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 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 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 Melvin Calvin Donald Campbell Anthony Cashmore Eric Chaisson Gregory Chaitin JeanPierre Changeux 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 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 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 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 Gilbert Lewis Benjamin Libet David Lindley Seth Lloyd Hendrik Lorentz Josef Loschmidt Ernst Mach Donald MacKay Henry Margenau Humberto Maturana 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 Henry Quastler Adolphe Quételet Jürgen Renn Juan Roederer Jerome Rothstein David Ruelle Tilman Sauer Jürgen Schmidhuber Erwin Schrödinger Aaron Schurger Thomas Sebeok 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 Libb Thims William Thomson (Kelvin) Giulio Tononi Peter Tse Francisco Varela Vlatko Vedral Mikhail Volkenstein Heinz von Foerster John von Neumann Jakob von Uexküll 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 
Hendrik A. Lorentz
Hendrik A. Lorentz was giant in theoretical physics who bridged the gap between classical electromagnetic field theory and modern relativity theories.
He put forward a theory of the electron and he developed the famous Lorentz transformations that describe how objects appear contracted in the direction of their motion to observers in a frame at rest. Lorentz's equations provided the basis for Albert Einstein's theory of special relativity. Lorentz had many unpublished conversations with Einstein, some of which provide insight into Einstein's thoughts on the mysterious relationship between discrete light quanta (particles) and the continuous waves of classical electromagnetic theory. It shows that Einstein had a statistical view of the quanta. The probability of finding quanta is determined by the continuous wave, which controls the interference even for one quantum at a time.
Lorentz also describes the twoslit experiment.
Excerpt from Problems of Modern Physics (1922 Lectures at Cal Tech)
50. Interference and the Quantum Theory. I tried to explain to
you how the production of light by quantum jumps can perhaps
be reconciled with our old views concerning radiation, so that
these would hold as to the constitution of the emitted radiation.
But the question arises, Can this constitution be really just what
we have thought; that is, can there be a propagation according
to Maxwell's laws, with a tendency to spread out in all directions
and the impossibility of a lasting concentration of energy?
You know that phenomena like those of photoelectricity have led Einstein to his hypothesis of lightquanta. According to this, quantities of energy equal to hν would be concentrated in small spaces, moving with the speed of light; they would even be light and would produce all optical effects. In this way we can understand that even very feeble light can give to an electron the amount of energy hv, for the smallness of the intensity would be due to the small number of quanta which it contains, the magnitude of each remaining the same.
Einstein described this difficulty in 1905.
So we should
escape the difficulty which, in the case of wavemotion, arises
from the continual spreading out and weakening of the energy.
The hypothesis of lightquanta, however, is in contradiction with the phenomena of interference. Can the two views be reconciled? I should like to put forward some considerations about this question, but I must first say that Einstein is to be given credit for whatever in them may be sound. As I know his ideas concerning the points to be discussed only by verbal communication, however, and even by hearsay, I have to take the responsibility for all that remains unsatisfactory. Let us suppose that in the emission and propagation of light there is something that conforms wholly to Maxwell's equations, but that it has practically no energy at all, the electric and magnetic forces being infinitely small.
Today this Fresnel (interference) radiation is the probability amplitude wave function ψ
Then in this, let
us say, Fresnel radiation we shall have the ordinary laws of
reflection, interference, and refraction, but we shall see nothing
of it. On a screen you will have something like an undeveloped
photographic image.
We can now imagine that in the production of light this Fresnel radiation is accompanied by the emission of certain quanta of energy that are of a different nature. Although their precise nature is unknown, we may suppose that energy is concentrated in small spaces and remains so. These quanta move in such a way in our "pattern" that they can never come to a place where in this pattern there is darkness. In thus traveling from the source outward each quantum has a choice between many paths.
The intensity of the radiation gives the probability of finding light quanta, just as Born's rule (1926) says the probability of finding material particles is proportional to the square of the wave function
The probability of following different paths is
proportional to the intensity of the radiation along these paths
in Fresnel's radiation.
Now in all real cases the act of emission is repeated a great many times. Suppose it is repeated N times, and let the Fresnel radiation be the same in these different cases. Then we shall have N quanta moving in this pattern, and if their number is very great and the probability of following different paths as stated, the number of quanta coming on different parts of a screen on which we observe an interference phenomenon will be proportional to the intensity which we have in Fresnel's pattern. These considerations can easily be extended. Take, for instance, polarization. The polarization will be in the Fresnel pattern, not in the quanta, but the quanta will illuminate a screen or a photographic plate or our retina to exactly the degree determined by the classical theory.
Or consider light passing through two slits, one particle at a time
When light falls on the surface of a piece of glass, there is
a partition between the reflected and refracted parts. The
probability of the quantum's following one path or another is
determined by the wellknown formulae of Fresnel for the intensities
of the reflected and the refracted light.
Suppose that in an elementary act of radiation there are a million waves; these exist in Fresnel's pattern; but the quantum of energy can have any place in the train of waves, either near the front or near the rear of these waves. If we have an ordinary beam of light consisting of the superposition of a great number of elementary beams, we have quanta in great number distributed all through the space occupied by the beam. For Teachers
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