In this installment on the history of atom theory, physics professor (and my dad) Dean Zollman discusses how Werner Heisenberg—he of the Uncertainty Principle—decided to take a mathematical approach to something he couldn’t observe. For those who need a refresher, Heisenberg’s Uncertainty Principle is that we cannot know both the position and momentum of a particle precisely, and that the more we know about one, the less we know about the other.—Kim
By Dean Zollman
In the last post, I discussed an experimental confirmation of Louis de Broglie’s hypothesis that matter could behave as waves do. In that case, Clinton Davisson and Lester Germer observed interference effects that could occur only if matter had wave-like behavior. In this post, we will back up in time just a little and consider the first of two theoretical developments that also occurred in the mid-1920s. The second approach will be discussed next time.
In 1925, Werner Heisenberg (1901-1976) was conducting research at the University of Goettingen in Germany. He was working under the direction of Max Born (1882-1970) and trying to resolve some of the mysteries that recent experimental discoveries had revealed. He had just spent about eight months working with Niels Bohr in Copenhagen. Thus, he was building on Bohr’s work and trying to find a fundamental basis to explain the Bohr Model of the Atom and the discrete spectrum of the hydrogen atom. Heisenberg had concluded that he needed to “reinterpret” classical mechanics in order to bring quantum ideas in to the picture.
Heisenberg’s basic approach was to avoid ideas such as orbiting electron because they were not observable. Instead, he pursued a mathematical theory. At one point in a letter to Wolfgang Pauli (1900-1958), he stated, “My entire meager efforts go toward killing off and suitably replacing the concept of orbital paths that one cannot observe.”
To do so, he looked first at a situation that was simpler than an atom—a certain kind of oscillating object whose behavior was not quite periodic. Heisenberg and his colleagues at Goettingen made some progress. They were able to base their theory on a new set of mathematical operations. While this approach showed some promise, it did not involve Planck’s constant and thus did bring in the latest quantum interpretations.
While working intensely on this issue, Heisenberg suffered an extreme attack of hay fever. He needed to get away from pollen, so on June 7, 1925, he left for the island of Helgoland. This German island in the North Sea has very little vegetation and therefore very little pollen. As he recovered from the hay fever, Heisenberg also had very little distractions. So, he was able to develop a mathematical approach to quantum physics.
When Heisenberg returned to Goettingen, he presented the ideas to Max Born and his young assistant Pascual Jordon (1902-1980). They recognized that Heisenberg’s formulation was quite similar to a relatively new mathematical concept called the matrix. So, they expanded the ideas to create a matrix approach to quantum physics.
While Heisenberg’s matrix mechanics worked to obtain observable results, it was very difficult to use to complete calculations. For example, Wolfgang Pauli obtained the energy levels in the hydrogen atom using matrices and thus connected it back to Bohr’s ideas and the spectrum of hydrogen. However, it took him 40 pages of calculations to get to a result that could be observed in an experiment.
One of Heisenberg’s biographers, David Cassidy, states, “The new mechanics was (and is) nearly incomprehensible to the technically uninitiated.”
Unfortunately, that statement does seem to be true. Part of the reason is that matrix mechanics, as it became to be known, is not easily visualized. During the years that I have been teaching quantum physics to non-science students, I have not found an acceptable way to present this approach to students who have not studied the detail of matrix algebra.
Fortunately, a different method that was developed about the same time is more easily visualized. We will look at that approach and learn about Erwin Schroedinger in the next post and the rivalry that developed between Heisenberg and Schroedinger.
Public domain images via Wikimedia Commons.
Dean Zollman is university distinguished professor of physics at Kansas State University, where he has been a faculty member for more than 40 years. During his career he has received four major awards — the American Association of Physics Teachers’ Oersted Medal (2014), the National Science Foundation Director’s Award for Distinguished Teacher Scholars (2004), the Carnegie Foundation for the Advancement of Teaching Doctoral University Professor of the Year (1996), and AAPT’s Robert A. Millikan Medal (1995). His present research concentrates on the teaching and learning of physics and on science teacher preparation.