Max Planck
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Planck in 1933
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| Born |
Max Karl Ernst Ludwig Planck
23 April 1858 |
| Died | 4 October 1947 (aged 89) |
| Nationality | German |
| Alma mater | Ludwig Maximilian University of Munich |
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| Children | 5 |
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| Scientific career | |
| Fields | Physics |
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| Thesis | On the Second Principles of Mechanical Heat Theory (1879) |
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Max Karl Ernst Ludwig Planck, ForMemRS[1] (German: [ˈplaŋk];[2] English: /ˈplæŋk/;[3] 23 April 1858 – 4 October 1947) was a German theoretical physicist whose discovery of energy quanta won him the Nobel Prize in Physics in 1918.[4]
Planck made many contributions to theoretical physics, but his fame as a physicist rests primarily on his role as the originator of quantum theory,[5] which revolutionized human understanding of atomic and subatomic processes. In 1948, the German scientific institution the Kaiser Wilhelm Society (of which Planck was twice president) was renamed the Max Planck Society (MPS). The MPS now includes 83 institutions representing a wide range of scientific directions.
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Life and career[edit]
Planck came from a traditional, intellectual family. His paternal great-grandfather and grandfather were both theology professors in Göttingen; his father was a law professor at the University of Kiel[6] and Munich. One of his uncles was also a judge.[7]
Planck was born in Kiel, Holstein, to Johann Julius Wilhelm Planck and his second wife, Emma Patzig. He was baptized with the name of Karl Ernst Ludwig Marx Planck; of his given names, Marx (a now obsolete variant of Markus or maybe simply an error for Max, which is actually short for Maximilian) was indicated as the "appellation name".[8] However, by the age of ten he signed with the name Max and used this for the rest of his life.[9]
He was the 6th child in the family, though two of his siblings were from his father's first marriage. War was common during Planck's early years and among his earliest memories was the marching of Prussian and Austrian troops into Kiel during the Second Schleswig War in 1864.[7] In 1867 the family moved to Munich, and Planck enrolled in the Maximilians gymnasium school, where he came under the tutelage of Hermann Müller, a mathematician who took an interest in the youth, and taught him astronomy and mechanics as well as mathematics. It was from Müller that Planck first learned the principle of conservation of energy. Planck graduated early, at age 17.[10] This is how Planck first came in contact with the field of physics.
Planck was gifted when it came to music. He took singing lessons and played piano, organ and cello, and composed songs and operas. However, instead of music he chose to study physics.
The Munich physics professor Philipp von Jolly advised Planck against going into physics, saying, "in this field, almost everything is already discovered, and all that remains is to fill a few holes."[11] Planck replied that he did not wish to discover new things, but only to understand the known fundamentals of the field, and so began his studies in 1874 at the University of Munich. Under Jolly's supervision, Planck performed the only experiments of his scientific career, studying the diffusion of hydrogen through heated platinum, but transferred to theoretical physics.
In 1877 he went to the Friedrich Wilhelms University in Berlin for a year of study with physicists Hermann von Helmholtz and Gustav Kirchhoff and mathematician Karl Weierstrass. He wrote that Helmholtz was never quite prepared, spoke slowly, miscalculated endlessly, and bored his listeners, while Kirchhoff spoke in carefully prepared lectures which were dry and monotonous. He soon became close friends with Helmholtz. While there he undertook a program of mostly self-study of Clausius's writings, which led him to choose thermodynamics as his field.
In October 1878 Planck passed his qualifying exams and in February 1879 defended his dissertation, Über den zweiten Hauptsatz der mechanischen Wärmetheorie (On the second law of thermodynamics). He briefly taught mathematics and physics at his former school in Munich.
By the year 1880, Planck had obtained the two highest academic degrees offered in Europe. The first was a doctorate degree after he completed his paper detailing his research and theory of thermodynamics.[7] He then presented his thesis called Gleichgewichtszustände isotroper Körper in verschiedenen Temperaturen (Equilibrium states of isotropic bodies at different temperatures), which earned him a habilitation.
Academic career[edit]
With the completion of his habilitation thesis, Planck became an unpaid Privatdozent (German academic rank comparable to lecturer/assistant professor) in Munich, waiting until he was offered an academic position. Although he was initially ignored by the academic community, he furthered his work on the field of heat theory and discovered one after another the same thermodynamical formalism as Gibbs without realizing it. Clausius's ideas on entropy occupied a central role in his work.
In April 1885 the University of Kiel appointed Planck as associate professor of theoretical physics. Further work on entropy and its treatment, especially as applied in physical chemistry, followed. He published his Treatise on Thermodynamics in 1897.[12] He proposed a thermodynamic basis for Svante Arrhenius's theory of electrolytic dissociation.
In 1889 he was named the successor to Kirchhoff's position at the Friedrich-Wilhelms-Universität in Berlin[13] – presumably thanks to Helmholtz's intercession – and by 1892 became a full professor. In 1907 Planck was offered Boltzmann's position in Vienna, but turned it down to stay in Berlin. During 1909, as a University of Berlin professor, he was invited to become the Ernest Kempton Adams Lecturer in Theoretical Physics at Columbia University in New York City. A series of his lectures were translated and co-published by Columbia University professor A. P. Wills.[14] He retired from Berlin on 10 January 1926,[15] and was succeeded by Erwin Schrödinger.[16]
Family[edit]
In March 1887 Planck married Marie Merck (1861–1909), sister of a school fellow, and moved with her into a sublet apartment in Kiel. They had four children: Karl (1888–1916), the twins Emma (1889–1919) and Grete (1889–1917), and Erwin (1893–1945).
After the apartment in Berlin, the Planck family lived in a villa in Berlin-Grunewald, Wangenheimstrasse 21. Several other professors from University of Berlin lived nearby, among them theologian Adolf von Harnack, who became a close friend of Planck. Soon the Planck home became a social and cultural center. Numerous well-known scientists, such as Albert Einstein, Otto Hahn and Lise Meitner were frequent visitors. The tradition of jointly performing music had already been established in the home of Helmholtz.
After several happy years, in July 1909 Marie Planck died, possibly from tuberculosis. In March 1911 Planck married his second wife, Marga von Hoesslin (1882–1948); in December his fifth child Hermann was born.
During the First World War Planck's second son Erwin was taken prisoner by the French in 1914, while his oldest son Karl was killed in action at Verdun. Grete died in 1917 while giving birth to her first child. Her sister died the same way two years later, after having married Grete's widower. Both granddaughters survived and were named after their mothers. Planck endured these losses stoically.
In January 1945, Erwin, to whom he had been particularly close, was sentenced to death by the Nazi Volksgerichtshof because of his participation in the failed attempt to assassinate Hitler in July 1944. Erwin was executed on 23 January 1945.[17]
Professor at Berlin University[edit]
As a professor at the Friedrich-Wilhelms-Universität in Berlin, Planck joined the local Physical Society. He later wrote about this time: "In those days I was essentially the only theoretical physicist there, whence things were not so easy for me, because I started mentioning entropy, but this was not quite fashionable, since it was regarded as a mathematical spook".[18] Thanks to his initiative, the various local Physical Societies of Germany merged in 1898 to form the German Physical Society (Deutsche Physikalische Gesellschaft, DPG); from 1905 to 1909 Planck was the president.
Planck started a six-semester course of lectures on theoretical physics, "dry, somewhat impersonal" according to Lise Meitner, "using no notes, never making mistakes, never faltering; the best lecturer I ever heard" according to an English participant, James R. Partington, who continues: "There were always many standing around the room. As the lecture-room was well heated and rather close, some of the listeners would from time to time drop to the floor, but this did not disturb the lecture". Planck did not establish an actual "school"; the number of his graduate students was only about 20, among them:
- 1897 Max Abraham (1875–1922)
- 1903 Max von Laue (1879–1960)
- 1904 Moritz Schlick (1882–1936)
- 1906 Walther Meissner (1882–1974)
- 1907 Fritz Reiche (1883–1960)
- 1912 Walter Schottky (1886–1976)
- 1914 Walther Bothe (1891–1957)[19]
Black-body radiation[edit]
In 1894 Planck turned his attention to the problem of black-body radiation. The problem had been stated by Kirchhoff in 1859: "how does the intensity of the electromagnetic radiation emitted by a black body (a perfect absorber, also known as a cavity radiator) depend on the frequency of the radiation (i.e., the color of the light) and the temperature of the body?". The question had been explored experimentally, but no theoretical treatment agreed with experimental values. Wilhelm Wien proposed Wien's law, which correctly predicted the behaviour at high frequencies, but failed at low frequencies. The Rayleigh–Jeans law, another approach to the problem, agreed with experimental results at low frequencies, but created what was later known as the "ultraviolet catastrophe" at high frequencies. However, contrary to many textbooks this was not a motivation for Planck.[20]
Planck's first proposed solution to the problem in 1899 followed from what Planck called the "principle of elementary disorder", which allowed him to derive Wien's law from a number of assumptions about the entropy of an ideal oscillator, creating what was referred-to as the Wien–Planck law. Soon it was found that experimental evidence did not confirm the new law at all, to Planck's frustration. Planck revised his approach, deriving the first version of the famous Planck black-body radiation law, which described the experimentally observed black-body spectrum well. It was first proposed in a meeting of the DPG on 19 October 1900 and published in 1901. This first derivation did not include energy quantisation, and did not use statistical mechanics, to which he held an aversion. In November 1900, Planck revised this first approach, relying on Boltzmann's statistical interpretation of the second law of thermodynamics as a way of gaining a more fundamental understanding of the principles behind his radiation law. As Planck was deeply suspicious of the philosophical and physical implications of such an interpretation of Boltzmann's approach, his recourse to them was, as he later put it, "an act of despair ... I was ready to sacrifice any of my previous convictions about physics."[20]
The central assumption behind his new derivation, presented to the DPG on 14 December 1900, was the supposition, now known as the Planck postulate, that electromagnetic energy could be emitted only in quantized form, in other words, the energy could only be a multiple of an elementary unit:
where h is Planck's constant, also known as Planck's action quantum (introduced already in 1899), and ν is the frequency of the radiation. Note that the elementary units of energy discussed here are represented by hν and not simply by ν. Physicists now call these quanta photons, and a photon of frequency ν will have its own specific and unique energy. The total energy at that frequency is then equal to hν multiplied by the number of photons at that frequency.
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At first Planck considered that quantisation was only "a purely formal assumption ... actually I did not think much about it..."; nowadays this assumption, incompatible with classical physics, is regarded as the birth of quantum physics and the greatest intellectual accomplishment of Planck's career (Ludwig Boltzmann had been discussing in a theoretical paper in 1877 the possibility that the energy states of a physical system could be discrete). The discovery of Planck's constant enabled him to define a new universal set of physical units (such as the Planck length and the Planck mass), all based on fundamental physical constants upon which much of quantum theory is based. In recognition of Planck's fundamental contribution to a new branch of physics, he was awarded the Nobel Prize in Physics for 1918 (he actually received the award in 1919).[21][22]
Subsequently, Planck tried to grasp the meaning of energy quanta, but to no avail. "My unavailing attempts to somehow reintegrate the action quantum into classical theory extended over several years and caused me much trouble." Even several years later, other physicists like Rayleigh, Jeans, and Lorentz set Planck's constant to zero in order to align with classical physics, but Planck knew well that this constant had a precise nonzero value. "I am unable to understand Jeans' stubbornness – he is an example of a theoretician as should never be existing, the same as Hegel was for philosophy. So much the worse for the facts if they don't fit."[23]
Max Born wrote about Planck: "He was, by nature, a conservative mind; he had nothing of the revolutionary and was thoroughly skeptical about speculations. Yet his belief in the compelling force of logical reasoning from facts was so strong that he did not flinch from announcing the most revolutionary idea which ever has shaken physics."[1]
Einstein and the theory of relativity[edit]
In 1905, the three epochal papers by Albert Einstein were published in the journal Annalen der Physik. Planck was among the few who immediately recognized the significance of the special theory of relativity. Thanks to his influence, this theory was soon widely accepted in Germany. Planck also contributed considerably to extend the special theory of relativity. For example, he recast the theory in terms of classical action.[24]
Einstein's hypothesis of light quanta (photons), based on Heinrich Hertz's 1887 discovery (and further investigation by Philipp Lenard) of the photoelectric effect, was initially rejected by Planck. He was unwilling to discard completely Maxwell's theory of electrodynamics. "The theory of light would be thrown back not by decades, but by centuries, into the age when Christiaan Huygens dared to fight against the mighty emission theory of Isaac Newton ..."[25]
In 1910, Einstein pointed out the anomalous behavior of specific heat at low temperatures as another example of a phenomenon which defies explanation by classical physics. Planck and Nernst, seeking to clarify the increasing number of contradictions, organized the First Solvay Conference (Brussels 1911). At this meeting Einstein was able to convince Planck.
Meanwhile, Planck had been appointed dean of Berlin University, whereby it was possible for him to call Einstein to Berlin and establish a new professorship for him (1914). Soon the two scientists became close friends and met frequently to play music together.
First World War[edit]
At the onset of the First World War Planck endorsed the general excitement of the public, writing that, "Besides much that is horrible, there is also much that is unexpectedly great and beautiful: the smooth solution of the most difficult domestic political problems by the unification of all parties (and) ... the extolling of everything good and noble."[26][27]
Nonetheless, Planck refrained from the extremes of nationalism. In 1915, at a time when Italy was about to join the Allied Powers, he voted successfully for a scientific paper from Italy, which received a prize from the Prussian Academy of Sciences, where Planck was one of four permanent presidents.
Planck also signed the infamous "Manifesto of the 93 intellectuals", a pamphlet of polemic war propaganda (while Einstein retained a strictly pacifistic attitude which almost led to his imprisonment, being spared by his Swiss citizenship). But in 1915 Planck, after several meetings with Dutch physicist Lorentz, revoked parts of the Manifesto. Then in 1916 he signed a declaration against German annexationism.[citation needed]
Post-war and the Weimar Republic[edit]
In the turbulent post-war years, Planck, now the highest authority of German physics, issued the slogan "persevere and continue working" to his colleagues.
In October 1920 he and Fritz Haber established the Notgemeinschaft der Deutschen Wissenschaft (Emergency Organization of German Science), aimed at providing financial support for scientific research. A considerable portion of the money the organization would distribute was raised abroad.
Planck also held leading positions at Berlin University, the Prussian Academy of Sciences, the German Physical Society and the Kaiser Wilhelm Society (which in 1948 became the Max Planck Society). During this time economic conditions in Germany were such that he was hardly able to conduct research. In 1926 Planck became a foreign member of the Royal Netherlands Academy of Arts and Sciences.[28]
During the interwar period, Planck became a member of the Deutsche Volks-Partei (German People's Party), the party of Nobel Peace Prize laureate Gustav Stresemann, which aspired to liberal aims for domestic policy and rather revisionistic aims for politics around the world.
Planck disagreed with the introduction of universal suffrage and later expressed the view that the Nazi dictatorship resulted from "the ascent of the rule of the crowds".[29]
Quantum mechanics[edit]
At the end of the 1920s Bohr, Heisenberg and Pauli had worked out the Copenhagen interpretation of quantum mechanics, but it was rejected by Planck, and by Schrödinger, Laue, and Einstein as well. Planck expected that wave mechanics would soon render quantum theory—his own child—unnecessary. This was not to be the case, however. Further work only cemented quantum theory, even against his and Einstein's philosophical revulsions. Planck experienced the truth of his own earlier observation from his struggle with the older views in his younger years: "A new scientific truth does not triumph by convincing its opponents and making them see the light, but rather because its opponents eventually die, and a new generation grows up that is familiar with it."[30]
Nazi dictatorship and the Second World War[edit]
When the Nazis came to power in 1933, Planck was 74. He witnessed many Jewish friends and colleagues expelled from their positions and humiliated, and hundreds of scientists emigrate from Nazi Germany. Again he tried to "persevere and continue working" and asked scientists who were considering emigration to remain in Germany. Nevertheless, he did help his nephew, the economist Hermann Kranold, to emigrate to London after his arrest.[31] He hoped the crisis would abate soon and the political situation would improve.
Otto Hahn asked Planck to gather well-known German professors in order to issue a public proclamation against the treatment of Jewish professors, but Planck replied, "If you are able to gather today 30 such gentlemen, then tomorrow 150 others will come and speak against it, because they are eager to take over the positions of the others."[32] Under Planck's leadership, the Kaiser Wilhelm Society (KWG) avoided open conflict with the Nazi regime, except concerning Fritz Haber. Planck tried to discuss the issue with Adolf Hitler but was unsuccessful. In the following year, 1934, Haber died in exile.
One year later, Planck, having been the president of the KWG since 1930, organized in a somewhat provocative style an official commemorative meeting for Haber. He also succeeded in secretly enabling a number of Jewish scientists to continue working in institutes of the KWG for several years. In 1936, his term as president of the KWG ended, and the Nazi government pressured him to refrain from seeking another term.
As the political climate in Germany gradually became more hostile, Johannes Stark, prominent exponent of Deutsche Physik ("German Physics", also called "Aryan Physics") attacked Planck, Sommerfeld and Heisenberg for continuing to teach the theories of Einstein, calling them "white Jews". The "Hauptamt Wissenschaft" (Nazi government office for science) started an investigation of Planck's ancestry, claiming that he was "1/16 Jewish", but Planck himself denied it.[33]
In 1938, Planck celebrated his 80th birthday. The DPG held a celebration, during which the Max-Planck medal (founded as the highest medal by the DPG in 1928) was awarded to French physicist Louis de Broglie. At the end of 1938, the Prussian Academy lost its remaining independence and was taken over by Nazis (Gleichschaltung). Planck protested by resigning his presidency. He continued to travel frequently, giving numerous public talks, such as his talk on Religion and Science, and five years later he was sufficiently fit to climb 3,000-metre peaks in the Alps.
During the Second World War the increasing number of Allied bombing missions against Berlin forced Planck and his wife to temporarily leave the city and live in the countryside. In 1942 he wrote: "In me an ardent desire has grown to persevere this crisis and live long enough to be able to witness the turning point, the beginning of a new rise." In February 1944 his home in Berlin was completely destroyed by an air raid, annihilating all his scientific records and correspondence. His rural retreat was threatened by the rapid advance of the Allied armies from both sides.
In 1944, Planck's son Erwin was arrested by the Gestapo following the attempted assassination of Hitler in the 20 July plot. He was tried and sentenced to death by the People's Court in October 1944. Erwin was hanged at Berlin's Plötzensee Prison in January 1945. The death of his son destroyed much of Planck's will to live.[34] After the end of the war Planck, his second wife, and his son by her were brought to a relative in Göttingen, where Planck died on October 4, 1947. His grave is situated in the old Stadtfriedhof (City Cemetery) in Göttingen.[35]
Religious views[edit]
Planck was a member of the Lutheran Church in Germany.[36] He was very tolerant towards alternative views and religions.[37] In a lecture in 1937 entitled "Religion und Naturwissenschaft" (Religion and Natural Science) he suggested the importance of these symbols and rituals related directly with a believer's ability to worship God, but that one must be mindful that the symbols provide an imperfect illustration of divinity. He criticized atheism for being focused on the derision of such symbols, while at the same time warned of the over-estimation of the importance of such symbols by believers.[38]
Planck was tolerant and favorable to all religions. Although he remained in the Lutheran Church, he did not promote Christian or Biblical views. He believed "the faith in miracles must yield, step by step, before the steady and firm advance of the facts of science, and its total defeat is undoubtedly a matter of time." [39]
In his 1937 lecture "Religion and Naturwissenschaft," Planck expressed the view that God is everywhere present, and held that "the holiness of the unintelligible Godhead is conveyed by the holiness of symbols." Atheists, he thought, attach too much importance to what are merely symbols. He was a churchwarden from 1920 until his death, and believed in an almighty, all-knowing, beneficent God (though not necessarily a personal one). Both science and religion wage a "tireless battle against skepticism and dogmatism, against unbelief and superstition" with the goal "toward God!"[39]
Planck said in 1944, "As a man who has devoted his whole life to the most clear headed science, to the study of matter, I can tell you as a result of my research about atoms this much: There is no matter as such. All matter originates and exists only by virtue of a force which brings the particle of an atom to vibration and holds this most minute solar system of the atom together. We must assume behind this force the existence of a conscious and intelligent spirit (orig. geist). This spirit is the matrix of all matter."[40]
Planck regarded the scientist as a man of imagination and Christian faith. He said: "Both religion and science require a belief in God. For believers, God is in the beginning, and for physicists He is at the end of all considerations… To the former He is the foundation, to the latter, the crown of the edifice of every generalized world view".[41]
On the other hand, Planck wrote, "...'to believe' means 'to recognize as a truth,' and the knowledge of nature, continually advancing on incontestably safe tracks, has made it utterly impossible for a person possessing some training in natural science to recognize as founded on truth the many reports of extraordinary occurrences contradicting the laws of nature, of miracles which are still commonly regarded as essential supports and confirmations of religious doctrines, and which formerly used to be accepted as facts pure and simple, without doubt or criticism. The belief in miracles must retreat step by step before relentlessly and reliably progressing science and we cannot doubt that sooner or later it must vanish completely."[42]
Later in life, Planck's views on God were that of a deist.[43] For example, six months before his death a rumour started that he had converted to Catholicism, but when questioned what had brought him to make this step, he declared that, although he had always been deeply religious, he did not believe "in a personal God, let alone a Christian God."[44]
Publications[edit]
- Planck, M. (1900a). "Über eine Verbesserung der Wienschen Spektralgleichung". Verhandlungen der Deutschen Physikalischen Gesellschaft. 2: 202–204. Translated in ter Haar, D. (1967). "On an Improvement of Wien's Equation for the Spectrum" (PDF). The Old Quantum Theory. Pergamon Press. pp. 79–81. LCCN 66029628.
- Planck, M. (1900b). "Zur Theorie des Gesetzes der Energieverteilung im Normalspectrum". Verhandlungen der Deutschen Physikalischen Gesellschaft. 2: 237. Translated in ter Haar, D. (1967). "On the Theory of the Energy Distribution Law of the Normal Spectrum" (PDF). The Old Quantum Theory. Pergamon Press. p. 82. LCCN 66029628.
- Planck, M. (1900c). "Entropie und Temperatur strahlender Wärme" [Entropy and Temperature of Radiant Heat]. Annalen der Physik. 306 (4): 719–737. Bibcode:1900AnP...306..719P. doi:10.1002/andp.19003060410.
- Planck, M. (1900d). "Über irreversible Strahlungsvorgänge" [On Irreversible Radiation Processes]. Annalen der Physik. 306 (1): 69–122. Bibcode:1900AnP...306...69P. doi:10.1002/andp.19003060105.
- Planck, M. (1901). "Über das Gesetz der Energieverteilung im Normalspektrum". Annalen der Physik. 309 (3): 553–563. Bibcode:1901AnP...309..553P. doi:10.1002/andp.19013090310. Translated in Ando, K. "On the Law of Distribution of Energy in the Normal Spectrum" (PDF). Archived from the original (PDF) on 6 October 2011. Retrieved 13 October 2011.
- Planck, M. (1903). Treatise on Thermodynamics. Ogg, A. (transl.). London: Longmans, Green & Co. OL 7246691M.
- Planck, M. (1906). Vorlesungen über die Theorie der Wärmestrahlung. Leipzig: J.A. Barth. LCCN 07004527.
- Planck, M. (1914). The Theory of Heat Radiation. Masius, M. (transl.) (2nd ed.). P. Blakiston's Son & Co. OL 7154661M.
- Planck, M. (1915). Eight Lectures on Theoretical Physics. Wills, A. P. (transl.). Dover Publications. ISBN 0-486-69730-4.
- Planck, M. (1943). "Zur Geschichte der Auffindung des physikalischen Wirkungsquantums". Naturwissenschaften. 31 (14–15): 153–159. Bibcode:1943NW.....31..153P. doi:10.1007/BF01475738.
The Genesis and Present State of Development of the Quantum Theory
If I take it correctly that the duty imposed upon me today is to give a public lecture on my writings, then I believe that this task, the importance of which I am well aware through the gratitude felt towards the noble-minded founder of our Foundation, cannot be more suitably fulfilled than by my trying to give you the story of the origin of the quantum theory in broad outlines and to couple with this, a picture in a small frame, of the development of this theory up to now, and its present-day significance for physics.
When I look back to the time, already twenty years ago, when the concept and magnitude of the physical quantum of action began, for the first time, to unfold from the mass of experimental facts, and again, to the long and ever tortuous path which led, finally, to its disclosure, the whole development seems to me to provide a fresh illustration of the long-since proved saying of Goethe’s that man errs as long as he strives. And the whole strenuous intellectual work of an industrious research worker would appear, after all, in vain and hopeless, if he were not occasionally through some striking facts to find that he had, at the end of all his criss-cross journeys, at last accomplished at least one step which was conclusively nearer the truth. An indispensable hypothesis, even though still far from being a guarantee of success, is however the pursuit of a specific aim, whose lighted beacon, even by initial failures, is not betrayed.
For many years, such an aim for me was to find the solution to the problem of the distribution of energy in the normal spectrum of radiating heat. Since Gustav Kirchhoff has shown that the state of the heat radiation which takes place in a cavity bounded by any emitting and absorbing substances of uniform temperature is entirely independent upon the nature of the substances, a universal function was demonstrated which was dependent only upon temperature and wavelength, but in no way upon the properties of any substance. And the discovery of this remarkable function promised deeper insight into the connection between energy and temperature which is, in fact, the major problem in thermodynamics and thus in the whole of molecular physics. To attain this there was no other way but to seek out from all the different substances existing in Nature one of known emissive and absorptive power, and to calculate the properties of the heat radiation in stationary energy exchange with it. According to Kirchhoff’s Law, this would have to prove independent of the nature of the body.
Heinrich Hertz’s linear oscillator, whose laws of emission, for a given frequency, Hertz had just previously completely developed, seemed to me to be a particularly suitable device for this purpose. If a number of such Hertzian oscillators are set up within a cavity surrounded by a sphere of reflecting walls, then by analogy with audio oscillators and resonators, energy will be exchanged between them by the output and absorption of electromagnetic waves, and finally stationary radiation corresponding to Kirchhoff’s Law, the so-called black-body radiation, should be set up within the cavity. I was filled at that time with what would be thought today naively charming and agreeable expectations, that the laws of classical electrodynamics would, if approached in a sufficiently general manner with the avoidance of special hypotheses, be sufficient to enable us to grasp the most significant part of the process to be expected, and thus to achieve the desired aim. I, therefore, developed first the laws of emission and absorption of a linear resonator on the most general basis, in fact I proceeded on such a detour which could well have been avoided had I made use of the existing electron theory of H.A. Lorentz, already basically complete. But since I did not quite trust the electron hypothesis, I preferred to observe that energy which flowed in and out through an enclosing spherical surface around the resonator at a suitable distance from it. By this method, only processes in a pure vacuum came into account, but a knowledge of these was sufficient to draw the necessary conclusions however, about the energy changes in the resonator.
The fruit of this long series of investigations, of which some, by comparison with existing observations, mainly the vapour measurements by V. Bjerknes, were susceptible to checking, and were thereby confirmed, was the establishment of the general connection between the energy of a resonator of specific natural period of vibration and the energy radiation of the corresponding spectral region in the surrounding field under conditions of stationary energy exchange. The noteworthy result was found that this connection was in no way dependent upon the nature of the resonator, particularly its attenuation constants – a circumstance which I welcomed happily since the whole problem thus became simpler, for instead of the energy of radiation, the energy of the resonator could be taken and, thereby, a complex system, composed of many degrees of freedom, could be replaced by a simple system of one degree of freedom.
Nevertheless, the result meant no more than a preparatory step towards the initial onslaught on the particular problem which now towered with all its fearsome height even steeper before me. The first attempt upon it went wrong, for my original secret hope that the radiation emitted from the resonator can be in some characteristic way or other distinguished from the absorbed radiation and thereby allow a differential equation to be set up, from the integration of which one could gain some special condition for the properties of stationary radiation, proved false. The resonator reacted only to those rays which it also emitted, and was not in the slightest bit sensitive to the adjacent spectral regions.
Furthermore, my hypothesis that the resonator could exercise a unilateral, i.e. irreversible, effect upon the energy in the surrounding radiation field, was strongly contested by Ludwig Boltzmann, who, with his riper experience in these problems, proved that according to the laws of classical dynamics each of the processes observed by me can proceed in exactly the opposite direction, in such a way, that a spherical wave emitted from the resonator, returns and contracts in steadily diminishing concentric spherical surfaces inwards to the resonator, and is again absorbed by it, thereby allowing the formerly absorbed energy to be re-transmitted into space in the direction from which it came. And when I excluded this kind of singular process, such as an inwardly directed wave, by means of the introduction of a limiting definition, the hypothesis of natural radiation, all these analyses still showed ever more clearly that an important connecting element or term, essential for the complete grasp of the core of the problem, must be missing.
So there was nothing left for me but to tackle the problem from the opposite side, that of thermodynamics, in which field I felt, moreover, more confident. In fact my earlier studies of the Second Law of Heat Theory stood me in good stead, so that from the start I tried to get a connection, not between the temperature but rather the entropy of the resonator and its energy, and in fact, not its entropy exactly but the second derivative with respect to the energy since this has a direct physical meaning for the irreversibility of the energy exchange between resonator and radiation. Since I was, however, at that time still too far oriented towards the phenomenological aspect to come to closer quarters with the connection between entropy and probability, I saw myself, at first, relying solely upon the existing results of experience. In the foreground of interest at that time, in 1899, was the energy distribution law established by W. Wien shortly before, whose experimental proof was taken up, on the one hand, by F. Paschen at the Technische Hochschule in Hannover, and, on the other hand, by O. Lummer and E. Pringsheim at the State Institution in Charlottenburg. This law brought out the dependence of the radiation intensity on the temperature, representing it by an exponential function. If one calculates the connection between the entropy and the energy of a resonator, determined by the above law, the remarkable result is obtained that the reciprocal value of the above-mentioned differential coefficient, which I will call R, is proportional to the energy. This extremely simple relationship can be considered as the completely adequate expression of Wien’s energy distribution law; for with the dependence upon the energy, the dependence upon the wavelength is always directly given through the general, well-established displacement law by Wien.
Since the whole problem concerned a universal law of Nature, and since at that time, as still today, I held the unshakeable opinion that the simpler the presentation of a particular law of Nature, the more general it is – though at the same time, which formula to take as the simpler, is a problem which cannot always be confidently and finally decided – I believed for a long time that the law that the quantity R is proportional to the energy, should be looked upon as the basis for the whole energy distribution law. This concept could not be maintained for long in the face of fresh measurements. Whilst for small values of the energy and for short waves, Wien’s law was satisfactorily confirmed, noteworthy deviations for larger wavelengths were found, first by O. Lummer and E. Pringsheim, and finally by H. Rubens and F. Kurlbaum, whose measurements on the infrared residual rays of fluorite and rock salt revealed a totally different, though still extremely simple relationship, characterized by the fact that the quantity R is not proportional to the energy, but to the square of the energy, and in fact this holds with increasing accuracy for greater energies and wavelengths.
So, through direct experiment, two simple limits were determined for the function R: for small energies, proportionality with the energy; for greater energies, proportionality with the square of the energy. There was no better alternative but to make, for the general case, the quantity R equal to the sum of two terms, one of the first power, and one of the second power of the energy, so that for small energies the first is predominant, whilst for the greater energies the second is dominant. Thus the new radiation formula was found, which, in the face of its experimental proof, has stood firm to a reasonable extent until now. Even today, admittedly, we cannot talk of final exact confirmation. In fact, a fresh attempt at proof is urgently required.
However, even if the radiation formula should prove itself to be absolutely accurate, it would still only have, within the significance of a happily chosen interpolation formula, a strictly limited value. For this reason, I busied myself, from then on, that is, from the day of its establishment, with the task of elucidating a true physical character for the formula, and this problem led me automatically to a consideration of the connection between entropy and probability, that is, Boltzmann’s trend of ideas; until after some weeks of the most strenuous work of my life, light came into the darkness, and a new undreamed-of perspective opened up before me.
I must make a small intercalation at this point. According to Boltzmann, entropy is a measure for physical probability, and the nature and essence of the Second Law of Heat Theory is that in Nature a state occurs more frequently, the more probable it is. Now one always measures in Nature the difference in entropies, never the entropy itself, and to this extent one cannot speak of the absolute entropy of a state, without a certain arbitrariness. Nevertheless, it is useful to introduce the suitably defined absolute value of entropy, namely for the reason that with its help certain general laws can be particularly easily formulated. The case seems to be parallel, as I see it, with that of energy. Energy itself cannot be measured, only its difference. For that reason one used to deal, not with energy, but with work, and even Ernst Mach, who had so much to do with the Law of Conservation of Energy, and who in principle kept away from all speculations beyond the field of observation, has always avoided speaking of energy itself. Likewise, in thermochemistry, one has always stuck to the thermal effect, that is, to energy differences, until Wilhelm Ostwald in particular emphatically showed that many detailed considerations could be significantly abbreviated if one dealt with energy itself instead of with calorimetric numbers. The additive constant which was at first still undetermined in the expression for energy, has later been finally determined through the relativistic law of the proportionality between energy and inertia.
In a similar way to that for energy, an absolute value can be defined also for entropy and, as a result thereof, for the physical probability too, e.g. by so fixing the additive constant that energy and entropy disappear together. On the basis of a consideration of this kind a specific, relatively simple combinatorial method was obtained for the calculation of the physical probability of a specified energy distribution in a system of resonators, which led exactly to that entropy expression determined by the radiation law, and it brought me much-valued satisfaction for the many disappointments when Ludwig Boltzmann, in the letter returning my essay, expressed his interest and basic agreement with the train of thoughts expounded in it.
For the numerical treatment of the indicated consideration of probability, knowledge of two universal constants is required, both of which have an independent physical meaning, and whose subsequent evaluation from the law of radiation must provide proof as to whether the whole method is to be looked upon as a mere artifice for calculation, or whether it has an inherent real physical sense and interpretation. The first constant is of a more formal nature and is connected with the definition of temperature. If temperature were to be defined as the average kinetic energy of a molecule in an ideal gas, that is, as a tiny, little quantity, then the constant would have the value 2/3. In conventional temperature measure, on the contrary, the constant has an extremely small value which stands, naturally, in close association with the energy of a single molecule, and an exact knowledge of which leads, therefore, to the calculation of the mass of a molecule and those parameters related to it. This constant is often referred to as Boltzmann’s constant, although, to my knowledge, Boltzmann himself never introduced it – a peculiar state of affairs, which can be explained by the fact that Boltzmann, as appears from his occasional utterances, never gave thought to the possibility of carrying out an exact measurement of the constant. Nothing can better illustrate the positive and hectic pace of progress which the art of experimenters has made over the past twenty years, than the fact that since that time, not only one, but a great number of methods have been discovered for measuring the mass of a molecule with practically the same accuracy as that attained for a planet.
At the time when I carried out the corresponding calculation from the radiation law, an exact proof of the number obtained was quite impossible, and not much more could be done than to determine the order of magnitude which was admissible. It was shortly afterward that E. Rutherford and H. Geiger succeeded in determining, by direct counting of the alpha particles, the value of the electrical elementary charge, which they found to be 4.65 x 10-10 electrostatic units; and the agreement of this figure with the number calculated by me, 4.69 x 10-10, could be taken as decisive confirmation of the usefulness of my theory. Since then, more sophisticated methods have led to a slightly higher value, these measurements being carried out by E. Regener, R.A. Millikan, and others.
The explanation of the second universal constant of the radiation law was not so easy. Because it represents the product of energy and time (according to the first calculation it was 6.55 x 10-27 erg sec), I described it as the elementary quantum of action. Whilst it was completely indispensable for obtaining the correct expression for entropy – since only with its help could the magnitude of the “elementary regions” or “free rooms for action” of the probability, decisive for the assigned probability consideration, be determined – it proved elusive and resistant to all efforts to fit it into the framework of classical theory. As long as it was looked upon as infinitely small, that is, for large energies or long periods of time, everything went well; but in the general case, however, a gap yawned open in some place or other, which was the more striking, the weaker and faster the vibrations that were considered. The foundering of all efforts to bridge the chasm soon left little doubt. Either the quantum of action was a fictional quantity, then the whole deduction of the radiation law was in the main illusory and represented nothing more than an empty non-significant play on formulae, or the derivation of the radiation law was based on a sound physical conception. In this case the quantum of action must play a fundamental role in physics, and here was something entirely new, never before heard of, which seemed called upon to basically revise all our physical thinking, built as this was, since the establishment of the infinitesimal calculus by Leibniz and Newton, upon the acceptance of the continuity of all causative connections.
Experiment has decided for the second alternative. That the decision could be made so soon and so definitely was due not to the proving of the energy distribution law of heat radiation, still less to the special derivation of that law devised by me, but rather should it be attributed to the restless forwardthrusting work of those research workers who used the quantum of action to help them in their own investigations and experiments. The first impact in this field was made by A. Einstein who, on the one hand, pointed out that the introduction of the energy quanta, determined by the quantum of action, appeared suitable for obtaining a simple explanation for a series of noteworthy observations during the action of light, such as Stokes’ Law, electron emission, and gas ionization, and, on the other hand, derived a formula for the specific heat of a solid body through the identification of the expression for the energy of a system of resonators with that of the energy of a solid body, and this formula expresses, more or less correctly, the changes in specific heat, particularly its reduction with falling temperature. The result was the emergence, in all directions, of a number of problems whose more accurate and extensive elaboration in the course of time brought to light a mass of valuable material. I cannot give here even an approximate report on the abundance of the work carried out. Only the most important and characteristic steps along the path of progressive knowledge can be high-lighted here.
First come thermal and chemical processes. As far as the specific heat of solid bodies is concerned, Einstein’s theory, which rested upon the assumption of a single natural vibration of the atom, was extended by M. Born and Th. von Kármán to the case of various kinds of natural vibrations, which approached more nearly to the truth. P. Debye succeeded, by means of a bold simplification of the stipulations for the character of natural vibrations, in producing a relatively simple formula for the specific heat of solid bodies which, particularly for low temperatures, not only satisfactorily reproduces the measurements obtained by W. Nernst and his pupils, but is also compatible with the elastic and optical properties of these substances. The quantum of action also comes to the fore in considering the specific heat of gases. W. Nernst had earlier suggested that to the quantum of energy of a vibration there must also correspond a quantum of energy of a rotation, and accordingly it was to be expected that the rotational energy of the gas molecules would disappear with falling temperature. The measurements by A. Eucken on the specific heat of hydrogen confirmed this conclusion, and if the calculations of A. Einstein and O. Stern, P. Ehrenfest and others have not until now afforded any completely satisfactory agreement, this lies understandably in our, as yet, incomplete knowledge of the model of a hydrogen molecule. The fact that the rotations of the gas molecules, as specified by quantum conditions, do really exist in Nature, can no longer be doubted in view of the work on absorption bands in the infrared by N. Bjerrum, E. von Bahr, H. Rubens, G. Hetmer and others, even though it has not been possible to give an all-round exhaustive explanation of this remarkable rotation spectra up to now.
Since, ultimately, all affinity properties of a substance are determined by its entropy, the quantum-theoretical calculation of the entropy opens up the way to all the problems of chemical relationships. The Nemst chemical constant, which O. Sackur calculated directly through a combinatorial method as applied to oscillators, is characteristic for the absolute value of the entropy of a gas. H. Tetrode, in close association with the data to be obtained by measurement, determined the difference in entropy values between vapour and solid state by studying an evaporation process.
Whilst in the cases so far considered, states of thermodynamic equilibrium are concerned, for which therefore the measurements can only yield statistically average values relating to many particles and lengthy periods of time, the observation of electron impacts leads directly to the dynamic details of the process under examination. Thus the determination of the so-called resonance potential carried out by J. Franck and G. Hertz, or that concerning the critical velocity is the minimum an electron must possess in order to cause emission of a light quantum or photon by impact with a neutral atom, supplied a method of measuring the quantum of action which was as direct as could be wished for. The experiments by D.L. Webster and E. Wagner and others resulted in the development of methods suitable for the Röntgen spectrum which also gave completely compatible results.
The production of photons by electron impact appears as the reverse process to that of electron emission through irradiation by light-, Röntgen-, or gamma-rays and again here, the energy quanta, determined by the quantum of action and by the vibration frequency, play a characteristic role, as could be recognized, already at an early time, from the striking fact that the velocity of the emitted electrons is not determined by the intensity of radiation, but only by the colour of the light incident upon the substance. Also from the quantitative aspect, Einstein’s equations with respect to the light quantum have proved true in every way, as established by R.A. Millikan, in particular, by measurements of the escape velocity of emitted electrons, whilst the significance of the photon for the initiation of photochemical reactions was discovered by E. Warburg.
If the various experiments and experiences gathered together by me up to now, from the different fields of physics, provide impressive proof in favour of the existence of the quantum of action, the quantum hypothesis has, nevertheless, its greatest support from the establishment and development of the atom theory by Niels Bohr. For it fell to this theory to discover, in the quantum of action, the long-sought key to the entrance gate into the wonderland of spectroscopy, which since the discovery of spectral analysis had obstinately defied all efforts to breach it. And now that the way was opened, a sudden flood of new-won knowledge poured out over the whole field including the neighbouring fields in physics and chemistry. The first brilliant acquisition was the derivation of Balmer’s series formula for hydrogen and helium including the reduction of the universal Rydberg constant to merely known numerical quantities, whereby even the small discrepancies for hydrogen and helium were recognized as essentially determined by the weak motion of the heavy atom nucleus. Investigation then turned to other series in the optical and the Röntgen spectrum using the extremely fruitful Ritz combination principle, which was at last revealed clearly in all its fundamental significance.
Whoever, in view of the numerous agreements which in the case of the special accuracy of spectroscopic measurements could lay claim to particularly striking confirmatory power, might have been still inclined to feel that it was all attributable to the play of chance, would been forced, finally, to discard even his last doubt, as A. Sommerfeld showed that from a logical extension of the laws of quantum distribution in systems with several degrees of freedom, and out of consideration of the variability of the inertial mass in accordance with the relativity theory, that magic formula arose before which both the hydrogen and the helium spectrum had to reveal the riddle of their fine structure, to such an extent that the finest present-day measurements, those of F. Paschen, could be explained generally through it – an achievement fully comparable with that of the famous discovery of the planet Neptune whose existence and orbit was calculated by Leverrier before the human eye had seen it. Progressing further along the same path, P. Epstein succeeded in fully explaining the Stark effect of the electrical splitting up of the spectral lines, P. Debye produced a simple explanation of the K-series of the Röntgen spectrum, which had been investigated by Manne Siegbahn, and now followed a great number of further experiments, which illuminated with more or less success the dark secrets of the construction of the atom.
After all these results, towards whose complete establishment still many reputable names ought essentially to have been mentioned here, there is no other decision left for a critic who does not intend to resist the facts, than to award to the quantum of action, which by each different process in the colourful show of processes, has ever-again yielded the same result, namely, 6.52 x 10-27 erg sec, for its magnitude, full citizenship in the system of universal physical constants. It must certainly appear a unique coincidence that just in that time when the ideas of general relativity have broken through, and have led to fantastic results, Nature should have revealed an “absolute” in a place where it could be least expected, an invariable unit, in fact, by means of which the action quantity, contained in a space-time element, can be represented by a completely definite non-arbitrary number, and thereby divested itself of its (until now) relative character.
To be sure, the introduction of the quantum of action has not yet produced a genuine quantum theory. In fact, the path the research worker must yet tread to it is not less than that from the discovery of the velocity of light by Olaf Römer to the establishment of Maxwell’s theory of light. The difficulties which the introduction of the quantum of action into the well-tried classical theory has posed right from the start have already been mentioned by me. During the course of the years they have increased rather than diminished, and if, in the meantime, the impetuous forward-driving research has passed to the order of the day for some of these, temporarily, the gaps left behind, awaiting subsequent filling, react even harder upon the conscientious systematologist. What serves in Bohr’s theory as a basis to build up the laws of action, is assembled out of specific hypotheses which, up to a generation ago, would undoubtedly have been flatly rejected altogether by every physicist. The fact that in the atom, certain quite definite quantum-selected orbits play a special role, might be taken still as acceptable, less easily however, that the electrons, circulating in these orbits with definite acceleration, radiate no energy at all. The fact that the quite sharply defined frequency of an emitted photon should be different from the frequency of the emitting electron must seem to a theoretical physicist, brought up in the classical school, at first sight to be a monstrous and, for the purpose of a mental picture, a practically intolerable demand.
But numbers decide, and the result is that the roles, compared with earlier times, have gradually changed. What initially was a problem of fitting a new and strange element, with more or less gentle pressure, into what was generally regarded as a fixed frame has become a question of coping with an intruder who, after appropriating an assured place, has gone over to the offensive; and today it has become obvious that the old framework must somehow or other be burst asunder. It is merely a question of where and to what degree. If one may make a conjecture about the expected escape from this tight comer, then one could remark that all the signs suggest that the main principles of thermodynamics from the classical theory will not only rule unchallenged but will more probably become correspondingly extended. What the armchair experiments meant for the foundation of classical thermodynamics, the adiabatic hypothesis of P. Ehrenfest means, provisionally, to the quantum theory; and in the same way as R. Clausius, as a starting point for the measurement of entropy, introduced the principle that, when treated appropriately, any two states of a material system can, by a reversible process, undergo a transition from one to the other, now the new ideas of Bohr’s open up a very similar path into the interior of a wonderland hitherto hidden from him.
There is in particular one problem whose exhaustive solution could provide considerable elucidation. What becomes of the energy of a photon after complete emission? Does it spread out in all directions with further propagation in the sense of Huygens’ wave theory, so constantly taking up more space, in boundless progressive attenuation? Or does it fly out like a projectile in one direction in the sense of Newton’s emanation theory? In the first case, the quantum would no longer be in the position to concentrate energy upon a single point in space in such a way as to release an electron from its atomic bond, and in the second case, the main triumph of the Maxwell theory – the continuity between the static and the dynamic fields and, with it, the complete understanding we have enjoyed, until now, of the fully investigated interference phenomena – would have to be sacrificed, both being very unhappy consequences for today’s theoreticians.
Be that as it may, in any case no doubt can arise that science will master the dilemma, serious as it is, and that which appears today so unsatisfactory will in fact eventually, seen from a higher vantage point, be distinguished by its special harmony and simplicity. Until this aim is achieved, the problem of the quantum of action will not cease to inspire research and fructify it, and the greater the difficulties which oppose its solution, the more significant it finally will show itself to be for the broadening and deepening of our whole knowledge in physics.