Pauling Amidst the Titans of Quantum Mechanics: Europe, 1926

Erwin Schrödinger and Fritz London in Berlin, Germany, 1928.

[Ed. Note: Spring 2010 marks the seventy-fifth anniversary of the publication of Linus Pauling and E. Bright Wilson, Jr.’s landmark textbook, Introduction to Quantum Mechanics.  This is post 1 of 4 detailing the authoring and impact of Pauling and Wilson’s book.]

…the replacement of the old quantum theory by the quantum mechanics is not the overthrow of a dynasty through revolution, but rather the abdication of an old and feeble king in favor of his young and powerful son.

-Linus Pauling, “The Development of the Quantum Mechanics,” February 1929.

Since 1925 the John Simon Guggenheim Memorial Foundation has annually awarded fellowships to promising individuals identified as advanced professionals who have “already demonstrated exceptional capacity for productive scholarship or exceptional creative ability in the arts.”  The selection process is extremely competitive and recipients are generally esteemed in their chosen field as applicants face rigorous screening and are selected based on peer recommendation and expert review.

Since the first awards in 1925, many Nobel and Pulitzer prize winners have received Guggenheim Fellowships including, but not limited to, Ansel Adams, Aaron Copland, Martha Graham, Langston Hughes, Henry Kissinger, Paul Samuelson, Wendy Wasserstein, James Watson and, of course, Linus Pauling.

As one of the program’s earliest honorees, Pauling was awarded his first Guggenheim fellowship in 1926.  Heeding the advice of his mentors, Pauling had applied for the fellowship in hopes of pursuing an opportunity for international study.  Pauling’s advisers had long been insisting that he go to Europe to study alongside the leading experts in the budding field of quantum physics, and the Guggenheim funding provided Pauling with the opportunity to do just that.  It was this fellowship that allowed Pauling to travel abroad in order to learn from the European geniuses of quantum physics and to later become one of the early American pioneers of the new field of quantum mechanics.

Linus and Ava Helen Pauling’s apartment in Munich, Germany. 1927.

The subject of quantum mechanics constitutes the most recent step in the very old search for the general laws governing the motion of matter.

–Linus Pauling and E. Bright Wilson, Introduction to Quantum Mechanics, 1935.

The mid-1920s – the time during which Pauling was awarded the prestigious Guggenheim fellowship – was an exciting period to begin an exploration of quantum theory.  The tides were dramatically shifting in this field of study and the acceptance of the old quantum theory was rapidly declining.

Linus and Ava Helen left for Europe on March 4, 1926, arriving in Europe in the midst of what was a great quantum theory reform.  At the inception of quantum theory, physicists and chemists had attempted to apply the classical laws of physics to atomic particles in an effort to understand the motion of and interactions between nuclei and electrons.  This application was grossly flawed as the classical laws, such as Newton’s laws, were originally generated to represent macroscopic systems.   Theorists soon discovered that the classical laws did not apply to atomic systems, and that the microscopic world does not consistently align with experimental observations.

A series of breakthroughs by prominent theorists in the early- to mid-1920s accelerated the decline of the old quantum theory.  In 1924 Louis de Broglie discovered the wave-particle duality of matter, and in the process introduced the theory of wave mechanics.  Then in 1925, just one year before Pauling began his European adventure, Werner Heisenberg developed his uncertainty principle and thus began applying matrix mechanics to the quantum world.

In 1926, shortly after the Paulings arrived in Europe, Erwin Schrödinger combined de Broglie’s and Heisenberg’s findings, mathematically proving that the two approaches produce equivalent results.  Schrödinger then proceeded to develop an equation, now know as the Schrödinger Equation, that treats the electron as a wave.  (The Schrödinger Equation remains a central component of quantum mechanics today.)  The adoption of wave and matrix mechanics led to the development of a new quantum theory and the overwhelming acceptance of a burgeoning field known as quantum mechanics.

Arnold Sommerfeld and Ava Helen Pauling in Munich, Germany. 1927.

Where the old quantum theory was in disagreement with the experiment, the new mechanics ran hand-in-hand with nature and where the old quantum theory was silent, the new mechanics spoke the truth.

–Linus Pauling, February 1929

Pauling began his work in Munich at Arnold Sommerfeld‘s Institute for Theoretical Physics, a scholarly environment described by biographer Thomas Hager as “a new wave-mechanical universe for Pauling.”  It was this atmosphere that opened the door for Pauling to leave his mark as a pioneer of quantum mechanics.

In the fall of 1926, Pauling began applying the new quantum mechanics to the calculation of light refraction, diamagnetic susceptibility, and the atomic size of large, complex atoms.  Through these types of applications, Pauling developed his valence-bond theory, in the process making significant advancements in the new field of quantum mechanics and expanding our understanding of the chemical bond.


The Guggenheim Trip, Part III: Unexpected Colleagues

Walter Heitler, Fritz London, and Ava Helen Pauling in Europe. 1926.

Walter Heitler, Fritz London, and Ava Helen Pauling in Europe. 1926.

The paper of Heitler and London on H2 for the first time seemed to provide a basic understanding, which could be extended to other molecules. Linus Pauling at the California Institute of Technology in Pasadena soon used the valence bond method. . . . As a master salesman and showman, Linus persuaded chemists all over the world to think of typical molecular structures in terms of the valence bond method.” – Robert Mulliken. Life of a Scientist, pp. 60-61. 1989.

After Linus Pauling’s publication of “The Theoretical Prediction of the Physical Properties of Many-Electron Atoms and Ions,” he was ready for an even greater challenge – the problem of the chemical bond was a tantalizing enigma for Pauling, and he wanted more time in Europe to work on it. In the winter of 1926, he applied for an extension of his Guggenheim fellowship and with the help of a particularly complementary cover letter from Arnold Sommerfeld, Pauling was granted six more months of support.

Boosted by this news, he quickly began planning visits to Copenhagen and Zurich, both cities boasting of some of Europe’s finest research facilities. His first stop was Copenhagen, where he hoped to visit Niels Bohr’s institute and discuss ongoing research with the renowned scientist. Unfortunately, he had arrived uninvited and found it almost impossible to obtain a meeting with the physicist. Bohr, with the help of Werner Heisenberg and Erwin Schrödinger, was deeply engaged in research on the fundamentals of quantum mechanics, and was specifically attempting to root out the physical realities of the electron, in the process developing a theory which would eventually be termed the “Copenhagen Interpretation.”

Pauling did, however, did make one valuable discovery in Denmark — that of a young Dutch physicist named Samuel Goudsmit. The two men quickly became friends and began discussing the potential translation of Goudsmit’s doctoral thesis from German to English. Their work did eventually get them noticed by Bohr, who finally granted Pauling and Goudsmit an audience. Unfortunately for the pair, Bohr was neither engaging nor encouraging. Nevertheless, the two continued to work together, their cooperation eventually culminating in a 1930 text, The Structure of Line Spectra, the first book-form publication for either scientist.

In 1926 though, frustrated by his unproductive time in Copenhagen, Pauling departed, stopping briefly at Max Born’s institute in Göttingen before traveling to Zurich where other advances in quantum mechanics promised an interesting stay. Unfortunately, the man Pauling was most interested in, Erwin Schrödinger, proved to be just as unavailable as Bohr. The quantum mechanics revolution was consuming the time and thoughts of Europe’s leading physicists and Pauling, a small-fry American researcher, simply wasn’t important enough to attract the interest of men like Bohr and Schrödinger.

Fritz London

Fritz London

As a result, Pauling chose to converse and work with men of his own status in the scientific community. Fritz London and Walter Heitler, acquaintances of the Paulings, had spent the past several months working on the application of wave mechanics to the study of electron-pair bonding.

Heitler and London’s work was an outgrowth of their interest in the applications and derivations of Heisenberg’s theory of resonance, which suggested that electrons are exchanged between atoms as a result of electronic attraction. Heitler and London determined that this process, under certain conditions, could result in the creation of electron bonds by cancelling out electrostatic repulsion via the energy from electron transfer. Their work on hydrogen bonds likewise agreed with existing theories, including Wolfgang Pauli’s exclusion principle and G.N. Lewis’ shared electron bond. The Heitler-London model was well on its way to contributing to a new truth about the physics of the atom

Walter Heitler

Walter Heitler

Pauling used his time in Zurich to experiment with the Heitler-London work. While he didn’t produce a paper during his stay, the new model made a great impression on him and he returned to Caltech with a renewed sense of purpose. He was preparing to tackle the problem of atomic structure, in all its manifestations, and make history as one of the greatest minds of the twentieth century.

For more information, view our post “Linus Pauling and the Birth of Quantum Mechanics” or visit the website “Linus Pauling and the Nature of the Chemical Bond: A Documentary History.”

The Heisenberg Uncertainty Principle

Werner Heisenberg

Werner Heisenberg

I learned mathematics from Born and physics from Bohr, and from Sommerfeld I learned optimism.”
– Werner Heisenberg

While the Bohr-Sommerfeld atom had proved revolutionary in the mid-1910s, a decade later the model was considered disordered and highly paradoxical. For years, researchers had tried to rebuild mathematics to fit the atomic model of the day.

Instead of struggling along the same path as his contemporaries, Werner Heisenberg, a young German physicist, chose to entirely ignore visual models and focus on the mathematics of spectral data. Over the course of several days, by limiting himself to hard, verifiable data, Heisenberg created the basis for matrix mechanics. In cooperation with Max Born and Pascual Jordan, he was able to refine his work, allowing scientists to approach particles as evolving matrices rather than stale, immobile ball-and-stick models. Through his study of particles using matrix mechanics, he was able to develop a detailed theory suggesting that it was impossible to pinpoint both the momentum and the exact location of any given particle at a specific point in time. Instead, he argued, it was possible to create a probability distribution which could be used to calculate the likelihood of a particle achieving an exact momentum and position at a particular moment.

In late March of 1927, Heisenberg published a manuscript entitled “On the perceptual content of quantum theoretical kinematics and mechanics.” The paper detailed the terms of his probability theory, eventually known as the indeterminacy principle, or more commonly, the Heisenberg Uncertainty Principle. According to David Cassidy, author of Uncertainty: The Life and Science of Werner Heisenberg, Heisenberg’s paper, coupled with Bohr’s complementarity principle and Born’s statistical interpretation of Schrodinger’s wave function, formed an integral part of the Copenhagen interpretation of quantum mechanics. Cassidy calls the Copenhagen interpretation “an explication of mechanics that fundamentally altered our understanding of nature and our relation to it,” and an event that “marked the end of a profound transformation in physics that has not been equaled since.” In this way, Heisenberg was able to reshape scientists’ understanding of the world at the molecular level.

Linus Pauling had the great fortune of touring Europe on a Guggenheim Fellowship during the time of Heisenberg’s discovery. During his stay in Germany, Pauling visited the Göttingen Institute of Physics, the home of Max Born, Arnold Sommerfeld, and of course, Werner Heisenberg. The institute’s renowned scientists, determined to educate their students on the newest developments in their fields, were known for presenting cutting-edge research in their day-to-day lectures. In true Göttingen fashion, Max Born, the famed physicist and mathematician, presented the young visitor with a pre-publication copy of Heisenberg’s paper. We are pleased to note the final pre-publication proof sheets, item corr155.1, is a part of the Ava Helen and Linus Pauling Papers.

Listen: Pauling discusses his contacts with some of Europe’s finest scientists in the mid-1920s

As groundbreaking as the Heisenberg Uncertainty Principle was, Pauling and many of his fellow scientists found the matrix approach to be frustratingly mathematical. Much of Pauling’s work was heavily influenced by Heisenberg’s discoveries and he commonly introduced some of the concepts in his lectures, but ultimately he struggled with the abstract, intangible aspects of the math-based matrix mechanics.

“Uber den anschauclichen Inhalt der quantentheoretischen Kinematik und Mechanik.” March 23, 1927.”

Erwin Schrödinger’s work, which complemented Heisenberg’s complex mathematics, was comparatively simple and conducive to visual representation. As such, it was much more widely adopted by the researchers of the day. Both individuals quickly became known as titans of twentieth-century science.

Learn more at the website “Linus Pauling and the Nature of the Chemical Bond: A Documentary History,” or by clicking on the multimedia link below.

“Valence and Molecular Structure”