Why the 3rd law of Thermodynamics made Einstein (& QM) Famous

In late October of 1911, 31-year-old Albert Einstein went to an elite and influential conference called the Solvay Congress to discuss quantum mechanics.  How elite?  Well, at the time 4 of the 23 scientists in attendance had already won a Nobel Prize (or 2), and a further 5 would eventually win a Nobel Prize, including Einstein.  Just three years earlier, however, Einstein couldn’t get a job as a professor and, although his views on relativity were slowly gaining traction, his radical theories of quantizing light were roundly ignored.  So, how did Einstein get invited to this influential conference and why was there a big conference about quantum mechanics way back in 1911 in the first place?  The answer has to do with a Chemist named Walther Nernst who had created the 3rd law of thermodynamics.  What is the 3rd law of thermodynamics, why did Nernst create it and why in the world would a thermodynamics law put Einstein at an elite conference?  Well, I’ll tell you.  Ready?  Let’s go.

Nernst was a funny character: small, chubby, and charming but also stubborn with a notorious vindictive streak.  For example, Nernst was nicknamed Chronos because the Greek god ate his sons and Nernst ate his students[1]!  (Although to be fair, Robert Millikan who was a former student of Nernst’s, wrote in Nernst’s obituary that Nernst was “in the main, popular in the laboratory[2]” although even Millikan admitted that, “in the academic world [Nernst] nearly always had a quarrel on with somebody[3]”.)  Nernst was known for his hurried sloppiness and his office and lab, “always presented aspects of extreme chaos which his coworkers termed appropriately, ‘the state of maximum entropy[4].”  [Entropy is a measure of the disorder (or messiness) of a system, and, yes, Physicists have an equation for messiness!]  Despite his disheveled methods Nernst was surprisingly effective at experimenting and even better at seeing the big picture, and he always had an eye for the practical and modern.  For example, in 1897, when Nernst was in his early thirties, he invented a new kind of electric lamp and wisely insisted on a huge lump payment for the lamp instead of royalty.  Supposedly, the next year Nernst went to the US and asked Edison how much he made off of his light bulb patent, when Edison replied “nothing” Nernst gleefully replied, “I got a million marks for mine!  The trouble with you Edison is that you are not a good businessman. [5]

Albert Einstein
Albert Einstein

Wealthy and famous, Nernst was free to study whatever appealed to him.  In the early 1900s Nernst decided to focus on creating nitrogen-based fertilizers out of the nitrogen in the air.  This was a common interest of Chemists ever since 1898 when a charismatic English scientist with a fabulous mustache named William Crookes correctly predicted that the current farming methods were depleting the ground of nitrogen and with population growth, they would soon run out of wheat and millions would starve.  Crookes then inspired that generation of Chemists by stating that, “it is through the laboratory that starvation may ultimately be turned into plenty[6]”.  Therefore, Nernst began examining a lot of data for different chemical reactions at different temperatures and pressures.  Nernst knew that at the lowest possible temperature, called absolute zero, the chemical terms he was looking at should be identified as he had an equation that the difference between these terms equals the temperature times the entropy (remember, entropy is the measure of the disorder or messiness).  However, in December of 1905, supposedly while giving a lecture, Nernst said that “the realization pressed itself forward[7]” that it looked like these terms not only became “identical at low temperatures”, but “they invariably become practically identical some distance before absolute zero is reached. [8]”  In other words, not only does the temperature go to zero at absolute zero, but also the entropy goes to zero too!  Within a few months, this “theorem” was being referred to as a “Third law of Thermodynamics[9]”.  What in the world does it mean if the entropy is zero?  As a biographer of Nernst’s poetically wrote in 1973: “The third law had transformed absolute zero from a state of complete rest into one of perfect orderliness. [10]”  Nernst called it his “heat theorem” although it wasn’t much of a theory as a “heat postulate” as it was based entirely on assumptions about experimental graphs without any theoretical basis behind it.  At first, this “theorem” was, according to one of Nernst’s students, “mainly regarded as a useful rule for calculating chemical equilibria. [11]”  Nernst thus had found a way forward towards the creation of fertilizer but was so entranced by the implications of his “theory” that he abandoned the production of fertilizer to a fellow scientist named Fritz Haber.  With the help of Nernst’s “heat law” Haber succeeded in producing ammonia in 1909 and, with fellow chemist Carl Bosch, mass-producing it the next year.  Currently, Haber’s discovery is responsible for around half of the food produced today[12]!  When World War 1 started, ammonia was also used to make explosives without which Germany arguably could have never had the firepower to attempt the war (being blockaded from natural sources of nitrates).  In addition, during WW1 Haber moved from making fertilizers to being at the forefront of making deadly chlorine gas for use in trench warfare, personally overseeing the deployment of poison gas at Ypres and becoming known as the “father of chemical warfare”[13].   

Einstein's Graph from 1907

Anyway, back in 1905, Nernst was so excited by his “theory” that according to a former student, “the Nernst laboratory swung away from chemical equilibria to an entirely new and strange aspect of physics: the world of very low temperatures.[14]”  Nernst set up his own ad-hock hydrogen liquefier, which only worked when the lab’s long-suffering mechanic used it.  Even then it was very temperamental, once exploding and burning or breaking the laboratories windows, a wall, and the mechanics’ mustache[15]!  It is impossible to directly measure the entropy of a body so Nernst and his team measured the specific heats at very low temperatures with the liquid hydrogen as a cooling agent.  [Specific heat is the energy needed to change the temperature per degree]  They sound found that all their materials had specific heats that fell to very low values at very low temperatures.  In fact, it seemed like the specific heats would vanish at absolute zero.  Now, what does that mean?  Well, specific heat, as I said before, is the heat needed to increase an object’s temperature per degree.  If the specific heat is zero, then the object needs no heat for its temperature to increase.  This means that the object will not stay at absolute zero.  In other words, not only was absolute zero the coldest temperature, there is no way to reach absolute zero.  It is the limit but also, an unobtainable limit.  Just as absolute order is unobtainable.  Nernst was more and more convinced that he was on the precipice of a profound idea.  However, he was still stymied by the fact that he had no theoretical basis for his “theory”.  Then, in 1909 or early 1910, Nernst became aware of an obscure 1907 paper from a patent clerk, Albert Einstein, that proved theoretically that the specific heat goes to zero, but only if you used quantum mechanics.

Quantum mechanics began in December of 1900 when a co-worker (and friend) of Nernst named Max Planck assumed that light was created in little energy elements equal to a constant, h, times the frequency of light.  Now, Planck just made this assumption to make a radiation equation work and wasn’t even convinced that the number of energy elements were whole numbers, or quantized.  Einstein, however, saw things in a different light, so to speak.  In 1905, he assumed that light was composed of “a finite number of energy quanta [energy packets] that are localized in points in space, move without dividing, and can be absorbed or generated only as a whole.[16]” Planck didn’t care much for thinking of light as a bunch of particles writing Einstein that he felt that light behaves like a wave and is, “described exactly by Maxwell’s equations.[17]”  Planck was far more interested in Einstein’s third paper that miracle year where Einstein created the theory of relativity. Planck wanted Einstein to focus on relativity and ignore the quantum stuff but Einstein was hooked, at least at the time. 

Two years later, Einstein decided that he could use Planck’s idea of energy elements to understand how solids emit and absorb heat.  In other words, Einstein derived the specific heat using Planck’s quanta (this is the paper that Nernst liked).  Einstein wrote, “For although one has thought before that the motion of molecules obeys the same laws that hold for the motion of bodies in our world of sense perception we now must assume that the diversity of states they can assume is less than for bodies within our experience [and] can only assume the values, 0, hf, 2hf, etc.[18]” In order to determine the specific heat, Einstein modeled the molecules as little oscillators vibrating independently in three dimensions.  By the way, Einstein knew this was a simplified model and admitted, “an exact agreement with the facts is out of the question[19]”.  Nevertheless, this simple model, he hoped, would give an equation for how the specific heat varied with temperature.  From Planck, Einstein had an equation for the average energy of the vibrating molecules as a function of temperature; he then multiplied it by 3 times the number of molecules (3 for the three directions) to find the total energy of the substance.  Finally, he took the derivative of that energy as a function of temperature (as a derivative is an instantaneous change), and presto change-o he got an equation for the specific heat!  The exact form of the equation is not that important (especially as Einstein’s assumption was a little too broad and a person named Debeye created a more accurate equation in 1912).  What is important is that in 1907, the equation he got seemed to fit very nicely with the data he had on hand from other people’s experiments.  Moreover, the specific heat went to zero asymptotically at zero degrees for all solids!  As the author, Douglas Stone elegantly put it, “Newtonian atoms had frozen to death. [20]”  

3rd Law of Thermodynamics

At first, everyone basically ignored Einstein’s 1907 paper, like they ignored his pioneering 1905 paper on quantum mechanics before it.  He tried for years to get other scientists interested in quantum mechanics or to believe that light behaves like a wave and a particle, to no avail.  Einstein wrote a friend in May of 1909, “This quantum question is so extraordinarily important and difficult that everybody should take the trouble to work on it.[21]”  Three months later, Max Planck invited Einstein to give his first important public talk.  Planck was probably hoping that Einstein would talk about relativity but, instead, he spoke about Quantum Mechanics once again pushing “a theory of light that can be understood as a kind of fusion of the wave and particle theories.”  Years later, a member of the audience recalled that this talk went nowhere as “the chairman of the meeting was Planck, and he immediately said that it was very interesting but he did not quite agree with it.[22]”  Meanwhile, Einstein was still working at the patent office.  In fact, Einstein’s first job as a low-level professor only started in October of 1909 and even then he wasn’t well known even by his own department.

This is when Nernst read Einstein’s 1907 paper.  You could see why Nernst was happy to discover it, finally, he had some theoretical backing for his ideas.  Nernst wrote a friend, “Einstein’s “quantum hypothesis” is probably among the most remarkable thought [constructions] ever; if it is correct, then it indicated completely new paths…for all molecular theories; if it is false, well, then it will remain for all times ‘a beautiful memory’.[23]”  In March of 1910, Nernst decided he had to visit the young scientist and see for himself if Einstein was a genius or a crackpot.  After the visit, Nernst was deeply impressed with Einstein and declared him a “Boltzmann reborn[24]” (that is a big compliment).   The effect on Einstein’s reputation was immediate.  An assistant professor at Zurich Polytechnic recalled, “Einstein in 1909 was unknown in Zurich.  Then Nernst came and people in Zurich said ‘that Einstein must be a clever fellow if the great Nernst comes all the way from Berlin to Zurich to talk to him.[25]”  Einstein was ecstatic, writing a friend, “For me, the theory of quanta is a settled matter.  My predictions regarding the specific heats apparently being brilliantly confirmed [and even] Nernst… has… been here to see me.[26]”  

In February of 1910, Nernst mentioned Einstein’s 1907 paper at a talk and suddenly many scientists were interested in quantum mechanics and quantum views of specific heats.  For example, before Nernst mentioned it in 1910, there were no other papers that referenced Einstein’s 1907 paper.  In the three years after Nernst referenced him over forty papers referenced Einstein’s 1907 paper[27].  By 1912, even Max Planck tackled the issue and proved that Nernst’s initial thought that the entropy would always go to zero at absolute zero temperature wasn’t true if an object was a mixture of more than one component, which rewrote the third law to be: “the entropy of a perfect crystal goes to zero at absolute zero temperature”.   At around the same time, in 1912, Nernst created his final version of the third law of thermodynamics: “It is impossible for any procedure to lead to … t=0 in a finite number of steps. [28]” Scientists to this very day are still arguing about the proper form of the law. 

Back in the summer of 1910, Nernst decided that he needed to big international meeting on radiation and quantum “issues”.  He talked to Planck but Planck wanted to delay writing “Such a conference will be more successful if you wait until more factual material is available . [29]”  The ever-impatient Nernst turned to a wealthy soda manufacturer, and common scientific philanthropist, Ernest Solvay.  Solvay had as many ideas as he had money and was eager to be at the forefront of science.  Soon, with Solvay’s money, Nernst put together the world’s first international physics meeting in Brussels and had Solvay send out 19 invitations to the top scientists in the world, and, to bolster Nernst’s “heat theorem”, send an additional invitation to Einstein (Nernst asked Solvay not to mention that he was the “initiator of the idea of the conference[30]”). Einstein received his invitation with mixed feelings, as he had, in just the preceding months, become completely flummoxed by quantum mechanics (Einstein had been trying to re-write Maxwell’s equations to include quantum terms and had found it intractable).  In fact, the month before being invited to the conference, Einstein dejectedly wrote a friend, “I no longer ask whether these quanta really exist.  Nor do I try to construct them any longer. [31]” He even started to refer to quantum problems as “the h-disease” which, “looks ever more hopeless. [32]”  Despite wanting to give up on quantum mechanics, Einstein accepted the invitation; it was just too big an honor to ignore.  However, in Einstein fashion, he complained to a friend that, “my twaddle for the Brussels congress weighs down on me. [33]

After the conference Einstein wrote Solvay a flowery thank-you note that the congress, “will remain forever one of the most beautiful memories of my life,[34]” but he told his friend Besso his true feelings, “In Brussels… they acknowledged the failure of [quantum] theory with much lamentation but without finding a remedy.“  Einstein also added that he, “heard nothing that I had not known before,” and felt that, “nothing positive has come out of it.[35]”  But Einstein didn’t know that his talk at the Solvay conference was to have major consequences.  First, even the most conservative of the attendees started to agree with Marcel Brillouin, a scientist from France, “From now on we will have to introduce into our physical and chemical ideas a discontinuity, something that changes in jumps, of which we had no notion at all a few years ago.[36]”  The second was the attendees went home and talked about his speech.  For example one of the secretaries, Maurice de Broglie, told his baby brother Luis who recalled, “I began to think about quanta from the moment that my brother gave me the notes of the Solvay Congress of 1911.[37]”  Also, another of the attendees, the great Ernest Rutherford, went back to England and discussed the meeting with his graduate student, a nice Danish man named Niels Bohr. 

But before I get to Niels Bohr and the Bohr model of atoms, or Luis de Broglie, and how he created the idea of the wave nature of all particles, I want to first mention a funny thing about the laws of thermodynamics.  For years I have been teaching a trick to remember the laws of thermodynamics: “You can’t win, you can’t break even, and you can’t get out of the game” as immortalized by the 1978 film “The Wiz”.  But wait, why does that phrase represent the three laws and why is it in an all-black version of the “Wizard of Oz”?  That is next time on the Lightning Tamers.


[1] Recalled in Coffey, P Cathedrals of Science (2008) p. 170

[2] Millikan, R “A Great Physicist Passes” Scientific Monthly Vol. 42 January 1942 p. 84

[3] Millikan, R “A Great Physicist Passes” Scientific Monthly Vol. 42 January 1942 p. 84

[4] Recalled by Mandelssohn, K The World of Walther Nernst (1973) p. 70

[5] Recalled in Coffey, P Cathedrals of Science (2008) p. 30

[6] Crookes, W “Address of the President before the British Association for the Advancement of Science” Science Vol. 8 No. 200 (October 28, 1898) p. 562

[7] Translated in Coffey, P Cathedrals of Science p. 102

[8] Nerst, W “Studies in Chemical Thermodynamics” Nobel Lecture, December 12, 1921 p. 358

[9] Yale Alumni Weekly (Sept 1906), p. 184

[10] Mandelssohn, K The World of Walther Nernst (1973) p. 68

[11] Simon, F “The Third Law of Thermodynamics, An Historical Survey” 40th Guthrie Lecture, Year Book of the Physical Society, 1956 p. 3

[12] Smil, V “Detonator of the population” Nature Vol. 400 (1999)

[13] For example see the movie: Faber: The Father of Chemical Warfare (2008)  haberfilm.com

[14] According to Mandelssohn, K The World of Walther Nernst (1973) p. 71

[15] According to Mandelssohn, K The World of Walther Nernst (1973) p. 71

[16] Einstein, A “On a Heuristic Point of View Concerning the Production and Transformation of Light” Translated and found in Einstein, A, Beck A, and Havas, P The Collected Papers of Albert Einstein, Vol. 2 Princeton University Press p. 87

[17] Max Planck to Albert Einstein (July 1907) translated in Einstein, A, Beck A, and Havas, P The Collected Papers of Albert Einstein, Vol. 5 Princeton University Press p. 31

[18] Einstain, A “Planck’s Theory of Radiation and the Theory of Specific Heat” (1907) Translated and found in Einstein, A, Beck A, and Havas, P The Collected Papers of Albert Einstein, Vol. 2 Princeton University Press p. 218

[19] Einstain, A “Planck’s Theory of Radiation and the Theory of Specific Heat” (1907) Translated and found in Einstein, A, Beck A, and Havas, P The Collected Papers of Albert Einstein, Vol. 2 Princeton University Press p. 218

[20] Stone, A Einstein and the Quantum p. 110

[21] Albert Einstein to Jakob Laub (May 17, 1909) translated in Einstein, A, Beck A, and Havas, P The Collected Papers of Albert Einstein, Vol. 5 Princeton University Press p. 119

[22] Paul Epstein quoted in Stone, A Einstein and the Quantum (2013) p. 140

[23] W. Nernst to A Schuster, (March 10, 1910) Royal Society, found in Barkan, D Walther Nernst, and the Transition to Modern Physical Science (2011) p. 183

[24] W. Nernst to A Schuster, (March 10, 1910) Royal Society, found in Barkan, D Walther Nernst, and the Transition to Modern Physical Science (2011) p. 183

[25] George Hevesy recalled in Kuhn, T Black-body Theory (1987) p. 215

[26] Albert Einstein to Jakob Laub (March 16, 1910) translated in Einstein, A, Beck A, and Havas, P The Collected Papers of Albert Einstein, Vol. 5 Princeton University Press p. 149

[27] p 147-8 “Einstein and the Quantum” Stone

[28] p 342 “A Survey Of Thermodynamics” Bailyn (1994) American Institute of Physics NY

[29] Max Planck to Walther Nernst (June 11, 1910) found in Barkan, D Walther Nernst and the Transition to Modern Physical Science (2011) p. 187

[30] Walther Nernst to Ernest Solvay (Nov 27, 1910) Translated and Found in Mehra, Jagdish The Solvay Conferences on Physics (2012) p. 7

[31] Albert Einstein to Michele Besso (May 13, 1911) translated in Einstein, A, Beck A, and Havas, P The Collected Papers of Albert Einstein, Vol. 5 Princeton University Press p. 187

[32] Albert Einstein to Lorentz (Nov 23, 1911) translated in Einstein, A, Beck A, and Havas, P The Collected Papers of Albert Einstein, Vol. 5 Princeton University Press p. 228

[33] Albert Einstein to Michele Besso (September 11, 1911) translated in Einstein, A, Beck A, and Havas, P The Collected Papers of Albert Einstein, Vol. 5 Princeton University Press p. 205

[34] Albert Einstein to Ernest Solvay (Nov 22, 1911) translated in Einstein, A, Beck A, and Havas, P The Collected Papers of Albert Einstein, Vol. 5 Princeton University Press p. 227

[35] Albert Einstein to Michele Besso translated in Einstein, A, Beck A, and Havas, P The Collected Papers of Albert Einstein, Vol. 5 Princeton University Press p. 241

[36] Brillouin, W from Solvay, E., Langevin, P., Broglie, M. D. D., & Institut international de physique Solvay (1912). La théorie du rayonnement et les quanta: rapports et discussions de la réunion tenue à Bruxelles du 30 octobre au 3 novembre 1911. Paris: Gauthier-Villars. p.

[37] De Broglie, L quoted in Stone, A Einstein and the Quantum (2011) p. 243

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