MAX KARL PLANCK & THE BLACK BODY RADIATION LAW

Max Planck

Today, The Grandma has been relaxing at home. She has read about Max Planck, the German theoretical physicist who discovered energy quanta, derived a formula for the observed spectrum and studied black body radiation.

Planck gives his surname to a constant. He is also one of the most famous scientist of the last century thanks to his discoveries and he won the the Nobel Prize in Physics in 1918.

Planck presented a theoretical derivation of his black-body radiation law on a day like today in 1900 and The Grandma wants to homage him talking about his life and his contribution to physics and science.

Before reading about Max Planck and his achievements, The Grandma has read a new chapter of Clare West's Treading on Dreams-Stories from Ireland.

The Planck constant, or Planck's constant, denoted h is a physical constant that is the quantum of electromagnetic action, which relates the energy carried by a photon to its frequency.

A photon's energy is equal to its frequency multiplied by the Planck constant. The Planck constant is of fundamental importance in quantum mechanics, and in metrology it is the basis for the definition of the kilogram.

The Planck constant is defined to have the exact value h = 6.62607015×10−34 J·s.

At the end of the 19th century, physicists were unable to explain why the observed spectrum of black body radiation, which is still considered to have been accurately measured, diverged significantly at higher frequencies from that predicted by existing theories.

In 1900, Max Planck empirically derived a formula for the observed spectrum. He assumed that a hypothetical electrically charged oscillator in a cavity that contained black-body radiation could only change its energy in a minimal increment, E, that was proportional to the frequency of its associated electromagnetic wave. He was able to calculate the proportionality constant, h, from the experimental measurements, and that constant is named in his honor.

Max Planck

In 1905, the value E was associated by Albert Einstein with a quantum or minimal element of the energy of the electromagnetic wave itself. The light quantum behaved in some respects as an electrically neutral particle, as opposed to an electromagnetic wave. It was eventually called a photon.

Max Planck received the 1918 Nobel Prize in Physics in recognition of the services he rendered to the advancement of Physics by his discovery of energy quanta. Since energy and mass are equivalent, the Planck constant also relates mass to frequency.

Max Karl Ernst Ludwig Planck, (April 1858-4 October 1947) was a German theoretical physicist whose discovery of energy quanta won him the Nobel Prize in Physics in 1918.

Planck made many contributions to theoretical physics, but his fame as a physicist rests primarily on his role as the originator of quantum theory, 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.

More information: Max Planck-Gesellschaff

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 and Munich. One of his uncles was also a judge.

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. However, by the age of ten he signed with the name Max and used this for the rest of his life.

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.

Max Planck & Albert Einstein

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.

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. 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.

More information: BBC

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.

Max Planck

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."

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:

E = h ν

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.

More information: Live Science

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. 

Planck's constant

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.

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.

More information: Quanta Magazine

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...

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.

Albert Einstein & Max Planck in a conference

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. 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.

More information: Physics

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.

Planck's constant

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. He hoped the crisis would abate soon and the political situation would improve.

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.

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.

More information: Science Direct

Scientific discovery and scientific knowledge have been achieved

only by those who have gone in pursuit of it

without any practical purpose whatsoever in view.

Max Planck