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
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
It is a sad fact that 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
At the 1927 Solvay conference on physics entitled "Electrons and Photons," Niels 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
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
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."
Copenhageners were proud of their limited ability to know
. 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
had put limits on reason. The British empiricist philosophers John Locke
and David 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
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
. 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
of the observer.
The exact location of that transition from the quantum to the classically describable world
was arbitrary, said Heisenberg. He called it a "cut" (Schnitt)
. Heisenberg's and especially John von Neumann
's and Eugene Wigner
's insistence on a critical role for a "conscious 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
in the behavior of the quantum system.
Today, a large number of panpsychists
, some philosophers, and a small number of scientists, still believe that the mind
of a conscious observer
is needed to cause the so-called "collapse" of the wave function
. 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
's 1952 "pilot-wave" interpretation of quantum mechanics
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
, Pascual Jordan
, Paul Dirac
, and of course Erwin Schrödinger
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. 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.
The complementarity of waves and particles, including a synthesis of the particle-matrix mechanics theory of Heisenberg, Max Born, and Pascual Jordan, with the wave mechanical theory of Louis deBroglie and Erwin Schrödinger.
Again ironically, wave-particle duality was first described by Einstein in 1909. Heisenberg had to have his arm twisted by Bohr to accept the wave picture.
- Indeterminacy principle. 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 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, but epistemically, common sense and everyday experience inclines us to see it as deterministic. Bohr and Heisenberg insisted we must use classical (deterministic?) concepts and language to communicate our 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 in the world than classical physics implies.
The wave function ψ evolves according to the unitary deterministic Schrödinger equation of motion, conserving that information. When one possibility becomes actual (discontinuously), new information may be irreversibly 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 and nonseparability, things not addressed at all by the Copenhagen interpretation.
- Irreversible 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 in 1929, and later by Leon Brillouin and Rolf 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). Born interpreted the square modulus of Schrödinger's complex wave function as the probability 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 (acausal, indeterministic ). 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. 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 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, 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, and microscopic irreversibility.
- 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 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 ψ, which is irreversible, upon interacting with the measurement apparatus and creating new information.
- 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
There are many more elements that play lesser roles, some making the Copenhagen Interpretation very unpopular among philosophers of science and spawning new interpretations
or even "formulations
" of quantum mechanics. Some of these are misreadings or later accretions. They include:
The "conscious 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).
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 and Eugene 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, 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.
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 for interaction,
- second, the indeterministic collapse randomly (acausally) selects one of those possibilities to become actual.
The original concern that the "collapse dynamics" (von Neumann Process 1) is not a part of the formalism (von Neumann Process 2) but is an ad hoc element, with no rules for when to apply it.
If there was a deterministic law that predicted a collapse, or the decay of a radioactive nucleus, it would not be quantum mechanics!
Decoherence theorists say that the measurement problem is the failure to observe macroscopic superpositions, such as Schrödinger's Cat.
- The many unreasonable philosophical claims for "complementarity:" e.g., that it solves the mind-body problem?,
The basic "subjectivity" of the Copenhagen interpretation. It deals with epistemological knowledge of things, rather than the "things themselves."
Opposition to the Copenhagen Interpretation
, Louis deBroglie
, and especially Erwin Schrödinger
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
and the decoherence
theorists H. D. Zeh
and Wojciech Zurek
deny the existence of particles and the collapse of the wave function
, 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
theorists and others favoring Everett
's Many-Worlds Interpretation reject 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
behavior, the "quantum postulate
" of unpredictable events that undermine the classical physics of causality
. 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
, a month before the 1927 Solvay conference, Bohr introduced his theory of "complementarity
" 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
. 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
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
astonished Heisenberg by actually deriving
(instead of Heisenberg's heuristic microscope argument) the uncertainty principle
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.
Copenhagen Interpretation on Wikipedia>
Copenhagen Interpretation on Stanford Encyclopedia of Philosophy>
"Copenhagen Interpretation of Quantum Theory"
, in Physics and Philosophy
, Werner Heisenberg, 1958, pp.44-58
"The Copenhagen Interpretation"
, American Journal of Physics
, 40, p.1098, Henry Stapp, 1972
"The History of Quantum Theory"
, in Physics and Philosophy
, Werner Heisenberg, 1958, pp.30-43
- Born's statistical interpretation - brings in Schrödinger waves, which upset Heisenberg
- uncertainty principle, March 1927
- complementarity - waves and particles, wave mechanics and matrix mechanics, again upsets Heisenberg
- the two-slit experiment
- measurements, observers, "disturb" a quantum system, - Microscope echo
- loss of causality (Einstein knew), unsharp space-time description (wave-packet)
- classical apparatus, quantum system
- our goal not to understand reality, but to acquire knowledge Rosenfeld quote
- Experimenter must choose either particle-like or wave-like experiment - need examples
- Heisenberg uncertainty was discontinuity, intrusion of instruments, for Bohr it was "the general complementary character of description" - wave or particle
- Complementarity a general framework, Heisenberg particle uncertainty a particular example
- Einstein/Schrödinger want a field theory and continuous/waves only? Bohr wants sometimes waves, sometimes particles. Bohr wants always both waves and particles.
- Combines Heisenberg's "free choice" of experimenter as to what to measure, with Dirac's "free choice" of Nature with deterministic evolution of possibilities followed by discontinuous and random appearance of one actual from all the possibles.