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”

6 Responses

  1. Hello Author,

    I am really interested in knowing more about the various theories and developments in the world of Quantum Physics. Though i have been very recently introduced to this dimension, I find it very appealing and something I would like to know in depth. Could you suggest some reading material for this young enthusiast?

    Thanking you,

    P.S. I have just completed my high school in India. Though we have been taught the wave-particle duality and uncertainty principle, it has been more of an overview. this means though I am familiar with this topic, I don’t have a very strong base in this. And i have just read John Gribbin’s ‘In search of Schrodinger’s cat’ to try and get a better picture.

  2. Gagan,

    We appreciate your interest both in our site and in the realm of quantum mechanics. Here is a brief list of books and websites that may help you further your understanding of the subject:

    Pauling, Linus, and E. Bright Wilson, Jr. Introduction to Quantum Mechanics: With Applications to Chemistry. New York: Dover Publications, 1985. ISBN: 0486648710

    Griffiths, David J. Introduction to Quantum Mechanics. New Jersey: Prentice Hall, 2005.
    ISBN: 0131118927

    For a graduate level text with a heavy emphasis on mathematics, you may wish to consider:

    Mackey, George W. Mathematical Foundations of Quantum Mechanics. New York: Dover Publications, 2004. ISBN: 0486435172

    For an online guide, you may wish to visit the The Modern Revolution in Physics by Benjamin Crowell. An Adobe Acrobat version of the text is available on the site. (

    MIT (The Massachusetts Institute of Technology) also offers an extensive open courseware program featuring a variety of materials on quantum physics. This may prove to be a valuable resource.

    Finally, you can locate additional physics texts using the OSU Libraries Physics Research Guide which you may find to be an excellent resource.

    Good luck in your research and please check back for future posts.

  3. Thank You

    I’ll go through these.

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  6. […] 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 […]

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