Planck's Faustian Deal: The Quantum

Here is a short excerpt from my book Dr Faustus of Modern Physics giving perspective on the birth in 1900 of Quantum Mechanics with Planck's mathematical analysis of blackbody radiation introducing $E=h\nu$ as a smallest quantum of energy. 

To boost his career and the science of the booming German Empire, Max Planck, professor at the University of Berlin with a background from thermodynamics, took on the main open problem of physics at the end of the 19th century, namely to explain why the ultra-violet catastrophe of blackbody radiation predicted by classical theoretical physics cannot be observed. At stake was the credibility of a science of physics (and the German Empire) predicting very intense high-frequency radiation which simply refused to exist. The stakes were thus very high and Planck with ambition stepped in:

• The whole procedure was an act of despair because a theoretical interpretation had to be found at any price, no matter how high that might be... 

The price was to give up his soul as very serious scientist with deep conviction to classical ideals, which paved the way for new quantum physics giving up classical principles of reality, causality and determinism, now in deep crisis.  

1. Nobel Prize to Planck

 The Nobel Prize in Physics 1918 was awarded (in 1919) to Max Planck:

• in recognition of the services he rendered to the advancement of Physics by his discovery of energy quanta.

It took the Nobel Committee more than 10 years to come to this conclusion, because Planck’s new concept of a smallest quantum of energy was so difficult to swallow, described by the Swedish mathematician Ivar Fredholm as “hardly plausible”. In 1918 the Committee gave in under pressure to give the prize to Bohr and Einstein, which required a prize to Planck first. The presentation speech by Ekstrand stated:

• Planck’s radiation theory is, in truth, the most significant lodestar for modern physical research, and it seems that it will be a long time before the treasures will be exhausted which have been unearthed as a result of Planck’s genius.
• Planck constant, proved, as it turned out, to be of still greater significance: The product $h\nu$, where $\nu$ is the frequency of vibration of a radiation, is actually the smallest amount of heat which can be radiated at the vibration frequency $\nu$. This theoretical conclusion stands in very sharp opposition to our earlier concept of the radiation phenomenon.

Planck was thus viewed as having “discovered” a physical phenomenon of “energy quanta”, which in fact was a “theoretical conclusion”. This contradiction has come to form the ideology of modern physics made possible by breaching the classical holy distinction between reality and mathematical model.

2. Planck's Confession

From Planck's self-biography:

• We shall now derive strange properties of heat radiation described by electromagnetic wave theory.
• ..the whole procedure was an act of despair because a theoretical interpretation had to be found at any price, no matter how high that might be... 
• Either the quantum of action was a fictional quantity, then the whole deduction of the radiation law was essentially an illusion representing only an empty play on formulas of no significance, or the derivation of the radiation law was based on sound physical conception. Mechanically, the task seems impossible, and we will just have to get used to it (quanta). 
• My futile attempts to fit the elementary quantum of action into classical theory continued for a number of years and cost me a great deal of effort. Many of my colleagues saw in this something bordering on a tragedy (Planck shortly before his death).
• 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.
• The assumption of an absolute determinism is the essential foundation of every scientific inquiry.
• All matter originates and exist only by virtue of a force which brings the particle of an atom to vibration and hold this most minute solar system of the atom together. We must assume behind the existence of this force the existence of a conscious and intelligent mind. This mind is the matrix of all matter...
• In order to find the correct resonator entropy S it must be assume that the energy U of a resonator with frequency ν can only take on discrete energy values, to wit, integer multiples of h times ν, in contrast to classical theory where U can be any multiple, integer or not, of ν. We now say that U is quantised.
• My maxim i always this: consider every step carefully in advance, but then, if you believe you can take the responsibility for it, let nothing stop you.
• For by nature I am peaceful and disinclined to questionable adventures...for unfortunately I have not been given the capacity to react quickly to intellectual stimulation.

3. Planck on Politics

Planck lost his son Karl in combat during 1st World War and his son Erwin was executed after a plot against Hitler at the end of the 2nd World War. Planck signed together with 93 German intellectuals the Appeal to the Cultured Peoples of the World on 4 October 1914:

• We declare the leaders of German art and science to be at one with the German army.

Planck reports as Rector of Berlin University in 1914:

• The German people ha found itself again. One thing only we know, that we members of our university...will stand together as one man and hold fast until - despite the slander of our enemies - the entire world comes to recognise the truth and German honor.
• But we shall also see an feel how, in the fearful seriousness of the situation, everything that a country could call its own in physical and moral power came together with the speed of lightning and ignited a flame of holy wrath blazing to the heavens, while so much that had been considered important and desirable fell to the side, unnoticed, as worthless frippery.