## Max Planck Quantum Theory “Why I Accidentally Created Quantum Mechanics”

In December of 1900, a conservative German scientist named Max Planck wrote a paper that included, according to the Nobel Prize-winning Physicist Max Born, “the most revolutionary idea whichever has shaken physics.[1]”  For this paper, Planck assumed that light came in little energy packets.  Why did he do this and why was it so revolutionary?  Good questions!  Let’s ask Planck.  No, not with an Ouija board silly.  Why don’t we just read his autobiography and his other papers and see what Planck himself said?  And that is exactly what I did.  Ready for the real story of how and why quantum mechanics was created?  Let’s go!

Statistical mechanics had been around since 1859 when James Clerk Maxwell (of Maxwell’s equations) decided to study gasses by using statistics.  The general idea is that gasses are filled with a ridiculous number of atoms moving in different directions at different speeds.  In order to study them, you need to determine what they are doing on average, which is why you need statistics and probability.  Five years after Maxwell, a 20-year-old physicist named Ludwig Boltzmann read Maxwell’s paper and devoted his life to this research and became Germany’s main champion of the existence of atoms.  Max Planck said that for most of his career up to this point he had been, “hostile to the atomic theory which was the foundation of [Boltzmann’s] entire research.[6]” Why did Planck hate statistical mechanics?  It wasn’t the math, it was what it meant about Physics, specifically what it meant about the second law of thermodynamics and entropy.

See, Planck had gotten his Ph.D. (at age 19!) in the second law of thermodynamics.  The second law can be written in many, many, forms but the basic idea is that things cannot become more ordered (or less messy) by themselves.  Physicists call the messiness of a system, the entropy, which is given the letter S for no reason I can see (maybe it was a convenient letter not used for other things).  However, if you believe in statistical mechanics then all of those atoms could randomly become more ordered, it was just really, really, unlikely.  In other words, the second law wasn’t a law as much a statistical certainty.  Maxwell elegantly put it this way, “The second law of Thermodynamics has the same degree of truth as the statement that if you throw a cup of water into the sea, you cannot get the same cup of water out again.[7]”   To Planck, that statistical certainty didn’t seem good enough.

However, desperate times called for desperate measures, and, holding his nose, Planck dived into, “the interrelation of entropy and probability – in other words, to pursue the line of thought inaugurated by Boltzmann.[8]”  Boltzmann had been writing about the idea that atoms in gasses could have different arrangements to produce their average energies, and had given the letter W (the German word for probability) for the measure of how many different arrangements there could be.  It made sense that the entropy, or the amount of messiness, S, would relate to the number of ways that one could arrange your materials, W, but how?  Planck recalled, “Since the entropy S is an additive magnitude but the probability W is a multiplicative one, I simply postulated that S = k log W, where k is a universal constant.[9]”  This became known as Boltzmann’s entropy equation and k is known as Boltzmann’s constant, despite the fact that it was created and defined by Planck.  In fact, this equation “S=k log W” is actually written on Boltzmann’s tombstone!  Ironically, Boltzmann did not determine “his” constant.  Planck did.

But then Planck had a problem.  He couldn’t seem to get the equation to work without another constraint because if the energy is, “considered to be continuously divisible quantity, this distribution is possible in infinitely many ways.[10]”  He, therefore, imagined that light was made of little bundles of  “energy elements” with energy that equaled a constant h times the frequency of the light.  In his paper, Planck stated clearly, “the most essential point of the whole calculation [is to consider the energy], E to be composed of a very definite number of equal parts[11].”  This is the delineation between classical and modern physics.  Let’s take a moment to recognize what a radical and strange idea this is.  Think of a water wave or a sound wave.  They do not come in little packages.  They are vibrations of water or molecules where the more the water or molecules vibrate, the more energy the wave has.  Planck was creating a brand new thing in physics, a wave packet!  Five years later Einstein called these packets “quanta of energy” although they are currently called photons.  This is the birth of the quantum.  It is a really, really big deal.

However, Planck did not realize what he had done to the whole nature of Physics.  Quantizing energy was, according to Planck, “a purely formal assumption, and I did not give it much thought.[12]”  Instead, he assumed that he could massage this new theory into classical theory and spent over a decade in a futile attempt to distance himself from his own idea.  The rest of the scientific world politely ignored Planck’s startling claim and most believed in a competing theory that used statistical mechanics but didn’t require energy to be in little packages.  The only problem with the other method is that as the frequency went up you got more and more possible states with no quantum limitations so that as you went to the ultraviolet range, the radiation went up exponentially, a situation poetically called the ultraviolet catastrophe!  Some people tried to solve this problem with a fudge factor or by just saying it didn’t work at high frequencies for some unknown reason.  One of the inventors of this theory said it was fine (this is fine) as the catastrophe was happening but just unevenly and very, very slowly.  By the way, Planck thought that man was an idiot, writing a friend that he, “is the model of the theorist as he should not be… [he just] ignores the facts if they don’t fit.[13]” However, at the time a theory that didn’t fit the facts seemed far preferable to a theory with an odd energy packet that didn’t follow the laws of physics.

Even a young college graduate named Albert Einstein had “mixed feelings” about Planck’s paper.  Then in May of 1901, Einstein read a paper about something called the photoelectric effect by Phillip Lenard and it all made sense.  Planck’s equation was not a “formal assumption” it was a fundamental discovery about the nature of light.   He wrote to his girlfriend, “I have just read a wonderful paper by Lenard …[and] under the influence of this beautiful piece I am filled with such happiness and joy that I absolutely must share it with you.”  By 1905, Einstein and his “dear kitten” became the first people to actually use Planck’s idea of energy packets to explain what light is.  Well over a hundred years later, this paper is still considered to be correct and Einstein actually won his Nobel Prize due to the photoelectric effect.   And I will get to that.  But first I want to answer another question.  What is the photoelectric effect, why did Lenard study it, and what did Lenard think he was seeing?  That is next time on the Lightning tamers!

[1] Born, M “Obituary Notices of Fellows of the Royal Society” Trans of the Roy Soc (1947) Issue 17, p. 167

[2] Planck, M “On an Improvement of Wien’s Equation for the Spectrum” English translation from Haar, D. The Old Quantum Theory (1967) p. 81

[3] Planck, M Scientific Autobiography and Other Papers p 41

[4] p 41 “Scientific Autobiography and Other Papers” Max Planck

[5] 1931 letter to R. Wood recounted in p 76 “From X-rays to Quarks: Modern Physicists and Their Discoveries” Emilio Segre.

[6] p 32 “Scientific Autobiography and Other Papers” Max Planck

[7] recalled on p 55 “Einstein and the Quantum” Stone

[8] Planck, M Scientific Autobiography and Other Papers (1947) p. 41

[9] Planck, M Scientific Autobiography and Other Papers (1947) p. 41

[10] Planck, M “On the Theory of the Energy Distribution Law of the Normal Spectrum” English translation by D. Haar The Old Quantum Theory (1967) p. 85

[11] Planck, M “On the Theory of the Energy Distribution Law of the Normal Spectrum” English translation by D. Haar The Old Quantum Theory (1967) p. 85

[12] Planck, M referenced in Kantorovich, A Scientific Discovery: Logic and Tinkering (1993) p. 164

[13] Planck, M to Wein Referenced in Stone, A Einstein and the Quantum (2013) p. 102

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