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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
Free Will
Mental Causation
James Symposium
 
Bell's Theorem
John Bell showed in 1964 how the 1935 "thought experiment" of Einstein, Podolsky, and Rosen (EPR) could be made into a real experiment.

Einstein was especially bothered by the "nonlocal" aspect of quantum mechanics exhibited by a measurement at one place instantaneously determining the properties (position and momentum, and later spin) of a particle detected at another place. The spacelike separation between the two measurements implied something "travelling" faster than the speed of light between the two.

Actually, at the 1927 Solvay Conference, Einstein had already complained about "action at a distance" and faster-than-light effects when, in the two-slit experiment, the detection of a single particle at one place instantaneously collapsed the probability (Ψ2) of finding it at a distant place.

And we now know that Einstein probably saw this implicit violation of his theory of special relativity as early as 1905, when he formulated both relativity theory and the light-quantum hypothesis. See our history of Einstein's thought.

EPR proposed the existence of supplementary parameters or "local hidden variables" that could communicate information between the two measurements.

Einstein's colleagues Erwin Schrödinger, Max Planck, David Bohm, and others hoped that the hidden variables would allow a return to deterministic physics.

They wanted to eliminate mysterious quantum phenomena like superposition of states, quantum entanglement and nonlocality, action at a distance, and - perhaps most important for Schrödinger - the irreducible statistical chance associated with the collapse of the wave function. Einstein's famous remark on quantum indeterminacy was that "God does not play dice."

According to Wolfgang Pauli (in correspondence with Max Born), Einstein was less concerned with the return of determinism than he was with the restoration of "local reality" and the elimination of "action at a distance."

In 1964, John Bell put limits on any supplementary parameters or "hidden variables" that might eliminate nonlocality and restore a deterministic physics in the form of what he called an "inequality," the violation of which would confirm standard quantum mechanics.

Bell also described his key assertions in the simple idea that "local hidden variables" will never be found that give the same results as quantum mechanics. This has come to be known as Bell's Theorem.

In a 1990 lecture at CERN, shortly before his untimely death, Bell made it plain that the violation of his inequality had shown the "Einstein program" to be a failure.

It just is a fact that quantum mechanical predictions and experiments, in so far as they have been done, do not agree with [my] inequality. And that's just a brutal fact of nature... No action at a distance led you to determinism, in the case of parallel polarisers, but determinism, in the case of off-parallel polarisers, leads you back to action at a distance. Now, in my opinion, in answer to the question that you posed at the beginning, I don't know this phrase is too strong and active an assertion, I cannot say that action at a distance is required in physics. But I can say that you cannot get away with no action at a distance. You cannot separate off what happens in one place and what happens in another. Somehow they have to be described and explained jointly. Well, that's just the fact of the situation; the Einstein program fails, that's too bad for Einstein, but should we worry about that?

See a 10-minute video of John Bell on the Einstein failure

Bell's Theorem has been tested in numerous real EPR experiments over the years, by John Clauser, Alain Aspect, Michael Horne, Albert Shimony, and Richard Holt (in various CHSH-type experiments) and most recently by Nicolas Gisin and his colleagues in Geneva with entangled photons sent over miles of fiber optics.

In the 1989 book, Sixty-two Years of Uncertainty, Abner Shimony summarized the significance of various versions of Bell's Theorem.

All versions of Bell's theorem are variations, and usually generalizations, of the pioneering paper of J.S. Bell of 1964, entitled "On the Einstein-Podolsky-Rosen Paradox." All of them consider an ensemble of pairs of particles prepared in a uniform manner, so that statistical correlations may be expected between outcomes of tests performed on the particles of each pair. If each pair in the ensemble is characterized by the same quantum state Φ, then the quantum mechanical predictions for correlations of the outcomes can in principle be calculated when the tests are specified. On the other hand, if it is assumed that the statistical behavior of the pairs is governed by a theory which satisfies certain independence conditions (always similar to the Parameter and Outcome Independence conditions stated below, though the exact details vary from version to version of Bell's theorem), then it is possible to derive a restriction upon the statistical correlations of the outcomes of tests upon the two particles. The restriction is stated in the form of an inequality, known by the collective name of "Bell's Inequality." Each version of Bell's theorem exhibits a choice of Φ and of the tests upon the two particles such that the quantum mechanical predictions of correlations violates one of the Bell's Inequalities. The theorem therefore asserts that no physical theory satisfying the specified independence conditions can agree in all circumstances with the predictions of quantum mechanics. The theorem becomes physically significant when the Experimental arrangement is such that relativistic locality prima facie requires that the independence conditions be satisfied. Because such arrangements are in principle possible (and, in fact, actually realizable, if certain reasonable assumptions are made), one can restate Bell's Theorem more dramatically as follows: no local physical theory can agree in all circumstances with the predictions of quantum mechanics.
Fig. 1. An ensemble of particle pairs 1 + 2 is emitted in a uniform manner from the source. Particle 1 enters an analyzer with a controllable parameter a, and the possible outcomes are sm (m = 1,2,...). Particle 2 enters an analyzer with controllable parameter b, and the possible outcomes are tn (n = 1,2,...).
Figure 1 shows a source from which particle pairs, labeled 1 and 2, are emitted in a uniform manner. The complete state of a pair 1+2 is denoted by k, where k belongs to a space K of complete states. No assumption is made about the structure of K, except that probability measures can be defined on it. Because of the uniform experimental control of emission, it is reasonable to suppose that there is a definite probability measure w defined over K which governs the ensemble of pairs; but the uniformity need not be such that w is a delta-function, i.e., that every pair of the ensemble is in the same complete state k. Particle 1 enters an analyzer with a controllable parameter a, which the experimenter can specify, for instance, by turning a knob. Likewise, particle 2 enters an analyzer with a controllable parameter b.

The reason philosophers like Shimony have difficulty with two-particle wave-function collapses is clear from his exposition. It is quite wrong to describe two distinct particles, 1 and 2, with 1 entering the right analyzer and 2 entering the left analyzer.

Just as a single particle cannot be localized in the two-slit experiment, neither particle in an EPR experiment is localizable until there is a measurement, at which time both become localized (to within the usual quantum indeterminacy) however far apart they are at that time (in the rest frame of the experiment).

The reason we know everything about the "other" particle as soon as we measure one is, as Einstein knew well, but later writers often ignore, found in the various conservation laws (of energy, momentum, spin, etc.). If Bell's inequalities were not violated, the much more fundamental laws of conservation of momentum, angular momentum and spin would be violated.

For a correct description of how quantum mechanics describes two particles in an entangled quantum state, see our description of the EPR experiment.

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