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Philosophers

Mortimer Adler
Rogers Albritton
Alexander of Aphrodisias
Samuel Alexander
William Alston
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 Belsham
Henri Bergson
Isaiah Berlin
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
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
John Martin Fischer
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
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
Jaegwon Kim
William King
Hilary Kornblith
Christine Korsgaard
Saul Kripke
Andrea Lavazza
Keith Lehrer
Gottfried Leibniz
Leucippus
Michael Levin
George Henry Lewes
C.I.Lewis
David Lewis
Peter Lipton
John Locke
Michael Lockwood
E. Jonathan Lowe
John R. Lucas
Lucretius
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
C. Lloyd Morgan
Thomas Nagel
Friedrich Nietzsche
John Norton
P.H.Nowell-Smith
Robert Nozick
William of Ockham
Timothy O'Connor
David F. Pears
Charles Sanders Peirce
Derk Pereboom
Steven Pinker
Plato
Karl Popper
Porphyry
Huw Price
H.A.Prichard
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
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
William Whewell
Alfred North Whitehead
David Widerker
David Wiggins
Bernard Williams
Timothy Williamson
Ludwig Wittgenstein
Susan Wolf

Scientists

Michael Arbib
Bernard Baars
Gregory Bateson
John S. Bell
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
Jean-Pierre Changeux
Arthur Holly Compton
John Conway
John Cramer
E. P. Culverwell
Charles Darwin
Terrence Deacon
Louis de Broglie
Max Delbrück
Abraham de Moivre
Paul Dirac
Hans Driesch
John Eccles
Arthur Stanley Eddington
Paul Ehrenfest
Albert Einstein
Hugh Everett, III
Franz Exner
Richard Feynman
R. A. Fisher
Joseph Fourier
Lila Gatlin
Michael Gazzaniga
GianCarlo Ghirardi
J. Willard Gibbs
Nicolas Gisin
Paul Glimcher
Thomas Gold
A.O.Gomes
Brian Goodwin
Joshua Greene
Jacques Hadamard
Patrick Haggard
Stuart Hameroff
Augustin Hamon
Sam Harris
Hyman Hartman
John-Dylan Haynes
Martin Heisenberg
John Herschel
Werner Heisenberg
Jesper Hoffmeyer
E. T. Jaynes
William Stanley Jevons
Roman Jakobson
Pascual Jordan
Ruth E. Kastner
Stuart Kauffman
Simon Kochen
Stephen Kosslyn
Ladislav Kovàč
Rolf Landauer
Alfred Landé
Pierre-Simon Laplace
David Layzer
Benjamin Libet
Seth Lloyd
Hendrik Lorentz
Josef Loschmidt
Ernst Mach
Donald MacKay
Henry Margenau
James Clerk Maxwell
Ernst Mayr
Ulrich Mohrhoff
Jacques Monod
Emmy Noether
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
Juan Roederer
Jerome Rothstein
David Ruelle
Erwin Schrödinger
Aaron Schurger
Claude Shannon
David Shiang
Herbert Simon
Dean Keith Simonton
B. F. Skinner
Roger Sperry
Henry Stapp
Tom Stonier
Antoine Suarez
Leo Szilard
William Thomson (Kelvin)
Peter Tse
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
H. Dieter Zeh
Ernst Zermelo
Wojciech Zurek

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 two-slit 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 photo-electricity have led Einstein to his hypothesis of light-quanta. According to this, quantities of energy equal to 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 wave-motion, arises from the continual spreading out and weakening of the energy.

The hypothesis of light-quanta, 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 well-known 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.

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