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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
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
 
Nonseparability
The idea of something measured in one place "influencing" measurements far away challenged what Einstein thought of as "local reality." It came to be known as "nonlocality," but it always contained something else called "nonseparability." Einstein called it "spukhaft Fernwirkung" or "spooky action at a distance." Erwin Schrödinger called two particles "verschrankt" or "entangled" when their quantum properties had become correlated by an interaction. Entangled particles cannot be separated without an external interaction.

The question for Einstein and Schrödinger was how long the particles could retain their correlation as they traveled a great distance apart. Once de-correlated or "decohered," their two-particle wave function can be described as the product of two single-particle wave functions and there will no longer be any quantum interference between them. But entangled particles, it turns out, cannot be decohered without an external interaction of some kind (like a measurement).

Einstein had objected to nonlocal phenomena as early as the Solvay Conference of 1927, when he criticized the collapse of the wave function as involving "instantaneous-action-at-a-distance" that prevents the spherical outgoing wave from acting at more than one place on the screen. He probably had seen nonlocality as early as his light-quantum hypothesis paper of 1905.

Single-particle nonlocality can be defined in terms of the volume in phase space where the wave function has non-zero values. There are possibilities of finding the particle anywhere in this volume (with a calculable probability for each possibility).

A particle appears when one of those possibilities becomes actual and the particle is localized. This can be the result of an observer making a measurement or a random environmental interaction. The "collapse" of the wave function is then simply the instantaneous disappearance, the going to zero, of all the non-actualized possibilities when the nonlocal wave becomes a localized particle.

We can now understand the nonseparability of two entangled particles in terms of this nonlocality. Two entangled particles are described by a two-particle wave function that can not be factored into the product of two single-particle wave functions. The entangled particles share the same volume of nonlocality, i.e., where the two-particle wave function has non-zero values.

This means that either particle has the same possibility (with calculable probability) of appearing at any particular location. Just as with the single-particle nonlocality, we cannot say where the particles "are." Either one may be anywhere inside the nonlocality volume up to the moment of "collapse" of the two-particle wave function.

So far this is what Richard Feynman called the "only mystery" in quantum mechanics. He mistakenly advised you not to try to understand it or visualize it, but information physics will help you to do both, for single particles, such as the two-slit experiment, and for the two-particle Einstein-Podolsky-Rosen thought experiment.

When the entangled particles experience a random environmental interaction (described as "decoherence"), or an experimental measurement by an observer, the two-particle wave function "collapses." All the possibilities/probabilities that are not actualized go to zero, just as with the single particle wave function. But now, two particles appear, simultaneously in a special frame in which their center of mass is not moving. In other frames, one may appear to appear before the other.

Just as with the single particle, the localization of the two particles can be anywhere there was a possibility. But now fundamental conservation principles constrain their local appearances.The two particles appear simultaneously, usually in a spacelike separation, now disentangled, and symmetrically located about the point of the interaction which entangled them.

Einstein's idea of "local reality" was that events at one point in spacetime could depend only on the values of continuous functions at that point. In a "complete" physical theory all physical variables should be locally determined by his four-dimensional continuous field of space-time. His 1905 light-quantum hypothesis, his 1909 study of wave-particle duality, and above all his 1927 illustration of a spherical wave hitting a screen as a single particle, showed Einstein that things appeared to happen simultaneously over a large distance in space, actions-at-a-distance, he called them. That appeared to violate his special theory of relativity. But these early concerns about nonlocality all involved just one photon or electron. In 1935, he raised another difficulty

In 1935 Einstein and his Princeton colleagues Boris Podolsky and Nathan Rosen proposed their "EPR" thought experiment that implied two particles could remain correlated, perhaps remain "in contact" over large spatial distances. As far as the probabilistic wave function is concerned, there is nothing different here. When the two-particle wave function "collapses," its value goes to zero everywhere, just as for a single particle, but it now preduces two places where particles will be found. At the moment of collapse, all their properties are still correlated. After the collapse they are decohered and describable as the product of separate single-particle wave functions.

Schrödinger wrote to Einstein immediately and explained that the two-particle wave function could not be "separated" (this came to be called "nonseparability," closely related to nonlocality). Schrödinger said they remain entangled until some interaction "disentangles" them. A measurement would be such an interaction. Einstein stubbornly insisted on what he called a "separation principle" (Trennungsprinzip) that obtains as soon as the particles are in a spacelike separation, beyond where subluminal signals could be exchanged between them. This was needed for his idea of "local reality."

But Schrödinger understood wave mechanics much better than Einstein. The wave function describes only the possibilities for particle locations (with calculable probabilities). In a two-particle wave function, the possibilities mean either particle can be found anywhere the two-particle wave function is non-zero. We cannot know where either one will be found until we make a measurement. At that moment, the other particle will instantly be located where the principles of conservation of energy, momentum, angular momentum, and spin require it to be. It is only after the measurement that we can say the particles are separated. This is the core idea of nonseparability.

And this means that any measurement that collapses the two-particle wave function measures both particles! It is not possible to measure "one" (now, here) and then the "other one" (far away, later). Because the particles are indistinguishable, either one could be anywhere just before the measurement, exactly as the single particle in Einstein's 1927 presentation (or in the two-slit experiment) can be anywhere just before the measurement. We cannot say that the two particles are separated beyond the possibility of speed-of-light contact before the measurement.

Einstein's Introduction of Asymmetry

Almost every presentation of the EPR paradox begins with something like "Alice observes one particle..." and concludes with the question "How does the second particle get the information needed so that Bob's later measurements correlate perfectly with Alice?"

There is a fundamental asymmetry in this framing of the EPR experiment. It is a surprise that Einstein, who was so good at seeing deep symmetries, did not consider how to remove the asymmetry.

Consider this reframing: Alice's measurement collapses the two-particle wave function. The two indistinguishable particles simultaneously appear at locations in a space-like separation. The frame of reference in which the source of the two entangled particles and the two experimenters are at rest is a special frame in the following sense.

As Einstein knew very well, there are frames of reference moving with respect to the laboratory frame of the two observers in which the time order of the events can be reversed. In some moving frames Alice measures first, but in others Bob measures first.

If there is a special frame of reference (not a preferred frame in the relativistic sense), surely it is the one in which the origin of the two entangled particles is at rest. Assuming that Alice and Bob are also at rest in this special frame and equidistant from the origin, we arrive at the simple picture in which any measurement that causes the two-particle wave function to collapse makes both particles appear simultaneously at determinate places with fully correlated properties (just those that are needed to conserve energy, momentum, angular momentum, and spin).

In the two-particle case (instead of just one particle making an appearance), when either particle is measured, we know instantly those properties of the other particle that satisfy the conservation laws, including its location equidistant from, but on the opposite side of, the source, and its other properties such as spin.

We can also ask what happens if Bob is not at the same distance from the origin as Alice. This introduces a positional asymmetry. But there is still no time asymmetry from the point of view of the two-particle wave function collapse.

When Alice detects the particle (with say spin up), at that instant the other particle also becomes determinate (with spin down) at the same distance on the other side of the origin. It now continues, in that determinate state, to Bob's measuring apparatus.

Einstein asked whether a particle has a determinate position just before it is measured. It does not, but we can say that before Bob's measurement the electron spin he measures was determined from the moment the two-particle wave function collapsed. The two-particle wave function describing the indistinguishable particles cannot be separated into a product of two single-particle wave functions. When either particle is measured, they both become determinate.

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