Another Werner Heisenberg Essay

Werner Heisenberg

One cannot fully appreciate the work of Werner Heisenberg unless one
examines his contributions in the context of the time in which he lived. Werner
Karl Heisenberg was born in Wuerzburg, Germany, on December 5, 1901, and grew up
in academic surroundings, in a household devoted to the humanities. His father
was a professor at the University of Munich and undoubtedly greatly influenced
young Werner, who was a student at the Maximilian Gymnasium.
Heisenberg had the opportunity to work with many of the top physicists
in the world including Niels Bohr and Max Born. Like many of the top physicists
of the time Heisenberg received his doctorate at an early age. In Heisenberg's
case he received it at the young age of twenty three. Heisenberg was not just a
researcher. He was also a professor and author. During his career he taught at
many prestigious universities, including the Universities of Leipzig, Goettingen,
and Berlin. He also wrote many important books including, Physical Principles
of the Quantum Theory, Cosmic Radiation, Physics and Philosophy, and
Introduction to the Unified Theory of Elementary Particles. In 1932 he won the
Nobel Prize in Physics for his work in Quantum Mechanics.
With the Nazi's in power, and World War two on the horizon it was
inevitable that his German heritage would play a crucial role in his career.
Before Germany's blitzkrieg on Poland Heisenberg decided to make one final visit
of his friends in the West. Many tried to convince him to stay and accept a
professorship at Columbia, but Heisenberg declined. He felt that it was his
duty to preserve the foundation of science in Germany during the war. He also
believed that by staying in Germany during the war, he could help individual
German scientists. In fact, he did offer jobs to Jewish scientists when they
were fired from their posts at other universities. As time passed, Heisenberg
found that he was powerless to protect his friends. Heisenberg himself was
personally attacked, and his appointment at the University of Munich was blocked.
For over a year Heisenberg was attacked in the SS newspaper, which referred to
him as a "white Jew." The attack became so threatening that Heisenberg's mother,
who had a slight connection to Himmler's family, wrote to Himmler's mother
asking Himmler to intercede. Himmler personally cleared Heisenberg of the
charges leveled against him a year later, but he was told to study science and
avoid discussing scientists. The strain of the investigation surely affected
Heisenberg's creativity.
During the war Heisenberg worked on the German A-bomb project along with
a number of other German scientists. It has been proposed in the novel
Heisenberg's War, written by Thomas Powers, that Heisenberg deliberately
sabotaged this project to keep the bomb out of Hitler's hands. After the war
was over, all of the scientists in Germany working on the A-bomb project,
including Heisenberg, were interned in England to be questioned about their work
on the project.
Heisenbergs nationalism eventually ruined many of his academic
friendships. His close relationship with Neils Bohr was destroyed by his
decision to remain in Germany during the war. His failure to be more specific
about his stand in whether or not to seriously work to develop a German bomb
played an important part in his inability to reestablish ties with friends who
moved to the West. The creative interaction with many leading scientists prior
to the war was not resumed at the war's end.
Heisenberg's most important finding, the Uncertainty Principle is the
corner stone of Quantum Mechanics. However, many advances in Quantum Mechanics
had to be made before Heisenberg found it. Everything started with Rutherford's
model of the atom. Consisting of a positively charged central nucleus,
surrounded by orbiting planetary electrons. Around the same time that
Rutherford was discovering the basic structure of the atom, Plank did some
important work also. Finding that energy from an oscillating particle is
emitted not continuously, but in packets of energy he developed the Quantum
Theory of Radiation. From this came the universal constant h which played a
large role in Heisenbergs uncertainty principle. Neils Bohr then made a new
model of the atom, which combined both Rutherford's and Plank's work. This new
model accounted for known patterns of atomic radiation as seen in spectra.
However, what Bohr wrote on paper about the electron activity and what other
physicists were observing were two different things. Bohr had developed his
quantum theory of the atom by discarding the idea of a classical frequency
associated with the orbit of an electron, but he still retained the concept of
the classical orbit. Heisenberg went one step further and discarded the concept
of the orbit itself. Rather than the classical idea of the position and the
motion, or momentum, of the electron at each instant in time, Heisenberg
introduced his square arrays or matrices, which depict the electron as existing
simultaneously in all possible Bohr orbits. After Heisenberg's discovery, the
classical concept of the electron as a particle was no longer justifiable.
Heisenberg was led to these revolutionary ideas by his insistence on
utilizing only those quantities in a theory that are directly observable. Since
the orbit of an electron is not observable, it can have no place in a theory.
Only the spectral lines are observed, and, since these involve pairs of orbits,
all quantities that are used to describe the electron inside the atom should be
associated with such pairs.
Such thinking led to Heisenberg's matrices. One of the important
features of matrices is that it is not commutative. If the array representing
the position of an electron is q and an array representing its momentum is p,
then the product pq is not the same as the product qp.
This showed Heisenberg that the uncertainty relationship is purely an
algebraic consequence of his matrix theory. If you picture the product pq as
representing a measurement of the position of the electron followed by a
measurement of its momentum; qp, on the other hand, represents the measurement
of the momentum of a particle followed by at the measurement of its position.
That these two sets of measurements give different results simply means that the
measurement of the momentum of a particle destroys our knowledge of its position,
and vice versa. It follows that it is impossible to obtain or to have precise
knowledge of the position and the momentum of a particle simultaneously; this is
the essence of the uncertainty principle.
Its significance for the structure of the atom is that we have no way of
determining the orbit of an electron inside the atom observationally. As
Heisenberg pointed out in his analysis of the Copenhagen interpretation of
quantum theory, an electron can be observed inside an atom only with a gamma-ray
microscope which, because of the short wavelength of gamma rays, has a high
resolving power. This microscope shows us where the electron is at any moment,
but at least one gamma-ray photon must be reflected from the electron. In this
very process the electron is knocked out of the atom. It is senseless then to
speak of its orbit.
Although the uncertainty relations can be derived mathematically from
theory, it is much more instructive to derive them from the physical picture.
This method shows clearly the interrelationship between the wave and the
particle. In fact, it is clear from Heisenberg's analysis that wave and
particle are complementary aspects, as are position and momentum. It was from
considerations such as these that Bohr developed his theory of complementarily,
which is essential for an understanding of modern atomic theories.
The uncertainty relations completely change our ideas of causality. If
we cannot determine the position and the momentum of a particle simultaneously
to any desired degree of accuracy, we cannot determine its future course. We
can solve equations for the motion of the particle. However, these solutions
can tell us its future history only if at some moment in the past or at the
present instant we know its position and momentum. The farther we try to look
into the future, the less accurate our predictions become because our present
uncertainty, however small leads to greater deviations from the predicted
pattern of the motion as the time increases. We can understand this situation
by considering the lunar missile probes carried out by the United States and
Soviet Union. To hit a target as gar away as the moon involves extreme accuracy
in aiming the rocket and giving it the correct initial momentum; if we wish to
hit targets at greater distances, our accuracy will have to be increased
considerably because the further the distance, the greater the multiplication of
any initial error.
Today we use the term quantum mechanics for the entire mathematical
scheme that is used to treat problems in atomic, nuclear, elementary-particle,
and field physics. The mathematics of quantum mechanics stems directly from
Heisenberg's matrix mechanics and is a consequence of his uncertainty principle.
If anyone were to prove his uncertainty principle wrong the foundations of
quantum mechanics would fall.
Heisenberg spent the final years of his career trying to derive the
properties of such elementary particles as electrons, protons, and so on, from a
departure from quantum field theory by having the field itself construct its own
particles. Unfortunately, this approach led to a very complex mathematical
formulation which some say spoiled the great beauty of quantum mechanics.