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 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 Daniel Boyd F.H.Bradley C.D.Broad Michael Burke Lawrence Cahoone C.A.Campbell Joseph Keim Campbell Rudolf Carnap Carneades Nancy Cartwright Gregg Caruso Ernst Cassirer David Chalmers Roderick Chisholm Chrysippus Cicero Tom Clark 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 Austin Farrer Herbert Feigl Arthur Fine John Martin Fischer Frederic Fitch Owen Flanagan Luciano Floridi Philippa Foot Alfred Fouilleé Harry Frankfurt Richard L. Franklin Bas van Fraassen 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 Frank Jackson William James Lord Kames Robert Kane Immanuel Kant Tomis Kapitan Walter Kaufmann Jaegwon Kim William King Hilary Kornblith Christine Korsgaard Saul Kripke Thomas Kuhn Andrea Lavazza Christoph Lehner Keith Lehrer Gottfried Leibniz Jules Lequyer Leucippus Michael Levin Joseph Levine George Henry Lewes C.I.Lewis David Lewis Peter Lipton C. Lloyd Morgan John Locke Michael Lockwood Arthur O. Lovejoy E. Jonathan Lowe John R. Lucas Lucretius Alasdair MacIntyre Ruth Barcan Marcus Tim Maudlin James Martineau Nicholas Maxwell 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 U.T.Place 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 John Duns Scotus Arthur Schopenhauer John Searle Wilfrid Sellars David Shiang Alan Sidelle Ted Sider Henry Sidgwick Walter Sinnott-Armstrong Peter Slezak 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 C.F. von Weizsäcker William Whewell Alfred North Whitehead David Widerker David Wiggins Bernard Williams Timothy Williamson Ludwig Wittgenstein Susan Wolf Scientists David Albert Michael Arbib Walter Baade Bernard Baars Jeffrey Bada Leslie Ballentine Marcello Barbieri Gregory Bateson Horace Barlow John S. Bell Mara Beller Charles Bennett Ludwig von Bertalanffy Susan Blackmore Margaret Boden David Bohm Niels Bohr Ludwig Boltzmann Emile Borel Max Born Satyendra Nath Bose Walther Bothe Jean Bricmont Hans Briegel Leon Brillouin Stephen Brush Henry Thomas Buckle S. H. Burbury Melvin Calvin Donald Campbell Sadi Carnot Anthony Cashmore Eric Chaisson Gregory Chaitin Jean-Pierre Changeux Rudolf Clausius Arthur Holly Compton John Conway Jerry Coyne John Cramer Francis Crick E. P. Culverwell Antonio Damasio Olivier Darrigol Charles Darwin Richard Dawkins Terrence Deacon Lüder Deecke Richard Dedekind Louis de Broglie Stanislas Dehaene Max Delbrück Abraham de Moivre Bernard d'Espagnat Paul Dirac Hans Driesch John Eccles Arthur Stanley Eddington Gerald Edelman Paul Ehrenfest Manfred Eigen Albert Einstein George F. R. Ellis Hugh Everett, III Franz Exner Richard Feynman R. A. Fisher David Foster Joseph Fourier Philipp Frank Steven Frautschi Edward Fredkin Benjamin Gal-Or Howard Gardner Lila Gatlin Michael Gazzaniga Nicholas Georgescu-Roegen GianCarlo Ghirardi J. Willard Gibbs James J. Gibson Nicolas Gisin Paul Glimcher Thomas Gold A. O. Gomes Brian Goodwin Joshua Greene Dirk ter Haar Jacques Hadamard Mark Hadley Patrick Haggard J. B. S. Haldane Stuart Hameroff Augustin Hamon Sam Harris Ralph Hartley Hyman Hartman Jeff Hawkins John-Dylan Haynes Donald Hebb Martin Heisenberg Werner Heisenberg John Herschel Basil Hiley Art Hobson Jesper Hoffmeyer Don Howard John H. Jackson William Stanley Jevons Roman Jakobson E. T. Jaynes Pascual Jordan Eric Kandel Ruth E. Kastner Stuart Kauffman Martin J. Klein William R. Klemm Christof Koch Simon Kochen Hans Kornhuber Stephen Kosslyn Daniel Koshland Ladislav Kovàč Leopold Kronecker Rolf Landauer Alfred Landé Pierre-Simon Laplace Karl Lashley David Layzer Joseph LeDoux Gerald Lettvin Gilbert Lewis Benjamin Libet David Lindley Seth Lloyd Werner Loewenstein Hendrik Lorentz Josef Loschmidt Alfred Lotka Ernst Mach Donald MacKay Henry Margenau Owen Maroney David Marr Humberto Maturana James Clerk Maxwell Ernst Mayr John McCarthy Warren McCulloch N. David Mermin George Miller Stanley Miller Ulrich Mohrhoff Jacques Monod Vernon Mountcastle Emmy Noether Donald Norman Alexander Oparin Abraham Pais Howard Pattee Wolfgang Pauli Massimo Pauri Wilder Penfield Roger Penrose Steven Pinker Colin Pittendrigh Walter Pitts Max Planck Susan Pockett Henri Poincaré Daniel Pollen Ilya Prigogine Hans Primas Zenon Pylyshyn Henry Quastler Adolphe Quételet Pasco Rakic Nicolas Rashevsky Lord Rayleigh Frederick Reif Jürgen Renn Giacomo Rizzolati A.A. Roback Emil Roduner Juan Roederer Jerome Rothstein David Ruelle David Rumelhart Robert Sapolsky Tilman Sauer Ferdinand de Saussure Jürgen Schmidhuber Erwin Schrödinger Aaron Schurger Sebastian Seung Thomas Sebeok Franco Selleri Claude Shannon Charles Sherrington Abner Shimony Herbert Simon Dean Keith Simonton Edmund Sinnott B. F. Skinner Lee Smolin Ray Solomonoff Roger Sperry John Stachel Henry Stapp Tom Stonier Antoine Suarez Leo Szilard Max Tegmark Teilhard de Chardin Libb Thims William Thomson (Kelvin) Richard Tolman Giulio Tononi Peter Tse Alan Turing C. S. Unnikrishnan Francisco Varela Vlatko Vedral Vladimir Vernadsky Mikhail Volkenstein Heinz von Foerster Richard von Mises John von Neumann Jakob von Uexküll C. H. Waddington John B. Watson Daniel Wegner Steven Weinberg Paul A. Weiss Herman Weyl John Wheeler Jeffrey Wicken Wilhelm Wien Norbert Wiener Eugene Wigner E. O. Wilson Günther Witzany Stephen Wolfram H. Dieter Zeh Semir Zeki Ernst Zermelo Wojciech Zurek Konrad Zuse Fritz Zwicky Presentations Biosemiotics Free Will Mental Causation James Symposium |
Stern-Gerlach Experiment
The first Stern-Gerlach experiment was in 1922, long before the discovery of electron spin with which it is now associated.
It was an attempt to prove the existence of "space quantization," the limitation of the direction of angular momentum to a few space directions, as hypothesized by Niels Bohr and Arnold Sommerfeld.
Even today, Stern-Gerlach is one of the experiments that most directly shows the quantization at the core of quantum mechanics. Understanding how it works sheds light on the problem of measurement.
Designing a Quantum Measurement Apparatus
The first step in quantum measurement is to build an apparatus that separates a quantum system physically into distinguishable paths or regions of space, where the different regions correspond to (are correlated with) the physical properties we want to measure.
We do not actually distinguish the atoms as following one of the paths at this first step. That would cause the probability amplitude wave function to collapse. This first step is reversible, at least in principle. It is deterministic and an example of John von Neumann's process 2, evolution of the system according to the Schrödinger equation of motion.
We need a beam of atoms (and the ability to reduce the intensity to one atom at a time). Spin-up atoms are deflected upward (shown in blue). Spin-down atoms go down (shown in red in a schematic diagram adapted from photons passing through birefringent filters as going straight). Any given atom has the possibility of being deflected up or down by the inhomogeneous magnetic field in the Stern-Gerlach apparatus. Quantum mechanics describes the single atom as being in a superposition of up and down states.
| ψ > = ( 1/√2) | up > + ( 1/√2) | down > (1)This does not mean that there are two atoms, one on each path. It is a statement about probabilities. There is an equal probability that the atom will be found (at random) with its spin up or its spin down. This is a superposition of probability amplitudes, which can interfere with one another, not a superposition of particles, which cannot. Whenever we measure, we do not find a fraction of a particle, but the whole particle. Nor does it become two particles, one spin-up and one spin-down, as in the popular but mistaken interpretation of the Schrödinger Cat as in a superposition of live and dead cats.
An Information-Preserving, Reversible Example of Process 2
To show that Von Neumann's process 2 is reversible, we can add a second Stern-Gerlach apparatus, in line with the superposition of the physically separated states,
An Information-Creating, Irreversible Example of Process 1
But now suppose we insert something between the two apparatuses that is capable of a measurement to produce observable information. We need a detector that locates the atom in one of the two paths.
Let's consider an ideal photographic plate capable of precipitating visible silver grains upon the receipt of a single particle (and subsequent development). Today photography cannot detect single particles, but detectors using charge coupled devices (CCDs) are approaching this sensitivity. We could also use a simple Geiger counter.
Note that we do not literally "see" a spin-up atom. All that we really see is a black spot on a photographic plate or an increment in the numeric display of a Geiger counter.
We can write a quantum description of the plate as containing two sensitive collection areas, the part of the apparatus measuring spin-up atoms, | Aup > (shown as the blue spot), and the part of the apparatus measuring spin-down atoms, | Adown > (shown as the red spot)
We infer that what we see was caused by a spin-up atom, since our detector is located in the path such a particle would travel. | ψ > + | Aup0 > => | ψ, Aup0 > => | up, Aup1 >These jumps destroy (unobservable) phase information (between the possible spin-up and spin-down states), raise the (Boltzmann) entropy of the apparatus, and increase information (Shannon entropy) in the form of the visible spot. The entropy increase takes the form of a large chemical energy release when a photographic spot is developed (or a cascade of electrons in a CCD or Geiger counter). We can animate these irreversible and reversible processes, here shown as polarized photons in a birefringent filter, but equally applicable to spin-up and spin-down atoms in the Stern-Gerlach apparatus.
|