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Philosophers

Mortimer Adler
Rogers Albritton
Alexander of Aphrodisias
Samuel Alexander
William Alston
Anaximander
G.E.M.Anscombe
Anselm
Louise Antony
Thomas Aquinas
Aristotle
David Armstrong
Harald Atmanspacher
Robert Audi
Augustine
J.L.Austin
A.J.Ayer
Alexander Bain
Mark Balaguer
Jeffrey Barrett
William Belsham
Henri Bergson
George Berkeley
Isaiah Berlin
Richard J. Bernstein
Bernard Berofsky
Robert Bishop
Max Black
Susanne Bobzien
Emil du Bois-Reymond
Hilary Bok
Laurence BonJour
George Boole
Émile Boutroux
F.H.Bradley
C.D.Broad
Michael Burke
C.A.Campbell
Joseph Keim Campbell
Rudolf Carnap
Carneades
Ernst Cassirer
David Chalmers
Roderick Chisholm
Chrysippus
Cicero
Randolph Clarke
Samuel Clarke
Anthony Collins
Antonella Corradini
Diodorus Cronus
Jonathan Dancy
Donald Davidson
Mario De Caro
Democritus
Daniel Dennett
Jacques Derrida
René Descartes
Richard Double
Fred Dretske
John Dupré
John Earman
Laura Waddell Ekstrom
Epictetus
Epicurus
Herbert Feigl
John Martin Fischer
Owen Flanagan
Luciano Floridi
Philippa Foot
Alfred Fouilleé
Harry Frankfurt
Richard L. Franklin
Michael Frede
Gottlob Frege
Peter Geach
Edmund Gettier
Carl Ginet
Alvin Goldman
Gorgias
Nicholas St. John Green
H.Paul Grice
Ian Hacking
Ishtiyaque Haji
Stuart Hampshire
W.F.R.Hardie
Sam Harris
William Hasker
R.M.Hare
Georg W.F. Hegel
Martin Heidegger
Heraclitus
R.E.Hobart
Thomas Hobbes
David Hodgson
Shadsworth Hodgson
Baron d'Holbach
Ted Honderich
Pamela Huby
David Hume
Ferenc Huoranszki
William James
Lord Kames
Robert Kane
Immanuel Kant
Tomis Kapitan
Jaegwon Kim
William King
Hilary Kornblith
Christine Korsgaard
Saul Kripke
Andrea Lavazza
Keith Lehrer
Gottfried Leibniz
Leucippus
Michael Levin
George Henry Lewes
C.I.Lewis
David Lewis
Peter Lipton
C. Lloyd Morgan
John Locke
Michael Lockwood
E. Jonathan Lowe
John R. Lucas
Lucretius
Alasdair MacIntyre
Ruth Barcan Marcus
James Martineau
Storrs McCall
Hugh McCann
Colin McGinn
Michael McKenna
Brian McLaughlin
John McTaggart
Paul E. Meehl
Uwe Meixner
Alfred Mele
Trenton Merricks
John Stuart Mill
Dickinson Miller
G.E.Moore
Thomas Nagel
Friedrich Nietzsche
John Norton
P.H.Nowell-Smith
Robert Nozick
William of Ockham
Timothy O'Connor
Parmenides
David F. Pears
Charles Sanders Peirce
Derk Pereboom
Steven Pinker
Plato
Karl Popper
Porphyry
Huw Price
H.A.Prichard
Protagoras
Hilary Putnam
Willard van Orman Quine
Frank Ramsey
Ayn Rand
Michael Rea
Thomas Reid
Charles Renouvier
Nicholas Rescher
C.W.Rietdijk
Richard Rorty
Josiah Royce
Bertrand Russell
Paul Russell
Gilbert Ryle
Jean-Paul Sartre
Kenneth Sayre
T.M.Scanlon
Moritz Schlick
Arthur Schopenhauer
John Searle
Wilfrid Sellars
Alan Sidelle
Ted Sider
Henry Sidgwick
Walter Sinnott-Armstrong
J.J.C.Smart
Saul Smilansky
Michael Smith
Baruch Spinoza
L. Susan Stebbing
Isabelle Stengers
George F. Stout
Galen Strawson
Peter Strawson
Eleonore Stump
Francisco Suárez
Richard Taylor
Kevin Timpe
Mark Twain
Peter Unger
Peter van Inwagen
Manuel Vargas
John Venn
Kadri Vihvelin
Voltaire
G.H. von Wright
David Foster Wallace
R. Jay Wallace
W.G.Ward
Ted Warfield
Roy Weatherford
William Whewell
Alfred North Whitehead
David Widerker
David Wiggins
Bernard Williams
Timothy Williamson
Ludwig Wittgenstein
Susan Wolf

Scientists

Michael Arbib
Bernard Baars
Gregory Bateson
John S. Bell
Charles Bennett
Ludwig von Bertalanffy
Susan Blackmore
Margaret Boden
David Bohm
Niels Bohr
Ludwig Boltzmann
Emile Borel
Max Born
Satyendra Nath Bose
Walther Bothe
Hans Briegel
Leon Brillouin
Stephen Brush
Henry Thomas Buckle
S. H. Burbury
Donald Campbell
Anthony Cashmore
Eric Chaisson
Jean-Pierre Changeux
Arthur Holly Compton
John Conway
John Cramer
E. P. Culverwell
Charles Darwin
Terrence Deacon
Louis de Broglie
Max Delbrück
Abraham de Moivre
Paul Dirac
Hans Driesch
John Eccles
Arthur Stanley Eddington
Paul Ehrenfest
Albert Einstein
Hugh Everett, III
Franz Exner
Richard Feynman
R. A. Fisher
Joseph Fourier
Lila Gatlin
Michael Gazzaniga
GianCarlo Ghirardi
J. Willard Gibbs
Nicolas Gisin
Paul Glimcher
Thomas Gold
A.O.Gomes
Brian Goodwin
Joshua Greene
Jacques Hadamard
Patrick Haggard
Stuart Hameroff
Augustin Hamon
Sam Harris
Hyman Hartman
John-Dylan Haynes
Martin Heisenberg
Werner Heisenberg
John Herschel
Jesper Hoffmeyer
E. T. Jaynes
William Stanley Jevons
Roman Jakobson
Pascual Jordan
Ruth E. Kastner
Stuart Kauffman
Martin J. Klein
Simon Kochen
Stephen Kosslyn
Ladislav Kovàč
Rolf Landauer
Alfred Landé
Pierre-Simon Laplace
David Layzer
Benjamin Libet
Seth Lloyd
Hendrik Lorentz
Josef Loschmidt
Ernst Mach
Donald MacKay
Henry Margenau
James Clerk Maxwell
Ernst Mayr
Ulrich Mohrhoff
Jacques Monod
Emmy Noether
Abraham Pais
Howard Pattee
Wolfgang Pauli
Massimo Pauri
Roger Penrose
Steven Pinker
Colin Pittendrigh
Max Planck
Susan Pockett
Henri Poincaré
Daniel Pollen
Ilya Prigogine
Hans Primas
Adolphe Quételet
Juan Roederer
Jerome Rothstein
David Ruelle
Erwin Schrödinger
Aaron Schurger
Claude Shannon
David Shiang
Herbert Simon
Dean Keith Simonton
B. F. Skinner
Roger Sperry
John Stachel
Henry Stapp
Tom Stonier
Antoine Suarez
Leo Szilard
William Thomson (Kelvin)
Peter Tse
Vlatko Vedral
Heinz von Foerster
John von Neumann
John B. Watson
Daniel Wegner
Steven Weinberg
Paul A. Weiss
John Wheeler
Wilhelm Wien
Norbert Wiener
Eugene Wigner
E. O. Wilson
H. Dieter Zeh
Ernst Zermelo
Wojciech Zurek

Presentations

Biosemiotics
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James Symposium
 
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."

Bohr seemed to deny the existence of an "objective reality," but 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."

The information 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
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 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 was only 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, some scientists, still believe that the mind of a conscious observer is needed to cause the collapse of the wave function.

In the mid 1950's, Heisenberg reacted to David Bohm's 1952 "pilot-wave" interpretation of quantum mechanics by calling his work the "Copenhagen Interpretation" and indeed the 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.

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, ignorant of the history (dominated by Bohr's account), many of today's textbooks teach the "Bohr atom" as emitting or absorbing photons - Einstein light quanta!

  • 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 it.

  • 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. Indeterminacy is another example of complementarity, between the non-commuting conjugate variables momentum and position, for example, Δp Δx ≥ h (also between energy and time and between action and the angle variable).

  • 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 discontinuously becomes actual, new information may be irreversibly created and recorded by a measurement apparatus.

    Einstein maintained that quantum mechanics is incomplete, because it provides only statistical information about ensembles of quantum systems. He also objected strenuously to nonlocality and nonseparability, things not addressed by the Copenhagen interpretation.

  • 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 Plank's quantum of action h can be neglected. They mistakenly described this as h -> 0. But h is a 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!

  • 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.

    All the founders of quantum mechanics mention the need for irreversibility. The need for entropy transfer to stabilize that information so it could be observed was first shown by Leo Szilard in 1929, 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," 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.

  • 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 earlier years.

    All the predicted properties of physical systems and the "laws of nature" are only probabilistic (acausal). All the 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 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.

  • No Visualizability?. Bohr and Heisenberg both thought we could not 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 it was a probability 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.

  • No Path?. Bohr, Heisenberg, Dirac and others said we cannot describe a particle as having a path.

    Einstein's "objective reality" hoped for a deeper level of physics in which particles do have paths and, in particular, they obey conservation principles.

    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.
  • 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.

    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 for interaction,
      • second, the indeterministic collapse randomly (acausally) selects one of those possibilities to become actual.

    2. 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!

    3. 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

Albert Einstein, 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.

Perhaps the main claim of those today denying the Copenhagen Interpretation (and standard quantum mechanics) is 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 that 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 upsetting to Heisenberg.

Bohr had astonished Heisenberg by deriving (in Bohr's Como Lecture) the uncertainty principle from the space-time wave picture alone, with no reference to the causal 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.

Bohr said these contradictory pictures were "complementary" and that both were needed for a "complete" picture. He co-opted Einstein's claim to a more "complete" picture of 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 seems more "complete."

Many critics of Copenhagen thought that Bohr 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 an objective nature - 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.

References

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

For Teachers
For Scholars
  • 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.

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