Werner Heisenberg
| Werner Heisenberg | |
|---|---|
| |
| Institutions | University of Göttingen; Leipzig University |
| Nationality | German |
| Awards | Nobel Prize in Physics (1932) |
| Known for | Uncertainty principle |
| Occupation | Physicist |
| Field | Quantum mechanics |
| Wikidata | Q40904 |
Werner Karl Heisenberg (1901–1976) was a German theoretical physicist who helped found quantum mechanics, the theory describing atoms and subatomic particles. He laid many of its foundations, formulating a new mathematical framework (matrix mechanics) in 1925 and discovering the famous uncertainty principle in 1927. Heisenberg won the 1932 Nobel Prize in Physics for creating quantum mechanics. In later life he directed West Germany’s postwar physics institutions. He remains a celebrated but sometimes controversial figure for his wartime role in nuclear research and his philosophical views on science.
Early life and education
Heisenberg was born on 5 December 1901 in Würzburg, Bavaria, into a scholarly family. His father was a respected professor of Greek in Munich, and the family moved there when Werner was about ten. Young Heisenberg showed great talent in mathematics and physics during school. He entered the University of Munich in 1920, studying under the physicist Arnold Sommerfeld. Heisenberg later moved to the University of Göttingen, where he worked with the leading physicist Max Born.
Heisenberg completed his doctoral degree in 1923 in Munich with a thesis on the mathematics of fluid flow (hydrodynamics). He immediately turned to atomic physics, influenced by Niels Bohr’s quantum theory of atoms. In 1924 he earned his habilitation (a second advanced degree needed to teach at a university in Germany) at Göttingen. Around this time he met Bohr and other leaders of the new physics and began doing research on the structure of atoms and spectra (the light emitted by atoms).
Major works and ideas
Heisenberg’s first major contribution came in 1925. He realized that the existing atomic model (electrons orbiting the nucleus, as in Bohr’s model) could not explain certain experimental data, such as the intensities of spectral lines. Working largely by mental calculation and thinking about observable quantities (the quantities that experiments actually measure), he developed a new formulation of quantum theory. In July 1925 he published a paper which reinterpreted mechanics in terms of arrays of numbers (later called matrices). These mathematical objects could represent how electrons jump between energy levels. Although the details were very abstract, this new “matrix mechanics” was shown by Max Born and Pascual Jordan to be a consistent theory of quantum behavior. Within months, Heisenberg, Born and Jordan had laid down the foundation of modern quantum mechanics – the set of rules physicists use to predict atomic-scale phenomena.
In 1927 Heisenberg introduced his uncertainty principle (also called the indeterminacy principle). Heveriging that one could never know with infinite precision both certain pairs of physical properties of a single particle (for example, its position and velocity). In simple terms, the more precisely one measures a particle’s position, the less precisely one can know its momentum (mass times velocity), and vice versa. This was not just a technical limitation of measuring instruments but a fundamental property of nature at small scales. He formalized this by showing that the uncertainties (often written Δ) in position x and momentum p always satisfy Δx·Δp ≥ h/4π, where h is a very small number known as Planck’s constant (about 6.6×10^-34 joule-seconds). This relation means that at atomic scales, perfect predictability is impossible; nature is inherently "fuzzy" at a basic level.
The uncertainty principle had profound implications. It implied that electrons and other microscopic particles cannot be pictured as little balls moving on well-defined orbits. Instead, Heisenberg argued, physics can only talk about probabilities of finding things in certain places. This idea became a pillar of the so-called Copenhagen interpretation of quantum mechanics (developed by Heisenberg, Bohr and others), which says that the theory does not describe particles having exact properties until they are measured. Although many physicists accept the formalism of quantum mechanics, Einstein and others found the loss of classical determinism (the idea that the future should be fully predictable if you know the present exactly) deeply troubling. Heisenberg’s work showed that such determinism cannot hold in quantum theory.
Beyond matrix mechanics and the uncertainty principle, Heisenberg made several other important contributions. He worked on the theory of atomic nuclei after James Chadwick discovered the neutron in 1932, proposing early models of how protons and neutrons interact. He also tackled problems in ferromagnetism (the physics of magnets like iron), turbulence in fluid flows (returning to his earlier studies of moving fluids), and the behavior of high-energy particles called cosmic rays. In the late 1920s he and Wolfgang Pauli developed the first steps toward relativistic quantum field theory, trying to reconcile quantum mechanics with Einstein’s theory of relativity. He introduced the concept of the Heisenberg group in mathematics of particle spin, and developed what is now called the Heisenberg picture of quantum mechanics, an equivalent way of describing quantum systems that emphasizes observables changing in time. In all these works, Heisenberg combined mathematical insight with physical reasoning to explore the new quantum world.
As the 1930s progressed, Heisenberg’s research broadened. He studied cosmic-ray showers – cascades of particles produced in the atmosphere by high-energy radiation from space – and contributed to the development of quantum electrodynamics. His growing reputation was cemented in 1932 when he was awarded the Nobel Prize in Physics (announced in 1933) “for the creation of quantum mechanics.”
Method
Heisenberg’s most famous methodology was his insistence on observables. Unlike classical physics, in quantum physics some concepts (like an exact particle trajectory) cannot be directly measured or even defined. Heisenberg proposed that a theory should only involve quantities that correspond to real measurements – such as the frequencies and intensities of light emitted by atoms. This led him to replace quantities like a particle’s exact position in an orbit with mathematical objects that described transitions between energy levels.
Mathematically, Heisenberg’s equations involved matrices: grids of numbers that can be added and multiplied. A key insight of his 1925 paper was that when dealing with atomic phenomena, one must use non-commuting matrices. In everyday arithmetic, the order of multiplication usually does not matter (for example, 2×3=3×2). But in Heisenberg’s mechanics, the product of two matrices A×B could differ from B×A. This non-commutativity effectively encoded the uncertainty principle: it implies a built-in limit to simultaneous knowledge of certain pairs of properties.
Although Heisenberg initially lacked formal training in matrix algebra, he justified this unusual step by requiring that the theory only refer to things that happen in measurements (such as discrete spectral lines). Thus his early papers introduced matrix rules by physical reasoning. Later, Max Born realized that Heisenberg’s symbols were literally matrices, and with Jordan he helped formulate the full matrix mechanics.
Philosophically, Heisenberg drew on ideas from Plato and ancient Greek thought. He felt that the elementary particles of nature were not empty billiard balls but more like mathematical forms or ideas, only indirectly accessible to us. He often emphasized that theoretical physics deals with our knowledge of nature rather than nature itself. In this view, the act of measurement by a scientist plays an active role in shaping what can be known. Heisenberg warned against trying to visualize quantum processes too concretely; instead he advocated following where the math and the experiments lead.
In practice, Heisenberg was a bold theorist who also collaborated widely. He was not just a lone thinker but worked with other great minds like Niels Bohr, Max Born and Eugene Wigner, and he enjoyed debating ideas with colleagues. He was known to check consistency by doing calculations in multiple ways, and by keeping only the simplest examples in mind (such as “harmonic oscillators,” which are like bouncing springs or waves). This focus on fundamental examples helped him guess general patterns.
World War II and the Uranium Project
When the Nazis came to power in Germany in 1933, Heisenberg publicly continued to embrace modern physics. He defended relativity and quantum theory against attacks by some Nazi ideologues who denounced them as “Jewish physics.” Nazi physicists Philipp Lenard and Johannes Stark accused him of following ideas by Einstein and others. Although he was briefly investigated by the SS, senior officials ultimately kept Heisenberg in place because his expertise was too valuable.
In December 1938 Otto Hahn and Fritz Strassmann in Berlin discovered nuclear fission – the splitting of the uranium atom – a finding quickly interpreted by Lise Meitner and Otto Frisch as a huge release of energy. Fission hinted that atomic bombs might be possible. Heisenberg, like other prominent physicists, took an interest. When World War II began in 1939, the German military (Heereswaffenamt) formalized a nuclear research project, known as the Uranverein (Uranium Club). Heisenberg was enlisted to help direct this project along with other top scientists.
Heisenberg organized experiments on uranium and a neutron moderator (heavy water) to try to build a self-sustaining chain reaction. Such a chain reaction would be the basis for both nuclear reactors and, with much more refinement, bombs. Working from 1939 until about 1942, Heisenberg and his team performed calculations and built small assemblies of uranium and carbon (graphite) aiming to measure neutron multiplication. In mid-1942, Heisenberg met Albert Speer, the German Minister of Armaments. Heisenberg reportedly told Speer that an atomic bomb would require extraordinary resources and time – beyond Germany’s practical capabilities during the war. By late 1942 the German program was scaled back and focused largely on producing reactor power for research, rather than bombs.
The German project did make some progress: Heisenberg’s team created uranium piles (chains of uranium and heavy water) and a small reactor experiment in a cave at Haigerloch in 1945. However, they never achieved a sustained chain reaction. Why the Nazi bomb effort faltered is still debated. Some historians suggest that Heisenberg and his colleagues deliberately downplayed the feasibility of a bomb, potentially as a moral choice or way to avoid potential destruction. Others argue that Germany simply lacked the industrial base and raw materials (enriched uranium or plutonium) to build a bomb quickly, and that Heisenberg’s estimates of critical mass late in the war were too large or the calculations incomplete. In later private letters, Heisenberg said he was relieved not to have to make a decision about building a bomb for Hitler.
A famous episode was Heisenberg’s meeting with his old mentor Niels Bohr in Copenhagen in 1941. (This meeting was later dramatized by Michael Frayn’s play Copenhagen.) According to various accounts, Heisenberg tried to discuss the implications of nuclear research – perhaps hinting that Germany was working on bomb physics – but Bohr, uneasy under occupation, abruptly cut off the conversation. The exact content remains uncertain, but the incident showed how science blurred into wartime secrets.
Near the end of the war in spring 1945, Allied forces captured many German scientists involved in uranium research. Heisenberg and others were detained for several months at a manor house in England called Farm Hall, secretly recorded by British intelligence. The transcripts (released decades later) show Heisenberg and colleagues reacting to news of the Hiroshima bombing with surprise and confusion, indicating they had not anticipated an American bomb so soon. The transcripts also confirm his earlier caution: he calculated a bomb would need many tons of U-235 (far more than Germany had) making such a weapon seem impractical at the time.
While in Farm Hall and after, Heisenberg defended his actions as primarily scientific and patriotic rather than ideological. He gained credit for keeping the German project alive under difficult conditions and then helping restart German physics after the war. But over time critics have remained divided. Some argue he was morally complicit by working for the Nazi regime, even if under duress. Others sympathize with the position he was placed in or suggest he may have subtly stymied the bomb effort. His own views seemed ambivalent. What is clear is that the German war program never came close to producing a bomb.
Influence
Heisenberg’s influence on physics was enormous. His matrix formulation and uncertainty principle became core parts of quantum theory. The mathematical methods he introduced (using matrices and operators) continue to underpin quantum mechanics and quantum field theory. The “Heisenberg picture” is taught alongside the Schrödinger picture as an equivalent way to calculate quantum dynamics. Many future scientists were inspired by his papers; famous physicists like Richard Feynman and Steven Weinberg built on foundations laid by Heisenberg’s generation. Concepts like Heisenberg’s energy–time uncertainty apply to processes like particle creation and the stability of atoms, influencing how scientists think about everything from lasers to elementary particle decays.
Heisenberg also played a key role in shaping postwar science. After the war he accepted a leadership position in what became the Max Planck Institute for Physics (first in Göttingen, then moved to Munich). In those roles he helped rebuild Germany’s physics community. Heisenberg advocated for scientific freedom and worked to restore international cooperation. In the 1950s and 1960s he advised the West German government on science and technology policy, and became president of the national research council. Under his guidance, West Germany developed its first nuclear reactors and revived its research universities.
Philosophically and culturally, Heisenberg influenced how people view science. His uncertainty principle entered popular discussions as a metaphor for limits of knowledge. In the history of science he is often contrasted with Einstein – both trusted but ultimately embraced mathematics of quantum theory, yet came to different conclusions about reality. His quotations (for example, “What we observe is not nature itself, but nature exposed to our method of questioning”) still appear in discussions of science and reality. Teachers often credit Heisenberg’s 1925 and 1927 papers as the starting point of modern quantum theory; his name is given to concepts (Heisenberg uncertainty, Heisenberg group, Heisenberg cut) and even to an academic fellowship (the German Research Foundation’s Heisenberg Programme supports promising researchers in physics and other fields).
Namesakes include minor planets (an asteroid 13149 Heisenberg), school scholarships, and statues. In Germany a statue stands on the island of Heligoland, where he often vacationed. Many physics journals and textbooks routinely reference Heisenberg’s work, and his collected works remain standard references. The Nobel Prize committee praised him as the “creator of quantum mechanics,” a title reflecting his lasting legacy.
Critiques
Heisenberg’s career and ideas have drawn criticism as well as praise. Among the scientific debates, Albert Einstein and others famously challenged the philosophical implications of his uncertainty principle. Einstein objected to the idea that reality is inherently probabilistic: “God does not play dice,” he remarked. He and other “realists” believed particles should have definite properties whether or not we measure them. Heisenberg insisted that designing a theory in terms of measurables was the only sensible approach, but the debate (embodied in the Einstein–Bohr discussions) continued for decades. Today, most physicists accept the formalism but still study interpretations; critics of the Copenhagen view have proposed alternate frameworks (like Bohmian mechanics) partly motivated by discomfort with Heisenberg’s view that unobserved variables have no meaning.
In the context of the 1930s political climate, Heisenberg faced attacks from Nazi supporters of “Deutsche Physik.” He was labeled a “white Jew” by those extremists for upholding Einstein’s relativity. Some have criticized Heisenberg for not speaking out more forcefully against Nazism or for continuing to work within the regime. On the other hand, many scholars note he risked his position by defending “Jewish” science and that he made difficult choices under authoritarian pressure. His correspondence after the war, including letters to his wife Elisabeth, reveal a man anxious about Gestapo attention and eager to protect his staff.
Perhaps the fiercest criticism comes from the controversy over his wartime work. Historian Paul Rose (in Heisenberg and the Nazi Atomic Bomb Project, 1998) argued that Heisenberg may have shown “anti-Semitic thinking” and willful self-deception, blaming him for poor science and a cover-up after the war. Rose portrayed Heisenberg as morally compromised by nationalist views. Others, like David Cassidy in his biography Uncertainty, offer a more sympathetic view: Heisenberg as a patriotic scientist caught in a terrible situation, possibly working in shades of gray between the Nazis and the Allies. The truth likely lies between: while Heisenberg did not join Nazi Party organizations, he cooperated with the war effort. Some critics feel he should have refused to work on any potential bomb; others note he at least did not engineer a weapon for Hitler.
In technical scholarship, some early misconceptions in Heisenberg’s physics were later sorted out. For example, his initial calculation of the neutron–proton forces had simplifying assumptions that later theory refined. His separation of “uncertainty” into language led to some confusion in terminology (Heisenberg himself translated his original German term “Ungenauigkeit” as “uncertainty” rather than “imprecision”). But these are relatively minor compared to the broader philosophical and ethical discussions he inspired.
Legacy
Werner Heisenberg is remembered as one of the towering figures of 20th-century physics. Many of the insights he contributed remain cornerstones of modern science. The uncertainty principle in particular has become part of the cultural vocabulary describing limits of knowledge in any field. In physics, it and the mathematics of quantum mechanics still underpin technologies like the semiconductor chips in computers and MRI machines in medicine.
In Germany and worldwide, institutions commemorate Heisenberg. The Heisenberg Programme of the German Research Foundation (Deutsche Forschungsgemeinschaft) supports senior researchers and is named in his honor. The physical institutes he led – now part of the Max Planck Society – continue research in fundamental physics. On Heligoland, a statue of Heisenberg overlooks the sea, and a museum at the University of Hamburg includes exhibits on his life and work. Physics conferences, lecture series and awards sometimes bear his name, and anniversary celebrations (for example, in 2001 on his centenary) brought together scientists to discuss his contributions.
His writings also live on. He wrote several books for general readers, such as Physics and Philosophy (1958), which explains modern physics and its implications, and Across the Frontiers (1974), an autobiographical account of his life. Quotes from his writings are often cited on the nature of science: for instance, he wrote that science “no longer confronts nature as an objective observer, but sees itself as an actor.” This perspective has influenced thinkers in science and philosophy beyond physics itself.
Heisenberg’s mixed legacy also serves as a reminder of the complex relation between science and society. He stands as a symbol of genius in theoretical physics and of the deep intellectual humility required by the quantum world. At the same time, his role in wartime science continues to provoke reflection on the moral responsibilities of scientists under any regime. In the classroom, his story is told as part of the fascinating narrative of quantum mechanics. In these ways, Werner Heisenberg’s life and work remain woven into the fabric of modern scientific culture.
Selected works
- 1925: “Über quantentheoretische Umdeutung kinematischer und mechanischer Beziehungen” (Quantum‐Theoretical Reinterpretation of Kinematic and Mechanical Relations). Foundational paper introducing matrix mechanics.
- 1927: “Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik” (On the Perceptual Content of Quantum Theoretical Kinematics and Mechanics). Published formulation of the uncertainty principle.
- 1930: Die physikalischen Prinzipien der Quantentheorie (The Physical Principles of the Quantum Theory). A textbook summarizing early quantum theory.
- 1958: Physics and Philosophy: The Revolution in Modern Science. A popular book discussing the conceptual foundations of quantum mechanics and their philosophical implications.
- 1974: Across the Frontiers: A Physicist’s Life Story. Heisenberg’s autobiographical memoir, recounting his life and work (translated to English).