# Werner Heisenberg: Explorer of the Limits of Human Imagination

(published in Resurgence, UK, September/October 2016)

Werner Heisenberg, who died forty years ago, was one of the founders of quantum theory and will be remembered, along with Albert Einstein and Niels Bohr, as one of the giants of modern physics. He played a leading role in the dramatic change of concepts and ideas that occurred in physics during the first three decades of the twentieth century. These concepts brought about a profound change in our worldview: from the mechanistic worldview of Descartes and Newton to a holistic and ecological view.

At the very core of this change of paradigms lies a fundamental change of metaphors from seeing the world as a machine to understanding it as a network. As Heisenberg put it in his classic *Physics and Philosophy*: “The world thus appears as a complicated tissue of events, in which connections of different kinds alternate or overlap or combine and thereby determine the texture of the whole.”

The new view of reality was by no means easy to accept for physicists at the beginning of the twentieth century. The exploration of the atomic and subatomic world brought them in contact with a strange and unexpected reality. In their struggle to grasp this new reality, scientists became painfully aware that their basic concepts, their language, and their whole way of thinking were inadequate to describe atomic phenomena. Their problems were not merely intellectual but amounted to an intense emotional and even existential crisis, as vividly described by Heisenberg in his book. I remember reading *Physics and Philosophy* as a young student in the late 1950s, soon after it was published. It had a tremendous influence on my thinking and determined the trajectory of my entire career as a scientist and writer.

At the beginning of the twentieth century, physicists, for the first time, probed deep into the atomic world, into a realm of nature far removed from their everyday environment, and in doing so they transcended the limits of sensory imagination. They found, to their great surprise and dismay, that they could no longer rely with absolute certainty on logic and common sense; that ordinary language was often completely inadequate to describe the newly discovered phenomena. Atomic physics forced scientists to think about nature in new categories. It was Heisenberg’s great achievement to recognize this clearly and to build a new conceptual foundation in terms of these categories.

Heisenberg became involved in atomic physics at the age of twenty when he was a student at the University of Munich. In 1922, his teacher Arnold Sommerfeld invited him to attend a series of lectures given by Niels Bohr in Göttingen. The topic of the lectures was Bohr’s new atomic theory, which had been hailed as an enormous achievement and was being studied by physicists throughout Europe.

In the discussion following one of these lectures, Heisenberg disagreed with Bohr about a particular technical point. Bohr was so impressed by the clear arguments of this young student that he invited him to come for a walk, so that they could carry on their discussion. This walk, which lasted for several hours, was the first meeting of two outstanding minds whose further interaction was to become a major force in the development of atomic physics.

Niels Bohr, sixteen years older than Heisenberg, was a man with supreme intuition and a deep appreciation for the mysteries of the world; a man influenced by the religious philosophy of Kierkegaard and the mystical writings of William James. Werner Heisenberg, on the other hand, had a clear, analytic, and mathematical mind, and was rooted philosophically in Greek thought, with which he had been familiar since his early youth. The dynamic, and often dramatic, interplay of these two complementary minds was a unique process in the history of modern science and led to one of its greatest triumphs.

At that time, the investigations of atomic physicists were plagued by a number of paradoxes and apparent contradictions between the results of different experiments. Many of these paradoxes were connected with the dual nature of subatomic matter, which appeared sometimes as particles, sometimes as waves; a most puzzling behavior that was also exhibited by light or, more generally, by electromagnetic radiation.

Light, for example, was found to be emitted and absorbed in the form of “quanta,” but when these particles of light (now known as photons) traveled through space, they appeared as vibrating electric and magnetic fields which showed all the characteristic behavior of waves. Electrons had always been considered to be particles, and yet when a beam of these particles was sent through a small slit, it was bent just like a beam of light — in other words, electrons, too, behaved like waves. The strange thing was that, the more physicists tried to clarify the situation, the sharper the paradoxes became.

Here, Heisenberg made his first crucial contribution. He saw that the paradoxes in atomic physics appeared whenever one tried to describe atomic phenomena in classical terms, and he was bold enough to throw away the classical conceptual framework. In 1925, Heisenberg published a paper in which he abandoned the classical description of electron motion in terms of the positions and velocities of the electrons. He replaced it with a much more abstract framework in which physical quantities were represented by sets of numbers known as matrices. The whole formalism is now known as Heisenberg’s matrix mechanics. It was the first logically consistent formulation of quantum theory.

One year later, it was supplemented by a different formalism, worked out by Erwin Schrödinger and known as “wave mechanics.” Both formalisms are logically consistent and are mathematically equivalent; the same atomic phenomena can be described in two different mathematical languages.

At the end of 1926, then, physicists had a complete and logically consistent mathematical formalism, but they did not always know how to use it to describe a given experimental situation. Heisenberg recognized that the root of these difficulties was the lack of a definite interpretation of the formalism, and he spent the following months in intensive, exhausting, and often highly emotional discussions with Bohr, Schrödinger, and others, until the situation was finally clarified.

Heisenberg recognized that the formalism of quantum theory cannot be interpreted in terms of our intuitive notions of space and time, or of cause and effect; but at the same time he realized that all our concepts are connected with these intuitive notions of space and time. He concluded that there was no other way out than to retain the classical intuitive notions, but to restrict their applicability.

Heisenberg’s great achievement was to express these limitations of classical concepts in a precise mathematical form, which now bears his name and is known as the Heisenberg uncertainty principle. It consists of a set of mathematical relations that determine the extent to which classical concepts can be applied to atomic phenomena and thus stake out the limits of human imagination in the subatomic world.

At the most fundamental level, Heisenberg’s uncertainty principle is a measure of the unity and interrelatedness of matter. We have come to realize in modern physics that the material world is not a collection of separate objects, but rather appears as a network of relations between the various parts of a unified whole. This shift from objects to relationships has far-reaching implications for science as a whole. It is most apparent in ecology, a science that was developed around the time Werner Heisenberg formulated his uncertainty principle. Like subatomic particles, the phenomena we observe in ecosystems do not have intrinsic properties but can only be understood in terms of their mutual relationships.

In quantum physics, our classical notions, derived from our ordinary experience, are not fully adequate to describe the atomic and subatomic world. The concept of a distinct particle, for example, is an idealization that has no fundamental significance. When we describe the properties of such an entity in terms of classical concepts — like position, energy, velocity, etc. — we always find pairs of concepts that are interrelated and cannot be defined simultaneously in a precise way. The more we impose the one concept of the physical “object,” the more the other concept becomes uncertain, and the precise relation between the two is given by the uncertainty principle.

Like no one else, Werner Heisenberg explored the limits of human imagination, the limits to which our conventional concepts can be stretched. His greatness was that he not only recognized these limitations and their profound philosophical implications, but was able to stake them out with mathematical clarity and precision.