## Provided by Larry Zamick, Physics, Rutgers University: “Max Born Founder of Lattice Dynamics”

From Vigyan Prasar Science Portal

Max Born

“I am now convinced that theoretical physics is actual philosophy.”

“The problem of physics is how the actual phenomena, as observed with the help of our sense organs aided by instruments, can be reduced to simple notions which are suited for precise measurement and used for the formulation of quantitative laws.”

**Max Born in his Experiments and Theory in Physics**

Max Born was a pioneer in developing quantum mechanics. The term “quantum mechanics” was introduced by Born. Born’s initial research interests were lattice dynamics and how atoms in solids one held together and vibrate. The Born-Haber cycle, a cycle of theoretical reactions and changes, allows calculation of the lattice energy of ionic crystals. In 1926, immediately after his student Warner Heisenberg had formulated his first laws of a new quantum theory of atoms. Born collaborated with him to develop the mathematical formulation that would adequately describe it. It was Born who first showed that the solution of Schroendinger’s quantum mechanical wave equation has a statistical meaning of physical significance. Born’s interpretation of the wave equation has proved to be of great importance in the new quantum theory. Born reformulated the first law of thermodynamics. Born produced a very precise definition of quantity of heat and thus provide the most satisfactory mathematical interpretation of the first law of thermodynamics.

Commenting on Born’s scientific contributions, the winner of 1977 Nobel Prize for Physics, Sir Neville Francis Mott (1905-1996) wrote: “As the founder of lattice dynamics, that is, the theory of how atoms in solids stick together and vibrate, Max Born is one of the pre-eminent physicists of this century. His celebrated work on cohesion in ionic crystals formed the bridge between the physicist’s and chemist’s ways of studying crystals. For the physicists, lattice energies of the crystals were of central interest and for the chemists, heats of reaction. Born showed that the ionization potentials of the atoms could be used to compare the chemical and physical concepts. This was a landmark.”

Max Born was born on December 11, 1882 at Breslau, Germany (now Worclaw, Poland). His father Gustav Born was a professor of embryology at the University of Breslau and his mother Margarete Born (nee Kaufmann) came from a Silesian family of industrialists. It was from his mother that Born inherited his love for music. Born’s mother died when he was four years old. In his childhood, Born badly suffered from bad colds and asthma and which continued to afflict him throughout his life. Because of his bad health, he was taught by private tutor for a year in home and then after spending two years in a preparatory school, he joined the Wilhelm’s Gymnasium in Breslau. At the Gymnasium, Born studied a wide range of subjects including mathematics, physics, history, modern languages, Latin, Greek, and German. At the School, Born did not display any sign of a gifted child. He was more interested in humanities than in science subjects.

In 1901, Born joined the University of Breslau. Following his father’s advice, Born did not specialize in any particular subject. He took a wide range of subjects including mathematics, astronomy, physics, chemistry, logic, philosophy, and zoology. At the Breslau University, Born became interested in mathematics and the credit for this goes to his teachers Rosanes and London. Rosanes, a student of Leopold Kronecker (1823-91), who developed algebraic number theory and invented the Kronecker delta, gave brilliant lectures on analytical geometry. It was Rosanes, who introduced Born the ideas of group theory and matrix calculus, which were later used successfully by Born to solve physical problems. London’s lectures on definite integrals and on analytical mechanics were clear and lucid. The resultant effect of the teachings of Rosanes and London was that Born was drawn towards mathematics. He was helped by some of his classmates to develop interest in science. One of his classmates named Lachmann awakened his interest in astronomy. His other classmate Otto Toeplitz introduced the lives and works of some of the greatest mathematicians like Euler, Lagrange, Cauchy and Riemann to Born. Toeplitz had learnt these from his father, who was a schoolmaster and mathematician. In his later life Born acknowledged his debt to Otto Toeplitz ‘for the first introduction to these pathfinders in mathematical science’.

In those days it was a common practice for a German student to move from university to university. And Born was no exception. In 1902 Born went to the University of Heidelberg and then in 1903 he went to the University of Zurich. It was at Zurich that Born attended his first course on advanced mathematics given by Adolf Hurwitz (1859-1919). After coming back to Breslau University, he was told by his classmates Toeplitz and Hellinger of the great teachers of mathematics, Christian Felix Klein (1849-1925), the founder of modern geometry unifying Euclidean and non-Euclidean geometry; David Hilbert (1862-1943), who originated the concept of Hilbert Space; and Hermann Minkowski (1864-1909), who developed the mathematics that played a crucial role in Einstein’s formulation of theory of relativity at the University of Gottingen. So Born went to the University of Gottingen to attend lectures by these great scientists. At the Gottingen University, Born served as an Assistant to David Hilbert. He attended lectures by Klein and Carl Runge (1856-1927) on elasticity and a seminar on electrodynamics by Hilbert and Minkowski. Klein was annoyed with Born because of Born’s irregular attendance at his lectures. Born then attended Schwarzschild’s astronomy lectures. During his student days at the Gottingen University, he had the opportunity to go for walks in the woods with Hilbert and Minkowski. During these walks, all matters of fascinating subjects were discussed in addition to mathematics including problems pertaining to philosophy, politics and social. Born was also interacting with non-mathematicians like Courant, Schmidt and Caratheodory.

Born earned his PhD in physics from the University of Gottingen in 1907. He then undertook compulsory military service. However, he did not have to complete the standard one year period because he suffered from asthma. Even his brief stint with the military made him loath all things military. After serving in the military Born visited Caius College, Cambridge for six months to study under Larmor and J. J. Thomson (1908-1909). He came back to Breslau and worked there with the physicists Lummer and Pringsheim. Around this time he was fascinated by Einstein’s work on relativity. Born’s work on combining ideas of Einstein and Minkowski led to an invitation to Gottingen in 1909, by Minkowski as his assistant. However, Minkowski died within weeks after Born’s coming to Gottingen. In 1912, Born joined the faculty of the Gottingen University and he started with working with Theodore von Karman (1881-1963), who discovered Karman vortices.

In 1915 Born was appointed as Professor (extraordinarius) at the Berlin University to assist Max Plunck. At the time Albert Einstein was also at the Berlin University. However, soon he had to join the Army. He was attached to a scientific office of the Army, where he worked on the theory of sound ranging. He could also manage to find time to work on the theory of crystals, which led to publication his first book entitled “Dynamics of Crystal Lattices” summarizing a series of investigations that Born had initiated at Gottingen.

In 1919, after the conclusion of the First World War, Born was appointed Professor at the University of Frankfurt-on-Main, where a laboratory was put at his disposal.. Here Born’s assistant was Otto Stern, the first of Stern’s well-known experiments, which were awarded with a Nobel Prize originated there.

In 1921, Born came back to the University of Gottingen as Professor of Physics, where he stayed for 12 years, interrupted only by a visit to USA in 1925. Among his collaborators at Gottingen were Pauli, Heisenberg, Jordan, Fermi, Dirac, Hund, Weisskopf, Oppenheimer, Joseph Mayer and Maria Goeppert- Mayer. During his stay Born’s most important contributions to physics were made. He published a modernized version of his book on crystals. Assisted by his students he undertook numerous investigations on crystal lattices, followed by a series of studies on quantum theory. He collaborated with Heisenberg and Jordan to develop further the principles of quantum mechanics discovered by Heisenberg. He also undertook his own studies on the statistical interpretation of quantum mechanics. Born proposed that what Schrodinger had described with his wave equation, not the electron itself, but the probability of finding the electron in any given location. Consider you are bombarding a barrier with electrons, when some will go through and some will bounce off. Born figured out that a single electron has, say 55 percent chance of going through the barrier, and a 45 percent chance of bouncing back. Because electrons cannot readily divide, Schrodinger’s quantum mechanical wave equation could not have describing the electron itself, what it was describing was its probable location. Born’s interpretation was hailed by Leon Lederman, as “the single most dramatic and major change in our world view since Newton”. However, at the beginning Born’s interpretation was not liked either by Schrodinger, the propounder of the wave equation or many other physicists including Einstein. Born corresponded with Einstein on the subject and the Born-Einstein letters were published in 1971. Born’s proposition of probability meant that the determinism of Newton’s classical physics was no more valid. There is no predetermined way in which absolute prediction can be made, as in classical physics. Everything depends on probability. A similar idea is embodied in the uncertainty principle of Werner Heisenberg. But Bohr, Sommerfeld, Heisenberg and many others took Born’s ideas seriously and they continued the exciting work of trying to get all pieces to fit.

Born introduced a useful technique, known as the Born Approximation, for solving problems concerning the scattering of atomic particles. Born and J. Robert Oppenheimer introduced a widely used simplification of the calculations dealing with electronic structures of molecules. This work known as “Born-Oppenheimer theory of molecules deals with interatomic forces.”

In 1933, like many other scientists of Jewish origin, Born was forced to leave Germany. He went to England and became Stokes lecturer at the University of Cambridge. He worked there for three years. During these years he mostly worked in the field of nonliniear electrodynamics, which he developed with Infeld.

During the winter of 1935-1936, Born spent six months at Bangalore at the invitation of C. V. Raman. Commenting on his coming to Bangalore and subsequent events, Born said: “ As I had no other job, I was willing to accept Raman’s offer namely, a permanent position at his institute, if he could obtain the consent of the Council. Then he insisted on my attending the next faculty meeting which had to decide on bringing my appointment before the Council.

The English professor Aston (who had joined around the same time) went up and spoke in a most unpleasant way against Raman’s motion declaring that a second rank foreigner driven out from his own his country was not good enough for them. I was so shaken that, when I returned home, I simply cried.”

Born was elected to the Tait Chair of natural philosophy at the University of Edinburgh in 1936. He became a British subject in 1936. One of Born’s research students described Born’s days at Edinburgh: “When Born arrived in the morning he first used to make the round of his research students, asking them whether they had any progress to report, and giving them advice, sometimes presenting them with sheets of elaborate calculations concerning their problems which he had himself done the day before…The rest of the morning was spent by Born in delivering his lectures to undergraduate honours students, attending to departmental business, and doing research work of his own. Most of the latter, however he used to carry out at home in the afternoons and evenings.”

After his retirement in 1953 Born went back to his native country and settled in Gottingen. In 1954 he was awarded the Nobel Prize in Physics “for his fundamental research in quantum mechanics, especially for his statistical interpretation of the wavefunction.” He shared the Prize with Walther Wilhelm Georg Franz Bothe (1891-1957).

Born was awarded Fellowships of many scientific academies—Gottingen, Moscow, Berlin, Bangalore, Bucharest, Edinburgh, London, Lima, Dublin, Copenhagen, Stockholm, Washington, and Boston. He was awarded honorary doctorates from a number of universities including Bristol, Bordeaux, Oxford, Freidburg/Breisgau, Edinburgh, Oslo, and Brussels. He received the Stokes Medal of Cambridge, the Max Planck Medal of the German Physical Society, the Hughes Medal of the Royal Society of London. He was also awarded the MacDougall-Brisbane Prize, the Gunning-Victoria Jubilee Prize of the Royal Society, Edinburgh and the Grand Cross of Merit with Star of the order of Merit of the German Federal Republic.

During his post-retirement life in Bad Pyrmomt, a town neer Gottingen, Born wrote many articles and books on philosophy of science and the impact of science on human affairs particularly the responsibility of scientists for the use of nuclear energy in war and peace. He was totally against the use contemporary scientific knowledge of nuclear energy for warfare. He took the initiative in 1955 to get a statement on this subject signed by a gathering of Nobel Laureates. Born is buried in Gottingen, where he died on January 05, 1970. His tombstone displays his fundamental equation of matrix mechanics that is pq-qp = (h/ 2??i.

References , [Sorry no lnks provided.]

Born. Max. My Life: Reflections of a Nobel Laureate. London: Taylor & Francis, 1978.

A Dictionary of Scientists. Oxford: Oxford University Press, 1999.

The Cambridge Dictionary of Scientists (Second Edition). Cambridge: Cambridge University Press, 2002.

Parthasarathy, R. Paths of Innovators in Science, Engineering & Technology. Chennai: East West Books (Madras) Pvt. Ltd., 2000.

Spangenburg, Ray and Diane K. Moser. The History of Science: From 1895 to 1945. Hyderabad: Universities Press (India) Ltd., 1999.

Dardo, Mauro. Nobel Laureates and Twentieth-Century Physics. Cambridge: Cambridge University Press, 2004.

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