2006.


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Bring vor, was wahr ist; Produce, what is true;Schreib so, dass es klar ist Write, that its clearUnd verfichts, bis es mit dir gar ist!34 And fight, until you are finished!

Boltzmanns funeral took place on Saturday, September 8, 1906, at the Dbling ceme-tery in the XIX District of Vienna at the unusually late hour of seven oclock in theevening. The tra in from Trieste bearing Boltzmanns coffin had been delayed for hou rsby heavy weekend traffic. Boltzmanns assistant Stefan Meyer was the last of themourners to speak at Boltzmanns open grave.35 He closed his eulogy on behalf ofBoltzmanns students with their teachers battle cry: Reinheit und K larheit im K ampfum die Wahrheit! [Purity and Clarity in the Struggle for Truth!] 36

Boltzmanns Legacy

At the center of Boltzmanns lifelong struggles in physics and philosophy was the

question of the rea lity of atoms. In the 1870s, when Boltzmann was at the zenith of his

intellectual powers, there was no conclusive experimental evidence for the existence

of atoms. He had to fight his lonely battle on two fronts: for his belief in the reality of

atoms against Mach and the empiricists, and for h is statistical interp retat ion of the sec-

ond law of thermodynamics, his most revolutionary and lasting contribution to

physics, against Loschmidt and o thers. Boltzmanns struggle on these two fronts was

ironic in retrospect, as pointed out by the American theoretical physicist Leo

Kadanoff:

Mach was wrong about atoms and wrong in demanding that science only include the

immediately visible, but r ight in demanding a different philosophic outlook forkinetic theory. Boltzmann was right about a toms but utterly wrong in believing thatatoms provided a necessary basis for thermodynamics. The second law does notrequire atoms.37

Thermodynamics, in other words, is neutral with respect to models of the microphysi-cal world.

Boltzmanns goal of translating the behavior of the physical world into rigorouslydefined mathematical entities that obey well-defined rules remains an open gametoday, one that is still centered upon the second law of thermodynamics, a law thatAlbert Einstein regarded as an unshakeable and fundamental pillar of the physicalworld. As he wrote:

A theory is the more impressive the greater the simplicity of its premises is, the moredifferent kinds of things it re lates, and t he more extended is its area of applicability.Therefore the deep impre ssion which classical thermodynamic made upon me. It isthe only physical theory of universal content concerning which I am convinced that ,within the framework of the applicability of its basic concepts, it will never be over-thrown (for t he special attention of those who are skept ics on principle).38

As E lliott H. Lieb and and Jakob Yngvason have remarked, to derive the second lawfrom statistical mechanics is a goal that has so far eluded the deepest thinkers. 39


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Their recent axiomatic approach has enabled them to formulate the second law in away that is entirely free of the concept of atoms that was so dear to Boltzmann.40

We are thus left with a final irony: The statistical formulation of the entropy that isengraved on Boltzmanns tombstone in Vienna can be defined unambiguously andmeasured with no re ference whatsoever to the atomic structure o f matter.* But this isa common occurrence in science: The conceptual framework in which the creator o f anew scientific concept worked is usually transformed by his or he r successors. Still, asEinstein also wrote, scientists work in the faith that facts by themselves can andshould yield scientific knowledge without free conceptual constriction. 41 Physicsinvolves more than producing a consistent mathematical formulation of Nature. Atomsdo exist, and Boltzmann was their passionate prophet.

Acknowledgment

I thank Jakob Yngvason for valuable discussions and helpful suggestions and Roger H .Stuewer for his careful and t houghtful editorial work on my paper.

References

1 For a recent discussion of Einsteins 1905 papers, see John S. Rigden,Einstein 1905:The Standardof Greatness (Cambridge, Mass. and London: Harvard Un iversity Press, 2005).

2 David Lindley,Boltzm anns Atom :The Great Debate That L aunched a Revolution in Physics (NewYork:Free Press, 2001).

3 Roger Penrose,Th e Em perors New M ind:Con cerning Computers, Minds, and the Laws of Physics(New York and Oxford: Oxford Un iversity Press, 1989), Chapter 7.

4 John Crepeau, Josef Stefan: His life and legacy in the thermal sciences, Experimental Thermal

and Fluid Science (2006), .5 Ludwig Boltzmann, ber die Bewegung der Elektrizitt in krummen Flchen, Sitzungsberichte

der kaiserlichen A kademie der Wissenschaften. Mathematisch-naturwissenschaftliche Classe. II.A bteilung 52 (1865),214221;reprinted in Wissenschaftliche A bhandlun gen. Band I. 18651874,ed .Fritz Hasenhrl (Leipzig: J.A. Barth, 1909; reprinted New York:Che lsea, 1968), pp. 1-8.

6 Ludwig Boltzmann, ber die mechanische Bedeutung des zweiten Hauptsatzes der Wrmetheo-rie, Sitz . d . k. Akad. d . Wissen. Math.-naturw. Cl. II . Abt. 53 (1866), 195220; reprinted in Wis-senschaftliche A bhandlungen. Band I (ref. 5), pp. 9-33.

7 For discussions of Loschmidts life and work, including a bibliography of his publications, see W.Fleischhacker and T. Schnfeld, ed., Pioneering Ideas for the Ph ysical and Chem ical Sciences:JosefL oschmidts Con tributions and Modern Developm ents in Structural Organic Chem istry, A tomistics,

and Statistical Mechanics. Proceedings of the Josef L oschmidt Sym posium, held June 2527, 1995,

in Vienna, A ustria (New York and London: Plenum Press, 1997).

* Boltzmanns identification of entropy as the logarithm of the area of the energy surface (whensuitably revised in quantum-mechanical language) was a crucial insight about many systems,but the reason that th is quantity obeys the second law, and the reason for the existence of thesecond law, are different questions. See Elliott H . Lieb,What if Boltzmann h ad known ab outQuan tum Mechanics, in Giovanni Gallavotti, Wolfgang L. Reiter, and Jakob Yngvason, ed.,Proceedings of the Sy mp osium Boltzm anns L egacy 2006 (Zrich: Europ ean MathematicalSociety Publishing House, 2008) forthcoming.


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8 Ludwig Boltzmann, Josef Stefan, in Populre Schriften (Leipzig: Verlag J. A. Barth, 1905), pp.92103; on pp. 100101. Quoted in Carlo Cercignani,Ludwig Boltzmann:T he Man W ho TrustedAtoms (Oxford and New York: Oxford University Press, 1998), p. 6.

9 Ludwig Boltzmann, Studien ber das Gleichgewicht der lebendigen Kraft zwischen bewegtenmateriellen Punkten, Sitz . d . k. Akad. d . Wissen. Math.-naturw. Cl. II . Abt . 58 (1868), 517560;reprinted in Wissenschaftliche A bhandlun gen. Band I (ref. 5), pp. 4996. For the velocity-distribu-tion law, see J. Clerk Maxwell,O n the D ynamical Theory of Gases, Philosoph ical Transactions o fthe Royal Society of L ondon 157 (1867), 4988; reprinted in The Scientific Papers of James ClerkMaxwell, W.D. Niven, ed. Vol. 2 (Cambridge: Cambridge University Press, 1909; reprinted NewYork: Dover, 1965), pp. 2678.

10 Ludwig Boltzmann,Weitere Studien ber das Wrmegleichgewicht unter G asmoleklen, Sitz. d.k. Akad. d. Wissen. Math.-naturw. Cl. II. Abt. 66 (1872), 275370; reprinted in WissenschaftlicheAb handlungen. Band I (ref. 5.), pp. 316402.

11 J. Loschmidt, ber den Zu stand des Wrmegleichgewichtes eines Systems von Krpern mitRcksicht auf die Schwerkraft. I, Sitz. d. k. Ak ad. Wissen. Math.-naturw. Cl. II. Abt. 73 (1876),

128139; idem ,II, ibid., 366372; idem ,III, ibid. 75 (1877) 287298; idem ,IV, ibid. 76 (1877),209225; Herber t Spohn, Loschmidts Reversibility Argument and the H -Theorem, in Fleis-chhacker and Schnfeld, Pioneering Ideas (ref. 7), pp. 153157.

12 For a discussion and excerpts of the original papers by Henri Poincar, Ernest Zerm elo,an d Lud-wig Boltzmann, see Stephen G. Brush, Kinetic Theory. Vol. 2. Irreversible Processes(Oxford: Per-gamon Press, 1966), pp. 194228.

13 For a discussion of the reversibility and recurrence par adoxes within the context of Boltzmannswork, see Stephen G. Brush,L udwig Boltzmann and the Foundations of Natural Science, in IlseM. Fasol-Boltzmann. ed., L udwig Boltzm ann. Principien der Naturfilosofi. L ectures on NaturalPhilosophy 19031906(Berlin and H eidelberg: Springer-Verlag 1990), pp. 4361, esp.p p. 4850.

14 Klemens Rumpf and Petra Gran itzer, Ludwig Boltzmann als Experimentalphysiker, Physik inunserer Z eit5 (2006), 228234.

15 Ludwig Boltzmann, Experimentelle Bestimmung der Dielektrizittskonstante von Isolatoren,Sitz. d.A kad.d. Wissen. Math.-naturw.Cl. II.A bt. 67 (1873), 1780; idem , Experimentelle Bestim-mung der Dielektrizittskonstante einiger Gase, ibid. 69 (1874), 795813; idem , ber einige an

meinen Versuchen ber die elektrostatische Fernwirkung dielektrischer Krper anzubringendeKorrektionen, ibid. 70 (1874), 307341;rep rinted in Wissenschaftliche A bhandlun gen. Band I (r ef.5.), pp. 411471, 537555, 556586.

16 Dieter Flamm, ed.,Hochgeehrter Herr Professor! Innig geliebter L ouis! L udwig Boltzm ann, Hen-riette von Aigentler, Briefwechsel (Wien, Kln,Weimar: Bhlau, 1995).

17 Ludwig Boltzmann, ber d ie Beziehung zwischen dem zweiten Hau ptsatze der mechanischenWrmetheorie un d der Wahrscheinlichkeitsrechnung, respective den Stzen ber das Wrme-gleichgewicht, Sitz. d. k. Ak ad. d.Wissen. Math.-naturw. Cl. II.A bt. 76 (1877), 373435; reprintedin Wissenschaftliche A bhandlun gen. Band II. 18751881, ed. Fritz Hasenhrl (Leipzig:J.A. Barth,1909; reprinted New York: Chelsea, 1968), pp. 164223; Albert Einstein, ber einen die Erzeu-gung und Verwandlung des Lichts betr effenden h euristischen G esichtspunkt,An nalen der Physik17 (1905), 132148, on 140;repr inted in John Stachel, ed. Th e Collected Papers of Albert Einstein.Vol. 2. The Swiss Years: Writings, 19001909 (Princeton: Princeton University Press, 1989), pp.150166, on p. 158. For a discussion, see Martin J. Klein, The Development of Boltzmanns Sta-tistical Ideas, in E.G.D. Cohen and W.Thirring, ed., The B oltzm ann Equation:Theory and A ppli-cations (Wien and New York: Springer-Verlag, 1973) [Acta Physica A ustriaca, Supplementum X(1973)], pp. 53106.

18 Martin J. Klein, Max Planck and the Beginnings of the Quantum Theory,Archive for H istory ofExact Sciences 1 (1962), 459479, esp. 471.

19 For this and other sites, see Wolfgang L. Reiter, Vienna:A R andom Walk in Science, Physics inPerspective 3 (2001), 462489.

20 Ludwig Boltzmann, ber die Eigenschaften monozyklischer und anderer damit verwandterSysteme, Journal fuer reine und angewandte Matematik 98 (1884), 6898; reprinted in Wissen-


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schaftliche A bhandlun gen. Band III . 18821905, ed. Fritz H asenhrl (Leipzig: J.A. Barth, 1909;reprinted New York: Chelsea, 1968), pp. 122152.

21 Cercignani,Ludwig Boltzmann (ref. 8), p. 18 and Chapter 7.22 For a d iscussion of Boltzmanns and Ma xwells introduction of the er godic hypothesis, with refer-

ences to the original literature, see Stephen G. Brush, Foundations of Statistical Mechanics18451915,Arch.H ist.Ex. Sci. 4 (1967), 145183,esp.168177; reprinted in Stephen G. Brush, TheKind of Motion We Call Heat. Book 2. Statistical Physics and Irreversible Processes (Amsterdam,New York, Oxford: North-Holland, 1976), pp. 335385,esp. pp. 363377.

23 rztliches Gutachten ber den nervlichen Zustand Boltzmanns, Graz, den 24. Juni 1888, in Her-bert H rz and Andre as Laass,L udwig B oltzmanns Wege nach B erlin: Ein Kapitel sterreichisch-deutscher Wissenschaftsbeziehungen (Berlin:A kademie-Verlag, 1989), pp. 109110; reproduced infacsimilie in A bb. 10a)-c). Using todays terminology, Boltzmann probably was in a d epressivephase o f a cyclothymic disorder.

24 Paul K. Feyerabend, Machs Theorie der Forschung und ihre Beziehung zu Einstein, in RudolfHaller and Friedrich Stadler, ed.,Ernst Mach Werk und W irkung (Wien:Verlag Hlder-Pichler-

Tempsky, 1988), pp. 435462, especially pp. 448458.25 Heinrich Gomperz,Ernst Mach,A rchiv fr Geschichte der Philosophie 29 (1916), 325326;John

T. Blackmore,Ernst Mach: His Work, L ife, and Influence (Berkeley, Los Angeles, London: Uni-versity of California Press, 1972), pp. 145163;[Machs] Briefwechsel mit Theodor Gomp erz, inHaller and Stadler,Ernst Mach (ref. 24), pp. 213228.

26 See, for example, Lewis S. Feuer,Einstein and the Generations of Science (New York:Basic Books,1974), pp. 335341.

27 Ludwig Boltzmann, Vorlesung ber die Principe der Mechanik. 2 Vols. (Leipzig:Johann Ambr osiusBarth, 1897, 1904).

28 Stefan Meyer, ed., Festschrift L udwig B oltzmann gewidmet zum sechzigsten Geburtstage 20. Feb-ruar 1904 (Leipzig:Johann Ambro sius Barth, 1904).

29 Quoted in Cercignani,Ludwig Boltzmann (ref. 8), p.30.30 Fasol-Boltzmann,Ludwig Boltzmann (ref. 13). For valuable new biographical material, see Ilse

Maria Fasold-Boltzmann and Gerhar d Lud wig Fasold, ed.,Lu dwig Boltzm ann (18441906). Z umhund ertsten Todestag (Wien, New York:Springer-Verlag, 2006).

31 Ludwig Boltzmann, The Relations of Applied Mathematics, in Howard J. Rogers, ed., Con-

gress of Arts and Science Universal Exp osition, St. L ouis, 1904. Vol. IV. Physics Chemistry

A stronomy S ciences of the Earth (Boston and New York: Houghton, Mifflin, 1906),pp. 591603;

reprinted in Katherine R. Sopka, ed., Physics for a N ew Century: Papers Presented at the 1904

St. L ouis Congress (New York: Tomash Publishers and American I nstitute of Physics, 1986), pp.

267279.

32 Ludwig Boltzmann, Reise eines deutschen Professors ins Eldorado, in Populre Schriften (ref.8), pp. 403435;E ingeleitet und ausgewhlt von E ngelbert Broda (Br aunschweig and Wiesbaden:Friedr.Vieweg & Sohn, 1979), pp. 258290;re printed in Flamm,Hochgeehrter Herr Professor(ref.16),p p. 235256;tr anslated into E nglish in Transport Theory and Statistical Physics 20 (December1991), 499523, Physics Today 45 (January 1992), 4451, and Cercignani,Ludwig Boltzmann (ref.8), pp. 231250.

33 Eugen Bleuler,L ehrbuch der Psychiatrie, 14.Auflage,neu bearbeitet von Manfred Bleuler (Berlin,Heidelberg, New York: Springer-Verlag, 1979), pp. 519522.

34 Boltzmann, Vorlesungen ber die Principe der Mechanik. Vol. 1 (ref. 27), p. v.35 For more on Meyer, see Wolfgang L. Reiter, Stefan Meyer: Pioneer of Radioactivity, Phys. Per-

spect. 3 (2001), 106127.36 Hofrat Prof. Boltzmann. Das Leichenbegngnis in Wien,Die Zeit, No. 1422 (September 9,1906),

p. 4;H ofrat Prof. Boltzmann. Das Leichenbegngnis,Neues W iener Tagblatt, No. 49 (September9, 1906), pp. 67.

37 Leo P. Kadanoff, Boltzmanns Science, Irony and Achievment [Review of David Lindley,Boltz-manns A tom (ref. 2)], Science 291 (Mar ch 30, 2001), 25532554; on 2553.

38 Albert E instein, Autobiographical Notes, in Paul Arthur Schilpp, ed.,Albert Einstein: Philoso-pher-Scientist(Evanston, Ill.:The L ibrary of Living Philosophers, 1949) p. 33.


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39 Ellliott H. Lieb and Jakob Yngvason, The Physics and Mathematics of the Second Law of Ther-modynamics, Physics Reports 310 (1999), 196; on 5.

40 Ellliott H. Lieb and Jakob Yngvason,A Fresh Look at E ntropy and the Second Law of Thermo-dynamics, Physics Today 53 (Apr il 2000), 3237;L etters: Entro py Revisited, Gorilla and All,ibid. (October 2000), 1112, 14, 106.

41 Einstein, Autobiographical Notes (ref. 38), p. 49.

The E rwin Schrdinger Intern ational Institutefor Mathematical Physics

Boltzmanngasse 9A-1090 Vienna,Austriae-mail: [email protected]

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