Ludwig Eduard Boltzmann (1844-1906)
It does not seem out of place to start off by dedicating to Boltzmann the words that he himself put at the beginning of his book “Principles of Mechanics”-
“Bring forward what is true
write it so that it's clear
defend it to your last breath”
Boltzmann was certainly true to his words, his life is almost an embodiment of the above tenet. His work in statistical mechanics using probability to describe how the properties of atoms determine the properties of matter, his work on entropy, his dedication to lecturing and his belief in the atomic theory in the face of stiff opposition from people like Ernst Mach and Ostwald serves as a great example of a life dedicated to Science. Boltzmann's most important scientific contributions were in kinetic theory, including the Maxwell-Boltzmann distribution for molecular speeds in a gas. In addition, Maxwell-Boltzmann statistics and the Boltzmann distribution over energies remain the foundations of classical statistical mechanics. They are applicable to the many phenomena that do not require quantum statistics and provide a remarkable insight into the meaning of temperature.
Boltzmann was born in Vienna on 20 th Feb, 1844. Boltzmann’s elementary education took place under a private tutor which was continued in Linz in a gymnasium. There he excelled in his studies of Mathematics and Science. Also, he learned to play the piano under the tutelage of the celebrated Austrian composer, Anton Bruckner. Boltzmann continued to play the piano throughout his life. He enjoyed classical music and played the piano accompanying his son Arthur. His favourite composer was Beethoven and he subscribed to the opera house in Vienna.
Youth and the most productive years
Boltzmann, at the age of nineteen enrolled in the University of Vienna as a student of Physics and mathematics in the Institute of Physics founded by Christian Doppler. At that point Josef Stefan was the director. He was deeply influenced by Stefan, who was one of the few German physicists at that time who was receptive to the idea of local action mediated by a field. Boltzmann was introduced to the works of Maxwell by Stefan. At that time he did not know any English. In fact, he studied English so as to understand Maxwell’s original papers.
Three years after enrolling Boltzmann had already received his PhD, and published two papers. In 1869 at the age of 25 Boltzmann was awarded the post of the Chair of Mathematical Physics in Graz, the second largest city in Austria. These were some of the most productive years of his life. In 1872, he published a paper very modestly titled as “Further researches on the thermal equilibrium of gas molecules”. It was here that he introduced the famous Boltzmann’s equation. This equation describes the statistical properties of a gas made out of molecules and was one of the first equations historically to govern the temporal evolution of probability. It was here that he tried to prove the irreversibility of macroscopic phenomenon. He understood that the irreversibility of certain phenomena can be attributed to the difference in scale between the molecules and the macroscopic objects we encounter in daily life. Thus in a volume of macroscopic size the huge number of molecules undergo a large number of collisions over very small length scales. The exact inverse process is not observed not because it is impossible but because it is extremely improbable.
It seems that at that time he was in close contact with his illustrious colleagues in Berlin, Helmholtz, Ohm and Kirchoff and was on more than one occasion tempted to move to Berlin to work alongside them. He also collaborated with Bunsen and Konigsberger in Heidelberg. Boltzmann once remarked, “On certain problems I can only talk to one person, and that is Helmholtz.” From 1873 -1876 he worked in the University of Vienna as a Professor of Mathematics before he again returned to Graz to the Institute of Physics.
However appointment to that post was not an easy task, one of his opponents was Ernst Mach. He was indeed one of the staunchest opposers to Boltzmann's atomistic hypothesis, one that Boltzmann strove to defend throughout his life. Mach was widely celebrated for his text on mechanics which had influenced an entire generation of scientists, including Einstein and was indeed a cornerstone in the philosophy of science. In this book Mach opposed the prevailing view that mechanics is the central phenomenon guiding all physical observations and drew examples from evolutionary biology to psychology to support his statements. He stressed that the main feature of Science is economy of thought; Science tries to formulate its principles in such a way so as to condense in a few concepts and propositions the wealth of experimental observations. Thus he was against experimental models and pictures that could go beyond observed facts, hence he denied the existence of atoms. According to Boltzmann, the economic formulation was the knell tolling for some dead branch of Science.
However Boltzmann secured his place in Graz and when he arrived there he was already married. His wife was Henriette von Aigentler, an orphan living in Keinzl, south of Graz. She was a teacher and after meeting Boltzmann decided to study mathematics. In the first semester the university authorities allowed her to listen to the lectures because there was no rule in place barring women from colleges. In the second semester the faculty approved a rule to keep her out. So she appealed to the Minister of education and obtained an exemption, however, sadly, she was debarred again in the following semester.
In 1877, Boltzmann published the paper “Probabilistic foundations of heat theory”, where he introduced the concept of entropy as a mathematically well defined measure of what one can call the disorder of atoms. Earlier the entropy was a rather mysterious quantity which figured only when certain processes were not allowed. Here Boltzmann showed that the entropy is nothing but the measure of probability of a macroscopic state described in terms of the probability of the microscopic state describing the world of molecules.
These were very productive years for Boltzmann. He worked on a number of problems. For instance, he gave a deduction of Stefan's law of radiant heat which states that the amount of heat radiated by a body is proportional to the fourth power of its absolute temperature. In 1886, Hertz experimentally verified the equivalence of electromagnetic waves and light, predicted by Maxwell's theory. Boltzmann spent considerable effort in redoing Hertz's experiments. Boltzmann in a paper started working with interacting molecules (earlier he had worked only on ideal gases). Some people argue from this paper that it was Boltzmann and not Gibbs who should be considered as the father of the method of ensembles.
At this time Boltzmann avoided discussions on philosophical aspects of science and knowledge, something that was forced upon him in his later years.
The Crisis Begins
Boltzmann was a restless person and never felt at ease for a long time in one university. He moved around, to the displeasure of the administrators and the Austrian Government. Indeed, after his stint in the University of Graz he never really stayed in one place. His scientific productivity was affected and he developed manic depressive symptoms. At one point of time he was even forced to visit an asylum near Munich. His depression was further deepened by the death of his mother and later of his son Ludwig at the age of eleven. He first negotiated for a position at Berlin which he had longed for many years, only to refuse it later on for reasons very unclear. Then he moved to Munich, only to feel homesick and return back to Vienna. However Boltzmann certainly enjoyed great reputation because inspite of his fickleness and rumours circulating about the state of his mental health, the University of Vienna did all within its power to bring him back. However he did not find Vienna to be a happy place. Ernst Mach was at that time the professor of philosophy and history of science and was violently hostile to an atomic picture of nature. Boltzmann in spite of his prowess in the fields of Physics was by all accounts a rather casual and amiable person. It seems that Mach had a condescending attitude towards him and once remarked “Boltzmann is not malicious, but incredibly naive and casual ..., he simply does not know where to draw the line. This applies to other things too which are important to him. “He had to fight the theory of energetics, an application of the ideas of Mach. This program proposed that if we cannot refer to things we cannot observe, we may try to reduce everything to exchanges of energy, because that is what we can measure and feel, in one way or the other and base on this the entire foundations of physics. Boltzmann was a strong adversary of energetics.
Very soon Boltzmann left Vienna to work in Leipzig, however here he again fell into foul weather. Leipzig was the stronghold of Ostwald, another champion of energetics. The argument between them became so bitter that Mach himself thought that the debate was becoming too violent and proposed a reconciliation of mechanistic and phenomenological physics. In 1895, at a scientific meeting in Lübeck, Wilhelm Ostwald presented a paper in which he stated:-
The actual irreversibility of natural phenomena thus proves the existence of processes that cannot be described by mechanical equations, and with this the verdict on scientific materialism is settled. Sommerfeld, who was at the meeting, described the resulting battle between Ostwald and Boltzmann. Sommerfeld wrote:-
... Boltzmann was seconded by Felix Klein. The battle between Boltzmann and Ostwald resembled the battle of the bull with the supple fighter. However, this time the bull was victorious…. The arguments of Boltzmann carried the day. We, the young mathematicians of that time, were all on the side of Boltzmann….
Boltzmann's ideas were opposed by many European scientists, led by Ostwald. They misunderstood them, not fully grasping the statistical nature of his reasoning.
In Leipzig Boltzmann made his first attempt at suicide.
Now he again tried to come back to Vienna, however rumours were rife about his mental state and whether he would be able to perform his duties as a University Professor. The Emperor Feanz-Josef and the minister had to consult his previous psychiatrists before they were convinced that Boltzmann was capable of assuming the position. His sight had deteriorated and he had to pay a lady to read scientific papers for him and it was his wife who wrote down his own papers. In Vienna Boltzmann started lecturing on philosophy. During his lectures, even though the largest hall was chosen people stood on the steps to hear him talk. However, after two or three lectures, his interest diminished and he stopped.
In 1904 Boltzmann visited the World's Fair in St Louis, USA. He lectured on applied mathematics and then went on to visit Berkeley and Stanford. Unfortunately he failed to realise that the new discoveries concerning radiation that he learnt about on this visit were about to prove his theories correct. In the United States he was welcomed as one of the most celebrated physicists of Europe.
Boltzmann continued to defend his belief in atomic structure and in a 1905 publication Populäre Schriften he tried to explain how the physical world could be described by differential equations which represented the macroscopic view without representing the underlying atomic structure. :-
May I be excused for saying with banality that the forest hides the trees for those who think that they disengage themselves from atomistics by the consideration of differential equations.
Boltzmann's life had a tragic end in 1906. At that time he was spending a few days with his wife and youngest daughter in Duino, a village near Trieste, famous for its castle perched on a rock, having the sea on one side and a forest of cork oak on the other. Boltzmann never worried much about his health but sacrificed it for science. However now he was suffering from very poor sight, asthma and severe depression. When even that vacation in Duino did not bring him any relief from his illness, in a moment of deep depression he committed suicide by hanging on the 5 th of September, 1906. The next day he was to go to Vienna to start his lectures.
The equation for entropy S=k lnW is engraved on his tombstone.
It can hardly be said that he committed suicide because of the antagonistic attitude of various researchers who strongly opposed his atomistic viewpoint of nature, or the lack of recognition for his work. By that time he was a celebrated physicist who was widely acclaimed not only for his contributions to the branch of statistical mechanics but also for his contributions as a mathematician. It is now accepted that the compounding of all the above factors along with his mood shifts and bouts of depression was responsible for his taking his own life.
Schrodinger expected to begin his studies in physics under the great master within the next few months.
He remarks
“For me his range of ideas played the role of a scientific young love, and no one has ever held me so spellbound.”
Boltzmann- the inventor
Although primarily a theoretician Boltzmann was keenly interested in scientific and technological inventions with a keen interest in experimental work.
Boltzmann believed that practitioners of Science should not look down upon technology as just something utilitarian because it owed its initial beginnings to the practical need of solving mundane problems.
In 1902, Nerst invented his electric lamp (a small cylinder of oxides of rare earth elements heated by platinum spirals). He sent Boltzmann some specimens. Greatly enthused Boltzmann wrote verses on them:
(originally in German)
Since for yourself you choose the most refractory of material
And oblige it to carry an electrical current
You’re able to create the most glittering light.
Boltzmann sent out invitations to the members of the Viennese Physical Society to witness demonstrations of his lamp. Fifty litres of beer were ordered and about 55 invitations were sent out but he got a turnup of only about 7, which quite disappointed him.
He also took a personal interest in the aeroplane that Kress invented in 1880 and gave a lecture on this invention at the German Society of Physicists and Scientists. Unfortunately Kress ran out of money and was all but forgotten.
During his appointment as a Faculty member at Munich he used experimental models to illustrate theoretical models. He built an apparatus called the bicykel to illustrate in mechanical terms the mutual influence of electrical circuits to help his students visualize electromagnetic theory better. Arnold Sommerfeld remarks of this machine which was kept at Munich: ”It is used less for electrodynamics than for mechanics, i.e. to make it understandable how differential gears in cars, which is completely analogous to Boltzmann’s Bicykel works.”
He himself built a sewing machine for his wife who used it to sew clothes for the family.
Boltzmann- The man.
From all accounts Boltzmann was an amiable and genial person, who took a delight not only in pursuing science but also in music, poetry and nature.
One gets a glimpse into his personality when one sees that during the intense negotiations which resulted when he had to move from one University to another he remarked
“I hate this continuous secret battle. I know much better how to integrate than to intrigue.”
He could never refuse a favour. Whenever a student in a poor financial condition failed, he felt strongly responsible. In the last years of his life, no student failed an examination with him. He was very conscientious and hence administrative work became a great load for him.
He was short and stout and had curly hair and blue eyes. His wife used to call him “sweet fat darling”. Boltzmann loved nature, he took long walks with his children which always kept him in good humour. On these walks he gave detailed accounts of botany to them. He also went ice-skating with them in winter. Although, in Graz, he had a flat assigned to him as a member of the Physics faculty, he lived in a farm in the country with his family. He had a herbarium, collected butterflies and knew his plants well. He lived in idyllic surroundings with farmers as his neighbours. It is also said that he himself drove a cow, which he had just bought through the roads of Graz, after consulting his colleagues in Zoology about the best way to milk her. Story goes that his Alsatian dog came down from the farm at noon each day, waited for him outside the Institute and accompanied his master to the nearby pub where he lay down at his feet during lunch.
Boltzmann was a modest man content with his position in society; he refused the title of nobility that was offered to him. He used to say “Our middle class name was good enough for our ancestors and it will be for our children and grandchildren as well”.
He was a social person and regaled his friends with parties that lasted till late hours. His all round personality is reflected from his knowledge of classical German literature, which he liked to quote. He was a great lover of the German poet Schiller whose poetry is permeated by the concept of personal freedom and never separates the ethical from the artistic message. Among composers he liked Ludwig Van Beethoven the most.
Boltzmann- characteristics of his work
A characteristic of his work was that many of his papers were written in great detail. They were forbiddingly long with tedious calculations and lacked a clear coherent structure. His 1872 paper on H-theorem and the Boltzmann equation is about 87 pages long. In 1872 he wrote to his mother that hardly anyone was able to follow him-apart from Helmholtz. In 1873, Maxwell wrote to his colleague Peter Tait:
By the study of Boltzmann I have been unable to understand him. He could not understand me on account of my shortness and his length was and is an equal stumbling block to me.
Once Felix Klein of Gottingen asked Boltzmann to contribute an article for the encyclopedia. He hesitated for a long time. Finally Klein wrote to him if he did not do that, he would ask Zermelo to write the article. Zermelo was one among the physicists who opposed the views of Boltzmann. Immediately Boltzmann accepted the assignment.
He pursued many lines of thought. Jos Uffink wrote:
He would follow a particular train of thought that seemed promising and fruitful, only to discard it in the next paper for another one, and then pick it up again year later... it makes it hard to pin down Boltzmann on a particular set of rock-bottom assumptions, that would bring his true colours in the modern debate on the foundations of statistical physics.
Boltzmann- The Teacher
He was an excellent teacher. He possessed amazing memory and lectured almost without notes. He was witty and humorous and livened up his lectures with unusual expressions like “gigantically small”.
He had students like Paul Ehrenfest, Stefen Mayer (the discoverer of uranium fission by slow neutrons),Leise Meitner, Arrhenius and Nerst. Hasen o hrl (whose main work anticipated the equivalence of mass and energy in 1904, though with an erroneous factor), remarks
“He never exhibited his superiority. Anyone was free to put questions and even to criticize him. The conversation took place quietly and the student was treated as a peer. Only later did they realize how much he had learned from him.”
Students were always welcome to him with any kind of problem, even at his home, always keeping his patience and good humour. According to Lise Meitner, his relationship to students was very personal. He not only saw their knowledge of physics but tried to understand their character. When offering his mechanics course to students in 1902, he said:
Everything (of the course) I have. ... myself, my entire way of this thinking and feeling ... strict attention, iron discipline, tireless strength of mind. But forgive me if I ask you that which means most to me: for your trust, your affection, your love in a world, further most you have the power to give, yourself.
After his death lectures in theoretical physics were cancelled for eighteen months, until Hasenohrl was appointed to the vacant position.
We end this article with passage from a poem by his favourite poet by Schiller:
Advance proud sailor, do not pay attention to the jokes about you
Let the lazy sailor give up the tiller!
Advance towards the West, always towards the West!
It is there that the coast will appear. Look at it shining in your head!
With the Genius stays nature in eternal bond;
What the former promises, the latter certainly keeps.
Bibliography:
- Large parts have been taken from Ludwig Boltzmann – The man who trusted atoms Oxford university press
- Rajasekar, S.; Athavan, N. ( 2006 - 09-07 ). Ludwig Edward Boltzmann (the part, Boltzmann-characteristics of his work) has actually been lifted from here.
- http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Boltzmann.html
