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 BoisReymond 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 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.NowellSmith 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 JeanPaul Sartre Kenneth Sayre T.M.Scanlon Moritz Schlick Arthur Schopenhauer John Searle Wilfrid Sellars Alan Sidelle Ted Sider Henry Sidgwick Walter SinnottArmstrong 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 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 JeanPierre 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 GalOr Lila Gatlin Michael Gazzaniga Nicholas GeorgescuRoegen 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 JohnDylan 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 PierreSimon 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 Emil Roduner Juan Roederer Jerome Rothstein David Ruelle Tilman Sauer Jürgen Schmidhuber Erwin Schrödinger Aaron Schurger Sebastian Seung Thomas Sebeok Franco Selleri Claude Shannon Charles Sherrington David Shiang 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 Francisco Varela Vlatko Vedral Mikhail Volkenstein Heinz von Foerster Richard von Mises John von Neumann Jakob von Uexküll C. S. Unnikrishnan C. H. Waddington John B. Watson Daniel Wegner Steven Weinberg Paul A. Weiss Herman Weyl John Wheeler Wilhelm Wien Norbert Wiener Eugene Wigner E. O. Wilson Günther Witzany Stephen Wolfram H. Dieter Zeh Ernst Zermelo Wojciech Zurek Konrad Zuse Fritz Zwicky Presentations Biosemiotics Free Will Mental Causation James Symposium 
A "Hidden" Constant of the Motion?
In an important article written before the 1964 Bell's Theorem paper, Eugene Wigner in 1963 said the symmetrically placed positions (for the EPR paper) are caused by conservation of linear momentum and the perfectly opposite electron spins (for David Bohm's 1952 version of nonlocality with electrons) are the result of conservation of angular momentum. Wigner wrote If a measurement of the momentum of one of the particles is carried out — the possibility of this is never questioned — and gives the result p, the state vector of the other particle suddenly becomes a (slightly damped) plane wave with the momentum p. This statement is synonymous with the statement that a measurement of the momentum of the second particle would give the result p, as follows from the conservation law for linear momentum. The same conclusion can be arrived at also by a formal calculation of the possible results of a joint measurement of the momenta of the two particles. We can ask why John Bell, and almost every other physicist, philosopher of science, or science writer, has never explicitly considered the conservation of angular momentum as explaining the perfect correlations between "entangled" particles, and the perfectly opposite electron spins found in Bohm's version of the EPR experiment. It seems likely that many were using the conservation law implicitly, for example, Einstein. In 2005, C.S.Unnikrishnan of the Tata Institute of Fundamental Research in Mumbai, India was an exception. He proposed that the conservation law of angular momentum can correlate measurements of entangled electrons, explaining the perfect correlations of entangled particles, without the fasterthanlight interactionsatadistance or "hidden variables" often invoked to explain nonlocaiity. Unnikrishnan wrote Bell’s inequalities can be obeyed only by violating a conservation law. Unnikrishnan argues that conservation of angular momentum (electron spin) produces the same perfect correlations (or anticorrelations) found in all Bell test experiments when both experimenters measure at the same (preagreed upon) measurement angle. However, Unnikrishnan is concerned that "for individual measurements of the twopoint correlation, the conservation law cannot be invoked, since only the conditional probabilities are predicted by quantum mechanics." He uses instead averages of measurements. Unnikrishnan's apparent concern is that individual measurements will have random outcomes of updown, downup, and possibly even some upup and downdown. He mistakenly thinks quantum mechanics predicts separate probabilities for each electron. The latter two product states would violate conservation of angular momentum. Conservation laws are the consequence of extremely deep properties of nature that arise from simple considerations of symmetry. We regard these laws as "cosmological principles." Physical laws do not depend on the absolute place and time of experiments, nor their particular direction in space. Conservation of linear momentum depends on the translation invariance of physical systems, conservation of energy the independence of time, and conservation of angular momentum the invariance under rotations. Conservation laws are the consequence of these spatial symmetries, as explained by Emmy Noether. David Bohm's version of the EPR experiment starts with two electrons (or photons) prepared in an entangled state that is a superposition of twoparticle states, each of which conserves the total angular momentum and, of course, conserves the linear momentum as in Einstein's original EPR example. Quantum mechanics describes the probability amplitude wave function Ψ_{12} of the twoparticle system as in a superposition of twoparticle states. It is not a product of singleparticle states, as Erwin Schrödinger told Einstein in his reaction to the EPR paper. We can write this as
Ψ_{12} = 1/√2)  1_{+}2_{} > + 1/√2)  1_{}2_{+} > (1)
The probability amplitude wave function Ψ_{12} travels away from the source (at the speed of light or less). The total spin zero wave function is rotationally symmetric and isotropic, the same in all directions. Let's assume that at t_{0} an observer finds a particle with spin up in the x direction. This measurement breaks the rotational symmetry. The new symmetry is planar, including the chosen x direction and the z direction back to the origin of the entangled particles. Before the measurement, the spin has a possibility of being found in any direction. Rotational symmetry says the probability is the same in all directions. This does not mean a particle has spins in all directions at all times, which is impossible. At the time of this "first" measurement, say by observer A, new information comes into existence telling us that the wave function Ψ_{12} has "collapsed" into the state  1_{+}2_{} >. Probabilities have now become certainties, one possibility is now an actuality. If the first measurement finds particle 1's xcomponent spin is up, so the same spin component of entangled particle 2 must be down to conserve total angular momentum. And conservation of linear momentum tells us that at t_{0} the second electron is equidistant from the source in the opposite direction. As with any wavefunction "collapse", the probability amplitude information changes. Nothing really "collapses." Nothing physical, no matter or energy, is moving. Only information is changing. The wave function is updated to reflect the new information that comes into existence as the result of the measurement. When the first measurement finds particle 1 as spinup at t_{0}, at that moment of new information creation, particle 2 will be found in a spindown state with probability unity (certainty). And the results of observer B's measurement at t_{0} or any later time t_{1} is therefore determined to be spin down (if and only if, B measures in a preagreed upon same direction). Notice that Einstein's intuition that observer B's result seems already "determined" or "fixed" before the second measurement is in fact correct. Observer B's outcome is determined by the law of conservation of momentum. But the measurement by observer B was not predetermined before observer A's measurement. It was simply determined by her measurement. The measured values of particle 1 spinup and particle 2 spindown did not exist before the "free choice" of observer A brought them into existence, as Werner Heisenberg insisted. Which of the twoparticle quantum states  +  > or   + > occurs is completely random. It is the result of "Nature's choice," as Paul Dirac described it. Note also that before the measurement the twoparticle wave function was rotationally symmetric. No preferred angular direction existed. The preferred angle also comes into existence as a result of what Heisenberg called the "free choice" of the ("first") experimenter.
This "free choice" of a measurement angle breaks the rotational symmetry of the original twoparticle wave function. As Erwin Schrödinger described it to Einstein in his 1935 response to the EPR paper, the measurement disentangles the particles and projects the purestate superposition into a mixedstate product of singleparticle wave functions, either The two particles cannot already have those spin values before the measurements. That would require them to have spin values in all three x, y, and z directions, which is impossible. They only need to acquire opposite spins when measured along an agreed upon direction that breaks the rotational symmetry of the twoparticle wave function. Finally note that conservation of total spin zero requires no superluminal influence or interaction by one particle on the other. It actually requires that there be no actions on either particle, to preserve the symmetry needed for the conservation law. That symmetry has become linear and planar, as the rotational symmetry disappears, leaving symmetry only along the plane between the electrons that includes the chosen measurement direction. If the two particles did not conserve total spin zero (and every Bell test shows that they do conserve total spin), the violation of the conservation law would likely be met with more criticism than hypothetical superluminal interactions, which are of course impossible. What about the uncertainty principle? In the case of EPR measuring the position x (or the momentum p) of the two particles, won't their values be "fuzzy" (ΔxΔp ~ħ) and therefore not conserve momentum exactly, but only statistically for large numbers of examples? No, the conservation laws require that if x_{1} is found less than the expected value by an amount δ, that x_{2} would be greater by the opposite amount +δ, so that the two particles are equidistant from the origin. This ensures the conservation of linear momentum, just as Einstein in 1924 proved that the BohrKramersSlater theory that energy is only conserved statistically was wrong. Momentum is conserved exactly in every measurement, although the uncertainty principle may prevent this from being shown experimentally. Furthermore, in the Bohm version of nonlocality the quantities are discrete spins, not continuous positions or momenta. Electron spins are always measured to be either up or down, with nothing fuzzy about these values. And all the experimental results from all the Bell tests have always found the two spins opposite as long as both measurements are made in exactly the same direction, thus conserving total spin zero. There is still indeterminism (uncertainty) in the spin measurement results. We don't know which electron will be up and which down. It is this property that "does not exist" before the measurement. Physics has not found any hidden variables, local or nonlocal, as the cause of the perfect opposite spins. Is the conserved total spin zero acceptable as what we call a "hidden constant of the motion" that completely accounts for the perfectly opposite spins?
Summary of the "hidden" constant hypothesis
Standard quantum mechanics plus the principle of angular momentum conservation (true for quantum and classical mechanics) predicts:
The "hidden constant" of the motion was introduced in chapter 45 of My God, He Plays Dice, How Albert Einstein Invented Most of Quantum Mechanics, 2019, p.376. If the conservation of angular momentum (spin) is not the proven "cause" of the perfect correlations, the vast experimental evidence for those correlations, so critical to the twin random bit strings needed for quantum cryptography, tells us that conservation is an experimentally proven fact of the matter! We can also note that a subsequent measurement by either observer at a different angle will destroy the planar symmetry. The original linear combination or superposition of states
Ψ_{12} = 1/√2)  1_{+}2_{} > + 1/√2)  1_{}2_{+} > (1)
have become a mixture of product states that have decohered (their purestate coherent phase relations lost). They are disentangled, as Erwin Schrödinger argued in 1936. Measuring one can still tell us about the other. he said. But they can no longer interfere with one another and remain correlated in future measurements. They have truly separated, but had not separated earlier, as Einstein hoped with his Trennungsprinzip.
