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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
Daniel Boyd
F.H.Bradley
C.D.Broad
Michael Burke
Jeremy Butterfield
Lawrence Cahoone
C.A.Campbell
Joseph Keim Campbell
Rudolf Carnap
Carneades
Nancy Cartwright
Gregg Caruso
Ernst Cassirer
David Chalmers
Roderick Chisholm
Chrysippus
Cicero
Tom Clark
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.Nowell-Smith
Robert Nozick
William of Ockham
Timothy O'Connor
Parmenides
David F. Pears
Charles Sanders Peirce
Derk Pereboom
Steven Pinker
U.T.Place
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
John Duns Scotus
Arthur Schopenhauer
John Searle
Wilfrid Sellars
David Shiang
Alan Sidelle
Ted Sider
Henry Sidgwick
Walter Sinnott-Armstrong
Peter Slezak
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
Horace Barlow
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
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
Augustin-Jean Fresnel
Benjamin Gal-Or
Howard Gardner
Lila Gatlin
Michael Gazzaniga
Nicholas Georgescu-Roegen
GianCarlo Ghirardi
J. Willard Gibbs
James J. Gibson
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
Jeff Hawkins
John-Dylan Haynes
Donald Hebb
Martin Heisenberg
Werner Heisenberg
John Herschel
Basil Hiley
Art Hobson
Jesper Hoffmeyer
Don Howard
John H. Jackson
William Stanley Jevons
Roman Jakobson
E. T. Jaynes
Pascual Jordan
Eric Kandel
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
Karl Lashley
David Layzer
Joseph LeDoux
Gerald Lettvin
Gilbert Lewis
Benjamin Libet
David Lindley
Seth Lloyd
Werner Loewenstein
Hendrik Lorentz
Josef Loschmidt
Alfred Lotka
Ernst Mach
Donald MacKay
Henry Margenau
Owen Maroney
David Marr
Humberto Maturana
James Clerk Maxwell
Ernst Mayr
John McCarthy
Warren McCulloch
N. David Mermin
George Miller
Stanley Miller
Ulrich Mohrhoff
Jacques Monod
Vernon Mountcastle
Emmy Noether
Donald Norman
Alexander Oparin
Abraham Pais
Howard Pattee
Wolfgang Pauli
Massimo Pauri
Wilder Penfield
Roger Penrose
Steven Pinker
Colin Pittendrigh
Walter Pitts
Max Planck
Susan Pockett
Henri Poincaré
Daniel Pollen
Ilya Prigogine
Hans Primas
Zenon Pylyshyn
Henry Quastler
Adolphe Quételet
Pasco Rakic
Nicolas Rashevsky
Lord Rayleigh
Frederick Reif
Jürgen Renn
Giacomo Rizzolati
A.A. Roback
Emil Roduner
Juan Roederer
Jerome Rothstein
David Ruelle
David Rumelhart
Robert Sapolsky
Tilman Sauer
Ferdinand de Saussure
Jürgen Schmidhuber
Erwin Schrödinger
Aaron Schurger
Sebastian Seung
Thomas Sebeok
Franco Selleri
Claude Shannon
Charles Sherrington
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
Alan Turing
C. S. Unnikrishnan
Francisco Varela
Vlatko Vedral
Vladimir Vernadsky
Mikhail Volkenstein
Heinz von Foerster
Richard von Mises
John von Neumann
Jakob von Uexküll
C. H. Waddington
John B. Watson
Daniel Wegner
Steven Weinberg
Paul A. Weiss
Herman Weyl
John Wheeler
Jeffrey Wicken
Wilhelm Wien
Norbert Wiener
Eugene Wigner
E. O. Wilson
Günther Witzany
Stephen Wolfram
H. Dieter Zeh
Semir Zeki
Ernst Zermelo
Wojciech Zurek
Konrad Zuse
Fritz Zwicky

Presentations

Biosemiotics
Free Will
Mental Causation
James Symposium
 
Wave-Particle Duality

In what sense can something be, at one and the same time, both a discrete particle (Werner Heisenberg) and a continuous wave (Erwin Schrödinger)? This is a source of great confusion.

The information interpretation of quantum mechanics argues that the wave function is purely abstract immaterial information about the probabilities where concrete material particles will be found statistically when a large number of particles are measured.

Waves and particles are the quantum physics version of the most fundamental philosophical dualism - Idealism versus Materialism.

Quantum waves are never seen. They are not "observables," which Heisenberg made his chief criterion for the new quantum mechanics. He declared that the electron orbits of the "old" quantum theory of the Bohr atom simply do not exist because they are not observable. Only the spectral lines of light given off by transitions between energy levels are observable, he said.

Following the traditional Copenhagen Interpretation, many physicists today describe a quantum object as either a wave or a particle, depending on the free choice of the experimenter. But we will argue that the continuous "waves" are never observable except as averages over a larger number of discrete particles.

The continuous waves are an idea, a mathematical invention, a calculation tool, that allows us to make amazingly accurate predictions about where discrete material particles will be found when we make experimental measurements.

Information philosophy sees wave-particle duality as an example of the many dualisms seen in the ideal (noumenal) and material (phenomenal) worlds of ancient and modern philosophy.

A physicist describing the evolution of a quantum system, an electron or a photon, for example, generally proceeds in two stages.

Between measurements there is a wave stage in which the wave function explores all the possibilities available, given the configuration of surrounding particles, especially those nearby, which represent the boundary conditions for the Schrödinger equation of motion for the wave function. Because the space where the possibilities are non-zero is large, we say that the wave function (or "possibilities function") is nonlocal. Albert Einstein always hoped for a local "objective reality" and not what might seem merely "subjective" possibilities.

An observer can not gain any empirical knowledge unless new information has first been irreversibly recorded, e.g., when a particle has been localized and recorded in the experimental apparatus.
The other stage is measurement, when the photon or electron interacts with one or more of the surrounding particles, including the measurement apparatus. At this point, one of the nonlocal possibilities may be "actualized" or localized.

We can characterize the wave stage as "theory" and the measurement stage as "experiment." Theories are our ideas. Experiments are our interactions with the material world.

When we "visualize" the quantum wave moving through space (in the time-dependent quantum theory) or even the "standing waves" we imagine (in the time-independent theory), there is absolutely no material or energy at all the positions in space. What we visualize in our minds is not "real."

So we can also characterize the wave stage as the statistical or probabilistic or "possibilities" stage, where the experiment stage gives us "actualities" or "realizations."

The quantum process raises deep metaphysical questions about possibilities, with their calculable probabilities, and their measurable actualities.

Information about the new interaction may or may not be recorded. If the new information is irreversibly recorded, it may later be observed. It must be recorded before it can be observed. A "conscious observer" is not involved in the recording of the measurement. The recording of a measurement happens before the observer makes an observation. In modern physics, that can be days or weeks before the observation which may require further lengthy calculations and "data reduction."

When you hear or read that electrons are both waves and particles, you might think "either-or" - between measurements a wave of possibilities, at the measurement an actual particle.

Or you might prefer Albert Einstein's deeply help belief that it is always a particle with a path and definite properties, despite the practical impossibility of making measurements everywhere along the path.

That a continuous light wave might actually be composed of discrete quantum particles was first proposed by Einstein in 1905 as his "light-quantum hypothesis."

He wrote:

On the modern quantum view, what spreads out is a "nonlocal" wave of probability amplitude ψ,
whose absolute square |ψ|2 gives us the possibilities and probabilities for absorption, followed by a whole photon actually being absorbed ("localized") somewhere.
In accordance with the assumption to be considered here, the energy of a light ray spreading out from a point source is not continuously distributed over an increasing space but consists of a finite number of energy quanta which are localized at points in space, which move without dividing, and which can only be produced and absorbed as whole units.

In 1909, Einstein speculated about the connection between wave and particle views:

This is wave-particle duality fourteen years before Louis deBroglie's matter waves and Erwin Schrödinger's wave equation and wave mechanics
When light was shown to exhibit interference and diffraction, it seemed almost certain that light should be considered a wave...A large body of facts shows undeniably that light has certain fundamental properties that are better explained by Newton's emission theory of light than by the oscillation theory. For this reason, I believe that the next phase in the development of theoretical physics will bring us a theory of light that can be considered a fusion of the oscillation and emission theories...

Even without delving deeply into theory, one notices that our theory of light cannot explain certain fundamental properties of phenomena associated with light. Why does the color of light, and not its intensity, determine whether a certain photochemical reaction occurs? Why is light of short wavelength generally more effective chemically than light of longer wavelength? Why is the speed of photoelectrically produced cathode rays independent of the light's intensity? Why are higher temperatures (and, thus, higher molecular energies) required to add a short-wavelength component to the radiation emitted by an object?

The fundamental property of the oscillation theory that engenders these difficulties seems to me the following. In the kinetic theory of molecules, for every process in which only a few elementary particles participate (e.g., molecular collisions), the inverse process also exists. But that is not the case for the elementary processes of radiation.

Einstein's view since 1905 was that light quanta are emitted in particular directions. There are no outgoing spherical waves (except probability amplitude or "possibilities" waves). Even less likely are incoming spherical waves, never seen in nature
According to our prevailing theory, an oscillating ion generates a spherical wave that propagates outwards. The inverse process does not exist as an elementary process. A converging spherical wave is mathematically possible, to be sure; but to approach its realization requires a vast number of emitting entities. The elementary process of emission is not invertible. In this, I believe, our oscillation theory does not hit the mark. Newton's emission theory of light seems to contain more truth with respect to this point than the oscillation theory since, first of all, the energy given to a light particle is not scattered over infinite space, but remains available for an elementary process of absorption.

Also in 1909, Einstein’s imagined an experiment in which the energy of an electron (a cathode ray) is converted to a light quantum and back.

Consider the laws governing the production of secondary cathode radiation by X-rays. If primary cathode rays impinge on a metal plate P1, they produce X-rays. If these X-rays impinge on a second metal plate P2, cathode rays are again produced whose speed is of the same order as that of the primary cathode rays.

As far as we know today, the speed of the secondary cathode rays depends neither on the distance between P1 and P2, nor on the intensity of the primary cathode rays, but rather entirely on the speed of the primary cathode rays. Let’s assume that this is strictly true. What would happen if we reduced the intensity of the primary cathode rays or the size of P1 on which they fall, so that the impact of an electron of the primary cathode rays can be considered an isolated process?

If the above is really true then, because of the independence of the secondary cathode rays’ speed on the primary cathode rays’ intensity, we must assume that an electron impinging on P1 will either cause no electrons to be produced at P2, or else a secondary emission of an electron whose speed is of the same order as that of the initial electron impinging on P1. In other words, the elementary process of radiation seems to occur in such a way that it does not scatter the energy of the primary electron in a spherical wave propagating in every direction, as the oscillation theory demands.

Extending his 1905 hypothesis, Einstein shows energy can not spread out like a wave continuously over a large volume, because it is absorbed in its entirety to produce an ejected electron at P2, with essentially the same energy as the original electron absorbed at P1.

Rather, at least a large part of this energy seems to be available at some place on P2, or somewhere else. The elementary process of the emission of radiation appears to be directional. Moreover, one has the impression that the production of X-rays at P1 and the production of secondary cathode rays at P2 are essentially inverse processes...Therefore, the constitution of radiation seems to be different from what our oscillation theory predicts.

The theory of thermal radiation has given important clues about this, mostly by the theory on which Planck based his radiation formula...Planck’s theory leads to the following conjecture. If it is really true that a radiative resonator can only assume energy values that are multiples of hν, the obvious assumption is that the emission and absorption of light occurs only in these energy quantities. On the basis of this hypothesis, the light-quanta hypothesis, the questions raised above about the emission and absorption of light can be answered. As far as we know, the quantitative consequences of this light-quanta hypothesis are confirmed. This provokes the following question. Is it not thinkable that Planck’s radiation formula is correct, but that another derivation could be found that does not rest on such a seemingly monstrous assumption as Planck’s theory? Is it not possible to replace the light-quanta hypothesis with another assumption, with which one could do justice to known phenomena? If it is necessary to modify the theory’s elements, couldn’t one keep the propagation laws intact, and only change the conceptions of the elementary processes of emission and absorption?

This conception seems to me the most natural: that the manifestation of light’s electromagnetic waves is constrained at singularity points, like the manifestation of electrostatic fields in the theory of the electron. I imagine to myself, each such singular point surrounded by a field that has essentially the same character as a plane wave, and whose amplitude decreases with the distance between the singular points. If many such singularities are separated by a distance small with respect to the dimensions of the field of one singular point, their fields will be superimposed, and will form in their totality an oscillating field that is only slightly different from the oscillating field in our present electromagnetic theory of light.

Einstein thus imagines many singular points (his light quanta) whose average behavior has the shape of a light wave.

Just as a large number of randomly distributed discrete points approaches the smooth continuous appearance of the normal distribution, Einstein imagines the “totality” of points would look like an oscillating light wave or field. Einstein never published the implicit idea that the light wave would be stronger where there are many particles, less where there are few. But he described to many friends, including Max Born, the idea of a “ghost field” (Gespensterfeld) or “guiding field” (Führungsfeld) that represents the probability of finding a particle at different positions.

Our modern view of the relationship between waves and particles is straightforward. The wave is a complex function with values at every place in space whose absolute square gives us the probability of finding a discrete particle there. The wave (later the wave function ψ) is similar to the continuous gravitational or electromagnetic fields that specify the force on a test particle at any place in space and time. These “probability” fields are not substantial or as Einstein called them “ponderable.”

The “fusion of wave and emission theories of light” that Einstein expected is now seen to consist of a theoretical continuous field that provides abstract information (calculable probabilities and predictions) about the outcomes of experiments on localized discrete particles.

Dueling Wave and Particle Theories
Not only do we have the problem of understanding wave-particle duality in a quantum system, we have a full-blown wave mechanical theory (deBroglie and Schrödinger) versus a particle mechanics theory (Heisenberg, Max Born, Pascual Jordan).

Before either of these theories was developed in the mid-1920's, Einstein in 1916 showed how both wave-like and particle-like behaviors are seen in light quanta, and that the emission of light is done at random times and in random directions. This was the introduction of ontological chance (Zufall) into physics, over a decade before Heisenberg announced that quantum mechanics is acausal in his "uncertainty principle" paper of 1927.

As late as 1917, Einstein felt very much alone in believing the reality (his emphasis) of light quanta:

I do not doubt anymore the reality of radiation quanta, although I still stand quite alone in this conviction

Einstein in 1916 had just derived his A and B coefficients describing the absorption, spontaneous emission, and (his newly predicted) stimulated emission of radiation. In two papers, "Emission and Absorption of Radiation in Quantum Theory," and "On the Quantum Theory of Radiation," he derived the Planck law (for Planck it was mostly a guess at the formula), he derived Planck's postulate E = , and he derived Bohr's second postulate
Em - En = . Einstein did this by exploiting the obvious relationship between the Maxwell-Boltzmann distribution of gas particle velocities and the distribution of radiation in Planck's law.

Einstein wrote:

The formal similarity between the chromatic distribution curve for thermal radiation and the Maxwell velocity-distribution law is too striking to have remained hidden for long. In fact, it was this similarity which led W. Wien, some time ago, to an extension of the radiation formula in his important theoretical paper, in which he derived his displacement law...Not long ago I discovered a derivation of Planck's formula which was closely related to Wien's original argument and which was based on the fundamental assumption of quantum theory. This derivation displays the relationship between Maxwell's curve and the chromatic distribution curve and deserves attention not only because of its simplicity, but especially because it seems to throw some light on the mechanism of emission and absorption of radiation by matter, a process which is still obscure to us.
But the introduction of Maxwell-Boltzmann statistical mechanical thinking to electromagnetic theory has produced what Einstein called a "weakness in the theory." It introduces the reality of an irreducible objective chance!

If light quanta are particles with energy E = hν traveling at the velocity of light c, then they should have a momentum p = E/c = hν/c. When light is absorbed by material particles, this momentum will clearly be transferred to the particle. But when light is emitted by an atom or molecule, a problem appears.

The "statistical interpretation" of Max Born, which was based on Einstein's ideas about a "ghost field" (Gespensterfeld) or "guiding field" (Führungsfeld), tells us the outgoing wave is the probability amplitude wave function Ψ, whose absolute square is the probability of finding a light particle in an arbitrary direction.
Conservation of momentum requires that the momentum of the emitted particle will cause an atom to recoil with momentum hν/c in the opposite direction. However, the standard theory of spontaneous emission of radiation is that it produces a spherical wave going out in all directions. A spherically symmetric wave has no preferred direction. In which direction does the atom recoil? Einstein asked:
Does the molecule receive an impulse when it absorbs or emits the energy ε? For example, let us look at emission from the point of view of classical electrodynamics. When a body emits the radiation ε it suffers a recoil (momentum) ε/c if the entire amount of radiation energy is emitted in the same direction. If, however, the emission is a spatially symmetric process, e.g., a spherical wave, no recoil at all occurs. This alternative also plays a role in the quantum theory of radiation. When a molecule absorbs or emits the energy ε in the form of radiation during the transition between quantum theoretically possible states, then this elementary process can be viewed either as a completely or partially directed one in space, or also as a symmetrical (nondirected) one. It turns out that we arrive at a theory that is free of contradictions, only if we interpret those elementary processes as completely directed processes.

An outgoing light particle must impart momentum hν/c to the atom or molecule, but the direction of the momentum can not be predicted! Neither can the theory predict the time when the light quantum will be emitted.

Such a random time was not unknown to physics. When Ernest Rutherford derived the law for radioactive decay of unstable atomic nuclei in 1900, he could only give the probability of decay time. Einstein saw the connection with radiation emission:

It speaks in favor of the theory that the statistical law assumed for [spontaneous] emission is nothing but the Rutherford law of radioactive decay.
But the inability to predict both the time and direction of light particle emissions, said Einstein in 1917, is "a weakness in the theory..., that it leaves time and direction of elementary processes to chance (Zufall, ibid.)." It is only a weakness for Einstein, of course, because his God does not play dice.

Einstein clearly saw, as none of his contemporaries did, that since spontaneous emission is a statistical process, it cannot possibly be described with classical physics.

The properties of elementary processes required...make it seem almost inevitable to formulate a truly quantized theory of radiation.

How Einstein Discovered Wave-Particle Duality
Einstein was bothered by Planck's discovery of the blackbody radiation law. He said that it "rests on a seemingly monstrous assumption."
Planck had assumed that energy levels were discrete (compare Bohr's stationery states in the old quantum theory). Einstein saw that transitions between those levels should be discrete quanta. When Bohr formulated his atom theory (and for the next dozen years), he ignored Einstein's light quanta, as did Planck for 24 years!
Planck's theory leads to the following conjecture. If it is really true that a radiative resonator can only assume energy values that are multiples of , the obvious assumption is that the emission and absorption of light occurs only in these energy quantities. On the basis of this hypothesis, the light-quanta hypothesis, the questions raised above about the emission and absorption of light can be answered. As far as we know, the quantitative consequences of this light-quanta hypothesis are confirmed. This provokes the following question. Is it not thinkable that Planck's radiation formula is correct, but that another derivation could be found that does not rest on such a seemingly monstrous assumption as Planck's theory? Is it not possible to replace the light-quanta hypothesis with another assumption, with which one could do justice to known phenomena? If it is necessary to modify the theory's elements, couldn't one keep the propagation laws intact, and only change the conceptions of the elementary processes of emission and absorption?

To arrive at a certain answer to this question, let us proceed in the opposite direction of Planck in his radiation theory. Let us view Planck's radiation formula as correct, and ask ourselves whether something concerning the composition of radiation can be derived from it.

Eight years later, in his paper on the A and B coefficients (transition probabilities) for the emission and absorption of radiation, Einstein carried through his attempt to understand the Planck law. He confirmed that light behaves sometimes like waves (notably when a great number of particles are present and for low energies), at other times like the particles of a gas (for few particles and high energies).

Dirac on Wave-Particle Duality
Quantum mechanics is able to effect a reconciliation of the wave and corpuscular properties of light. The essential point is the association of each of the translational states of a photon with one of the wave functions of ordinary wave optics. The nature of this association cannot be pictured on a basis of classical mechanics, but is something entirely new. It would be quite wrong to picture the photon and its associated wave as interacting in the way in which particles and waves can interact in classical mechanics. The association can be interpreted only statistically, the wave function giving us information about the probability of our finding the photon in any particular place when we make an observation of where it is.

Note that the information about the possibility of a photon at a given point does not have to be "knowledge" for some conscious observer. It is statistical information about the photon, even if it is never observed
Some time before the discovery of quantum mechanics people [viz., Einstein!] realized that the connexion between light waves and photons must be of a statistical character. What they did not clearly realize, however, was that the wave function gives information about the probability of one photon being in a particular place and not the probable number of photons in that place.
Einstein, deBroglie, and Schrödinger had all argued that the light wave at some point might be the probable number of photons at that point.

But if we accept that Einstein always conceived the particle as indivisible and located at a given point in space and time (his local "objective reality"), we can agree with Dirac that the wave function gives us the probability of the individual particle "being in a particular place."

Feynman on Wave-Particle Duality
(The "One Mystery" of Quantum Mechanics)
Let us start with the history of light. At first light was assumed to behave very much like a shower of particles, of corpuscles, like rain, or like bullets from a gun. Then with further research it was clear that this was not right, that the light actually behaved like waves, like water waves for instance. Then in the twentieth century, on further research, it appeared again that light actually behaved in many ways like particles. In the photo-electric effect you could count these particles — they are called photons now. Electrons, when they were first discovered, behaved exactly like particles or bullets, very simply. Further research showed, from electron diffraction experiments for example, that they behaved like waves. As time went on there was a growing confusion about how these things really behaved — waves or particles, particles or waves? Everything looked like both...

How they behave, therefore, takes a great deal of imagination to appreciate, because we are going to describe something which is different from anything you know about...

It will be difficult. But the difficulty really is psychological and exists in the perpetual torment that results from your saying to yourself, 'But how can it be like that?' which is a reflection of uncontrolled but utterly vain desire to see it in terms of something familiar. I will not describe it in terms of an analogy with something familiar; I will simply describe it...

I will take just this one experiment, which has been designed to contain all of the mystery of quantum mechanics, to put you up against the paradoxes and mysteries and peculiarities of nature one hundred per cent. Any other situation in quantum mechanics, it turns out, can always be explained by saying, 'You remember the case of the experiment with the two holes ? It's the same thing'. I am going to tell you about the experiment with the two holes. It does contain the general mystery; I am avoiding nothing; I am baring nature in her most elegant and difficult form.

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