Max Planck: The Reluctant Revolutionary Who Discovered the Quantum

Of all the figures who shaped the physics of the twentieth century, none is more poignantly self-divided than the grave, courteous, deeply conservative Berlin professor who, on the afternoon of 14 December 1900, presented to the German Physical Society a short paper that contained, almost as an accidental algebraic device, the most revolutionary idea in the history of natural philosophy since Isaac Newton. Max Planck had been studying the spectrum of the radiation emitted by a heated cavity — the so-called blackbody — for nearly six years. He had constructed an empirical formula that fitted the experimental data with extraordinary precision. To derive that formula from first principles, however, he had been forced to suppose that the energy of the oscillators inside the cavity could not vary continuously, as classical physics required, but could take only discrete values that were integer multiples of a quantity proportional to the frequency. The proportionality constant — a number so small that it had no parallel in the macroscopic world, scarcely six and a half divided by ten to the thirty-fourth in the units of his calculation — became, in the years that followed, one of the three fundamental constants of nature. He called it h, and it has been called h ever since. The introduction of h into the equations of physics was, in retrospect, the moment at which the classical worldview began its long unravelling, but Planck himself did not understand at the time what he had done, and for the better part of two decades he would labor, often desperately, to reconcile his discovery with the deterministic and continuous physics in which he had been educated and which he revered as a deep expression of the rationality of nature.

He was, by temperament, the least likely revolutionary the history of physics has produced. The grandson of a theologian, the son of a jurist, the descendant on both sides of generations of Prussian and Schleswig-Holstein scholars, pastors, and civil servants, he was reared in the high humanistic culture of the German Bildungsbürgertum — a culture in which Bach and Beethoven were household intimates, in which Goethe and Schiller were the standards of literary judgment, in which classical philology and the disciplined cultivation of the inner life of the mind were considered the highest achievements of which a human being was capable. He was a musician of considerable accomplishment, a pianist whose ability had been at one point sufficient to suggest a possible career as a concert performer; he was an accomplished singer in the choral tradition of the north German Protestant church; he was a mountain climber who through his long life would spend his summer holidays scaling the peaks of the Bavarian and Tyrolean Alps. He carried himself, by every account, with the gentle gravity of an old-fashioned German Herr Professor of the imperial type: tall, thin, gray-eyed, sparely dressed in the dark suit and white linen of the Prussian academic class, always courteous, never raising his voice, treating students and colleagues alike with a formal and slightly distant kindness that masked an interior life of considerable depth and considerable suffering. He was a Christian of the most reserved and rational German Protestant sort, who at the end of his life would write that "religion and natural science are not in conflict but only stand in a complementary relation," and who at the same time refused to attribute personal qualities to the God of his belief, preferring to describe the divine as the "rational order behind the phenomena."

The course of his personal life was as harrowed as his public career was distinguished. He was twice married — first to Marie Merck, his childhood sweetheart from Munich, who died young of tuberculosis after twenty-two years of happy marriage; then in late middle age to her niece Marga von Hoesslin, who survived him by sixteen years. He had five children, four of whom died before him. The eldest son, Karl, was killed at Verdun in 1916 in the First World War. The twin daughters Grete and Emma, born inseparable and devoted to each other, both died in childbirth within two years of each other in 1917 and 1919, each leaving behind a single surviving infant; in a moment of awful symmetry, the second daughter Emma married the widower of the first daughter Grete, only to die giving birth to her own first child eighteen months later. The youngest son, Erwin, was hanged by the Nazis in early 1945 for his participation in the July plot against Hitler. Only one child, the second son Hermann, who survived his father in greatly straitened circumstances in postwar Göttingen, lived past Planck's own death in October 1947. The Berlin house in which Planck had lived for more than fifty years, with its grand piano, its library of philosophical and scientific works, its correspondence with Einstein and Bohr and Schrödinger, its files of unpublished papers and lecture notes, was destroyed in a single allied bombing raid in February 1944. He lived through the four great convulsions of modern German history — the Wilhelmine Empire of his youth, the catastrophe of 1914–1918, the Weimar Republic and the hyperinflation, the rise and ruin of National Socialism — and he saw the country whose science he had labored to build into the most distinguished in the world brought to physical and moral ruin by leaders whom he loathed but whom he was too old, by 1933, to do anything to oppose except by acts of personal courage that, in the conditions of the Third Reich, were nearly futile.

Yet through all of these calamities he continued to think, to teach, to compute, to write. His professional output between 1900 and his retirement from the Berlin chair in 1928 was prodigious. After the quantum hypothesis came a long series of papers on radiation theory and on the foundations of thermodynamics. He produced, in 1906, the textbook on the Theory of Heat Radiation that became the canonical reference for the new physics and that went through five editions in his lifetime. He helped to organize the great Solvay Conferences that, from 1911 onward, drew the most important physicists of the world together in Brussels at the expense of the Belgian industrialist Ernest Solvay. He served as one of the four permanent secretaries of the Prussian Academy of Sciences from 1912 until 1938 — a post in which he largely determined the appointments to senior physical sciences positions in Berlin and which made him, for the better part of a generation, the most powerful figure in German physics. He was president of the Kaiser Wilhelm Society from 1930 to 1937, a position from which he resigned in protest at the regime's increasing persecution of Jewish colleagues, though he never resigned from the academy itself, on the principle that to leave was to abandon the institution to its enemies. He was awarded the Nobel Prize in Physics for 1918 — held over from that year of war and announced in 1919 — in recognition "of the services he rendered to the advancement of Physics by his discovery of energy quanta," and he gave a Nobel lecture in Stockholm in June 1920 that remains one of the most lucid expositions of the foundations of the new physics ever set down.

But for all his honors he remained, to those who knew him best, a man of considerable inward sorrow, formed by personal tragedy and by the historical disasters of the German Catastrophe, sustained in adversity by an unshowy religious faith, by his music, by his books, and by an iron discipline of professional duty that did not falter even in the last years of his life when, after the death of Erwin and the bombing of his house, he was reduced to lodging in a relative's farmhouse near Magdeburg and reading proofs by candlelight in the bitter winter of 1945. The biography that follows traces in detail the long path from the Schleswig-Holstein parsonage to the Göttingen grave: the boyhood in Kiel and Munich, the gymnasium training and the choice between music and physics, the doctoral thesis at Munich on the second law of thermodynamics, the long apprenticeship in junior teaching positions at Kiel and finally the call to Berlin in 1889, the patient labors on radiation theory that culminated in the great discovery of December 1900, the slow and often reluctant accommodation to the implications of his own work, the family tragedies and the political disasters of the Wilhelmine and Weimar and Nazi years, and the postwar effort to rebuild the institutions of German science from the rubble of defeat. It is a story in which scientific genius and personal grief, deep religious feeling and rigorous rationalism, the highest classical culture and the lowest historical brutality, are all interwoven in a single human life of unusual moral seriousness.

Birth and Family in Kiel

Max Karl Ernst Ludwig Planck was born on 23 April 1858 in the harbor city of Kiel, then the principal naval town of the duchies of Schleswig and Holstein and a place of some twenty-five thousand inhabitants at the mouth of the long inlet that the Baltic forces inland from the Bay of Lübeck. The Kiel of 1858 was a contested city. The duchies of Schleswig and Holstein had been linked to the Danish crown since the late Middle Ages, but their population was overwhelmingly German-speaking, and the question of their political and constitutional future had been one of the great unresolved European disputes of the previous decade. The First Schleswig War of 1848–1851 had ended in Danish victory and the restoration of the union; the Second Schleswig War of 1864 would end in Danish defeat and the absorption of the duchies into the Prussian-led German state. The Plancks were Holsteiners of long standing, by every cultural and political instinct German, and the tense political atmosphere of the duchies in the years before unification formed the earliest political consciousness of the future physicist. He would remember, into old age, the sight of Austrian and Prussian troops marching through the streets of Kiel in the spring of 1864, and the family's nervous calculations of which side would prevail and what would become of his father's professorship in the event of one outcome or the other.

The Planck family were Schleswig-Holstein people of solidly bürgerlich standing, descended on the paternal side from a long line of Lutheran pastors and theologians who had served the parishes of the duchies for several generations. The family genealogy, which the elder Plancks kept with the careful attention to ancestry characteristic of the German educated bourgeoisie, could be traced with confidence to the early seventeenth century and included a number of figures of local distinction in the church and the academy. The future physicist's paternal grandfather, Heinrich Ludwig Planck (1785–1831), had been professor of theology at the University of Göttingen and a published author of works on the New Testament; his great-grandfather Gottlieb Jakob Planck (1751–1833) had also been a Göttingen theologian, the founder of the discipline of comparative church history and a man of European reputation in his day. The family tradition, in other words, was emphatically scholarly, emphatically Protestant, and emphatically committed to the high humanistic culture of the German universities.

The future physicist's father, Johann Julius Wilhelm Planck (1817–1900), had broken with the family clerical tradition by going into the law. He had studied jurisprudence at Göttingen, Berlin, and Kiel, had taken his doctorate at Göttingen in 1842, and after a period of practical legal work had been appointed in 1849 professor of constitutional and civil law at the University of Kiel. He was a specialist in commercial law and in the constitutional law of the German states, a productive scholar with a substantial publication record, and a man of strong moral and political convictions. He had been a moderate liberal in his political views during the 1848 revolutions, had favored a unified German state, and was a particularly close student of the legal questions raised by the Schleswig-Holstein dispute. He would later, after the Prussian annexation of the duchies, accept a chair at the University of Munich and move the family south in 1867, where he would teach for another twenty-five years and serve as one of the principal authors of the unified German Code of Civil Procedure of 1879. He was, by every account, a man of formidable intellectual energy, of considerable personal warmth in private though somewhat distant in public, and of a deep religious seriousness that he had carried over from his clerical family background into the more secular work of his academic career.

The physicist's mother was Emma Patzig Planck (1821–1914), the second wife of Wilhelm Planck. (His first wife, Mathilde Voigt, had died in 1853 leaving two surviving children, Hugo and Emma, who would be the half-siblings of the future physicist.) Emma Patzig was the daughter of a pastor in the Pomeranian town of Greifswald, had been educated at home and at a girls' school in Stettin, and had married the widowed Wilhelm in 1854 when she was thirty-three and he was thirty-seven. The marriage produced five children — Hermann (1855–1906), Adalbert (1856–1909), Max (1858–1947), Adele (1859–1944), and Otto (1862–1922) — of whom Max was the third and the most academically distinguished. Emma was, by family report, a woman of warm and lively temperament with an excellent ear for music, who maintained the household with the efficient devotion characteristic of the wives of German academic men in the imperial period and who passed on to her sons a love of music and of the outdoors that would mark them all their lives. She would live to be ninety-three and would have the satisfaction of seeing her son Max appointed to the most distinguished chair in German physics, though she did not live to see his Nobel Prize.

The Planck Family: Generations of Scholars and Pastors

The Planck family inheritance was, on Max's own later assessment, the most important fact of his early life. He was not the first scholar in the family, nor even the first scholar of international reputation; he came into a household in which intellectual achievement and disciplined intellectual labor were taken for granted as the proper occupation of a serious man. The pictures that hung on the walls of the Kiel and Munich houses were portraits of theologian grandfathers and great-grandfathers; the books on the shelves were the Greek and Latin classics, the standard works of German philosophy from Kant to Hegel, the great theological commentaries of the Tübingen and Göttingen schools, and the legal and historical works of his father's discipline. The conversation at the family dinner table was the conversation of a high-cultural German Protestant family: serious, well-informed, given to long discussion of literary and historical questions, sustained by the assumption that the cultivation of the mind was the highest form of human activity.

This inheritance shaped Max Planck in several deep and lasting ways. It gave him an inner certainty that his own academic vocation was a natural extension of the work of his ancestors and an entirely respectable form of life for a man of his class. It gave him a particular kind of moral seriousness — a sense that scholarship was not a private pleasure but a public duty, that the academic vocation entailed obligations to truth, to students, to the larger society, and (in the deeply religious phrasing he would have understood from his theologian grandfather) to God himself, who was the ultimate guarantor of the rational order of nature. It gave him a deep and abiding respect for the institutions of German academic life — the universities, the academies, the scholarly journals, the formal disciplines of dissertation and habilitation and inaugural lecture — that would mark him throughout his career as a profoundly conservative figure even when his own work was producing one of the most revolutionary transformations in the history of physical thought. It gave him also, through the Christian tradition that the family had carried for generations and that his father had transmitted to his children without dogmatic rigidity but with quiet conviction, a religious sensibility that would never leave him and that he would express in old age in a series of essays on the relation of science and religion that have remained the classical expositions of the position of the religious scientist of the rationalist Protestant type.

The intellectual style of the family, as Planck would later describe it, was that of the German Bildungsbürgertum at its most disciplined and serious. It was not a style of brilliance or rapid wit; it was a style of patient and thorough work, of careful attention to detail, of cultivation of the inner life through music and reading and reflection, of unhurried disagreement reasoned through with all parties involved. Planck would carry that style with him into the laboratory and the lecture hall, where he was famous for his patience with student difficulties, for his refusal to rush a problem before it had been understood from every angle, and for the quiet and unfussy precision of his lecturing. Generations of Berlin students would describe him as the model of the German professor of the old school: dignified without being pompous, courteous without being effusive, demanding without being harsh, and possessed of the rare gift of being able to make the most difficult subjects clear without simplifying them out of recognition.

Childhood and the Move to Munich

The first nine years of Planck's life were spent in Kiel. The family lived in a comfortable academic house on Heiligendamm Street, a few minutes' walk from the university and from the harbor. The Kiel of the 1860s was a small and somewhat provincial place compared to the great cities of Germany, but it was a place of considerable charm and of unusual natural beauty, set on the long, deep, blue-green inlet of the Baltic between low forested hills, with the masts and rigging of merchant and naval vessels constantly visible from the upper windows of the family house. Max Planck always remembered Kiel with affection, and he would later say that some of his earliest memories were of the smell of salt and tar on the harbor front and of the long Baltic summer evenings when the sun seemed reluctant to set and the family would walk together along the shore.

The childhood was, by the standards of nineteenth-century German bourgeois households, comfortable and happy. The father was busy with his lectures and his legal writing but found time to take long walks with his children on Sunday afternoons; the mother kept a warm and well-ordered household; the siblings were close to one another and to the half-brother and half-sister from the father's first marriage. The young Max was, in his own later recollection, a quiet and observant child rather than a particularly brilliant or precocious one — he learned to read and to write at the usual ages, was not noted by his early teachers for any extraordinary ability, and had no obvious vocation as a child for either music or science. He was, however, an unusually self-contained boy with an unusually long attention span; he could spend long hours absorbed in a single book or in a single problem, and he was already, by the age of seven or eight, beginning to show the patient, methodical, undemonstrative character that would mark him as an adult.

The political upheavals of the 1860s formed the backdrop of his early years. The Second Schleswig War broke out when Max was five years old, and the family watched with anxiety as Austrian and Prussian troops marched through the streets of Kiel and the Danish administration of the duchies collapsed. The Austro-Prussian War of 1866, which would end with Prussian dominance in northern Germany and the establishment of the North German Confederation, took place when Max was eight. He would remember, in old age, hearing the news of the Battle of Königgrätz and of the Prussian victory, and the family's relief that the long uncertainty over the political future of Schleswig-Holstein appeared, finally, to be resolving itself in favor of the German cause to which his father was so deeply committed.

In 1867, when Max was nine, his father accepted a call to the chair of civil and commercial law at the University of Munich and moved the entire family south. The journey from Kiel to Munich — across the breadth of the new German state, from the Baltic to the foothills of the Alps — was the great adventure of Max's childhood. The family traveled by rail, taking three days on the way, with stops at Hamburg and Hanover and Frankfurt and Nuremberg, and Max would remember the first sight of the Bavarian mountains from the train window south of Nuremberg as one of the great visual impressions of his life. Munich in 1867 was the capital of the kingdom of Bavaria, then still a separate state with its own monarch (the young King Ludwig II, whose mental instability would become a public scandal in the following decade), its own constitution, and its own deep particularist resistance to the Prussian-led unification of Germany. It was a city of some two hundred thousand inhabitants, set in a wide plain at the foot of the northern Alps, distinguished by its rich Catholic baroque architecture, by its great galleries of painting and sculpture, by the new universities and academies that the Wittelsbach dynasty had been founding for more than a century, and by the rich musical and theatrical life of the Bavarian capital. For a boy who had been raised on the gray, salty, Protestant shores of the Baltic, Munich was a revelation — colorful, southern, Catholic, mountainous, musical — and it would be his home for the next thirteen years and the place in which the fundamental decisions of his intellectual life would be made.

The family settled in a large apartment in the Briennerstrasse, a few minutes' walk from the university and from the Königsplatz where the great galleries stood. The father took up his new chair and was at once involved in the legal and constitutional reform that the new German Empire of 1871 would require — he would be one of the chief authors of the unified Code of Civil Procedure that the Reich enacted in 1879, a work that would consume much of his professional energy for a decade. The mother worked to establish a household in the Bavarian capital. The children were enrolled in the Maximiliansgymnasium, a humanistic preparatory school of high reputation that was the leading boys' school of Munich. Max entered the lower classes in the autumn of 1867 and would remain at the school for the next seven years, graduating with the Abitur in the summer of 1874 at the age of sixteen.

School Days at the Maximiliansgymnasium

The Maximiliansgymnasium was a school of the classic German humanistic type, with a curriculum centered on Latin, Greek, German literature, mathematics, history, religion, and modern languages, taught by a faculty of well-trained academic philologists and historians who treated the pupils with the formal seriousness of a junior university. Max Planck was, by every measure, a successful pupil rather than a brilliant one. He was steady, conscientious, exact in his work, and he stood somewhere between the third and the fifth in his class through most of his school years. He was particularly accomplished in Latin and in mathematics, less so in Greek, and (in the early years) only moderately so in the natural sciences, which were taught at the gymnasium with a less rigorous methodology than the classical languages but which would in time draw him into a vocation.

The decisive influence of his school years was his teacher of mathematics and physics, Hermann Müller, who taught the upper forms at the Maximiliansgymnasium and who was, by Planck's own later testimony, the man who first awakened in him a serious interest in physical science. Müller was a Bavarian schoolmaster of unusual ability — a doctorate from the University of Munich, an active interest in current developments in physics and mathematics, a particular enthusiasm for the new principle of the conservation of energy that had been formulated in the 1840s by Julius Mayer and Hermann Helmholtz. He taught his classes with a kind of philosophical intensity that was unusual in German secondary education, taking the position that the principle of the conservation of energy was the most important discovery in the history of physics and that the understanding of energy and its transformations was the central project of physical science. He would describe to his classes the way in which the principle of conservation linked together mechanics, heat, electricity, magnetism, and chemistry into a single coherent system, and he would, with a quiet enthusiasm that Planck never forgot, present the principle of conservation as one of the great achievements of the human mind in the understanding of nature.

The young Planck was deeply impressed. The idea of an underlying conservation principle linking all the disparate phenomena of physics — that something is preserved through all the changes of nature, that the apparent diversity of physical processes is in fact governed by an iron and exact accounting — appealed to his temperament more than any other idea he had encountered in his schooling. It gave him a first glimpse of the kind of science he would later spend his life pursuing: a science not of accumulated facts but of fundamental principles, a science that sought to find behind the appearances of the physical world the deep regularities that the human mind could grasp and could express in mathematical form. He would later say that Müller's lessons on the conservation of energy were "the first to convey to me a real sense of what physics is about," and the principle of conservation, in its more general formulation as the laws of thermodynamics, would be the subject both of his doctoral dissertation and of the long line of papers that led, by an inner logical necessity, to the discovery of the quantum.

The Choice Between Music and Physics

By the time Planck took his Abitur in the summer of 1874 he was sixteen years old and faced with the choice of a university subject. The choice was harder than it would have been for most boys of his class, because he was a musician of considerable promise as well as a mathematician. He had begun piano lessons at the age of six and had quickly shown an unusual talent. By his teens he was singing in choirs of the Munich Protestant churches, was playing the organ at services, and was an accomplished pianist with a particular gift for the chamber music of Schumann and Brahms. He had been, in his last year at the gymnasium, the principal accompanist for the school choir, and he had composed several short pieces — choral works, a piano fantasy, a song cycle on poems by Heine — that had been performed at school concerts and that his teachers had thought showed real talent.

The question of whether he should make music his profession was discussed seriously in the family. The Munich musical establishment of the 1870s was one of the most distinguished in Europe — the city was the location of Wagner's first complete cycle of the Ring (which Planck attended as a student at Bayreuth in 1876), of the Royal Bavarian Opera, of the Royal Conservatory of Music; if he had wished to pursue a musical career, Planck would have had every resource available to him. He consulted, in the spring of 1874, the kapellmeister of the Munich Royal Court Orchestra, who heard him play and who gave him a candid assessment: he was a talented amateur, but he was not, in the kapellmeister's view, a future Liszt or Brahms; he could have a respectable career as a music teacher or as a provincial church organist, but he would not be a major figure in the musical life of his country. Planck thought about this judgment for some weeks, discussed it with his parents, and concluded that he would not be content with a second-tier career in music. He would go to the university and study a subject in which he might still hope to become a figure of consequence.

The choice within the university was between philosophy, mathematics, and physics. He was attracted to all three, and the dividing lines between them were less sharp in the 1870s than they would later become. He had been, at the gymnasium, a particularly strong mathematics student, and his teacher Hermann Müller had urged him to consider physics. He took the advice. In October 1874 he matriculated at the University of Munich and registered for courses in mathematics, physics, and philosophy, with the intention of working out within the first year or two of his university course which of the three would be his principal study.

He found himself, in his first semester, disappointed by the physics that the University of Munich offered. The professor of physics at Munich was the elderly Philipp von Jolly (1809–1884), an able experimental physicist of the old school but not a man of great theoretical depth. When Planck consulted him about the prospects of a career in physics, Jolly famously discouraged him with the often-quoted (and probably apocryphal in its precise wording) remark that "the most important discoveries in physics have already been made — what remains is a matter of filling in the details to the next decimal place." Planck would later, with characteristic self-deprecating humor, observe that he was glad he had not listened to that particular piece of advice. But Jolly's broader view of physics — that the discipline was essentially complete in its principles and that the remaining work was the careful working out of consequences — was widely shared in the 1870s, and it discouraged the most ambitious young men of Planck's generation from pursuing the subject. Planck nevertheless persevered, and within a few semesters he had decided that physics, and particularly the theoretical and mathematical analysis of physical phenomena, was the field in which his abilities and his interests most naturally lay.

University Years in Munich and Berlin

Planck spent three years at the University of Munich, from the autumn of 1874 to the spring of 1877, taking the broad curriculum of mathematics, physics, and philosophy that the German universities offered to ambitious students of his class. He attended lectures by Jolly in experimental physics and by Ludwig Seidel in mathematics; he studied the philosophy of Kant under Jacob Frohschammer; he took courses in chemistry, in astronomy, and in the theoretical mechanics that was still the foundation of the German physical curriculum. He worked steadily, accumulating a sound general education in the physical sciences but without finding in Munich a mentor who could direct him toward the most important developments of contemporary research.

In the autumn of 1877, in accordance with the German student tradition of spending a portion of one's university course at a second institution, Planck transferred to the University of Berlin for a year of advanced study. The decision was, in retrospect, the most important academic choice of his life. Berlin in 1877 was, with Heidelberg and Göttingen, one of the three great German universities, and its faculty of physics included the two most distinguished physicists in the country: Hermann von Helmholtz, the formidable polymath who held the chair of physics and who was the leading figure in the German scientific establishment of the imperial era; and Gustav Robert Kirchhoff, the older theoretician who held the chair of mathematical physics and who had already done the fundamental work on spectral analysis, on the radiation of heated bodies, and on the foundations of electrodynamics. Planck spent two semesters in Berlin, the winter of 1877–78 and the summer of 1878, and the experience transformed his sense of what physics was and of what could be done within it.

The Berlin he found in those years was the bustling new capital of the German Empire, a city in the midst of an explosive growth that would, within a generation, make it one of the great cities of the world. The university occupied the old palace of Prince Heinrich on Unter den Linden, a few blocks east of the Brandenburg Gate; the physics laboratories were a short walk south, on Reichstagufer overlooking the Spree. Planck lodged in modest student rooms in the Friedrichstadt and walked each morning to the lecture halls, attending courses by Helmholtz and Kirchhoff and Karl Weierstrass (in mathematics) and the young experimentalist Heinrich Hertz, who was Helmholtz's assistant and who would within a few years discover the electromagnetic waves whose existence was predicted by Maxwell's theory.

The intellectual experience of the Berlin year was, in Planck's later assessment, distinctly mixed. Helmholtz, though widely revered, was a notoriously poor lecturer — he prepared his lectures inadequately, often appeared to be working out his thoughts in front of his audience, and lost his place in the calculations on the blackboard. Planck, who had been raised on the well-prepared and beautifully delivered lectures of his Munich teachers, was at first disappointed in the great man. He soon came, however, to see beyond the surface awkwardness of Helmholtz's classroom manner to the depth and originality of his thinking. He attended Helmholtz's seminars, found himself drawn into discussions of the foundations of mechanics, of the principle of least action, of the theoretical basis of the second law of thermodynamics; and he formed, through these contacts, the personal connection with Helmholtz that would later be decisive in his appointment to the Berlin chair.

Kirchhoff was the more impressive lecturer — his presentations were models of rigor and clarity, and his exposition of the theory of light and heat radiation, which Planck attended in the summer semester of 1878, was the most lucid systematic treatment of the subject then available. But Kirchhoff was, by his own admission, a reserved and forbidding man who did not encourage personal contact with his students. Planck would never form a close personal relationship with him, though he would in due course inherit Kirchhoff's chair at Berlin and would take up, as the central problem of his career, the very questions of blackbody radiation that Kirchhoff had first formulated in 1860.

The deeper intellectual influence on Planck during the Berlin year was, characteristically, not a teacher at all but a book. He had begun, while at Munich, to read the papers of Rudolf Clausius on the foundations of thermodynamics — the great Bonn theoretician who, between 1850 and 1865, had given the modern formulation of the second law of thermodynamics and who had introduced the concept of entropy into the vocabulary of physics. Planck found in Clausius's clean, austere, mathematically rigorous treatment of the second law exactly the kind of physics that engaged his temperament. The first law of thermodynamics, the conservation of energy, was the principle that Hermann Müller had taught him at the gymnasium; the second law, the law of the increase of entropy, was its mysterious and consequential companion. Where the first law spoke of a quantity that was preserved through all the transformations of nature, the second law spoke of a quantity that increased — a quantity whose increase gave the direction of physical processes, that distinguished past from future, that made the cooling of a hot body and the warming of a cold one a phenomenon governed by an inviolable mathematical principle. Planck read Clausius's papers with rapt attention through the Berlin winter, and by the time he returned to Munich in the summer of 1878 he had decided that the foundations and consequences of the second law of thermodynamics would be the subject of his doctoral thesis.

Doctoral Thesis on the Second Law of Thermodynamics

Planck returned to the University of Munich in the autumn of 1878 to begin work on his doctoral dissertation. The dissertation, submitted in the spring of 1879 and defended in July of that year, was titled "On the Second Law of the Mechanical Theory of Heat" — a dense, mathematically careful treatment of the foundations of the second law of thermodynamics with particular attention to the question of the precise mathematical statement of entropy increase and to the conditions under which various physical processes could be considered reversible or irreversible. It was a notably independent piece of work for a twenty-one-year-old doctoral candidate. Planck took the position, against several of the leading authorities of his day, that the second law of thermodynamics was a strictly universal and rigorously valid principle of physics, on the same logical footing as the first law, and that the various proposals then in circulation to weaken or qualify the second law — by allowing exceptions to it in microscopic processes, by deriving it as a statistical regularity rather than an exact principle, or by attempting to reduce it to mechanical considerations — were all in error. The position would, ironically enough, be one that he would later have to abandon, but it was the position from which his entire subsequent career in physics would unfold.

The dissertation was received politely by the Munich faculty but with little enthusiasm. Jolly, the experimental physicist, considered the question rather too abstract for his taste; the mathematician Ludwig Seidel found the mathematical apparatus competent but unremarkable; the philosopher Frohschammer thought the work technically beyond his competence. The thesis was accepted, Planck was awarded the doctorate summa cum laude in July 1879, and the document was published in the standard form of the Munich dissertations of the time. It received almost no attention from the wider physics community. Clausius, to whom Planck sent a copy with a respectful covering letter, did not reply. Helmholtz, who had probably read it, made no public comment. The dissertation that contained Planck's first sustained scientific contribution lay unread on the shelves of the German university libraries, and Planck would later observe with characteristic dry humor that the work had probably been read only by the members of his dissertation committee and by his own family.

He did not, however, lose confidence in the importance of his subject. He continued, in the year after his doctorate, to work on questions in thermodynamics, and in 1880 he submitted to the University of Munich a Habilitationsschrift — the second dissertation required for permission to teach as a Privatdozent — on the equilibrium states of isotropic bodies at various temperatures. The Habilitation thesis was a more substantial piece of work than the doctoral dissertation, applied the principles of thermodynamics to a variety of specific physical systems, and showed clearly that the young Planck had mastered the technical apparatus of his discipline. The Habilitation was accepted in the summer of 1880, and in October of that year, at the age of twenty-two, Planck was qualified to teach at the University of Munich as a Privatdozent — an unpaid lecturer whose income depended on the fees of his students and whose principal hope was to attract sufficient attention to be called eventually to a regular professorship.

Early Academic Struggles and the First Appointments

The years 1880 to 1885 were the most professionally difficult of Planck's career. He was a Privatdozent in Munich, lecturing on thermodynamics and on mathematical physics to small audiences of students who were not particularly interested in the rather abstract subjects he taught. His income from student fees was modest; he supplemented it by tutoring and by occasional translation work; he lived in the family apartment in the Briennerstrasse with his parents and younger siblings. He continued to publish papers on thermodynamics — on the dissociation of gases, on the equilibrium of dilute solutions, on the thermodynamics of chemical reactions — and these papers were of high quality, but they attracted little attention. The leading German physicists of the day — Helmholtz, Kirchhoff, Clausius, Boltzmann — were occupied with their own problems and showed little interest in the work of a young provincial Privatdozent.

The frustration of these years was deepened by Planck's growing realization that the position he had taken in his doctoral thesis — the strict and exact universality of the second law of thermodynamics — was being challenged by the most original work of the period. Ludwig Boltzmann in Vienna had been developing, through the late 1870s and the 1880s, a statistical interpretation of the second law in which the increase of entropy was treated not as an exact and inviolable principle but as a statistical regularity following from the random motions of large numbers of molecules. On Boltzmann's view, the second law was not a fundamental principle but a derived consequence of the mechanics of many-particle systems; the entropy of a gas could in principle decrease, but the probability of such a decrease was so vanishingly small that it could be ignored in practice. The position was, in its mathematical foundations, brilliantly original, and it pointed toward what would become the modern statistical mechanics. But Planck was, at first, deeply unsympathetic to it. The statistical foundation seemed to him to weaken the second law in a way that compromised its dignity as a fundamental principle of physics; he resisted Boltzmann's approach for nearly two decades before, under the pressure of the blackbody problem, he would be forced to adopt it.

The breakthrough in his professional career came in the spring of 1885. The University of Kiel — the town of his birth — had a vacancy for an extraordinary professor of theoretical physics, and a candidate was needed who would not be exorbitantly expensive (Kiel was a provincial university with limited resources) and who would be willing to take up the post on relatively short notice. Through the recommendations of his Munich teachers and of Helmholtz, with whom he had maintained sporadic correspondence since his Berlin year, Planck was offered the position. He accepted at once. In May 1885 he moved north to Kiel, took up residence in the same town in which he had been born twenty-seven years before, and began teaching as a regularly paid professor with the security and the social standing that the German academic system reserved for its tenured ranks.

The Kiel years (1885–1889) were the formative years of his mature scientific career. He produced a steady stream of papers on thermodynamics and on the physics of dilute solutions; he wrote a small monograph, The Conservation of Energy (1887), that won the prize offered by the philosophical faculty of the University of Göttingen for the best essay on the history and foundations of the conservation principle; he established his reputation as a thoughtful and rigorous theoretical physicist of the German school. The Kiel position was modest in salary but offered him the leisure to do the work that would, within five years, lead to the call to Berlin.

It was during the Kiel years, too, that Planck's personal life acquired its first lasting form. He had been engaged for several years to Marie Merck, the daughter of a Munich banking family who had been a childhood friend of his sister Adele and whom he had courted with quiet persistence through the long years of his Munich Privatdozent struggles. Marie Merck was a young woman of warm and lively temperament, with an excellent musical education and a gift for languages, who had waited patiently through the years of Planck's professional uncertainty for him to be in a position to support a family. With the Kiel professorship secured, they were married in March 1887, in the Lutheran church of Munich, in a ceremony attended by the assembled families and by a small number of academic friends. They moved together to Kiel and set up housekeeping in a modest professorial villa near the university. Their first child, Karl, was born in 1888.

The Chair at Berlin and the Inheritance of Kirchhoff

In October 1887, Gustav Kirchhoff died in Berlin at the age of sixty-three. The chair of theoretical physics at the University of Berlin — the most distinguished theoretical position in Germany and one of the two or three most distinguished in the world — became vacant, and the question of his successor was immediately taken up by the Berlin faculty and by the Prussian ministry of culture. The first choice of the faculty was Ludwig Boltzmann of Vienna, the most original theoretical physicist of the German-speaking world. Boltzmann was approached, but for reasons of family and of his deep attachment to Vienna he declined the call. The faculty then considered Heinrich Hertz, the brilliant experimentalist who had just (in late 1887 and 1888) confirmed the existence of Maxwellian electromagnetic waves by his experiments at Karlsruhe; but Hertz was at this point an experimentalist rather than a theoretician, and the chair was specifically designated as theoretical. The faculty's third choice was Max Planck of Kiel.

The decision to call Planck to Berlin was, by every account, primarily the work of Helmholtz. Helmholtz had read with attention Planck's prize essay on the conservation of energy; he had been impressed by Planck's papers on thermodynamics; he had remembered the quiet, careful, well-mannered young man who had attended his Berlin lectures a decade before; and he proposed Planck's name to the ministry as the candidate of best fit for the position. The proposal was accepted. In November 1888 Planck was offered the call to Berlin as extraordinary professor of theoretical physics, with the promise of promotion to ordinarius (the full professorship) within a year or two if he proved equal to the responsibilities of the post. He accepted at once. In the spring of 1889, after the Kiel summer semester had been concluded, he moved with Marie and the infant Karl to Berlin and took up his duties at the university in October of that year.

The Berlin appointment transformed Planck's life. He was now, at the age of thirty-one, the holder of the most distinguished theoretical chair in German physics. He was a colleague of Helmholtz, of Werner von Siemens, of Emil du Bois-Reymond, of the leading lights of the imperial German scientific establishment. He was, within a few years, elected to the Prussian Academy of Sciences (in 1894), and he was given the responsibility of editing the great journal Annalen der Physik — the journal that, between 1900 and 1920, would publish the foundational papers of quantum theory and relativity, many of them through Planck's own editorial selection. He was, by 1892, promoted to ordinarius professor with a substantial salary and a permanent house in the academic quarter of the new capital. He was settled, for the next four decades, in the institution that would be the center of his professional life.

The Plancks took a large apartment in the Grunewald, the wooded suburb west of the city center where the Berlin academic and professional class was beginning to settle in the new villas of the Wilhelmine boom. They were soon joined in the household by Marie's elder sister Helene, who would live with them as housekeeper and companion through the years of Marie's pregnancies. Three more children arrived in quick succession: Erwin in 1893, the twin daughters Grete and Emma in 1889 (born in fact in Kiel and brought to Berlin as infants — there is some dating confusion in the literature, but the twins were born in 1889 and Erwin in 1893), and the youngest son Hermann in 1893 as well. The family settled into the rhythm of professorial life: lectures in the morning, work in the study or laboratory in the afternoon, music in the evenings, weekend walks in the Grunewald forest, summer holidays in the Alps. Marie maintained the household with the efficient devotion of the wife of a German academic of the imperial period; the children were educated at home and at the local gymnasium; the Plancks became one of the established academic families of Wilhelmine Berlin.

The Problem of Blackbody Radiation

The scientific problem that would consume Planck's attention through the 1890s and the early 1900s — and that would lead, almost against his will, to the discovery of the quantum — was the problem of blackbody radiation. The problem had been first clearly formulated by Kirchhoff himself in 1859 and 1860, in a series of papers on the relation between the emission and absorption of radiation by heated bodies. A blackbody, in Kirchhoff's idealized formulation, is a body that absorbs all radiation that falls upon it (regardless of wavelength, regardless of angle) and that, when heated, emits radiation of a characteristic spectrum that depends only on its temperature. The blackbody is in this sense the perfect emitter and the perfect absorber, and the spectrum of its radiation — the function relating the intensity of the emitted radiation to the wavelength and to the temperature — is a universal function of nature, independent of the material of the body or of any other physical characteristic of the source. Kirchhoff had recognized in 1860 that the determination of this universal function was one of the central problems of theoretical physics, and he had challenged the physicists of his generation to derive the function from first principles.

The challenge had been taken up by the most distinguished physicists of the second half of the nineteenth century. Boltzmann, in a paper of 1884, had derived from thermodynamic considerations the total energy radiated by a blackbody per unit area per unit time — the famous Stefan-Boltzmann law, which states that the total radiated power per unit area is proportional to the fourth power of the absolute temperature. Wilhelm Wien, then a young physicist at the Physikalisch-Technische Reichsanstalt in Berlin, had derived in 1893 the so-called Wien displacement law, which states that the wavelength of maximum emission is inversely proportional to the absolute temperature. By 1896, Wien had gone further and had proposed, on the basis of a heuristic argument from kinetic theory, a definite functional form for the entire spectral distribution — the so-called Wien distribution law, which expressed the spectral energy density as a particular function of the frequency and the temperature.

The Wien distribution law fitted the experimental data extremely well for the short-wavelength (high-frequency) portion of the spectrum. By the late 1890s, with the development of increasingly sensitive bolometers and the construction of experimental cavities at well-controlled temperatures, the empirical data on blackbody radiation had become very precise, and the Wien law appeared to be a satisfactory description of the spectrum. The principal experimental work was being done in Berlin at the Reichsanstalt, the national physical and metrological laboratory that had been established in 1887 under the direction first of Helmholtz and then of Friedrich Kohlrausch. Otto Lummer and Ernst Pringsheim, two of the principal experimentalists at the Reichsanstalt, had constructed in the 1890s a series of cavity radiators that approached the ideal blackbody as closely as the technology of the period allowed, and they had measured the spectrum of their cavities with unprecedented precision.

Planck took up the theoretical analysis of blackbody radiation in the early 1890s, partly as an extension of his thermodynamic interests and partly as a problem that lay at the boundary of thermodynamics and electrodynamics — exactly the kind of foundational issue that engaged his temperament. His approach was characteristic. He represented the contents of a blackbody cavity as a collection of small, harmonically oscillating electrical resonators of varying frequencies. Each resonator could, by virtue of its accelerated electrical motion, absorb and emit electromagnetic radiation. The equilibrium between the resonators and the radiation field would, by thermodynamic argument, determine the spectrum of the radiation. The problem reduced to the question of how to assign an average energy to a resonator of given frequency at a given temperature, and from there the spectrum of the radiation could be computed by standard electrodynamic methods.

Through the late 1890s, Planck published a series of papers on the thermodynamics of resonators and on the foundations of the second law as applied to radiation processes. The work was meticulous, deeply mathematical, and conducted with the slow, patient thoroughness that was Planck's characteristic style. By 1899 he had reached the conclusion that the Wien distribution law could be derived from the thermodynamic properties of the resonators on the assumption of a particular relation between the entropy of a resonator and its energy. The derivation was elegant, and it appeared to settle the question of the blackbody spectrum on a thermodynamic basis. Planck was, by the end of 1899, confident that he had found a fundamental theoretical foundation for the empirical Wien law and that the problem of blackbody radiation was essentially solved.

The Interpolation Formula of October 1900

The triumph was short-lived. In the spring and summer of 1900, the Reichsanstalt experimentalists Lummer and Pringsheim, working with longer-wavelength (infrared) radiation than had previously been studied, found that the Wien distribution law systematically failed to describe the spectrum at low frequencies. The measured intensity at long wavelengths was higher than the Wien law predicted, and the discrepancy grew with increasing wavelength and increasing temperature. By October 1900, the experimental position had become clear: the Wien law was an excellent approximation at high frequencies but failed badly at low frequencies, and a new theoretical description of the spectrum was needed.

The new measurements were communicated to Planck personally by Heinrich Rubens, another Reichsanstalt experimentalist who had been making particularly precise measurements at the longest wavelengths then accessible. On the afternoon of Sunday, 7 October 1900, Rubens called at Planck's house in the Grunewald to discuss the new results over coffee. He showed Planck the measurements and explained in detail the systematic deviation of the data from the Wien law. Planck, who had been working that morning on a related theoretical question, listened with the close attention that the news required. After Rubens had left, he set to work on the problem of finding a formula that would fit the new data.

By that evening — within a few hours, by his own later account, of Rubens's departure — Planck had constructed an interpolation formula. He had been thinking about the relation between the entropy and the energy of a resonator. The Wien law followed from a particular assumption about the second derivative of the entropy with respect to the energy. Planck found, by trial, that if he assumed a slightly different functional form for that second derivative — a form that interpolated between the Wien limit at high frequencies and a different limit (the so-called Rayleigh limit) at low frequencies — he obtained a formula that fitted the new data with remarkable precision. He wrote the formula on a postcard and mailed it to Rubens the same evening. Rubens compared it with his measurements over the following few days and reported back to Planck that the formula fitted the data within experimental error across the entire spectral range.

Planck presented the new formula to the German Physical Society at its meeting of 19 October 1900, in a short paper titled "On an Improvement of Wien's Radiation Law." The paper was modest in its claims. Planck described the empirical formula, showed that it fitted the experimental data better than the Wien law, but did not attempt at this point to derive it from first principles. He left the derivation for a later occasion. The Berlin physicists who heard the paper were impressed by the empirical fit but did not at first appreciate the theoretical significance of what they had been shown. The interpolation formula, taken simply as an empirical fit to the data, was a useful piece of work but did not, on its face, signal a revolution.

The Quantum Hypothesis of December 1900

Planck himself, however, could not be content with an empirical formula. From the moment he had presented the interpolation in October, he had set himself the task of deriving the formula from physical principles. The derivation would be the test of whether the formula was merely a happy accident or whether it pointed to something fundamental about the nature of radiation and of heat. He spent the following six weeks in what he later called the most intensive period of theoretical work of his life. He read and reread Boltzmann's statistical-mechanical papers of the 1870s and 1880s. He worked through the mathematical derivation of the second law of thermodynamics in its statistical form. He tested various hypotheses about the nature of the resonators and about the way in which their energy was related to their entropy.

The decisive step came, by his own later testimony, in the early days of December 1900. He had been led, by the logic of his derivation, to adopt — for the first time in his career — the Boltzmann statistical interpretation of entropy. The entropy of a system, on Boltzmann's formulation, was proportional to the logarithm of the number of microscopic configurations that produced a given macroscopic state — the famous formula S = k log W, where W is the number of configurations and k is what would later be called Boltzmann's constant. To apply Boltzmann's formula to a collection of resonators, one had to count the number of ways in which a given total energy could be distributed among the resonators of different frequencies. The counting, however, only worked if the energy was assumed to come in discrete portions rather than in continuous quantities — for otherwise the number of possible distributions would be infinite, and the formula S = k log W would be meaningless.

Planck therefore made what he later called "an act of desperation" — a desperate mathematical assumption that he hoped would yield the correct interpolation formula and that he could later, perhaps, justify by a more satisfactory argument. He assumed that the total energy of the resonators of a given frequency was distributed among them in discrete portions of magnitude ?, where ? was proportional to the frequency — ? = h?, with h a constant of proportionality. He worked out the number of possible distributions of these discrete energy portions among the resonators by a standard combinatorial argument, took the logarithm to obtain the entropy, and derived from the entropy by thermodynamic argument the spectral distribution of the radiation. The result was exactly the interpolation formula he had constructed in October. The constant h emerged from the derivation as a fundamental constant of nature, whose numerical value he could determine from the experimental data: h was approximately 6.55 × 10?²? erg-seconds, an extraordinarily small number that nevertheless represented the fundamental scale of the discreteness of the energy distribution.

Planck presented the derivation to the German Physical Society at its meeting of 14 December 1900, in a paper titled "On the Theory of the Energy Distribution Law of the Normal Spectrum." The paper introduced into the equations of physics, for the first time, the constant that would later be called Planck's constant — the constant that, together with the velocity of light c and the gravitational constant G, would be one of the three fundamental constants by which physicists characterize the elementary scales of nature. The introduction of h marked the beginning of quantum theory and the end of the long classical period that had begun with Newton in 1687. The date 14 December 1900 has been called, with some justice, the birthday of modern physics.

THE DERIVATION AND THE MEANING OF h

What Planck had done, in his December 1900 paper, was simultaneously a small and a vast thing. On the small side, he had constructed a clever combinatorial derivation of an empirical formula. On the vast side, he had — by the assumption that the energy of his resonators could take only discrete values of magnitude h? — introduced into theoretical physics a hypothesis that was incompatible with the foundations of classical mechanics and classical electrodynamics. In classical physics, the energy of an oscillator could take any continuous value; nothing in the equations of Newtonian mechanics or of Maxwellian electrodynamics suggested any discrete restriction on the energies of physical systems. Planck's hypothesis broke that classical principle in a way that he himself did not at first appreciate but that would, within the next thirty years, transform every department of physical theory.

Planck, in 1900, did not believe that he had discovered anything quite so revolutionary. He thought of the discretization of resonator energy as a mathematical device, perhaps a temporary expedient, that he hoped would eventually be replaced by a more satisfying classical derivation. He spent the better part of the next fifteen years trying to find such a classical derivation. He examined the question of whether the discretization was a real property of nature or merely an artifact of his particular method of counting; he investigated whether the same result could be obtained by some other route that avoided the assumption of discrete energy; he probed the relation of the new formula to the various classical theories of radiation that had been proposed by Lord Rayleigh, by James Jeans, and by his own younger Berlin colleague Albert Einstein. Through all of these investigations he held to the view that the quantum was, at bottom, a calculational device that would in due course be superseded by a continuous classical theory of the radiation field.

He was wrong. The quantum, as Einstein would show in 1905 and as the subsequent development of physics would confirm beyond reasonable doubt, was not a calculational device but a deep fact about the structure of nature. Energy in microscopic systems is, in fact, quantized; the equations of classical physics, which had served so well for two and a half centuries, were merely the large-scale approximation to a deeper underlying theory in which discreteness, probability, and the uncertainty principle were ineliminable features. The path from Planck's December 1900 paper to the mature quantum mechanics of Heisenberg and Schrödinger in 1925 and 1926 was a long and tortuous one, and Planck himself, deeply conservative in his physical instincts, did not always grasp the implications of his own discovery. But the discovery had been made, and physics would never again be the same.

Einstein and the Light Quantum

The first physicist to grasp the full implications of Planck's hypothesis was the young Albert Einstein, then a clerk at the Swiss Patent Office in Bern, who in the spring of 1905 published a paper titled "On a Heuristic Point of View Concerning the Production and Transformation of Light." Einstein took up Planck's hypothesis of discrete energy elements, generalized it beyond the resonators of the blackbody to electromagnetic radiation itself, and proposed that light consisted not of continuous waves (as the Maxwell theory required) but of discrete particles or quanta — "light quanta," as he called them, that we would later call photons — each of energy h?. He showed that this hypothesis explained at once a number of experimental phenomena that classical electrodynamics had been unable to account for: the photoelectric effect, in which light incident on a metal surface releases electrons of a definite kinetic energy that depends on the frequency but not on the intensity of the incident radiation; the photochemical equivalence law; and (with some additional argument) the spectroscopic series of the lighter elements.

Planck, who as editor of Annalen der Physik received Einstein's paper and approved its publication, was deeply impressed by the originality and the boldness of the work but was also deeply uneasy about its implications. He could accept the quantization of energy in the resonators of his cavity, but he could not accept the quantization of the radiation field itself. Light, on the Maxwell theory, was a wave phenomenon — it exhibited interference, diffraction, polarization, all the unmistakable properties of waves — and to declare that it was actually composed of particles seemed to Planck a step backward in physics, a return to the corpuscular theory of light that had been definitively overthrown by Young, Fresnel, and Maxwell in the nineteenth century. He wrote to Einstein, with characteristic courtesy, that he found the paper "of the greatest interest" but that he could not yet accept its conclusions. Through the following years he would maintain a position of partial acceptance — he agreed that energy was somehow quantized in its interaction with matter, but he believed that the radiation field itself remained continuous.

The disagreement between Planck and Einstein on the light quantum was, in retrospect, the first of the great disputes within the developing quantum theory. Both men maintained their positions with the courtesy and the mutual respect that characterized their long friendship — Einstein would be Planck's colleague at the Prussian Academy from 1914, and the two men would correspond and meet regularly throughout the next thirty years — but the underlying difference was real and deep. Planck wanted to preserve as much of classical physics as possible; Einstein, increasingly, wanted to follow the quantum logic wherever it led. The history of physics in the first two decades of the twentieth century would be the history of Einstein's view gradually prevailing over Planck's.

The Struggle with the Quantum and Planck's Resistance

The decade between 1905 and 1915 was, for Planck, a period of intense and often painful struggle with the implications of his own discovery. He continued to publish papers on the theory of radiation, on the foundations of thermodynamics, on the relation of the quantum hypothesis to the rest of physical theory. He produced, in 1906, the textbook on the Theory of Heat Radiation that became the canonical reference work on the new subject. He worked, through these years, on what he called the "second quantum theory" — a series of papers in which he tried to develop a version of the quantum hypothesis in which only the emission of radiation by the resonators was quantized, while absorption remained continuous. The theory was elegant in its mathematics but unsuccessful in its physics — it failed to account for the observed phenomena and was abandoned, by Planck himself, around 1913 in favor of a more thoroughgoing quantum treatment.

Through these years Planck served as one of the principal interpreters of the quantum hypothesis to the broader scientific public. He gave lectures on the new physics at Vienna in 1908, at Columbia in 1909 (where he delivered the so-called Columbia Lectures, published in 1910 as Eight Lectures on Theoretical Physics — a series that remained for a generation the most lucid systematic introduction to the new physics available in any language), at the Solvay Congress in Brussels in 1911. He was, by virtue of his position at Berlin and of the prestige of his discovery, the leading spokesman in Germany for quantum theory, and his calm, measured, conservative exposition of the new physics did much to gain acceptance for ideas that were, in their inner content, radically subversive of the classical worldview that he himself had been raised in.

He was, throughout these years, the slowest of the great quantum theorists to give up on the classical foundation. The young men who were doing the most original work on quantum theory in the second decade of the century — Einstein, Bohr, Sommerfeld, Born, Heisenberg, Pauli — were prepared, with varying degrees of enthusiasm, to abandon the deterministic and continuous classical worldview in favor of the new framework that the quantum was making necessary. Planck held back. He could see the experimental evidence as clearly as anyone; he could follow the mathematics as well as any of his younger colleagues; but he could not bring himself, until quite late in his career, to accept that the classical worldview had been definitively overthrown. He continued to hope, into the 1920s, that some way would be found to reconcile the quantum results with the underlying classical principles of continuity and determinism. He was, in this respect, the most poignant of the quantum revolutionaries — the man who had begun the revolution and who spent the rest of his life trying, with declining success, to limit its scope.

The Solvay Conferences and the New Physics

In October 1911 the first of the great Solvay Conferences of physics opened in Brussels under the chairmanship of Hendrik Lorentz of Leiden. The conference had been organized by the German chemist Walther Nernst at the expense of the Belgian industrialist Ernest Solvay, who had made a fortune in the soda industry and who wished to use a portion of his wealth to support fundamental scientific research. The first conference was devoted to the topic of "the theory of radiation and the quanta," and its participants included the most distinguished theoretical and experimental physicists of Europe: Lorentz, Planck, Einstein, Madame Curie, Sommerfeld, Wien, Rubens, Rutherford, Jeans, Poincaré, and several others. The conference lasted a week, and the discussions ranged across the foundations of the new quantum physics with a depth and a candor that the published proceedings preserved for the scientific public.

Planck was, at the 1911 Solvay Conference, a senior figure rather than a leading participant in the discussions. He was now fifty-three, the established occupant of the most distinguished chair in German physics, the man whose hypothesis of 1900 was the subject of the meeting. But the most active discussions were carried on by the younger men — by Einstein, by Sommerfeld, by Nernst, by Lorentz — and Planck listened more than he spoke. He maintained his position that the quantum was a hypothesis that needed further investigation but that should not be taken as definitively established; he resisted the more radical proposals of Einstein and his collaborators. The conference ended without consensus, but with a clearer sense than before of the magnitude of the problems that quantum theory was raising.

The Solvay Conferences would continue at irregular intervals through the rest of Planck's life — there would be conferences in 1913, 1921, 1924, 1927, 1930, 1933, and 1948 (the last after his death) — and Planck would attend most of them, though increasingly as a senior elder statesman of the discipline rather than as an active participant in the technical discussions. The most famous of the Solvay Conferences, that of 1927, would witness the great debate between Einstein and Bohr over the interpretation of the new quantum mechanics; Planck attended but took no active part in the dispute, finding himself, by that point, somewhat outside the technical apparatus of the new theory but unwilling to take sides between the two friends whose positions he understood and partially shared.

Marriage to Marie Merck

The personal life that had been established in Kiel in 1887 and that had continued through the early Berlin years was, by the time of the great scientific discoveries of 1900, a settled and happy domestic establishment. Marie Planck managed the household with the warm efficiency that her husband relied upon. The four children — Karl, Erwin, Grete, Emma (Hermann had died as an infant; some confusion in the secondary sources arises here because Hermann is the name both of Planck's elder brother who died in 1906 and a name that occasionally appears in early biographies; the surviving four children of Max and Marie were Karl, the twins Grete and Emma, and Erwin) — were growing up in the comfortable bourgeois atmosphere of the Grunewald villa. The household kept the kind of musical, scholarly, religiously serious atmosphere that the Plancks had themselves grown up in. There were regular family concerts in the parlor, in which Max played the piano and Marie sang; there were Sunday morning church services at the local Protestant church; there were long summer holidays in the Bavarian Alps, where the family rented a chalet at Murnau and where the children learned to climb the mountains that would, for Max in particular, remain a lifelong love.

The happiness of these years was cut short by tragedy. In the late summer of 1909 Marie Planck developed a persistent cough that her doctors diagnosed, after some weeks of uncertainty, as pulmonary tuberculosis. The disease progressed rapidly, despite a course of treatment at a Swiss sanatorium in the autumn of 1909, and on 17 October 1909 Marie Planck died at the age of forty-eight, twenty-two years after her marriage and one day before the twentieth anniversary of her husband's arrival in Berlin to take up the chair of theoretical physics. She left her husband devastated and her four children, ranging in age from twenty-one to sixteen, motherless. Marie's elder sister Helene, who had lived with the Plancks as housekeeper through the years of Marie's pregnancies, stepped into the management of the household, and the family struggled to reconstitute itself around the absence at its center.

Planck, in the months after Marie's death, was reported by his friends to be a man transformed — quieter than usual, more withdrawn, more visibly burdened by the responsibilities of his position. He did not, however, allow his grief to interrupt his professional work. He continued to lecture, to write, to attend the meetings of the Academy and of the Physical Society. He had been raised in a tradition in which personal sorrow was borne in private and in which the professional obligations of a serious man were not allowed to slacken under the pressure of private misfortune. His character, in this respect, was that of the Prussian academic of the imperial period at its most disciplined and most reticent. But the private letters of these years, particularly those to his old friend Helmholtz (who would die in 1894) and to his sister Adele, show clearly the depth of the wound.

World War I and the Manifesto of the Ninety-Three

In August 1914 the long European peace that had held since the Franco-Prussian War of 1870–71 collapsed in the catastrophe of the First World War. The German declaration of war on Russia on 1 August, the invasion of Belgium on 4 August, the British declaration of war on Germany on the same day — events that within ten days had drawn the whole of Europe into a conflict that no one in 1913 had thought possible — found the German academic community as deeply unprepared as the rest of the country. Planck, like the great majority of his colleagues, supported the German war effort. He believed, in the autumn of 1914, that Germany had been forced into the war by the aggression of its enemies and that the country was fighting a just defensive struggle for its existence. He would, in the four years that followed, gradually come to a more critical view, but in the first months of the war he was a German patriot of the conventional type.

The most visible expression of his patriotism, and the one that he would later most deeply regret, was his signature on the so-called Manifesto of the Ninety-Three — "An die Kulturwelt!" or "To the Civilized World!" — an open letter signed in October 1914 by ninety-three of the most distinguished German scholars, scientists, and intellectuals. The manifesto denied, in the face of well-documented Allied accounts, that German troops had committed atrocities in Belgium, defended the German invasion of that country as a military necessity, and asserted the unity of German culture with the German war effort. The signatories included nearly every prominent figure in German academic life: Adolf von Harnack, the great church historian; Wilhelm Wundt, the founder of experimental psychology; Wilhelm Roentgen, the discoverer of X-rays; Fritz Haber, the chemist; and many others. Planck signed.

He signed, by his own later account, hastily and without having read the manifesto in detail. He had been approached at his office by the organizers (the writers Ludwig Fulda and Hermann Sudermann), shown the document, and asked to add his name to the list of distinguished signatories. He did so, and the manifesto was published in October 1914 to immediate international scandal. The Allied press treated it as evidence of the moral collapse of German intellectual life under the pressure of war; foreign academics broke off correspondence with their German colleagues; the manifesto became, for the next thirty years, a symbol of the alignment of German academic culture with German militarism.

Planck would, by the spring of 1915, come to regret his signature deeply. He had not, on his later reading of the document, agreed with all of its assertions, and he had not realized at the time of his hasty signing how the document would be received outside Germany. He attempted, in 1915 and 1916, to withdraw his signature, but the political conditions of wartime made retraction difficult. He would, after the armistice, write a personal letter to each of his foreign scientific correspondents apologizing for his signature on the manifesto and expressing his regret at having allowed himself to be drawn into a piece of nationalist propaganda. He would say, in the 1920s, that it was the worst single act of moral judgment in his life. The episode reveals both the moral seriousness with which Planck approached his public obligations and the considerable pressure that the patriotic mood of August 1914 exerted on even the most measured of German academics.

The Loss of Karl Planck

The personal cost of the First World War to the Planck family was harrowing. The eldest son, Karl, had been twenty-six in 1914 and had volunteered for military service in the first weeks of the war. He was commissioned as a junior officer in an infantry regiment and was sent first to the eastern front and then, in the autumn of 1915, to the western. In the spring of 1916 his regiment was committed to the great German offensive at Verdun, which had been launched in February by the German chief of staff Erich von Falkenhayn with the explicit aim of bleeding the French army to death in a battle of attrition before the strategic fortress of Verdun. The battle of Verdun was, by every measure, the most terrible single engagement of the war: it lasted ten months, consumed nearly a million casualties on both sides, and ended in February 1917 with the German lines back almost exactly where they had started. Karl Planck was killed at Verdun on 16 May 1916, in one of the obscure local actions that made up the larger battle.

The news reached the Berlin household some weeks later through the standard military channels — a brief letter from his commanding officer, followed by the personal effects sent back through the army postal service. Planck was at his office at the university when the news arrived. He came home, spoke quietly with his sister-in-law Helene about the news, and went into his study. He emerged some hours later with the composure that his family had come to expect of him in moments of grief. He continued his work; he attended his lectures and his meetings of the academy; he wrote to his foreign scientific correspondents to inform them of his loss. The private letters of these months, however, show a man whose interior had been shattered. He wrote to his sister Adele that "the worst is bearable only with the help of God, and I have come to understand that one must take the strength of others, even from those whose presence one has lost, as well as from God." It was the kind of sentence that Planck wrote rarely and that suggests, more clearly than any of his more public statements, the depth of his religious feeling and the depth of his pain.

The remaining war years were, for the Plancks, a slow accumulation of further losses. The twin daughter Grete, who had married the Heidelberg classical philologist Ferdinand Fehling in 1916, became pregnant in early 1917 and died in childbirth in May of that year at the age of twenty-eight; her infant daughter survived. The widower Fehling, in a strange but not at the time unusual arrangement, married the surviving twin Emma in early 1918, and Emma in turn became pregnant in late 1918. She died in childbirth in November 1919, also at twenty-eight, also leaving a surviving infant daughter. The two granddaughters — Grete's daughter (also called Grete) and Emma's daughter (Emma the younger) — would be raised partly by Fehling and partly by their grandfather in the Grunewald house, and they would be a great comfort to Planck in the long years of his widowhood and old age. But the loss of the two daughters, on top of the loss of Karl, was a blow from which the family never fully recovered. Of the four children that Marie had borne and that had survived infancy, only two — Erwin and Hermann — were still alive at the end of 1919, and even of these only Erwin would be physically robust enough to face the political dangers of the years that lay ahead.

The Nobel Prize of 1918

In the midst of these family tragedies, in November 1918, came the announcement of the Nobel Prize in Physics for the year 1918. The award had been held over from the year itself because of the wartime difficulties of holding the Stockholm ceremonies, and it was formally announced in 1919 with the citation "for the services he rendered to the advancement of Physics by his discovery of energy quanta." The prize was the most important formal recognition that Planck would receive in his lifetime, and it confirmed, on the international stage, the centrality of his work to the development of twentieth-century physics.

The formal lecture, however, could not be delivered until June 1920, when the disrupted scientific intercourse between Germany and the Allied countries had been at least partially restored and when Planck was able to travel to Stockholm. He delivered the Nobel Lecture on 2 June 1920, in a packed lecture hall at the Royal Swedish Academy of Sciences, in the presence of the king of Sweden and of the assembled Swedish scientific establishment. The lecture, titled "The Origin and Development of the Quantum Theory," was a model of the kind of public exposition at which Planck excelled — measured in tone, careful in its historical reconstruction, generous in its acknowledgment of the contributions of others, philosophically reflective on the meaning of the developments he had set in motion. He told the story of his early thermodynamic work, of the blackbody problem, of the construction of the interpolation formula, of the December 1900 derivation; he traced the subsequent development of quantum theory through the work of Einstein, Bohr, Sommerfeld, and the others; and he closed with an extended meditation on the philosophical meaning of the new physics — on its implications for the relation of cause and effect, for the deterministic worldview of classical science, for the future of physical theory.

The Stockholm lecture would be the most widely circulated of Planck's public statements on the quantum theory, and it would, in its German and English versions, become one of the standard introductions to the new physics for educated readers throughout the world. Planck returned to Berlin with the Nobel medal, with the prize money (which the Swedish Academy paid in Swedish kronor — a fortunate currency choice, given the catastrophic German inflation that was about to begin), and with a heightened sense of the historical significance of the work that he had been carrying on, almost in solitude, through the previous twenty years.

The Weimar Years and Planck as Dean of German Science

The Germany to which Planck returned from Stockholm in the summer of 1920 was not the Germany in which he had grown up. The Wilhelmine Empire had collapsed in November 1918, the Kaiser had abdicated and fled to the Netherlands, the Treaty of Versailles had been signed in June 1919 under conditions of acute national humiliation, the Weimar Republic had been proclaimed at Weimar in February 1919 with a constitution that no major political faction was wholly committed to defend. The country was wracked by political violence — the Spartacist uprising of January 1919, the Kapp Putsch of March 1920, the assassination of foreign minister Walther Rathenau in June 1922 — and was sliding, by 1922, into the hyperinflation that would, by the autumn of 1923, render the German currency worthless and devastate the savings of the German middle class.

For Planck and for the academic class to which he belonged, the years 1919 to 1923 were a period of acute personal and professional difficulty. His pension and his savings, denominated in the depreciating mark, lost most of their value in the inflation. The Berlin academic establishment was harassed by demands from the new ministry of culture for democratic reforms that the conservative academic majority resisted. The international scientific community, which had broken off relations with German science during the war and which was slow to restore them after the armistice, treated German scholars with a coldness that wounded Planck personally and that he worked patiently to overcome. He was active, through the 1920s, in the reconstruction of international scientific relations — he wrote letters of explanation and apology to his foreign colleagues, he organized the participation of German physicists in the international scientific congresses that were being slowly resumed, he served on the executive council of the International Council of Scientific Unions when German science was at length readmitted in 1926.

Within Germany, Planck became through the 1920s the most influential single figure in the organization of physical science. He held simultaneously his professorship at Berlin, his position as permanent secretary of the Prussian Academy of Sciences (a post he had held since 1912 and would continue to hold until 1938), and the editorship of Annalen der Physik. He served on the boards of the Kaiser Wilhelm Society, the Reichsanstalt, the Notgemeinschaft der Deutschen Wissenschaft (the Emergency Society for German Science, founded in 1920 to support research in the impoverished post-war environment), and a half-dozen other scientific bodies. His judgment on appointments, on the direction of research, on the allocation of scarce resources, was central to the institutions of German physics. He was, by the late 1920s, the dean of German science in the most literal sense — the senior figure whose word carried decisive weight in the academic establishment of the country.

He used this influence, in the main, with great wisdom. He was a powerful advocate within the academic establishment for the support of younger physicists doing work in quantum theory and in atomic physics. He was a defender, against considerable institutional resistance, of the appointment of foreign and Jewish physicists to senior positions in Berlin — most famously of Einstein, whom he had personally recruited to the Prussian Academy in 1913 and whose continued presence in Berlin he protected through the troubled years of the early 1920s. He was a generous reviewer of papers submitted to Annalen der Physik, particularly of work by young authors, and he edited the journal with a light hand that allowed the great variety of the new physics to find its way into print. The papers of Heisenberg on matrix mechanics, of Schrödinger on wave mechanics, of Born and Jordan on the foundations of quantum theory, of Pauli on the exclusion principle — all of them passed through Planck's editorial office, and all of them were treated by him with the courteous and rapid handling that he believed serious scientific work deserved.

Marriage to Marga Von Hoesslin

Planck's personal life, after the death of Marie in 1909, had been the bachelor establishment of a widower in his sixties, with the household managed by Marie's sister Helene and the children long since grown to adulthood. In March 1911, however, eighteen months after Marie's death, Planck married Marga von Hoesslin, a young woman of forty years his junior who was the niece of his first wife (more precisely, the daughter of Marie's elder sister). The marriage was, by Planck's own account, a marriage of late-life companionship rather than of romantic passion, undertaken in part to provide the household with a younger mistress who could share the burden of raising the children of Karl and Erwin and to manage the establishment as the older Helene began to age. Marga was a Munich woman, well educated, accomplished in music and in languages, of the same broad cultural background as Marie had been; she would prove a devoted second wife and stepmother, and the marriage, despite the considerable age difference, was a happy one.

A son, Hermann, was born to Max and Marga in 1911 — Planck's fifth and last child. (There is a confusion in the secondary literature here, because Marie's youngest son was sometimes called Hermann in early biographies, and Marga's son was certainly named Hermann; the family's preference for the name caused some confusion in the death records of the early biographers, but the genealogical facts are clear: Marie bore Karl, Grete, Emma, and Erwin, while Marga bore the second-marriage son Hermann.) Hermann Planck would grow up in the Grunewald house, would attend the local gymnasium, would study at the universities of Berlin and Munich, and would in due course become a state official in the German diplomatic service. He would survive his father by many years and would be the only one of Planck's children to outlive him.

The household that Planck and Marga maintained in the Grunewald through the 1910s, 1920s, and into the 1930s was a place of considerable distinction in the academic and musical life of Berlin. The Plancks held regular musical evenings on Tuesday or Sunday nights, at which the senior man would play the piano (often accompanying Marga in lieder by Schubert and Schumann, or playing chamber music with visiting violinists and cellists who included, on different occasions, Albert Einstein on his beloved violin and the young pianist Artur Schnabel). The guests were drawn from the cream of Berlin intellectual society — the physicists Einstein, Nernst, Laue, Born, Schrödinger when he visited; the mathematicians David Hilbert and Hermann Weyl; the philosopher Ernst Cassirer; the theologian Adolf von Harnack; the politician Walther Rathenau before his murder; and a constant traffic of foreign visitors. The Sunday afternoon walks in the Grunewald forest, in which Planck would gather around him a small group of younger physicists for unhurried conversation on the foundations of physical theory, became a celebrated institution of Berlin academic life. Generations of physicists would later remember those walks as among the formative intellectual experiences of their youth.

Philosophy of Physics and the Nature of Science

Planck's philosophical reflections on the nature of physical theory occupied an increasing portion of his later professional output. He had been, from the beginning of his career, a physicist of strongly philosophical temperament — a man who thought always about the foundations of the discipline as well as its technical content, who was attracted to questions of the relation between physical theory and the broader human enterprise of knowing the world, who was unwilling to confine himself to the technical specialisms that were beginning, in the 1920s, to dominate the discipline. From about 1909 onward he gave a regular series of public lectures, in Germany and abroad, on the philosophy of physics and on the relation of physical science to other forms of human knowledge. These lectures, collected and published in several volumes — the Eight Lectures on Theoretical Physics of 1909, A Survey of Physical Theory of 1925, Where Is Science Going? of 1932, Scientific Autobiography and Other Papers of 1949 — established him as the most influential philosophical interpreter of physics of his generation.

The principal position that Planck took in these lectures was the position of metaphysical realism. He held that the external world possessed an objective existence independent of the human observer; that the task of physical science was to construct mathematical descriptions of that objective world that were, as far as could be managed, true to its actual structure; that the criteria by which the success of such descriptions should be judged included not only the conformity of the descriptions with experimental data but also their internal coherence, their simplicity, and their fruitfulness in suggesting further investigations. He was a determined opponent of the positivist philosophy that had been developed in Vienna and elsewhere in the late nineteenth and early twentieth centuries, which held that scientific concepts were merely convenient summaries of observational regularities and that questions about the underlying reality of the physical world were meaningless. He was a particular antagonist of the position of Ernst Mach, the Vienna physicist and philosopher whose Anti-Atomism and whose general phenomenalism had been influential in the development of modern positivism. Planck and Mach engaged in a notable public exchange of views in 1908 and 1909, in which Planck argued vigorously for the reality of atoms and of the deeper constituents of matter that the new physics was beginning to disclose.

In his lectures on the philosophical implications of the quantum theory, Planck took a position of cautious conservatism. He accepted that the equations of quantum mechanics, as developed by Heisenberg and Schrödinger in the late 1920s, gave the correct mathematical description of microscopic processes. He accepted, with considerable reluctance, the probabilistic interpretation of quantum mechanics that had been advanced by Born in 1926 and that had been worked into a coherent philosophical position by Bohr through the late 1920s. But he resisted the more radical implications of the Copenhagen interpretation — the view that physical reality at the microscopic level was indeterminate, that the act of observation played a constitutive role in the existence of physical states, that the categories of cause and effect lost their applicability at the quantum scale. He continued to hold, into the last years of his life, that the apparent indeterminism of quantum mechanics was a temporary feature of the present state of the theory and that a deeper underlying determinism would eventually be discovered. His position was, in this respect, very close to the position of his old friend Einstein, who famously declared that "God does not play dice with the universe" and who maintained, through three decades of debate with Bohr, that quantum mechanics in its existing form was incomplete.

Religion and the Question of God

Planck's religious views, which he expressed publicly with increasing willingness in the last two decades of his life, were closely connected to his philosophical realism and to his interpretation of the new physics. He was a Christian of the German Protestant rationalist tradition — a man who had been baptized and confirmed in the Lutheran church, who attended Sunday services through most of his life, who served as a presbyter of his local congregation in Berlin from 1920 onward, who took the practices of personal devotion seriously without making them a matter of public display. He was not, however, a Christian of any orthodox or dogmatic sort. He did not believe in the personal immortality of the soul in the traditional Christian sense; he did not accept the literal truth of the resurrection accounts; he was skeptical of the kinds of miraculous interventions in nature that some of his colleagues in the theological faculty would have considered essential to a Christian worldview. His religion was, rather, a religion of the rational order of nature — a religion in which God was identified with the deep mathematical regularities that physical science was disclosing, and in which religious devotion took the form of the disciplined cultivation of the human mind in the pursuit of understanding.

His most extended statements on the relation of religion and science were given in a public lecture of 1937, "Religion and Natural Science," and in his 1947 lecture "Sinn und Grenzen der exakten Wissenschaft" (Meaning and Limits of Exact Science), both of which were widely reprinted and translated. In these lectures Planck took the position that religion and natural science were not in conflict but were rather complementary forms of human engagement with the same underlying reality. Science, he held, was concerned with the description of the regularities of nature, with the analysis of what happens and why; religion was concerned with the moral orientation of human life and with the apprehension of the larger meaning of the world that physical science describes. The two disciplines addressed different aspects of human experience, both of them essential, neither of them reducible to the other. He held also that there was, at the bottom of both science and religion, a single ultimate reality — what he called variously "the rational order of the world," "the spirit of God expressing itself in nature," "the world spirit" — that was the proper object of religious devotion and the source of the laws that physical science was charged with discovering.

The position was, in its philosophical content, a version of the rational theism that had been developed in the German Enlightenment tradition by Leibniz and by Kant. It was a position to which Planck came naturally as the descendant of a long line of Lutheran theologians and as the inheritor of the German academic tradition in which physical science and Christian piety had long been understood to be reconcilable. It would, in the last years of his life, lend Planck a kind of moral authority within the German academic world that few of his colleagues commanded, and it would sustain him through the personal and political tragedies of the 1930s and 1940s with a strength that his more secular colleagues sometimes noted with envy.

Music and Private Interests

Through all the years of his professional eminence and personal sorrow, Planck remained the accomplished musician of his youth. He was, by every account, a pianist of considerable technical ability and of unusual interpretive depth, particularly in the chamber music of the German Romantic tradition. He sang in a number of Berlin choral societies, including the prestigious Singakademie. He composed occasional pieces of music for family and academic occasions — a song cycle for his second wedding, a piece of chamber music for Helmholtz's seventieth birthday celebration in 1891, several short works for piano and voice that circulated in manuscript among his musical friends. He was a particular devotee of Bach, whose music he played and studied with the kind of religious seriousness that the composer's own life and works invited. He attended the great Bach festivals at Leipzig, took part in the Berlin performances of the Bach cantatas, organized a private group of friends in the 1890s for the regular performance of Bach chamber works at his Grunewald house.

His other recreations were the standard recreations of the educated German bourgeoisie of his class. He was a determined mountaineer, who climbed the major peaks of the Bavarian Alps in his youth and continued to take long walking holidays in the mountains into his sixties. He kept up an extensive personal correspondence on scientific and philosophical questions with friends and colleagues across Europe — letters of substance, written in his careful old-fashioned German hand, that have been preserved in the academic archives of Berlin and Göttingen and that constitute one of the major personal records of European intellectual life in the first half of the twentieth century. He read widely in the German classics — Goethe, Schiller, Hölderlin, Lessing — and in the standard works of German philosophy, with a particular love for Kant. He was, in short, the model of the cultivated German academic of his generation, a man whose private interests reinforced rather than competed with his public vocation as a physicist.

Confrontation with National Socialism

The political events of January 1933, when Adolf Hitler was appointed Chancellor of Germany by the aged President Hindenburg, found Planck at the age of seventy-four, presiding over the Kaiser Wilhelm Society (the predecessor of what would later be the Max Planck Society) as its president since 1930. The new regime moved with extraordinary speed against the German academic establishment. The Civil Service Restoration Act of 7 April 1933, which dismissed from public employment all civil servants of Jewish ancestry or of left-wing political associations, was applied at once to the universities and to the research institutes of the Kaiser Wilhelm Society. Within a few months, the leading Jewish physicists of Germany — Einstein (who had been on a lecture tour in California and refused to return), Max Born (who emigrated to Britain), James Franck (who emigrated to the United States), Lise Meitner (who would later be forced to flee to Sweden in 1938), Otto Frisch, Otto Stern, Walter Elsasser, and dozens more — had either lost their positions or were in the process of doing so.

Planck was confronted, in the spring and summer of 1933, with the central moral dilemma of his late life. He could remain at his post and try, through whatever influence the regime might allow him, to protect the institutions and the individuals of German science from the worst consequences of the new policies; or he could resign in public protest at the regime's actions and risk being silenced and his institutions taken over by less scrupulous officials. He chose the first course, and the choice would expose him to bitter criticism, both at the time and in the decades after the war, from those who felt that he had compromised himself by remaining in office under a regime whose policies he should have publicly denounced. He defended his choice on the grounds that no public protest from him would change the policies of the regime, while a determined and patient effort from inside the institutions might at least mitigate some of the worst injustices and preserve the long-term capacity of German science to recover after the eventual end of the National Socialist period. The choice was a difficult one and the verdict of history on it has been mixed, but Planck himself maintained the position to the end of his life.

The Meeting with Hitler

In May 1933 Planck obtained, in his capacity as president of the Kaiser Wilhelm Society, a personal audience with Hitler in the chancellery in Berlin. His purpose was to plead with the new Chancellor for moderation in the dismissal of Jewish scientists and, in particular, to argue for the retention of certain individuals whose work was of fundamental importance to German science. He singled out, in his opening remarks, the chemist Fritz Haber, whose research on the synthesis of ammonia had saved Germany from defeat by starvation during the First World War and whose continued service to German chemistry was, in Planck's view, indispensable. He attempted to explain to Hitler that the dismissal of Haber and of other Jewish scientists would damage German science for generations and would forfeit the international leadership in physical and chemical research that the country had spent fifty years building up.

The audience went badly. Hitler, by Planck's later account in conversation with friends, responded to his arguments with a tirade against "the Jews" that was both intemperate and incoherent. Hitler shouted, gestured, accused Jewish scientists of being part of an international conspiracy against Germany, refused to consider any individual exceptions to the new dismissal policies, and dismissed Planck's plea for Haber with the remark that "a Jew is a Jew." Planck left the chancellery after about twenty minutes, recognizing that he had failed entirely and that the regime would not be moved by rational argument from its course of persecution. He would never again meet Hitler personally, and he would resign from the presidency of the Kaiser Wilhelm Society in 1937, in part because of his deepening despair at the impossibility of working with the regime.

The meeting with Hitler became, in the decades after the war, one of the central anecdotes by which Planck's character under the Nazi regime was discussed. Those who saw in him a man of moral courage cited the meeting as evidence of his willingness to plead with the dictator personally on behalf of his Jewish colleagues; those who saw in him a man of insufficient moral resolve cited his choice to remain in office afterward as evidence of accommodation with the regime. Both judgments contain elements of truth, but neither captures the full complexity of Planck's situation. He was a seventy-five-year-old man, surrounded by a regime whose violence and irrationality he found incomprehensible, charged with the institutional welfare of an academy and a research society whose continued existence depended on some minimum of cooperation with the political authorities, and possessed of no political tools with which to oppose the regime more directly. He did what he could; it was, in the end, very little.

Defense of Jewish Colleagues and Einstein

Through the late 1930s, while remaining publicly silent on the political questions of the regime, Planck worked through private channels to assist as many of the dismissed Jewish scientists as he could. He wrote letters of recommendation that helped Born, Franck, Schrödinger, and many others to find positions in foreign universities; he intervened with the ministry of culture on behalf of partial-Jewish (Mischlinge) scientists who were attempting to retain their positions; he traveled to Cambridge and to Oxford in 1937 and 1938 to maintain personal contact with his former colleagues in their British exile. He continued to correspond with Einstein, who had settled at the Institute for Advanced Study at Princeton; the correspondence was scientific and philosophical rather than political, and both men were careful, in those dangerous years, not to commit to writing remarks that might be intercepted by the German authorities.

The defense of Einstein had taken a particularly dramatic public form. In April 1933, in the immediate aftermath of the Civil Service Restoration Act, the Prussian Academy of Sciences had been required to take a position on Einstein's continued membership. Einstein had, from California, denounced the Nazi regime in unmistakable terms; the academy had been pressed by the ministry of culture to expel him. Planck, who as one of the four permanent secretaries had to participate in the decision, attempted to find a compromise that would preserve Einstein's connection to the institution he had served since 1914. The attempt failed; Einstein, learning of the academy's vacillation, resigned his membership of his own accord in March 1933, and the academy's awkward subsequent decision to "regret" his resignation rather than to expel him was a small consolation. Planck's role in the affair was the role of a man trying to behave decently in conditions that made decency nearly impossible; the affair pained him for the rest of his life.

The War Years and the Loss of Erwin

The Second World War broke out in September 1939 with the German invasion of Poland, and Planck — by then eighty-one years old, retired from his professorship for a decade, in poor health, with diminished personal influence in the Berlin academic establishment — watched with mounting horror as the catastrophe he had foreseen since 1933 unfolded. He continued his philosophical writing through the early war years, traveling occasionally to give public lectures (his last major lecture tour, in 1942, took him to Holland and to Italy, where he spoke to large audiences on the foundations of physics and the relation of science and religion). He maintained his correspondence with surviving scientific colleagues. He spent the longer holidays at the family chalet at Murnau in the Bavarian Alps and at the country estate of the von Hoesslin family near Augsburg.

The decisive personal disaster of his last years was the arrest and execution of his youngest son Erwin. Erwin Planck had been, throughout the Weimar years, a senior civil servant — state secretary in the office of the Chancellor under Heinrich Brüning and (briefly) under Franz von Papen between 1932 and 1933. He had been dismissed by the Nazis in 1933 along with most of the senior officials of the late Weimar government and had spent the years since in a conservative political opposition that had drawn him gradually into the circle of resistance figures around Carl Friedrich Goerdeler and Ludwig Beck. He was a peripheral but real participant in the planning of the conspiracy that culminated in the failed assassination attempt on Hitler of 20 July 1944, when Colonel Claus von Stauffenberg planted a bomb at Hitler's East Prussian military headquarters and was executed within twenty-four hours when the plot collapsed.

Erwin Planck was arrested in the immediate aftermath of the July 20 plot, in late July 1944, on charges of conspiracy and treason. He was held in the Gestapo prison in Berlin through the autumn and winter of 1944, was tried by the People's Court (Volksgerichtshof) under the notorious Roland Freisler in October 1944, was sentenced to death, and was executed by hanging at Plötzensee prison in Berlin on 23 January 1945. His father, by then eighty-six years old, was in the small Bavarian town of Rogätz near Magdeburg when the news of the execution arrived. The execution destroyed whatever capacity Planck had left for sustained intellectual work; he never fully recovered.

Evacuation and the Final Months of War

The Berlin house in the Grunewald that had been the Plancks' home for fifty-four years was destroyed by allied bombs on the night of 15 February 1944, in one of the great raids on the German capital. The entire library — the manuscripts of unpublished works, the correspondence with Einstein and Bohr and Schrödinger, the lecture notes of a lifetime, the family photographs and personal papers — went up in flames. Planck and Marga, who had been visiting friends at Rogätz, returned to find the house a smoking ruin. They moved permanently to Rogätz, where they were taken in by the family of Marga's nephew Wilhelm Roloff, a country doctor in the small town. The remaining months of the war were spent in this provincial Saxon retreat, with the family living in straitened conditions in the doctor's house, with sporadic news of the disaster in Berlin and on the eastern and western fronts, with the steady accumulation of grief that the loss of Erwin and the destruction of the house had brought.

The Soviet army reached the Magdeburg region in April 1945. Rogätz lay on the line of the advance and was briefly the scene of a small but bitter battle between the retreating Wehrmacht and the advancing Red Army. The Planck household sheltered in the cellar of the Roloff house for several days while the artillery fire passed over the town. After the fighting ended, the area came under American military administration (it was within the zone that would later be exchanged with the Soviets for the western sectors of Berlin); Allied officers, learning that the eminent physicist was living in the town, came to inquire after his welfare and to offer assistance. Through this Allied assistance, Planck and Marga were eventually moved, in the summer of 1945, to the small university town of Göttingen, where Planck had family connections (his theologian grandfather had taught there a century before) and where the University of Göttingen, which had escaped the worst of the war damage, was beginning slowly to resume its operations.

Postwar Years and the Max Planck Society

The Göttingen years (1945–1947) were the last years of Planck's life. He was eighty-seven when he settled in the small Lower Saxon university town in the autumn of 1945. His health was poor — he was suffering from the after-effects of a serious fall that he had taken at Rogätz in early 1945 and from the strain of the war years — but his mind remained clear, and he was able, in the small house that the Göttingen university authorities provided for him, to continue his correspondence with foreign colleagues, to receive visitors, and to take a continuing if necessarily limited interest in the rebuilding of German science.

The most important institutional development of these last years was the reconstitution of the Kaiser Wilhelm Society, of which Planck had been president from 1930 to 1937, as the Max Planck Society for the Advancement of Science (Max-Planck-Gesellschaft zur Förderung der Wissenschaften). The Kaiser Wilhelm Society had been thoroughly compromised by its involvement with the Nazi regime — many of its research institutes had been engaged in war-related research, and the name itself bore associations with the imperial and Nazi periods that the postwar authorities found unacceptable. The British occupation authorities, working through Otto Hahn (the chemist who had discovered nuclear fission in 1938 and who was, in 1945, perhaps the most distinguished German scientist still in the country), proposed the reorganization of the society under a new name and with reformed governance. Planck was approached, in early 1946, with the proposal that the new society be named after him. He was at first reluctant, on the characteristic ground that such public honors were inappropriate for a living scientist, but he was eventually persuaded to accept on the grounds that his name would help to distance the new society from the discredited associations of the old. The Max Planck Society was formally constituted in February 1948, four months after Planck's death, with Otto Hahn as its first president. It has remained the most distinguished research organization in Germany ever since, with the Max Planck Institutes of physics, chemistry, biology, mathematics, history, and the social sciences carrying on the tradition of fundamental research that Planck had spent his life building up.

The reconstruction of German science in the immediate postwar years was, in the larger view, the unfinished work of Planck's lifetime. He had spent fifty years building up the German physical research establishment to the position of international preeminence that it had occupied between roughly 1900 and 1933; he had watched, with mounting despair, that establishment dismantled by the National Socialist regime; he could see, in 1946 and 1947, the slow beginning of its reconstitution under wholly different political conditions. He gave to that reconstruction whatever moral support and personal authority his name commanded, and he died with the satisfaction of knowing that the Max Planck Society had been founded and that the great tradition of German physical research, however damaged, would continue.

Death in Gottingen

Max Planck died in Göttingen on 4 October 1947, eight months after his eighty-ninth birthday. The death came after a fall — he had slipped on a polished floor in the small university house where he and Marga were living — and the subsequent confinement to bed in a body weakened by age and by long suffering. He retained his clarity of mind to the end; in the last weeks of his life he received visits from former students and colleagues, dictated brief letters to his correspondents, and prepared, with characteristic thoroughness, the final disposition of his papers and his affairs. He died peacefully on the morning of 4 October, in the presence of Marga and his surviving son Hermann.

He was buried in the city cemetery at Göttingen, in a simple grave whose modest marker bore only his name, his dates, and the equation E = h? — the equation by which his constant h enters into the most basic formula of quantum theory, the equation that has been called the shortest summary of his life's work. The funeral was attended by a small gathering of family and academic friends. There were short tributes from Otto Hahn, from Werner Heisenberg, from the rector of the University of Göttingen, and from the British military governor of the region. The world press, distracted by the great political and economic crises of the postwar transition, gave the news of his death less attention than it would have received a decade before, but the leading scientific publications of Germany, Britain, and the United States carried substantial obituaries that recognized the centrality of Planck's contribution to the physics of his century.

Legacy: the Father of Quantum Theory

The place that Max Planck occupies in the history of modern physics is the place of the founder of quantum theory — the man whose introduction of the constant h on 14 December 1900 marked the beginning of the long revolution that, by the 1930s, had transformed the foundations of physical science. The revolution that Planck initiated was not, like the relativistic revolution of Einstein, a revolution carried through by a single mind in a few years of intense activity; it was a slow, collective, often confused process that occupied two generations of physicists and that drew on the work of dozens of contributors. But the initial step — the introduction of discreteness into the equations of physics, the abandonment of the strict continuity that had been the unstated assumption of Newtonian and Maxwellian science — was Planck's, and it remained his most personal contribution to the development of the new physics.

The full meaning of that initial step took the better part of two decades to become clear. Einstein's paper of 1905 on the light quantum, his 1907 application of the quantum hypothesis to the heat capacity of solids, Bohr's quantum theory of the hydrogen atom in 1913, Sommerfeld's extension of the Bohr theory to the heavier elements between 1915 and 1920, de Broglie's hypothesis of matter waves in 1924, Heisenberg's matrix mechanics in 1925, Schrödinger's wave mechanics in 1926, Born's probabilistic interpretation later in 1926, Dirac's relativistic electron theory in 1928 — all of these were extensions, elaborations, and consequences of the original quantum hypothesis. The cumulative effect was to produce, by the late 1920s, a mathematical framework — what we now call quantum mechanics — that gave a complete and quantitative description of the behavior of microscopic systems and that has remained, for a hundred years, the most thoroughly tested and most precisely confirmed theory in the history of natural science.

Planck himself, as has been noted, did not in his lifetime fully accept all the implications of the framework that his discovery had set in motion. He could not finally embrace the probabilistic interpretation of quantum mechanics that had become standard by the late 1920s; he held to the end of his life the hope that a deeper deterministic theory would be found underlying the apparent indeterminism of the Copenhagen formulation. The hope has not, in the seventy-five years since his death, been realized — quantum mechanics in something close to the Copenhagen form remains the standard theory of microscopic physics, with no satisfactory deterministic alternative — but Planck's resistance is a reminder of the conservatism of his physical instincts and of the depth of his attachment to the classical worldview in which he had been formed.

The Quantum Revolution in Physics and Culture

The cultural impact of the quantum revolution, like the cultural impact of the relativistic revolution that Einstein had set in motion at almost the same moment, has been profound and is still working itself out a century later. The discovery that the deepest layer of physical reality is not the deterministic, continuous, fully describable layer of classical Newtonian science but a layer of probabilistic, discrete, and (in important respects) only partially describable phenomena has changed the way that educated people think about the nature of physical reality, about the relation of mind and world, about the possibility and the limits of scientific knowledge. The quantum revolution has affected philosophy (through its bearing on questions of determinism, of causality, of the relation of observer and observed), theology (through its bearing on questions of divine action in nature and the relation of mind and matter), and even art and literature (through its diffuse influence on the modernist sensibility of the early twentieth century and on the more recent contemporary culture).

Within physics itself, the quantum revolution has produced almost the whole of the technological infrastructure of modern civilization. The semiconductor electronics that powers all modern computers, smartphones, telecommunications systems, and digital networks is fundamentally a quantum technology — the behavior of electrons in solid-state devices being governed by the principles of quantum mechanics in ways that classical physics simply cannot describe. The laser, which has revolutionized optics, surgery, telecommunications, and manufacturing, is a fundamentally quantum device. The nuclear technologies that have provided both nuclear electrical power and the nuclear weapons that have shaped the strategic geography of the modern world are products of the application of quantum mechanics to the structure of the atomic nucleus. The chemistry that has produced the modern pharmaceutical industry, the modern plastics industry, the modern food industry, is in the last analysis a chemistry whose foundations are quantum mechanical. The magnetic resonance imaging that has transformed medical diagnostics, the photovoltaic cells that are slowly transforming the energy economy, the satellite positioning systems that are now ubiquitous in modern life — all of these are downstream applications of the quantum theory whose foundation was laid on that December afternoon in 1900.

Planck Units and the Fundamental Constants

A small but characteristic part of Planck's legacy is the set of so-called Planck units, the system of natural units of measurement based on the fundamental constants of physics. Planck observed, in his 1899 paper on the foundations of radiation theory, that the three fundamental constants of nature then known — the velocity of light c, the gravitational constant G, and his own newly introduced constant h — could be combined to produce units of length, time, mass, and other physical quantities that did not depend on any arbitrary human standard and that should be intelligible to any technical civilization anywhere in the universe. The Planck length (about 1.6 × 10?³? meters), the Planck time (about 5.4 × 10??? seconds), the Planck mass (about 2.2 × 10?? kilograms), and the Planck energy (about 1.96 × 10? joules, or equivalently 1.22 × 10¹? giga-electron-volts) define the natural scales at which quantum and gravitational effects become comparable in magnitude. These scales are far removed from the scales of everyday physics — the Planck length is some twenty orders of magnitude smaller than the size of a proton — and they represent, in the current view, the scales at which the as-yet-undiscovered quantum theory of gravity must operate. The Planck units have become the standard system of natural units in theoretical physics and cosmology, and they constitute Planck's most direct posthumous influence on the foundational questions of the discipline.

The constant h itself, the original constant of December 1900, is now known with extraordinary precision — its 2019 redefinition as exactly 6.62607015 × 10?³? joule-seconds, which fixes the value of h by definition and uses h to define the kilogram, ensured that the constant became one of the foundations of the international system of units. The kilogram, which had previously been defined as the mass of a particular cylinder of platinum-iridium kept in a vault at Sèvres outside Paris, was redefined in 2019 in terms of Planck's constant — a poignant recognition of the way in which Planck's discovery has become woven into the basic vocabulary of modern measurement.

The Max Planck Institutes and German Science

The Max Planck Society, founded in 1948 in the year after Planck's death, has grown to be one of the most important basic research organizations in the world. Its eighty-three institutes (as of 2024), spread across Germany and operating in fields from astrophysics to molecular biology to social anthropology, employ some twenty-three thousand scientists and produce a steady stream of fundamental research at the highest international standard. Members of the Max Planck Institutes have won, in the seventy-five years since the society's founding, more than thirty Nobel Prizes — a record that places the society among the most productive research organizations in the history of science. The institutes are funded by the federal and state governments of Germany on the explicit basis that basic, curiosity-driven research is a public good that justifies long-term public investment, and they represent, in their continued vitality, the most successful long-term consequence of Planck's institutional work in the first half of the twentieth century.

The institutes preserve, in their daily practice, the values that Planck embodied — the commitment to rigorous fundamental research, the impatience with administrative interference in scientific judgment, the conviction that the long-term contributions to human knowledge can come only from researchers who are free to follow their own scientific instincts. The administrative structure of the Max Planck Society, in which each institute is headed by a small group of distinguished scientists with substantial autonomy from central direction, was designed by Otto Hahn and his successors in deliberate imitation of the institutional ideals that Planck had defended throughout his career. The success of the model has been so substantial that it has been imitated, in whole or in part, by basic research organizations in Britain, France, Italy, Japan, China, and the United States.

Conclusion: the Meaning of Max Planck

The life of Max Planck is, in the perspective of a century, the life of one of the most consequential individuals of the twentieth century, and at the same time the life of a deeply private, even reticent man whose public influence was always exercised through the formal channels of academic institutions rather than through the kind of celebrity that became available to scientists in the later twentieth century. He was not a public figure in the sense that Einstein or Bohr or Oppenheimer would become; he was a German Herr Professor of the old school, who avoided the press, who declined honorary degrees that he thought inappropriate, who kept his political views to himself when he could and expressed them in measured private correspondence when he could not. The public statements he made on the great questions of his time — on the relation of science and religion, on the philosophical foundations of physics, on the moral obligations of the scientist — were almost all delivered in formal academic lectures and were published in the formal academic press. He was, in his public bearing, the model of a kind of scientist that has now largely vanished: the academic gentleman of the imperial German tradition, whose authority derived from his institutional position and whose public statements were governed by the dignity of his professional rank.

Yet behind that formal public face was, as the correspondence and the recollections of his closest friends show, a man of considerable inward depth and inward suffering, sustained through a long life of professional eminence and private tragedy by an unshakable belief in the rational order of nature, by a deep though undogmatic Christian faith, by the daily exercise of music and scholarship and disciplined intellectual work, and by the steady devotion of his two wives and his surviving family. He lost his first wife to tuberculosis in middle age, his eldest son in the trenches of the First World War, both of his twin daughters in childbirth, his youngest son to the gallows of the Nazi regime, his Berlin house and library to the bombs of the Royal Air Force, and his country, twice in his lifetime, to the catastrophes of war and totalitarianism. Through all of these losses he continued to think, to teach, to write, to insist on the basic dignity of the scientific vocation and the basic decency of human conduct that the German academic tradition had stood for. He emerged from the wreckage of the Second World War, at the age of eighty-seven, to lend his name and his moral authority to the reconstitution of German science under the wholly new political conditions of the postwar period, and he died with the satisfaction of knowing that the great tradition to which he had dedicated his life would, however damaged, continue.

The constant h that he had introduced into physics on a winter afternoon in 1900 has long since been woven into the deepest fabric of physical theory and of the modern technological civilization that physical theory has made possible. The Max Planck Institutes that bear his name continue to do the fundamental research that he believed was the highest calling of the scientific vocation. The Planck units, defined by the fundamental constants of nature, set the scales at which the foundational questions of contemporary physics — the quantum theory of gravity, the structure of spacetime at the smallest scales, the unification of the fundamental forces — must finally be addressed. And the example of his life — measured, conscientious, religiously serious, devoted to the patient and disciplined pursuit of truth, sustained in adversity by the inner resources of a fully developed humanistic culture — remains, in the very different conditions of the early twenty-first century, a model of what the scientific life can be at its best. The reluctant revolutionary who began the most important transformation in the history of modern physics died, after eighty-nine years of patient labor, in the small German university town where his ancestors had taught and where his own grave bears the single equation that summarizes his work. He had wanted, all his life, to find the rational order behind the phenomena of nature. He had found, in his quiet way, more of that order than any other human being of his century.