Citation for this page in APA citation style.

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 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 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 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 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 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 Gregory Bateson 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 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 Lila Gatlin Michael Gazzaniga Nicholas Georgescu-Roegen GianCarlo Ghirardi J. Willard Gibbs 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 John-Dylan Haynes Donald Hebb Martin Heisenberg Werner Heisenberg John Herschel Basil Hiley Art Hobson Jesper Hoffmeyer Don Howard William Stanley Jevons Roman Jakobson E. T. Jaynes Pascual Jordan 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 David Layzer Joseph LeDoux Gilbert Lewis Benjamin Libet David Lindley Seth Lloyd Hendrik Lorentz Josef Loschmidt Ernst Mach Donald MacKay Henry Margenau Owen Maroney Humberto Maturana James Clerk Maxwell Ernst Mayr John McCarthy Warren McCulloch N. David Mermin George Miller Stanley Miller Ulrich Mohrhoff Jacques Monod Emmy Noether Alexander Oparin 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 Henry Quastler Adolphe Quételet Lord Rayleigh Jürgen Renn Juan Roederer Jerome Rothstein David Ruelle Tilman Sauer Jürgen Schmidhuber Erwin Schrödinger Aaron Schurger Sebastian Seung Thomas Sebeok Claude Shannon David Shiang Abner Shimony Herbert Simon Dean Keith Simonton B. F. Skinner Lee Smolin Ray Solomonoff Roger Sperry John Stachel Henry Stapp Tom Stonier Antoine Suarez Leo Szilard Max Tegmark Libb Thims William Thomson (Kelvin) Giulio Tononi Peter Tse Francisco Varela Vlatko Vedral Mikhail Volkenstein Heinz von Foerster Richard von Mises John von Neumann Jakob von Uexküll John B. Watson Daniel Wegner Steven Weinberg Paul A. Weiss Herman Weyl John Wheeler Wilhelm Wien Norbert Wiener Eugene Wigner E. O. Wilson Stephen Wolfram H. Dieter Zeh Ernst Zermelo Wojciech Zurek Konrad Zuse Fritz Zwicky Presentations Biosemiotics Free Will Mental Causation James Symposium |
Erwin Schrödinger
Erwin Schrödinger is perhaps the most complex figure in twentieth-century discussions of quantum mechanical uncertainty, ontological chance, indeterminism, and the
statistical interpretation of quantum mechanics.
In his early career, Schrödinger was a great exponent of fundamental chance in the universe. He followed his teacher Franz S. Exner, who was himself a colleague of the great Ludwig Boltzmann at the University of Vienna. Boltzmann used intrinsic randomness in molecular collisions (molecular chaos) to derive the increasing entropy of the Second Law of Thermodynamics. The macroscopic
irreversibility of entropy increase depends on Boltzmann's molecular chaos which depends on the randomness in microscopic irreversibility.
Before the twentieth century, most physicists, mathematicians, and philosophers believed that the chance described by the calculus of probabilities was actually completely determined. The "bell curve" or "normal distribution" of random outcomes was itself so consistent that they argued for underlying deterministic laws governing individual events. They thought that we simply lack the knowledge necessary to make exact predictions for these individual events. Pierre-Simon Laplace was first to see in his "calculus of probabilities" a universal law that determined the motions of everything from the largest astronomical objects to the smallest particles. In a Laplacian world, there is only one possible future.
On the other hand, in his inaugural lecture at Zurich in 1922, Schrödinger argued that evidence did not justify our assumptions that physical laws were deterministic and strictly causal. His inaugural lecture was modeled on that of Franz Serafin Exner in Vienna in 1908.
"Exner's assertion amounts to this: It is quite possible that Nature's laws are of thoroughly statistical character. The demand for an absolute law in the background of the statistical law — a demand which at the present day almost everybody considers imperative — goes
Several years later, Schrödinger presented a paper on "Indeterminism in Physics" to the June, 1931
"Fifty years ago it was simply a matter of taste or philosophic prejudice whether the preference was given to determinism or indeterminism. The former was favored by ancient custom, or possibly by an a priori belief. In favor of the latter it could be urged that this ancient habit demonstrably rested on the actual laws which we observe functioning in our surroundings. As soon, however, as the great majority or possibly all of these laws are seen to be of a statistical nature, they cease to provide a rational argument for the retention of determinism.
Despite these strong arguments against determinism, just after he completed the wave mechanical formulation of quantum mechanics in June 1926 (the year Exner died), Schrödinger began to side with the determinists, including especially Max Planck and Albert Einstein (who in 1916 had discovered that ontological chance is involved in the emission of radiation).
Schrödinger's wave equation is a
continuous function that evolves smoothly in time, in sharp contrast to the discrete, discontinuous, and indeterministic "quantum jumps" of the Born-Heisenberg matrix mechanics. His wave equation seemed to Schrödinger to restore the continuous and deterministic nature of classical mechanics and dynamics. And it suggests that we may visualize particles as wave packets moving in spacetime, which was very important to Schrödinger. By contrast, Bohr and Heisenberg and their Copenhagen Interpretation of quantum mechanics insisted that visualization of quantum events is simply not possible. Einstein agreed with Schrödinger that visualization (Anschaulichkeit) should be the goal of describing reality.
Max Born, Werner Heisenberg's mentor and the senior partner in the team that created matrix mechanics, shocked Schrödinger with the interpretation of the wave function as a "probability amplitude."
The motions of particles are indeterministic and probabilistic, even if the equation of motion for the probability is deterministic.
It is true, said Born, that the wave function itself evolves deterministically, but its significance is that it predicts only the probability of finding an atomic particle somewhere. When and where particles would appear - to an observer or to an observing system like a photographic plate - was completely and irreducibly random, he said. Born credited Einstein for the idea that the relationship between waves and particles is that the waves give us the probability of finding a particle, but this "statistical interpretation" of the wave function came to be known as "Born's Rule.".
Einstein had seen clearly for many years that quantum transitions involve chance, that quantum jumps are random, but he did not want to believe it. Although the Schrödinger equation of motion is itself continuous and deterministic, it is impossible to restore continuous deterministic behavior to material particles and return physics to strict causality. Even more than Einstein, Schrödinger hated this idea and never accepted it, despite the great success of quantum mechanics, which today uses Schrödinger's wave functions to calculate Heisenberg's matrix elements for atomic transition probabilities and all atomic properties. Discouraged, Schrödinger wrote to his friend Willie Wien in August 1926 "[That discontinuous quantum jumps]...offer the greatest conceptual difficulty for the achievement of a classical theory is gradually becoming even more evident to me."...[yet] today I no longer like to assume with Born that an individual process of this kind is "absolutely random." i.e., completely undetermined. I no longer believe today that this conception (which I championed so enthusiastically four years ago) accomplishes much. From an offprint of Born's work in the
Why did Schrödinger not simply welcome Born's absolute chance? It provides strong evidence that Boltzmann's assumption of chance in atomic collisions (molecular disorder) was completely justified. Boltzmann's idea that entropy is statistically irreversible depends on microscopic irreversibility. Exner thought chance is absolute, but did not live to see how fundamental it was to physics. And the early Epicurean idea that atoms Could it be that senior scientists like Max Planck and Einstein were so delighted with Schrödinger's work that it turned his head? Planck, universally revered as the elder statesman of physics, invited Schrödinger to Berlin to take Planck's chair as the most important lecturer in physics at a German university. And Schrödinger shared Einstein's goal to develop a unified (continuous and deterministic) field theory. Schrödinger won the Nobel prize in 1933. But how different our thinking about absolute chance would be if perhaps the greatest theoretician of quantum mechanics had accepted random quantum jumps in 1926? In his vigorous debates with Neils Bohr and Werner Heisenberg, Schrödinger attacked the probabilistic Copenhagen interpretation of his wave function with a famous thought experiment (which was actually based on another Einstein suggestion) called Schrödinger's Cat.Schrödinger was very pleased to read the Einstein-Podolsky-Rosen paper in 1935. He immediately wrote to Einstein in support of an attack on Bohr, Born, and Heisenberg and their "dogmatic" quantum mechanics. "I was very happy that in the paper just published in P.R. you have evidently caught dogmatic q.m. by the coat-tails...My interpretation is that we do not have a q.m. that is consistent with relativity theory, i.e., with a finite transmission speed of all influences. We have only the analogy of the old absolute mechanics . . . The separation process is not at all encompassed by the orthodox scheme.' Einstein had said in 1927 at the Solvay conference that nonlocality (faster-than-light signaling between particles in a space-like separation) seemed to violate relativity in the case of a single-particle wave function with non-zero probabilities of finding the particle at more than one place. What instantaneous "action-at-a-distance" prevents particles from appearing at more than one place, Einstein oddly asked. [The answer, one particle becoming two particles never appears in nature. That would violate the most fundamental conservation laws.]
In his 1935 EPR paper, Einstein cleverly introduced asymmetry that Einstein, and Schrödinger, have mistakenly introduced into a perfectly symmetric situation, making entanglement such a mystery.
Schrödinger challenged Einstein's idea that two systems that had previously interacted can be treated as ψ and _{1}ψ.
_{2}
Einstein called this his "separability principle ( When two systems, of which we know the states by their respective representatives, enter into temporary physical interaction due to known forces between them, and when after a time of mutual influence the systems separate again, then they can no longer be described in the same way as before, viz. by endowing each of them with a representative of its own. I would not call thatIn the following year, Schrödinger looked more carefully at Einstein's assumption that the entangled system could be separated enough to be regarded as two systems with independent wave functions: Years ago I pointed out that when two systems separate far enough to make it possible to experiment on one of them without interfering with the other, they are bound to pass, during the process of separation, through stages which were beyond the range of quantum mechanics as it stood then. For it seems hard to-imagine a complete separation, whilst the systems are still so close to each other, that, from the classical point of view, their interaction could still be described as an unretarded Schrödinger says that the entangled system may become disentangled (Einstein's separation) and yet some perfect correlations between later measurements might remain. Note that the entangled system could simply decohere as a result of interactions with the environment, as proposed by decoherence theorists. The perfectly correlated results of Bell-inequality experiments might nevertheless be preserved, depending on the interaction. And of course they will be separated by a measurement of either particle, for example, by Alice or Bob in the case of Bell's Theorem.
Bell's Theorem
Following David Bohm's version of EPR, John Bell considered two spin-1/2 particles in an entangled state with total spin zero. We can rewrite Schrödinger's separation equation above as
| ψ > = (1/√2) | + - > - (1/√2) | - + >
This is a superposition of two states, either of which conserves total spin zero. The minus sign ensures the state is anti-symmetric, changing sign under interchange of identical electrons.
Schrödinger does not mention
Let's assume that Alice makes a measurement of a spin component of one particle, say the x-component. First, her measurement projects the entangled system into either the | + - > or
Whenever Alice measures spin up, Bob measures spin down, but that is
Bell's inequality was a study of how these perfect correlations fall off as a function of the angle between measurements by Alice and Bob. Bell predicted local hidden variables would produce a
Bell wrote that "Since we can predict in advance the result of measuring any chosen component of
But note that these values were not determined (they did not even exist according to the Copenhagen Interpretation) before Alice's measurement. According to Werner Heisenberg and Pascual Jordan, the spin components are
Quantum Jumping
In 1952, Schrödinger wrote two influential articles in the British Journal for the Philosophy of Science denying quantum jumping. These papers greatly influenced generations of quantum collapse deniers, including John Bell, John Wheeler, Wojciech Zurek, and H. Dieter Zeh.
On Determinism and Free Will
In Schrödinger's mystical epilogue to his essay What Is Life? (1944), he "proves God and immortality at a stroke" but leaves us in the dark about free will.
As a reward for the serious trouble I have taken to expound the purely scientific aspects of our problem Order, Disorder, and Entropy
Chapter 6 of What Is Life?
Normal | Teacher | ScholarNec corpus mentem ad cogitandum, nec mens corpus ad motum, neque ad quietem, nec ad aliquid (si quid est) aliud determinare potent.' SPINOZA, Ethics, Pt III, Prop.2 |