Werner Heisenberg: the Columbus of quantum mechanics

This year marks the centenary of the birth of Werner Heisenberg, pioneer of quantum mechanics and theoretical
high-energy physics. Helmut Rechenberg, Heisenberg’s last postgraduate, co-editor of his collected
works and co-author of the multivolume opus The Historical Development of Quantum Theory, traces
the life of a quantum figurehead.

This year, 5 December marks the centenary of Werner Heisenberg’s birth. It is to him that we owe the first
breakthrough of modern atomic theory – the invention of quantum mechanics. His famous uncertainty relations
were a central part of its interpretation. He also established several fundamental quantum mechanics
applications and pioneered the extension of the theory to high-energy phenomena.

Werner Heisenberg,
born in Würzburg, came from an academic family and after 1910 grew up in Munich, where he graduated with
distinction from high school in 1920. He studied under Arnold Sommerfeld at the University of Munich,
obtaining his PhD in July 1923 and then went on to work under Max Born in Göttingen. In 1924 Niels Bohr
invited him to Copenhagen. Thus he became a member of the great international post-First World War
community of quantum and atomic theorists, including such brilliant talents as Paul Dirac, Enrico Fermi,
Friedrich Hund, Pascual Jordan, Oskar Klein, Hendrik Kramers, Wolfgang Pauli and Gregor Wentzel.

the very first semester Sommerfeld gave Heisenberg the difficult problem of explaining the anomalous Zeeman
effect of sodium spectral lines. The freshman found a perfect solution – exhibiting, however, unusual
half-integral quantum numbers and a strangely behaving atomic core. Simultaneously he studied the classical
hydrodynamical turbulence problem. On the publication of Heisenberg’s first paper in this field in 1922,
Sommerfeld remarked to Heisenberg’s father: “You belong to an irreproachable family of philologists, and now
you have the misfortune of seeing the sudden appearance of a mathematical-physical genius in your family.” In
his PhD thesis, Heisenberg suggested the first method for deriving the critical Reynolds number, marking the
transition from laminar to turbulent motion. In spite of this brilliant work, he nearly failed the experimental
part of the doctoral exam with Willy Wien.

The breakthrough

In 1923, contemporary atomic theory
was in a deep crisis. As a way out of the situation, Pauli, who was in Copenhagen, and Born and Heisenberg
who were in Göttingen, proposed replacing the semiclassical differential expressions of Bohr and Sommerfeld
by corresponding discrete difference terms to predict experimental quantum results (the 1925
Kramers-Heisenberg formula, which predicted the Raman effect, for example). Heisenberg and Pauli claimed
that fundamental concepts of the old theory, notably electron orbits, had to be abandoned completely.

May 1925, in Göttingen, Heisenberg began to describe atomic systems by observables only
(“quantum-theoretical” Fourier series). With this, the usual physical quantities, like position q and momentum
p of an electron, did not commute but satisfied instead the relation pq – qp = h/2pi.
In June 1925 when Heisenberg was recovering from a severe attack of hay fever on the island of Heligoland, he
found that he could satisfy the necessary requirement of energy conservation in atomic processes. His
“quantum-theoretical reformulation” was the breakthrough to modern quantum mechanics. Soon Born and
Jordan reformulated it as “matrix mechanics” and Paul Dirac as “q number theory”, and applied it successfully,
as Heisenberg and Pauli did, to various atomic problems.

It was in 1926 that Erwin Schrödinger created
wave mechanics, formally equivalent to matrix mechanics, but working with differential equations and
continuous wavefunctions. Schrödinger claimed that nature exhibited no “quantum jumps” at all. Heisenberg,
from spring 1926 a lecturer and Bohr’s principal assistant in Copenhagen, contradicted this and in early 1927
derived the central result of the physical interpretation: simultaneous measurements of momentum and position
of an atomic particle were limited by the famous uncertainty relation: Dp. Dq ~ h. This relation had radical consequences – the classical causality law or, expressed
more generally, the possibility of a strict separation of object and subject, ceased to be valid in quantum

In the fall of 1927, Heisenberg became professor of theoretical physics at Leipzig. Together with
Peter Debye and Friedrich Hund he established a new centre of atomic physics there. His first students, Felix
Bloch and Rudolf Peierls, pioneered with him the quantum mechanics of solids (ferromagnetism, metals and

High-energy theory and elementary particles

Heisenberg’s main interest, however,
was a relativistic extension of quantum mechanics: with Pauli he formulated Lagrangian quantum field theory
(1929). They tried to cope with the emerging divergence difficulties, achieving some progress with
“renormalization” procedures (Heisenberg 1934; Weisskopf 1934). Originally they were led to expect that
quantum mechanics would not apply any more at high energy. However, after the discovery of the neutron in
1932, Heisenberg proposed a quantum-mechanical theory of the atomic nucleus based on new exchange forces.

During the 1930s, nuclear theory progressed enormously, mainly through work in the US and in Japan
(notably by Hideki Yukawa with his meson theory) and further at Leipzig (despite the Nazi government
depriving Heisenberg of excellent students and collaborators after 1933).

From 1932 Heisenberg also
turned his attention to the high-energy phenomena observed in cosmic radiation. He suggested several new
ideas, such as “explosive showers”, and in 1938, with his student Hans Euler, he solved the problem of the
so-called “hard component” (unstable “mesotrons”). These efforts aimed ultimately at an ambitious goal that he
and Pauli had envisaged: a unified quantum field theory, describing all elementary particles and their
interactions, without any divergences and allowing all of their properties (such as masses and coupling
constants) to be calculated. More than 30 years later they still had not reached their goal.

during their labours, Heisenberg and Pauli created many concepts of modern high-energy physics, such as
isotopic spin (Heisenberg, 1932), spin-statistics theory (Pauli and Fierz, from 1937 to 1941), and the
symmetry breaking caused by a degenerate vacuum (Heisenberg and Pauli 1958). In addition, in 1942
Heisenberg proposed the so-called “S-Matrix theory”, which was widely discussed after the Second World War
as a phenomenological approach in quantum electrodynamics and strong-interaction theory. Another noteworthy
result was the logarithmically rising total cross-section for particle collisions at higher energies (Heisenberg

Science, politics and international relations

During the Third Reich (1933-1945),
Heisenberg’s life and work was made difficult not only by racism directed against his Jewish teachers,
colleagues and students, but also by outright attacks on him and his scientific work. Nazi partisans considered
quantum and relativity theories to be “degenerate, Jewish physics”, the defenders of which “had to disappear like
the Jews”. In spite of these attacks, and in spite of generous offers to accept prestigious chairs in the US,
Heisenberg remained in Germany, believing that he did not have the moral right to abandon his students and his
country during such difficult times.

During the Second World War he was drafted into the secret German
atomic energy project, working on a nuclear reactor, but not on a bomb. In 1942 he moved to Berlin to take
over the directorship of the Kaiser Wilhelm-Institut für Physik (which eventually became the Max Planck

After the war he successfully helped to renew science in the Federal Republic of Germany and
to re-establish international scientific relations, assisted by many friends in Europe and beyond. Thus he
became a co-founder and ardent supporter of CERN (and the first chairman of its scientific policy committee).
He considered international co-operation, especially in the most fundamental fields of science (such as
high-energy physics), to be a “main tool to reach understanding between peoples”. As president of the
Alexander von Humboldt Foundation, he invited hundreds of young research scholars from all around the world
to work at German universities and scientific institutes, and high-energy physics received a substantial share of
these fellowships.

Werner Heisenberg died on 1 February 1976 in Munich. To commemorate his 80th
anniversary, the Max Planck Institute for Physics (which he had transferred in 1958 from Göttingen to Munich)
was given the additional name “Werner-Heisenberg-Institut”.

The centenary is being marked by several
special events. From 26-30 September a meeting with the title “100 years of Werner Heisenberg” was held by
the Alexander von Humboldt Foundation at Bamberg; from 4-7 December a Heisenberg centennial event at the
Max Planck Institute and Ludwig-Maximilians University, Munich, includes a two-day symposium with nine
distinguished speakers from abroad; and from 3 December to January 2002 there is a Heisenberg exhibition at
the University of Leipzig and at the Max-Planck-Haus, Munich. For more information, see http://www.heisenberg-centennial.de.

Further reading

David Cassidy 1992 Uncertainty: the life and science of Werner Heisenberg
Jagdish Mehra and Helmut Rechenberg The Historical Development of Quantum
5 volumes (Springer).

About the author

Helmut Rechenberg, Max Planck Institute for Physics, Munich.