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 F.H.Bradley C.D.Broad Michael Burke Lawrence Cahoone 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 Arthur Fine John Martin Fischer Frederic Fitch 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 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 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.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 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 Hans Briegel Leon Brillouin Stephen Brush Henry Thomas Buckle S. H. Burbury Donald Campbell Anthony Cashmore Eric Chaisson Gregory Chaitin JeanPierre Changeux Arthur Holly Compton John Conway 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 Albert Einstein Hugh Everett, III Franz Exner Richard Feynman R. A. Fisher David Foster Joseph Fourier Philipp Frank Steven Frautschi Edward Fredkin Lila Gatlin Michael Gazzaniga GianCarlo Ghirardi J. Willard Gibbs Nicolas Gisin Paul Glimcher Thomas Gold A. O. Gomes Brian Goodwin Joshua Greene Jacques Hadamard Mark Hadley Patrick Haggard J. B. S. Haldane Stuart Hameroff Augustin Hamon Sam Harris Hyman Hartman JohnDylan 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 William R. Klemm Christof Koch Simon Kochen Hans Kornhuber Stephen Kosslyn Ladislav Kovàč Leopold Kronecker Rolf Landauer Alfred Landé PierreSimon Laplace David Layzer Joseph LeDoux Benjamin Libet Seth Lloyd Hendrik Lorentz Josef Loschmidt Ernst Mach Donald MacKay Henry Margenau James Clerk Maxwell Ernst Mayr John McCarthy Warren McCulloch 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 Adolphe Quételet Jürgen Renn Juan Roederer Jerome Rothstein David Ruelle Tilman Sauer Jürgen Schmidhuber Erwin Schrödinger Aaron Schurger Claude Shannon David Shiang 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 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 Stephen Wolfram H. Dieter Zeh Ernst Zermelo Wojciech Zurek Konrad Zuse Fritz Zwicky Presentations Biosemiotics Free Will Mental Causation James Symposium 
Satyendra Nath Bose
Quantum Statistics for Photons (1924)
In 1924, Albert Einstein received an amazing very short paper from India by Satyendra Nath Bose. Einstein must have been pleased to read the title, "Planck's Law and the Hypothesis of Light Quanta." It was more attention to Einstein's 1905 work than anyone had paid in nearly twenty years. The paper began by claiming that the "phase space" (a combination of 3dimensional coordinate space and 3dimensional momentum space) should be divided into small volumes of h^{3}, the cube of Planck's constant. By simply counting the number of possible distributions of light quanta over these cells, Bose claimed he could calculate the entropy and all other thermodynamic properties of the radiation, including the famous Planck law.
ρ_{ν}dν = (8πhν^{2}/c^{3}) / (e^{  hν / kT } 1)
Maxwell and Boltzmann had derived their distribution law for material particles by analogy with the Gaussian exponential tail of probability in the theory of errors. The number of gas particles with velocity between v and v + dv is
N ( v ) dv = (4 / α^{2} √π) v^{2} e^{  v2 / α2 } dv.
Max Planck had simply guessed his expression from Wien's law for high frequency radiation
ρ_{ν}dν = aν^{3} e^{  bν/T}.
and from Lord Rayleigh's expression for lowfrequency (longwavelength) radiation.
ρ_{ν}dν = ν^{2}T.
Planck simply added the term  1 in the denominator of Wien's expression (1 / e^{  bν / T}). Planck later acknowledged that his breakthrough was luckily finding a mathematical expression that interpolates between Wien's Law at high frequencies and the RayleighJeans Law at low frequencies. He called it a glückliche Interpolationformel. Einstein said Planck's work was "monstrous," but obviously in perfect agreement with experiment. How had Planck done it? All Einstein's derivations of the Planck law, including that of 191617 (which Bose called "remarkably elegant"), used classical electromagnetic theory to derive the density of radiation as the number of "modes" or "degrees of freedom" of the radiation field,
ρ_{ν}dν = (8πν^{2}dν / c^{3}) dE
In 1906, Einstein had criticized Planck's use of this classical expression in deriving his "quantum" radiation law. He called it a contradiction... "this assumption...contradicts the theoretical basis from which [this expression] was developed." But now Bose showed he could get this quantity with a simple statistical mechanical argument remarkably like that Maxwell used to derive his distribution of molecular velocities. Where Maxwell said that the three directions of velocities for particles are independent of one another, but of course equal to the total momentum,
p_{x2} + p_{y2} + p_{z2} = p^{2} ,
Bose just used Einstein's 1917 relation for the momentum of a photon, its energy hν divided by its velocity c,
p = hν / c,
and he wrote
p_{x2} + p_{y2} + p_{z2} = h^{2}ν^{2} / c^{2} .
This led him to calculate a frequency interval in phase space as
∫ dx dy dz dp_{x} dp_{y} dp_{z} = 4πV ( hν / c )^{2} ( h dν / c ) = 4π ( h^{3} ν^{2} / c^{3} ) V dν,
which he simply divided by h^{3}, multiplied by 2 to account for two polarization degrees of freedom, and he had derived the number of cells belonging to dν,
ρ_{ν}dν = (8πν^{2}dν / c^{3}) E ,
without using classical radiation laws, a correspondence principle, or even Wien's law. His derivation was purely statistical mechanical, based only on the number of cells in phase space and the number of ways N photons can be distributed among pcells. Einstein immediately translated the Bose paper into German and had it published in Zeitschrift für Physik, without even telling Bose. More importantly, Einstein then went on to discuss a new quantum statistics that predicted lowtemperature condensation of any particles with integer values of the spin. So called BoseEinstein statistics were quickly shown by Dirac to lead to the quantum statistics of halfinteger spin particles called FermiDirac statistics. Fermions are halfinteger spin particles that obey Pauli's exclusion principle so a maximum of two particles, with opposite spins, can be found in the fundamental h^{3} volume of phase space identified by Bose. Einstein's 1916 work on transition probabilities predicted the stimulated emission of radiation that brought us lasers (light amplification by the stimulated emission of radiation). Now his work on quantum statistics brought us the BoseEinstein condensation. Either work would have made their discoverer a giant in physics, but these are more often attributed to Bose, just as Einstein's quantum discoveries before the Copenhagen Interpretation are mostly forgotten by historians and today's textbooks, or attributed to others. This work with Bose is often seen as Einstein's last positive contribution to quantum physics. Some judge his later efforts as purely negative attempts to discredit quantum mechanics, by graphically illustrating quantum phenomena that seem logically impossible or at least in violation of fundamental theories like his relativity. But in some ways the phenomena of nonlocality (seen as early as 1905 but made clear at the Solvay conference in 1927), and nonseparability, and entanglement (which were introduced by the 1935 EinsteinPodolskyRosen paper) are as amazing as anything Einstein ever did. As we shall see, just like his visions of light quanta and ontological chance that were denied or ignored for so long, the “founders” of quantum mechanics told us to not even try to visualize the “mysteries” produced by Einstein’s last insights. They told us not to try to understand what is happening in “quantum reality.” Despite them, Einstein’s visions of entanglement and “spooky action at a distance” have been confirmed by the latest experiments. He didn’t like them, but he saw them first. They can only be understood by trying to see what it is that Einstein saw so long ago. Information philosophy will try to illustrate his vision. They may not be made intuitive by our explanations, but they can be made understandable. And they can be visualized in a way that Einstein and Schrödinger might have liked, even if they would still find the phenomena impossible to believe. We hope even the layperson will see our animations as providing them an understanding of what quantum mechanics is doing in the microscopic world. The animations present standard quantum physics as Einstein saw it, though Schrödinger never accepted the "collapse" of the wave function and the existence of particles.
References
Planck's Law and the Hypothesis of Light Quanta
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