Copenhagen interpretation
In 1925, Werner Heisenberg presented a treatment of electron behavior based on discussing only observable quantities. He defined these as the frequencies of light that atoms absorbed and emitted. Max Born then realized that classical variables like position and momentum were represented by matrices in this theory. These mathematical objects could be multiplied together like numbers, but the order of multiplication mattered. Erwin Schrödinger later presented an equation treating the electron as a wave. Born discovered that the wave function served as a tool for calculating probabilities rather than describing physical reality directly. This transition from old quantum theory to full-fledged quantum physics began in 1925 after decades of heuristic corrections. The Bohr-Sommerfeld model had failed to extend beyond hydrogen to helium. Physicists worked with approximations until the mid-1920s when the revision reached coherent status.
Werner Heisenberg coined the phrase Copenhagen interpretation around 1955 while criticizing alternative interpretations developed by David Bohm. He delivered lectures titled The Copenhagen Interpretation of Quantum Theory and Criticisms and Counterproposals to the Copenhagen Interpretation in 1955. Before his book was released for sale, Heisenberg privately expressed regret for having used the term. He stated that it suggested other interpretations existed which he considered nonsense. Léon Rosenfeld called the term ambiguous in a 1960 review and suggested discarding it. Despite this criticism, the term entered widespread use. The city of Copenhagen refers to where Bohr and Heisenberg worked during the mid-1920s. At the 1927 Solvay Conference, Max Born and Heisenberg declared quantum mechanics a closed theory. No definitive historical statement exists about what the interpretation entails because their writings contradict each other on important issues.
Quantum mechanics is intrinsically indeterministic according to core principles accepted across versions of the Copenhagen interpretation. The Born rule gives the probability density of finding a particle at a given point when measured. This probability is proportional to the square of the magnitude of the particle's wave function at that point. Formulated by Max Born in 1926, it allows calculation of individual transition process probabilities. Complementarity states that certain properties cannot be jointly defined for the same system at the same time. Observable quantities corresponding to mutually exclusive laboratory arrangements cannot be predicted together. A particular experiment can demonstrate particle behavior or wave behavior but not both simultaneously. Hans Primas and Roland Omnès added that quantum physics applies to individual objects without requiring an ensemble. Results from measuring devices are essentially classical and should be described in ordinary language. Statements about measurements that are not actually made do not have meaning.
Much criticism has focused on the need for a classical domain where observers or measuring devices can reside. This boundary came to be termed the Heisenberg cut while John Bell derisively called it the shifty split. As typically portrayed, interpretations involve two different kinds of time evolution for wave functions. One follows deterministic flow according to the Schrödinger equation while the other involves probabilistic jumps during measurement. There is no clear criterion for when each kind applies. Steven Weinberg writes that traditional presentation gives no way to locate the boundary between realms. The problem becomes particularly acute in quantum cosmology where the quantum system is the universe itself. How does an observer stand outside the universe to measure it? Rudolf Peierls noted that the observer does not have to be contemporaneous with the event. Asher Peres argued physicists are conceptually outside those degrees of freedom that cosmology studies.
Albert Einstein was an early and persistent supporter of objective reality while Bohr and Heisenberg advanced opposing positions. Abraham Pais recalled a walk with Einstein discussing quantum mechanics. Einstein suddenly stopped and asked whether he really believed the moon exists only when looked at. Einstein maintained that quantum theory could not be complete despite giving correct predictions. His most famous product was the Einstein-Podolsky-Rosen thought experiment published in 1935. This paper pointed out that if position of one particle were measured, the result of measuring momentum of another could be predicted. They invoked what later became known as the EPR criterion of reality. Bohr responded in Physical Review later that same year arguing their reasoning was fallacious. Einstein said he was convinced God does not throw dice regarding randomness in nature. Bohr reputedly replied that it cannot be for us to tell God how he runs the world. Einstein never proposed a hidden variable theory though he explored the possibility before withdrawing his paper.
A cat is put in a sealed box with its life or death made dependent on state of a subatomic particle. Schrödinger resisted so naively accepting as valid a blurred model for representing reality. The description of the cat during the course of the experiment becomes a blur of living and dead cat states. But this implies the cat is actually both dead and alive until the box is opened to check on it. In Copenhagen-type views, the wave function reflects our knowledge of the system once observed. There is a 50% chance the cat will be dead and 50% chance it will be alive. Some versions reject assigning a wave function to physical systems meeting everyday definitions like cats. Wigner's friend thought experiment involves two conscious beings traditionally known as Wigner and his friend. The external observer believes the system is in one state while his friend is convinced the cat is alive. Different interpretations take different positions on whether observers can be placed on quantum side of the cut.
According to an informal poll conducted at a quantum mechanics conference in 1997, the Copenhagen interpretation remained most widely accepted label physicists applied to their own views. A similar result was found in polls conducted in 2011 and 2025. A large number of alternative interpretations have appeared sharing some aspects while providing alternatives to others. The ensemble interpretation offers an interpretation of the wave function but not for single particles. Consistent histories advertises itself as Copenhagen done right. More recently, interpretations inspired by quantum information theory like QBism and relational quantum mechanics have appeared. Under realism and determinism if wave function is regarded as ontologically real and collapse entirely rejected, many-worlds results. Bohmian mechanics shows it possible to reformulate quantum mechanics to make it deterministic at price of making it explicitly nonlocal. John Archibald Wheeler began career as apostle of Niels Bohr then supervised PhD thesis of Hugh Everett proposing many-worlds interpretation. Late in life he wrote that while Copenhagen might fairly be called fog from north, it remains best interpretation we have.
Common questions
When did Werner Heisenberg coin the phrase Copenhagen interpretation?
Werner Heisenberg coined the phrase Copenhagen interpretation around 1955 while criticizing alternative interpretations developed by David Bohm. He delivered lectures titled The Copenhagen Interpretation of Quantum Theory and Criticisms and Counterproposals to the Copenhagen Interpretation in 1955.
What is the origin of the name Copenhagen interpretation for quantum mechanics?
The city of Copenhagen refers to where Bohr and Heisenberg worked during the mid-1920s. Physicists worked with approximations until the mid-1920s when the revision reached coherent status after decades of heuristic corrections.
How does Max Born define probability density in the Copenhagen interpretation?
Formulated by Max Born in 1926, the Born rule gives the probability density of finding a particle at a given point when measured. This probability is proportional to the square of the magnitude of the particle's wave function at that point.
Why did Albert Einstein criticize the Copenhagen interpretation of quantum theory?
Einstein maintained that quantum theory could not be complete despite giving correct predictions and famously said he was convinced God does not throw dice regarding randomness in nature. His most famous product was the Einstein-Podolsky-Rosen thought experiment published on the 2nd of May 1935 which pointed out flaws in their reasoning.
What happens to Schrödinger's cat according to Copenhagen-type views?
In Copenhagen-type views, there is a 50% chance the cat will be dead and 50% chance it will be alive before the box is opened to check on it. The description of the cat during the course of the experiment becomes a blur of living and dead cat states until observed.