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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
Jules Lequyer
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
Otto Neurath
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
Walter Baade
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
Richard Dawkins
Terrence Deacon
Lüder Deecke
Richard Dedekind
Louis de Broglie
Max Delbrück
Abraham de Moivre
Paul Dirac
Hans Driesch
John Eccles
Arthur Stanley Eddington
Gerald Edelman
Paul Ehrenfest
Albert Einstein
Hugh Everett, III
Franz Exner
Richard Feynman
R. A. Fisher
Joseph Fourier
Philipp Frank
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
Donald Hebb
Martin Heisenberg
Werner Heisenberg
John Herschel
Art Hobson
Jesper Hoffmeyer
E. T. Jaynes
William Stanley Jevons
Roman Jakobson
Pascual Jordan
Ruth E. Kastner
Stuart Kauffman
Martin J. Klein
Simon Kochen
Hans Kornhuber
Stephen Kosslyn
Ladislav Kovàč
Leopold Kronecker
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
John McCarthy
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
Max Tegmark
William Thomson (Kelvin)
Giulio Tononi
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
Konrad Zuse
Fritz Zwicky

Presentations

Biosemiotics
Free Will
Mental Causation
James Symposium
 
The False Asymmetry in Entanglement

In 1935 Albert Einstein and Erwin Schrödinger mistakenly introduced an asymmetry into a perfectly symmetric situation, making entanglement the mystery that it is considered today. Every follower of their early thinking introduces this false 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's?"

In between the two experimenters, two entangled particles leave the center in opposite directions. Alice makes a measurement and finds an electron or photon in a certain spin state (say up). When Bob makes his measurement, at the same time or later, he always finds a spin state (say down) that is perfectly correlated (or anti-correlated) with Alice's. The final spin is the same as at the start of the experiment (say zero). Spin is a conserved quantity.

The simplest explanation of the mystery of entanglement is that any measurement, either Alice or Bob, whichever is actually first, "collapses" the two-particle wave function and determines both particles' properties. Conservation of those properties means that they have been continuously correlated perfectly since the experiment started, unless an external interaction changes one or both of them.

It is a surprise that Einstein, who was so good at seeing deep symmetries, did not consider how to remove the false asymmetry favoring the supposed "first" measurement..

This description privileges the "here" and the "now" of Alice's point of view. In the special frame of reference in which Alice's and Bob's labs are at rest along with the central source emitting the entangled particles, the two-particle wave function Ψ12 "collapses" in both places at the same instant in "world-time." Either Alice or Bob "collapses" the wave function, depending on who measures first in this special frame. We can say that like the initial entanglement, disentanglement affects both particles simultaneously.

Bob's "then" and "there" are thought by Alice to happen later because they are in a space-like separation and it takes time for Bob's results to reach Alice. But the overall situation is perfectly symmetric. Bob can think his measurement is first when it is not, unless it is actually made at a later time t1 in the special frame above.

Einstein's 1935 EPR paper asked about two electrons fired in opposite directions from a central source with equal velocities. He imagined them starting at t0 some distance apart and approaching one another with high velocities. Then for a short time interval from t1 to t1 + Δt the particles are in contact with one another and become entangled.

Einstein said correctly in the EPR paper that at a later time t2, a measurement of one electron's position would instantly establish the position of the other electron - without measuring it explicitly. And this is correct, just as after the collision of two billiard balls, measurement of one ball tells us exactly where the other one is due to conservation of momentum. But this is not "action at a distance." It is more properly "knowledge at a distance."

Note that Einstein used conservation of linear momentum to calculate the position of the second electron. Although conservation laws are rarely cited as the explanation, they are the physical reason that entangled particles always produce correlated results. If the results were not always correlated, the implied violation of a fundamental conservation law would be a much bigger story than the mysterious entanglement itself, as interesting as that is.

Now linear momentum is not the only quantity that is always strictly conserved. Others are mass, energy, angular momentum, and particle spin. It is the spin (of electrons or photons) that is measured in the modern tests of entanglement inspired by Bell's 1964 theorem and inequality.

Now Einstein's idea of an "objective reality" is that the particles have properties like position, momentum, and spin at all times. By contrast, Niels Bohr's "Copenhagen Interpretation" claims that particles have no such properties until they are measured.

While it is true that particles acquire some specific properties that depend on what the experimenter measures for, conservation laws require that particle motions and other properties are continuous in space and time. It is only our knowledge of the particle positions that appears to be discontinuous (the "quantum jumps").

But just because we cannot know their properties does not mean, as Einstein insisted, that they do not have objective properties. We cannot prove (without continuous measurements) that the particle ceases to exist or has discontinuous properties, between measurements. What forces would cause such changes? We imagine the particles are not interacting with other particles!

One property that is particularly difficult to visualize as conserved is spin. When measured in a particular direction, electrons always are measured as having a spin of +1/2 or -1/2. They can be measured in the x, y, or z direction, so it is tempting to see them as having spin 1/2 simultaneously in these directions, but that is not the case. They have a certain probability of measuring 1/2 or -1/2 in any direction, but it is the measurement that "projects" the spin 1/2 into the direction of measurement.

left right
σx σy σz σx σy σz
+ +/- +/- - +/- +/-
+/- + +/- +/- - +/-
+/- +/- + +/-- +/- -
- +/- +/- + +/- +/-
+/- - +/- +/- + +/-
+/- +/- - +/-- +/- +
Below is an animation that starts with two electrons produced with the left spin up in the y direction and the right spin down (the yellow row). The animation illustrates the assumption, unprovable but consistent with conservation principles, that particles remain in those states no matter how far they separate, provided neither interacts with anything else before the measurement.

This illustrates Einstein's "objective reality" idea, that particles have properties like position before they are measured. Spin is different, in that the measurement projects the electron spins along the chosen measurement direction, with projection preserving the opposite directions of spin.

Since each electron has only one unit of electron spin (a magnetic moment equal to one Bohr magneton), we can only say that if measured in a given direction, the spin will be instantly projected, in our example as spin up (1/2 ) for the left electron and the opposite spin down (-1/2) for the right electron.

The table shows six possible outcomes. The spins in directions not measured are indeterminate. A superposition of spin up and down is our best possible prediction +/-.

 

Werner Heisenberg and later Paul Dirac and others refer to the "free choice" of the experimenter as to which direction is chosen to measure. But then Dirac adds that nature makes an indeterministic choice as to whether we find the electron spin is up (1/2 ) or down (-1/2) in that freely chosen direction.

In his description of three polarizers, Dirac showed that unmeasured directions are in a superposition of states.

Now entanglement adds the nonlocality and non-separability that is caused by the (single) two-particle wave function Ψ12 collapsing symmetrically and simultaneously into single-electron wave functions Ψ1 and Ψ2 in our special frame.

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