# Copenhagen Interpretation of Quantum Mechanics The idea that there was a Copenhagen way of thinking was christened as the "_Kopenhagener Geist der Quantentheorie_" by [Werner Heisenberg](https://www.informationphilosopher.com/solutions/scientists/heisenberg/) in the introduction to his 1930 textbook _The Physical Principles of Quantum Theory_, based on his 1929 lectures in Chicago (given at the invitation of [Arthur Holly Compton](https://www.informationphilosopher.com/solutions/scientists/compton/)). It is a sad fact that [Einstein](https://www.informationphilosopher.com/solutions/scientists/einstein/), who had found more than any other scientist on the quantum interaction of electrons and photons, was largely ignored or misunderstood at this Solvay, when he again clearly described [nonlocality](https://www.informationphilosopher.com/freedom/nonlocality.html) At the 1927 Solvay conference on physics entitled "Electrons and Photons," [Niels Bohr](https://www.informationphilosopher.com/solutions/scientists/bohr/) and Heisenberg consolidated their Copenhagen view as a "complete" picture of quantum physics, despite the fact that they could not, or would not, visualize or otherwise explain exactly what is going on in the microscopic world of "quantum reality." From the earliest presentations of the ideas of the supposed "founders" of quantum mechanics, [Albert Einstein](https://www.informationphilosopher.com/solutions/scientists/einstein/) had deep misgivings of the work going on in Copenhagen, although he never doubted the calculating power of their new mathematical methods. He described their work as _incomplete_ because it is based on the statistical results of many experiments so only makes probabilistic predictions about individual experiments. Einstein hoped to _visualize_ what is going on in an underlying "objective reality." Bohr seemed to deny the existence of a fundamental "reality," but he clearly knew and said that the physical world is largely independent of human observations. In classical physics, the physical world is assumed to be completely independent of the act of observing the world. In quantum physics, Heisenberg said that the result of an experiment depends on the [free choice](https://www.informationphilosopher.com/freedom/free_choice.html) of the experimenter as to what to measure. The quantum world of photons and electrons might look like waves or look like particles depending on what we look for, rather than what they "are" as "things in themselves." The [information interpretation](https://www.informationphilosopher.com/introduction/physics/interpretation/) of quantum mechanics says there is only one world, the quantum world. Averaging over large numbers of quantum events explains why [large objects appear to be classical](https://www.informationphilosopher.com/introduction/physics/quantum_to_classical.html) Copenhageners were proud of their limited ability [to know](https://www.informationphilosopher.com/knowledge/). Bohr said: > There is no quantum world. There is only an abstract quantum physical description. It is wrong to think that the task of physics is to find out how nature is. Physics concerns what we can say about nature. Bohr thus put severe epistemological limits on knowing the Kantian "things in themselves," just as [Immanuel Kant](https://www.informationphilosopher.com/solutions/philosophers/kant/) had put limits on reason. The British empiricist philosophers [John Locke](https://www.informationphilosopher.com/solutions/philosophers/locke/) and [David Hume](https://www.informationphilosopher.com/solutions/philosophers/hume/) had put the "primary" objects beyond the reach of our "secondary" sensory perceptions. In this respect, Bohr shared the positivist views of many other empirical scientists, [Ernst Mach](https://www.informationphilosopher.com/solutions/scientists/mach/) for example. Twentieth-century analytic language philosophers thought that philosophy (and even physics) could not solve some basic problems, but only "dis-solve" them by showing them to be conceptual errors. Neither Bohr nor Heisenberg thought that macroscopic objects actually are classical. They both saw them as composed of microscopic quantum objects. On the other hand, Bohr and Heisenberg emphasized the importance of conventional classical-physics language as a tool for [knowledge](https://www.informationphilosopher.com/knowledge/). Since language evolved to describe the familiar world of "classical" objects in space and time, they insisted that somewhere between the quantum world and the classical world there must come a point when our observations and measurements can be expressible in classical concepts. They argued that a measurement apparatus and a particular observation must be describable classically in order for it to be understood and become knowledge in the [mind](https://www.informationphilosopher.com/mind/) of the observer. The exact location of that [transition from the quantum to the classically describable world](https://www.informationphilosopher.com/introduction/physics/quantum_to_classical.html) was arbitrary, said Heisenberg. He called it a ["cut" (_Schnitt_)](https://www.informationphilosopher.com/introduction/physics/heisenberg_cut.html). Heisenberg's and especially [John von Neumann](https://www.informationphilosopher.com/solutions/scientists/neumann/)'s and [Eugene Wigner](https://www.informationphilosopher.com/solutions/scientists/wigner/)'s insistence on a critical role for a "[conscious observer](https://www.informationphilosopher.com/quantum/observer/)" has led to a great deal of nonsense being associated with the Copenhagen Interpretation and in the philosophy of quantum physics. Heisenberg may only have been trying to explain how knowledge reaches the observer's mind. For von Neumann and Wigner, the mind was considered a [causal factor](https://www.informationphilosopher.com/freedom/causality.html) in the behavior of the quantum system. Today, a large number of [panpsychists](https://www.informationphilosopher.com/mind/panpsychism), some philosophers, and a small number of scientists, still believe that the [mind](https://www.informationphilosopher.com/mind/) of a [conscious observer](https://www.informationphilosopher.com/quantum/observer/) is needed to cause the so-called ["collapse" of the wave function](https://www.informationphilosopher.com/quantum/collapse/). A relatively large number of scientists opposing the Copenhagen Interpretation believe that there are never any "collapses" in a _universal wave function_. In the mid 1950's, Heisenberg reacted to [David Bohm](https://www.informationphilosopher.com/solutions/scientists/bohm/)'s 1952 "pilot-wave" [interpretation of quantum mechanics](https://www.informationphilosopher.com/introduction/physics/interpretations.html) by calling his own work the "Copenhagen Interpretation" and the only correct interpretation of quantum mechanics. A significant fraction of working quantum physicists say they agree with Heisenberg, though few have ever looked carefully into the fundamental assumptions of the Copenhagen Interpretation. This is because they pick out from the Copenhagen Interpretation just the parts they need to make quantum mechanical calculations. Most textbooks start the story of quantum mechanics with the picture provided by the work of Heisenberg, Bohr, [Max Born](https://www.informationphilosopher.com/solutions/scientists/born/), [Pascual Jordan](https://www.informationphilosopher.com/solutions/scientists/jordan/), [Paul Dirac](https://www.informationphilosopher.com/solutions/scientists/dirac/), and of course [Erwin Schrödinger](https://www.informationphilosopher.com/solutions/scientists/schrodinger/). ## What Exactly Is in the Copenhagen Interpretation? There are several major components to the Copenhagen Interpretation, which most historians and philosophers of science agree on: - **[The quantum postulates](https://www.informationphilosopher.com/solutions/scientists/bohr/quantum_postulate.html)**. Bohr postulated that quantum systems (beginning with his "Bohr atom" in 1913) have "stationary states" which make discontinuous "quantum jumps" between the states with the emission or absorption of radiation. Until at least 1925 Bohr insisted the radiation itself is continuous. Einstein said radiation is a discrete "light quantum" (later called a photon) as early as 1905. Ironically, largely ignorant of the history of quantum mechanics (dominated by Bohr's account), many of today's textbooks teach the "Bohr atom" as emitting or absorbing photons - Einstein light quanta! Also, although Bohr made a passing reference, virtually no one today knows that discrete energy states or quantized energy levels in matter were first discovered by Einstein in his 1907 work on specific heat. - **[Wave-particle duality](https://www.informationphilosopher.com/introduction/physics/wave-particle_duality.html)**. The [complementarity](https://www.informationphilosopher.com/introduction/physics/complementarity.html) of [waves and particles](https://www.informationphilosopher.com/quantum/copenhagen/wave-particle_duality.html), including a synthesis of the particle-matrix mechanics theory of Heisenberg, [Max Born](https://www.informationphilosopher.com/solutions/scientists/born/), and [Pascual Jordan](https://www.informationphilosopher.com/solutions/scientists/jordan/), with the wave mechanical theory of [Louis deBroglie](https://www.informationphilosopher.com/solutions/scientists/debroglie/) and [Erwin Schrödinger](https://www.informationphilosopher.com/solutions/scientists/schrodinger/). Again ironically, [wave-particle duality](https://www.informationphilosopher.com/quantum/copenhagen/wave-particle_duality.html) was first described by Einstein in 1909. Heisenberg had to have his arm twisted by Bohr to accept the wave picture. - **[Indeterminacy principle](https://www.informationphilosopher.com/freedom/indeterminacy.html)**. Heisenberg sometimes called it his "uncertainty" principle, which could imply human ignorance, implying an epistemological (knowledge) problem rather than an ontology (reality) problem. Bohr considered indeterminacy as another example of his complementarity, between the non-commuting conjugate variables momentum and position, for example, _Δp Δx ≥ h_ (also between energy and time and between action and angle variables). - **Correspondence principle**. Bohr maintained that in the limit of large quantum numbers, the atomic structure of quantum systems approaches the behavior of classical systems. Bohr and Heisenberg both described this case as when Planck's quantum of action _h_ can be neglected. They mistakenly described this as _h -> 0_. But _h_ is a fundamental constant. The [_quantum-to-classical transition_](https://www.informationphilosopher.com/introduction/physics/quantum_to_classical.html) is when the action of a macroscopic object is large compared to _h_ . As the number of quantum particles increases (as mass increases), large macroscopic objects behave like classical objects. Position and velocity become arbitrarily accurate as _h / m -> 0_. _Δv Δx ≥ h / m_. There is only one world. It is a quantum world. Ontologically it is [indeterministic](https://www.informationphilosopher.com/freedom/indeterminism.html), but epistemically, common sense and everyday experience inclines us to see it as [deterministic](https://www.informationphilosopher.com/freedom/determinism.html). Bohr and Heisenberg insisted we must use classical (deterministic?) concepts and language to communicate our [knowledge](https://www.informationphilosopher.com/knowledge/) about quantum processes! - **Completeness**. Schrödinger's wave function _ψ_ provides a "complete" description of a quantum system, despite the fact that conjugate variables like position and momentum cannot both be known with arbitrary accuracy, as they can in classical systems. There is less [information](https://www.informationphilosopher.com/introduction/information/) in the world than classical physics implies. The wave function _ψ_ evolves according to the unitary [deterministic](https://www.informationphilosopher.com/freedom/determinism.html) Schrödinger equation of motion, _conserving_ that information. When one possibility becomes actual (discontinuously), new information may be [irreversibly](https://www.informationphilosopher.com/problems/reversibility/) created and recorded by a measurement apparatus, or simply show up as a new information structure in the world. By comparison, Einstein maintained that quantum mechanics is _incomplete_, because it provides only _statistical_ information about _ensembles_ of quantum systems. He also was deeply concerned about [nonlocality](https://www.informationphilosopher.com/problems/nonlocality/) and [nonseparability](https://www.informationphilosopher.com/problems/nonseparability/), things not addressed at all by the Copenhagen interpretation. - **[Irreversible](https://www.informationphilosopher.com/problems/reversibility/) recording** of information in the measuring apparatus. Without this record (a pointer reading, blackened photographic plate, Geiger counter firing, etc.), there would be nothing for observers to see and to know. Information must come into the universe long before any scientist can "observe" it. In today's high-energy physics experiments and space research, the data-analysis time between the initial measurements and the scientists seeing the results can be measured in months or years. All the founders of quantum mechanics mention the need for irreversibility. The need for positive entropy transfer away from the experiment to stabilize new information (negative entropy) so it can be observed was first shown by [Leo Szilard](https://www.informationphilosopher.com/solutions/scientists/szilard/) in 1929, and later by [Leon Brillouin](https://www.informationphilosopher.com/solutions/scientists/brillouin/) and [Rolf Landauer](https://www.informationphilosopher.com/solutions/scientists/landauer/). - **Classical apparatus?**. Bohr required that the macroscopic measurement apparatus be described in ordinary "classical" language. This is a third "complementarity," now between the quantum system and the "classical apparatus" But Born and Heisenberg never said the measuring apparatus _is_ "classical." They knew that everything is fundamentally a quantum system. Lev Landau and Evgeny Lifshitz saw a circularity in this view, "quantum mechanics occupies a very unusual place among physical theories: it contains classical mechanics as a limiting case [correspondence principle], yet at the same time it requires this limiting case for its own formulation. - **Statistical interpretation ([acausality](https://www.informationphilosopher.com/quantum/copenhagen/freedom/chance.html))**. Born interpreted the square modulus of Schrödinger's complex wave function as the [probability](https://www.informationphilosopher.com/quantum/copenhagen/freedom/probability.html) of finding a particle. Einstein's "ghost field" or "guiding field," deBroglie's pilot or guide wave, and Schrödinger's wave function as the distribution of the electric charge density were similar views in much earlier years. Born sometimes pointed out that his direct inspiration was Einstein. All the predicted properties of physical systems and the "laws of nature" are only [probabilistic](https://www.informationphilosopher.com/freedom/probability.html) ([acausal](https://www.informationphilosopher.com/freedom/causa_sui.html), [indeterministic](https://www.informationphilosopher.com/freedom/indeterminacy.html) ). All results of physical experiments are _statistical_. Briefly, theories give us probabilities, experiments give us statistics. Large numbers of identical experiments provide the statistical evidence for the theoretical probabilities predicted by quantum mechanics. Bohr's emphasis on epistemological questions suggests he thought that the statistical uncertainty may only be in our [knowledge](https://www.informationphilosopher.com/knowledge/). They may not describe nature itself. Or at least Bohr thought that we can not describe a "reality" for quantum objects, certainly not with classical concepts and language. However, the new concept of an _immaterial_ possibilities function (pure information) moving through space may make quantum phenomena "visualizable." Ontological acausality, chance, and a probabilistic or statistical nature were first seen by Einstein in 1916, as Born later acknowledged. But Einstein disliked this chance. He and most scientists appear to have what [William James](https://www.informationphilosopher.com/solutions/philosophers/james/) called an "antipathy to chance." - **No Visualizability?**. Bohr and Heisenberg both thought we could never produce models of what is going on at the quantum level. Bohr thought that since the wave function cannot be observed we can't say anything about it. Heisenberg said probability is real and the basis for the statistical nature of quantum mechanics. Whenever we draw a diagram of the waves impinging on the [two-slits](https://www.informationphilosopher.com/solutions/experiments/two-slit_experiment/), we are in fact visualizing the wave function as possible locations for a particle, with calculable probabilities for each possible location. Today we can visualize with animations many puzzles in physics, including the two-slit experiment, [entanglement](https://www.informationphilosopher.com/quantum/entanglement/), and [microscopic irreversibility](https://www.informationphilosopher.com/quantum/copenhagen/). - **No Path?**. Bohr, Heisenberg, Dirac and others said we cannot describe a particle as having a path. The path comes into existence when we observe it, Heisenberg maintained. (_Die “Bahn” entsteht erst dadurch, dass wir sie beobachten_) Einstein's "objective reality" hoped for a deeper level of physics in which particles do have paths and, in particular, they obey conservation principles, though intermediate measurements needed to observe this fact would interfere with the experiments. - **[Paul Dirac](https://www.informationphilosopher.com/solutions/scientists/dirac/)** formalized quantum mechanics with these three fundamental concepts, all very familiar and accepted by Bohr, Heisenberg, and the other Copenhageners: - **_Axiom of measurement_**. Bohr's stationary quantum states have eigenvalues with corresponding eigenfunctions (the eigenvalue-eigenstate link). - **_Superposition principle_**. According to Dirac's transformation theory, _ψ_ can be represented as a linear combination of vectors that are a proper basis for the combined target quantum system and the measurement apparatus. - **_Projection postulate_**. The [collapse of the wave function](https://www.informationphilosopher.com/solutions/experiments/wave-function_collapse/) _ψ_, which is irreversible, upon interacting with the measurement apparatus and creating new information. - **[Two-slit experiment](https://www.informationphilosopher.com/solutions/experiments/two-slit_experiment)**. A "gedanken" experiment in the 1920's, but a real experiment today, exhibits the combination of wave and particle properties. Note that what two-slit experiment really shows is - first, the wave function [deterministically](https://www.informationphilosopher.com/freedom/determinism.html) and continuously exploring all the _[possibilities](https://www.informationphilosopher.com/freedom/possibilities.html)_ for interaction, - second, the particle [randomly](https://www.informationphilosopher.com/freedom/chance.html) and discontinuously choosing one of those possibilities to become _[actual](https://www.informationphilosopher.com/freedom/actualism.html)_. There are many more elements that play lesser roles, some making the Copenhagen Interpretation very unpopular among philosophers of science and spawning new [interpretations](https://www.informationphilosopher.com/introduction/physics/interpretations/) or even "[formulations](https://www.informationphilosopher.com/introduction/physics/formulations/)" of quantum mechanics. Some of these are misreadings or later accretions. They include: - **The "[conscious observer](https://www.informationphilosopher.com/quantum/observer/)."** The claim that quantum systems cannot change their states without an observation being made by a conscious observer. Does the collapse only occur when an observer "looks at" the system? How exactly does the mind of the observer have causal power over the physical world? (the [mind-body problem](https://www.informationphilosopher.com/problems/mind-body/)). Einstein objected to the idea that his bed had diffused throughout the room and only gathered itself back together when he opened the bedroom door and looked in. [John von Neumann](https://www.informationphilosopher.com/solutions/scientists/neumann/) and [Eugene Wigner](https://www.informationphilosopher.com/solutions/scientists/wigner/) seemed to believe that the mind of the observer was essential, but it is not found in the original work of Bohr and Heisenberg, so should perhaps not be a part of the Copenhagen Interpretation? It has no place in standard quantum physics today - **The [measurement problem](https://www.informationphilosopher.com/problems/measurement/)**, including the insistence that the measuring apparatus must be described classically when it is made of quantum particles. There are actually at least three definitions of the measurement problem. 1. The claim that the two dynamical laws, unitary deterministic time evolution according to the Schrödinger equation and indeterministic collapse according to Dirac's projection postulate are logically inconsistent. They cannot both be true, it's claimed. The proper interpretation is simply that the two laws laws apply at different times in the evolution of a quantum object, one for possibilities, the other for actuality (as Heisenberg knew): - first, the unitary deterministic evolution moves through space exploring all the _[possibilities](https://www.informationphilosopher.com/freedom/possibilities.html)_ for interaction, - second, the indeterministic collapse [randomly](https://www.informationphilosopher.com/freedom/chance.html) (acausally) selects one of those possibilities to become _[actual](https://www.informationphilosopher.com/freedom/actualism.html)_. 2. The original concern that the "collapse dynamics" ([von Neumann Process 1](https://www.informationphilosopher.com/solutions/scientists/neumann/#process1)) is not a part of the formalism ([von Neumann Process 2](https://www.informationphilosopher.com/solutions/scientists/neumann/#process2)) but is an _ad hoc_ element, with no rules for when to apply it. If there was a [deterministic](https://www.informationphilosopher.com/freedom/determinism.html) law that predicted a collapse, or the decay of a radioactive nucleus, it would not be quantum mechanics! 3. [Decoherence theorists](https://www.informationphilosopher.com/knowledge/decoherence.html) say that the measurement problem is the failure to observe macroscopic superpositions, such as [Schrödinger's Cat](https://www.informationphilosopher.com/quantum/copenhagen/schrodingerscat). - The many unreasonable philosophical claims for "complementarity:" e.g., that it solves the [mind-body problem](https://www.informationphilosopher.com/problems/mind-body/)?, - The basic "subjectivity" of the Copenhagen interpretation. It deals with epistemological knowledge of things, rather than the "things themselves." ## Opposition to the Copenhagen Interpretation [Albert Einstein](https://www.informationphilosopher.com/solutions/scientists/einstein/), [Louis deBroglie](https://www.informationphilosopher.com/solutions/scientists/debroglie/), and especially [Erwin Schrödinger](https://www.informationphilosopher.com/solutions/scientists/schrodinger/) insisted on a more "complete" picture, not merely what can be said, but what we can "see," a visualization (_Anschaulichkeit_) of the microscopic world. But de Broglie and Schrödinger's emphasis on the wave picture made it difficult to understand material particles and their "quantum jumps." Indeed, Schrödinger and more recent physicists like [John Bell](https://www.informationphilosopher.com/solutions/scientists/bell/) and the [decoherence](https://www.informationphilosopher.com/knowledge/decoherence.html) theorists [H. D. Zeh](https://www.informationphilosopher.com/solutions/scientists/zeh/) and [Wojciech Zurek](https://www.informationphilosopher.com/solutions/scientists/zurek/) deny the existence of particles and the [collapse of the wave function](https://www.informationphilosopher.com/solutions/experiments/wave-function_collapse/), which is central to the Copenhagen Interpretation. Perhaps the main claim of those today denying the Copenhagen Interpretation (and standard quantum mechanics) began with Schrödinger's (nd later Bell's) claim that "there are no quantum jumps." [Decoherence](https://www.informationphilosopher.com/knowledge/decoherence.html) theorists and others favoring [Everett](https://www.informationphilosopher.com/solutions/scientists/everett/)'s Many-Worlds Interpretation reject [Dirac](https://www.informationphilosopher.com/solutions/scientists/dirac/)'s _projection postulate_, a cornerstone of quantum theory. Heisenberg had initially insisted on his own "matrix mechanics" of particles and their discrete, discontinuous, [indeterministic](https://www.informationphilosopher.com/freedom/indeterminism.html) behavior, the "[quantum postulate](https://www.informationphilosopher.com/solutions/scientists/bohr/quantum_postulate.html)" of unpredictable events that undermine the classical physics of [causality](https://www.informationphilosopher.com/freedom/causality.html). But Bohr told Heisenberg that his matrix mechanics was too narrow a view of the problem. This disappointed Heisenberg and almost ruptured their relationship. But Heisenberg came to accept the criticism and he eventually endorsed all of Bohr's deep philosophical view of quantum reality as _unvisualizable_. In his September [Como Lecture](https://www.informationphilosopher.com/solutions/scientists/bohr/quantum_postulate.html), a month before the 1927 Solvay conference, Bohr introduced his theory of "[complementarity](https://www.informationphilosopher.com/introduction/physics/complementarity.html)" as a "complete" theory. It combines the contradictory notions of wave and particle. Since both are required, they complement (and "complete") one another. Although Bohr is often credited with integrating the dualism of waves _and_ particles, it was Einstein who predicted this would be necessary as early as [1909](https://www.informationphilosopher.com/solutions/scientists/einstein/1909.html). But in doing so, Bohr obfuscated further what was already a mysterious picture. How could something possibly be both a discrete particle and a continuous wave? Did Bohr endorse the continuous [deterministic](https://www.informationphilosopher.com/freedom/determinism.html) wave-mechanical views of Schrödinger? Not exactly, but Bohr's accepting Schrödinger's wave mechanics as equal to and complementing his matrix mechanics was most upsetting to Heisenberg. [Bohr's Como Lecture](https://www.informationphilosopher.com/solutions/scientists/bohr/quantum_postulate.html) astonished Heisenberg by actually _deriving_ (instead of Heisenberg's heuristic microscope argument) the [uncertainty principle](https://www.informationphilosopher.com/freedom/uncertanty.html) from the space-time wave picture alone, with no reference to the _acausal_ dynamics of Heisenberg's picture! After this, Heisenberg did the same derivation in his 1930 text and subsequently completely accepted _complementarity_. Heisenberg spent the next several years widely promoting Bohr's views to scientists and philosophers around the world, though he frequently lectured on his mistaken, but easily understood, argument that looking at particles disturbs them. His microscope is even today included in many elementary physics textbooks. Bohr said these contradictory wave and particle pictures are "complementary" and that both are needed for a "complete" picture. He co-opted Einstein's claim to a more "complete" picture of an objective" reality, one that might restore simultaneous knowledge of position and momentum, for example. Classical physics has twice the number of independent variables (and twice the information) as quantum physics. In this sense, it does seem more "complete." Many critics of Copenhagen thought that Bohr deliberately and provocatively embraced logically contradictory notions - of _continuous_ deterministic waves and _discrete_ indeterministic particles - perhaps as evidence of Kantian limits on reason and human knowledge. Kant called such contradictory truths "antinomies." The contradictions only strengthened Bohr's epistemological resolve and his insistence that physics required a _subjective_ view unable to reach the _objective_ nature of the "things in themselves." As Heisenberg described it in his explanation of the Copenhagen Interpretation, > This again emphasizes a subjective element in the description of atomic events, since the measuring device has been constructed by the observer, and we have to remember that what we observe is not nature in itself but nature exposed to our method of questioning. Our scientific work in physics consists in asking questions about nature in the language that we possess and trying to get an answer from experiment by the means that are at our disposal. > > > ("[The Copenhagen Interpretation of Quantum Mechanics," in _Physics and Philosophy_, 1955)](https://www.informationphilosopher.com/solutions/scientists/heisenberg/Copenhagen_Interpretation.html) ## References [Copenhagen Interpretation on Wikipedia](http://en.wikipedia.org/wiki/Copenhagen_interpretation) [Copenhagen Interpretation on Stanford Encyclopedia of Philosophy](http://plato.stanford.edu/entries/qm-copenhagen/) ["Copenhagen Interpretation of Quantum Theory"](https://www.informationphilosopher.com/quantum/copenhagen/Heisenberg_Copenhagen_Interpretation.pdf), in _Physics and Philosophy_, Werner Heisenberg, 1958, pp.44-58 ["The Copenhagen Interpretation"](https://www.informationphilosopher.com/quantum/copenhagen/Stapp_Copenhagen_Interpretation.pdf), _American Journal of Physics_, 40, p.1098, Henry Stapp, 1972 ["The History of Quantum Theory"](https://www.informationphilosopher.com/quantum/copenhagen/Heisenberg_History_of_QT.pdf), in _Physics and Philosophy_, Werner Heisenberg, 1958, pp.30-43