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Max Karl Ernst Ludwig Planck
The Originator of Quantum Theory
 
 
 
Dr Subodh Mahanti

“Fortunately science, like that nature to which it belongs, is neither limited by time nor by space. It belongs to the world, and is of no country and no age. The more we know, the more we feel our ignorance: the more we feel how much remains unknown….”

Humphry Davy

“Scarcely any other discovery in the history of science has produced such extraordinary results within the short span of our generation as those which have directly arisen from Max Planck’s discovery of the elementary quantum of action. This discovery has been prolific, to a constantly increasing degree of progression, in furnishing means for the interpretation and harmonizing of results obtained from the study of atomic phenomena, which is a study that has made marvelous progress within the past thirty years.”

Niels Bohr



“Planck’s love of fundamental and general problems drove him to take up the blackbody problem, which was independent of atomic models or particular hypotheses. He loved the absolute, and such was the blackbody.”

Emilio Gino Segre



Max Karl Ernst Ludwig Planck is ranked with Albert Einstein as one of the two founders of 20th-century physics. Planck’s discovery of a world of discrete, discontinuous “quanta” of energy ushered in the era of modern physics. His discovery was in direct contrast with the apparent continuity of classical Newtonian mechanics. In 1900 Planck postulated the universal constant in nature that came to be known as Planck’s constant. It was Planck’s discovery, which directly led to the formulation of quantum mechanics 20 years later. As an editor of the Annalen der Physik, Germany’s leading physics journal, he played an important role in the development of physics as a whole. As an editor, he also welcomed and promoted Einstein’s theory of relativity. In fact Planck was the first prominent physicist to endorse Einstein’s special theory of relativity. Planck supported the right of women to study science at the university. Planck loved music. He played piano and organ extremely well. It is said that at one time Planck considered music as career. He also loved walking and climbing in the mountains. Planck was a man of deep philosophical and religious conviction. He is one of the very few scientists to be immortalized on a coin (the German DM 2 piece of 1958).

Planck was born on April 23, 1858 in Kiel, Schleswig-Holstein, Germany. His father, Julius Wilhelm Planck was Professor of Constitutional Law in the University of Kiel, and later in Gottingen. Planck’s family was truly an academic family. His grandfather and great-grandfather had been professors of theology at Gottingen. Plank’s mother Emma Planck (nee Patzig) was his father’s second wife. Planck was his father’s sixth child (two of the children were from his first marriage to Mathilde Vogt). He was brought up in a tradition, which highly cherished scholarship, honesty, fairness and generosity.

Plank had his early schooling in Kiel before his family moved to Munich in 1867. At Munich Planck joined the prestigious Maximilian Gymnasium in May 1867. At school he performed well but at the same time he did not show any sign of outstanding talent. His school report of the year 1872 while commenting his performance noted: “Justifiably favoured by both teachers and classmates…and despite having ways, he has a very clear, logical mind. Shows great promise.” It is said that at the beginning his best subject at school was perhaps music. Almost every year he won the school prize in catechism and good conduct. Towards the end of his schooling at the Maximilian Gymnasium he was drawn to physics and mathematics by his mathematics teacher Hermann Muller.

In July 1874 he passed his school leaving examination with distinction. Plank had not decided about his future career. He even explored the possibility of pursuing a musical career. Finally he entered the Munich University on 21 October 1874, where he was taught physics by Philipp von Jolly and Wilhelm Beetz, and Mathematics by Ludwig Seidel and Gustav Bauer. It seems Planck was not much impressed with his teachers at the Munich University. Remembering his student days at the Munich University Planck later wrote: “I did not have the good fortune of a prominent scientist or teacher directing the specific course of my education.” At the beginning Planck took mostly mathematics classes. His physics teacher Philipp von Jolly presented a very bleak picture of the prospect of research career in physics. Jolly described physics as essentially a complete science. A few loose ends remained to be tidied up but on the whole all the major discoveries had already been made. So there was very little prospect of further development. In those days it was not uncommon for a physicist to believe that study of physics was essentially a dead end. It was almost a common belief that everything of importance had already been discovered. But finally Planck decided to study theoretical physics. On describing why he chose physics, Planck later wrote: “The outside world is something independent from man, something absolute, and the quest for the laws which apply to this absolute appeared to me as the most sublime scientific pursuit in life.” He was inspired by the discovery that “pure reasoning can enable man to gain an insight into the mechanism of the world.” In October 1877 Planck moved to the Berlin University, where he was taught by Hermann Ludwig Ferdinand von Helmholtz and Gustav Robert Kirchoff. At Berlin, Planck made independent study of Rudolf Clausius’ writings on thermodynamics. Planck returned to Munich and from where he received his doctorate degree in July 1879. His PhD thesis was on the second law of thermodynamics and it was titled “On the Second Law of Mechanical Theory of Heat.” Planck’s decision to study theoretical physics was a revolutionary step. Theoretical physics was yet to be recognized as a discipline on its own right.

After completing his PhD Planck became a Privatdozent at Munich University, a post he held for five years. It was not a salaried post and Plank lived with his Parents. On May 02, 1885, Planck was appointed as an Associate Professor of Theoretical physics at the Kiel University. This appointment, which he held for four years, made Planck financially independent. Planck married Marie Merck on March 31, 1887. Marie was the daughter of a Munich banker. At Kiel Planck worked on thermodynamics. In this he was influenced by his teacher Gustav Kirchoff and by reading Rudolf Julius Emmanuel Clausius’ publications. He published three excellent research papers on applications to physical chemistry and thermoelectricity.

On November 29, 1888, Planck was appointed as an Associate Professor of Theoretical Physics at the University of Berlin. He succeeded his former teacher Kirchoff. Planck was not the first choice. The authorities of the Berlin University was looking for a world-renowned physicist to replace Kirchoff and first they approached Ludwig Boltzman but he did not accept the offer. After Boltzman, the post was offered to Heinrich Hertz but he also refused the offer. Finally the Department of Philosophy of the Berlin University proposed Planck’s name for the post. Planck was strongly recommended by Helmholtz, who was also Planck’s former teacher. While recommending Planck, Helmholtz wrote: “Planck’s papers are very favourably distinguished from those of the majority of his colleagues in that he tries to carry through the strict consequences of thermomechanics constructively, without adding additional hypotheses, and carefully separates the secure from the doubtful…His papers…clearly show him to be a man of original ideas who is making his own paths (and) that he has a comprehensive overview of the various areas of science.” In 1892 Planck was promoted to full professorship. He remained at the Berlin University until his retirement in 1926. In 1914 Planck succeeded in bringing Albert Einstein to Berlin and later Max von Laue, his favourite student and a Nobel Laureate. His lectures on all branches of theoretical physics at the Berlin University were held in high regard within the scientific community for many years. After Planck’s retirement in 1927, Erwin Schrodinger was chosen as his successor.

Planck was fascinated with absolutes in nature, which led him to the laws of thermodynamics and which in turn to the problem of blackbody radiation. It was Gustav Robert Kirchhoff, who in 1859-60 introduced the concept of a blackbody—an object that does not reflect any surface light. A black body is a perfect emitter and absorber of radiation at all frequencies. It should be noted that explaining the radiation given off by a hot body was one of the major challenges in physics at the end of 19th-century. It was known that the intensity of the radiation given off by a hot body increased with wavelength up to a maximum value but then fell off with increasing wavelength and that the radiation was caused by the vibrating atoms in the body. For an idealized emitter like a so-called blackbody it should have been possible to develop a theoretical expression using thermodynamics for its radiation. But there was a problem with the blackbody radiation. Since a blackbody absorbs all frequencies so when heated it should logically radiate all frequencies as well. Based on this assumption, physicists expected the number of radiations in the high-frequency range should vastly outnumber in the low-frequency range. This is because high frequencies have shorter wave lengths and so more number of high frequencies could be packed into the blackbody. But this does not happen in reality. And it could not be explained in terms of physical theories of blackbody radiation developed in 1890s, though a number of radiation laws were indeed developed. In 1896 Wilhelm Wen derived a radiation law that applied only at short wavelengths. Lord Rayleigh and James Jeans developed a law that applied at long wavelengths. Planck decided to find an equation that would be applicable to all wavelengths of the radiation emitted by a hot body. He hit upon the idea of correlating the entropy of the oscillator with its energy.

Planck argued that the atoms of a heated black body, an idealized solid, did not radiate energy continuously. They radiated energy in ‘discrete amounts’. Based on this idea he deduced a formula, which proved valid for all frequencies or wavelengths of the emitted light. Planck visualized a heated solid as being composed oscillating atoms. These oscillating atoms caused the emission of electromagnetic waves like tiny elementary antennae. And like the receiving antenna of a television set, the oscillating atoms absorbed the radiation falling upon them. But unlike an antenna, which absorbs the incoming waves at all frequencies or in a continuous way, the oscillating atoms emitted or absorbed the energy carried by the electromagnetic radiation in discrete packets or quanta (quanta is plural; the singular form is quantum). In other words the atoms absorbed energy – only at definite frequencies and not at all frequencies. The energy (E) of each quantum had to be related to the frequency (v) of the wave by the formula E = hv, where the Greek letter v is the frequency, and h corresponds to the Planck constant or elementary quantum of action. The value of h, which is a fundamental constant, is 6.63 X 10-34 joule-second. Planck’s radiation law was expressed as E = nhv, where n = 0, 1, 2, 3, 4, etc. According to this formula the energy of each quantum is proportional to the frequency. This means radiation at low frequencies is easy, as it requires only small packets or quanta of energy. And so a frequency twice as high, radiation would require twice the amount of energy. Thus based on Planck’s idea it can be said that the quantum-energy requirements to radiate at high frequency end of the spectrum will be so great that it is very unlikely to happen. Planck thus explained why blackbodies do not radiate all frequencies equally. If temperature is raised it would become easier for the larger quanta of energy to form and accordingly radiation at higher frequencies will become more likely.

Planck announced his discovery at a meeting of the German Physical Society, held in Berlin on December 14, 1900. His results were later presented in a paper published in the German physics journal Annalen der Physik in March 1901. The paper was titled “Zur Theorie der Gesetzes der Energieverteilung im Normal-Spectrum” (“On the Theory of the Law of Energy Distribution in the Continuous Spectrum”). It is from this paper that quantum theory originated.

For his discovery Planck was awarded Nobel Prize in Physics in 1919 for the year 1918. This his how he began his Nobel Lecture, which he delivered on June 01, 1920: “When I look to the time…when the concept…of the physical quantum of action began, for the first time, to unfold from the mass of experimental facts…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 journey, at last accomplished at least one step which was conclusively near the truth.”

Further he continued: “For many years, my aim was to solve the problem of energy distribution in the normal spectrum of radiating heat. After Gustav Kirchoff has shown that the state of the heat radiation which takes place in a cavity bounded by any emitting and absorbing material at uniform temperature is totally independent of the nature of the material, a universal function was demonstrated which was dependent only on temperature and wavelength, but not in any way on properties of the material. 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 so in all molecular physics…

At that time I held what would be considered today naively charming and agreeable expectations, that the laws of classical electrodynamics would, if approached in a sufficiently general manner avoiding special hypotheses, allow us to understand the most significant part of the processes we would expect, and so to achieve the desired aim…

A number of different approaches showed more and more clearly that an important connecting element or term, essential to completely grasp the basis of the problem, had to be missing…

I was busy…from the day I established a new radiation formula, with the task of finding a real physical interpretation of the formula, and this problem led me automatically to consider the connection between entropy and probability, that is Boltzmann’s train of ideas; eventually after some weeks of the hardest work of life, light entered the darkness, and a new inconceivable perspective opened before me...”

Planck himself reluctantly accepted the implications of his discovery. Being a conservative physicist, he did not want to see classical physics destroyed. He later wrote: “I tried immediately to weld the elementary quantum of action somehow in the framework of classical theory. But in the face of all such attempts this constant showed itself to be obdurate…My futile attempts to put the elementary quantum of action into the classical theory continued for a number of years and they cost me a great deal of effort.”

There was something unusual about the Plank’s formula. While seeking a relationship between the energy emitted or absorbed by a body and the frequency of radiation Planck had introduced a constant of proportionality, which could only take integral multiples of a certain quantity. However, initially Planck himself and his contemporaries did not feel it necessary to pay much serious attention to the quantum discontinuity. In 1900, neither Planck nor other physicists recognized that the new radiation law necessitated a break with classical physics. To them what mattered was the impressive accuracy in explaining the blackbody radiation and it also included the radiation laws developed by Wien and Boltzmann. Thus the Plank’s radiation law was quickly accepted by the community of physicists. In 1902 Planck’s radiation law appeared in the second volume of Heinrich Kayser’s authoritative Handbook of Spectroscopy. However, it did not mention of the nature of quantum assumption. In fact at the beginning the quantum concept was subject to a great deal of skepticism. The Dutch physicist Peter Debye later recalled: “We did not know whether the quanta were something fundamentally new or not.” Thus Max Jammer commented: “Never in the history of physics was there such an inconspicuous mathe-matical interpolation with such far-reaching physical and philosophical consequences.”

Plank’s introduction of quantum was a revolutionary idea. It was a radical break with classical physics. The concept of quanta is fundamental to physics. Commenting upon the implication of Planck’s discovery, Einstein wrote: “This discovery (Planck’s discovery) became the basis of all twentieth-century research in physics and has almost entirely conditioned its development ever since. Without this discovery it would not have been possible to establish a workable theory of molecules and atoms and the energy processes that govern their transformations. Moreover, it has shattered the whole framework of classical mechanics and electrodynamics and set science a fresh task: that of finding a new conceptual basis for all physics. Despite remarkable partial gains, the problem is still far from a satisfactory solution.”

Rapid acceptance of far-reaching implication Planck’s idea came with its use in Einstein’s prediction of the photoelectric effect. In 1905 Einstein used Planck’s discovery in his explanation of the photoelectric effect. Einstein said that light is composed of not only of waves, but also of particles, named photons.

After Einstein, Niels Bohr demonstrated the far-reaching significance of Planck’s theory. In 1913, Bohr developed the first quantum theory of atomic structure. Bohr proposed that like Planck’s atomic oscillator, the atoms can exist only in certain states. According to Bohr these quantum states correspond to specific energy values and orbits and atoms remaining in these states should not radiate. Finally Planck’s quantum concept became the basis of a new theory, named quantum mechanics, which explained all phenomena of the atomic and subatomic world. Quantum mechanics dominated physics of the whole twentieth century.

Planck was a great patriot. He could not think of leaving Germany, his beloved country, even during the two world wars. During the First World War, he prevented the Berlin Academy of Sciences from expelling members belonging to enemy countries. He publicly denied of his signature of the Manifesto of the Ninety-Three Intellectuals, a declaration in support of the German invasion of Belgium. Planck was the only one of the ninety-three intellectuals to deny publicly. After the First World War, he played an important role in rebuilding German science. He became the President of the Kaiser-Wilhelm Society, which administered some of the best-known scientific and technological research institutes. Planck’s reputation was tarnished when he decided to retain his position of influence even after the Nazis came to power. Though Planck did not publicly protest against persecution of the Jewish scientists but he raised the issue with Adolf Hitler himself in 1933. Planck argued that racial laws barring Jews from government positions would endanger the preeminence of German science. Hitler did not accept Planck’s suggestion. In 1938, Planck was forced from his positions of influence.

Planck, while explaining why he was still in Germany said in 1942: “I have been here in Berlin University since 1889…so I am quite an old-timer. But there really are not any genuine old Berliners, people who were born here; in the academic world everybody moves around frequently. People go from one university to the next one, but in that sense I am actually very sedentary. But once I arrived in Berlin, it was not easy to move away; for ultimately, this is the centre of all intellectual activity in the whole of Germany.”

Planck endured many personal tragedies in later part of his life. His elder son Karl died from wounds suffered in action in the First World War. His twin daughters Grete and Emma died during childbirth in 1917 and 1919 respectively. During the Second World War, Planck was forced to witness devastation of his country. German science and its institutions were destroyed. Planck’s own home was completely destroyed by Allied bombing in 1944 and he suffered great hardship. His youngest son and the last surviving child Erwin was executed for his part in an unsuccessful attempt to assassinate Hitler in 1944. By the end of the war, Planck, his second wife and his son by her, moved to Gottingen.
Planck summarized his work in two books: Thermodynamik (Thermodynamics, 1897) and Theorie der Warmestrahlung (Theory of Heat Radiation, 1906).

Planck wrote extensively on the philosophy of science and on religion. He believed in the existence of an almighty, omniscient and beneficent God, identical in character with the power of physical laws. Planck was of the view that science is based on the recognition of a reality external to the observer. He argued that there is only apparent contradiction between causal laws and the freedom of the will. He thought that causality is valid in nature even though it could not be proved.

Planck died on October 4, 1947 in Gottingen. The value “h + 6.62 x 10–27 erg.sec” is engraved on his tombstone.

References

  1. Kragh, Helge. Quantum Generations: A History of Physics in the Twentieth Century. Hyderabad: Universities Press (India) Ltd., 2001.

  2. Spangenburg, Ray and Diane K. Moser. The History of Science: From 1895 to 1945. Hyderabad: Universities Press (India) Ltd., 1994.

  3. A Dictionary of Scientists. Oxford: Oxford University Press, 1999.

  4. The Cambridge Dictionary of Scientists (Second Edition). Cambridge: Cambridge University Press, 2002.

  5. Jammer, Max. Concepts of Mass in Classical and Modern Physics. Cambridge, Mass.: Harvard University Press, 1961.

  6. Segre, Emilio. From X-rays to Quaks: Modern Physicists and Their Discoveries. San Fransisco: W. H. Freeman and Co., 1980.

  7. Einstein, Albert. Idea’s and Opinions. New Delhi: Rupa & Co., 1994.

  8. Dardo, Mauro. Nobel Laureates and Twentieth-Century, Physics. Cambridge: Cambridge University Press, 2004.

  9. Planck, Max. Where Is Science Going?. Woodbridge, CT: Ox Bow Press, 1981.

  10. Planck, Max. The Genesis and Present State of Development of the Quantum Theory. Nobel Lectures: Physics 1901-1921. The Nobel Foundation. Amsterdam: Elsevier, 1967.