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 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 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 |
Max Planck
In 1900, Max Planck's hypothesized a quantum of action h and restricted the energy in oscillators radiating electromagnetic energy to integer multiples of hν, where ν is the radiant frequency. He then discovered a formula for the distribution of radiant energy in a black body at any temperature.
Bν (v, T) = (2hν3 / c2) (1 / ( e hν / kT - 1) )
Planck solved the great problem of blackbody radiation by applying the statistical mechanics of the Maxwell-Boltzmann velocity distribution law for particles to the distribution of energy in a radiation field. Planck did not suggest that light actually came in quantized (discrete) bundles of energy. That was the work of Albert Einstein five years later in his photo-electric effect paper (for which he won the Nobel Prize), in which he proposed his "light-quantum hypothesis." For Einstein, the particle equivalent of light (later called a "photon") contains hν units of energy, where h is Planck's constant and ν is the frequency of the light wave.
Planck did not actually believe that light radiation itself existed as light quanta. His quantization assumption was for an ensemble of "oscillators" or "resonators" that were emitting and absorbing the radiation. Although the Lorentz theory of the electron was already complete, Planck did not accept electrons and instead described "the energy flowing across a spherical surface of a certain radius containing the resonator." He assumed the resonators could be described as having energy values limited to multiples of hν.
Note the resemblance to the Bohr theory of the atom thirteen years later, where Bohr postulated stationary states of the electron and transitions between those states with the emission or absorption of continuous waves of energy equal to hν!
Planck's assumption was simply a mathematical device to make the distribution of light as a function of frequency (and thus energy) resemble the Maxwell-Boltzmann distribution of molecular velocities in a gas as a function of velocity (and thus energy). In 1925, he called his work "a fortunate guess at an interpolation formula" and "the quantum of action a fictitious quantity... nothing more than mathematical juggling."
Note the resemblance between the distribution of blackbody radiation as a function of temperature and the Maxwell-Boltzmann distribution of velocities.
The similarity between the two is the rise to a maximum with a power law on one side and an exponential decline on the other. The difference is because the radiant energy (the number of photons) increases greatly as temperature goes up, but the number of molecules is held constant.
Planck in 1900 explained the spectral distribution of colors (wavelengths) in blackbody electromagnetic radiation by using Boltzmann’s principle that the entropy S of a gas is related to the probabilities W for the possible random distributions of molecules in different places in its container and with different velocities. S = k logW, where k is Boltzmann’s constant (so named by Planck. Boltzmann and Einstein used R/N) ). Boltzmann’s calculations of probabilities used the number of ways that particles can be distributed in various volumes of phase space. Planck used the same combinatorial analysis, but now for the number of ways that discrete elements of energy could be distributed among a number of radiation oscillators.
To simplify calculations, both Boltzmann and Planck assumed that energies could be considered multiples of a unit of energy, E = ε, 2ε, 3ε ... Plank regarded this quantum hypothesis as a mathematically convenient device, but not representing reality. He found the density of radiation with frequency ν to be
ρν = (8πhν3/c2) / (ehν/kT - 1).Planck's "blackbody" radiation law was the first known connection between the mechanical laws of matter and the laws of electromagnetic energy. Planck realized that he had made a great step in physical understanding, "the greatest discovery in physics since Newton," he reportedly told his seven-year-old son in 1900. In particular, Planck found that Boltzmann's statistical mechanics constant k = R/N, derived from the distribution of velocities of material gas particles, appears in his new law for the distribution of electromagnetic radiation energy. Boltzmann himself had never described this constant k as such. It was Planck who gave it a symbol and a name, although it is inscribed on Boltzmann's tomb in his famous formula relating entropy to probability, S = k logW Planck established an independent and very accurate value for Boltzmann's constant. His blackbody radiation distribution law of course also includes the new Planck constant h. He called it the "quantum of action" because it had the units of position times momentum. Planck's formula led him to a value for Avogadro's number of molecules in a mole (the gram molecular weight) of a gas and an estimate of the fundamental unit of electrical charge. These gave Planck great confidence that his "fictitious" formula must be correct. Five years later, Albert Einstein explained the photoelectric effect using "light quanta," discrete units of light energy, later called photons. Since the momentum of a particle is the energy divided by velocity of a particle, the momentum p of a photon is p = hν/c, where c is the velocity of light. To make the dual aspect of light as both waves and particles (photons) more plausible, Einstein interpreted the square of the light wave amplitude as the probable density of photons. In fact, Planck fundamentally disliked the idea that physical quantities might be discrete and not continuous. He did not truly accept quanta of light until many years after Einstein had shown the quantization of light in his 1905 explanation of the photoelectric effect. Nevertheless, Planck's constant h lies at the heart of quantum mechanics, which introduced an irreducible and ontological randomness or indeterminacy into physics, first recognized by Einstein in his 1916 work on transition probabilities for the emission and absorption of light quanta. Planck, along with Einstein, Erwin Schrödinger and others, opposed such indeterminism. Einstein called chance a "weakness in the theory." Planck remained convinced that determinism and strict causality were essential requirements for physical science and so must be true. "Just as no physicist will in the last resort acknowledge the play of chance in human nature, so no physiologist will admit the play of chance in the absolute sense." "the assumption of chance in inorganic nature is incompatible with the working principle of natural science." "We must admit that the mind of each one of our greatest geniuses — Aristotle, Kant or Leonardo, Goethe or Beethoven, Dante or Shakespeare — even at the moment of its highest flights of thought or in the most profound inner workings of the soul, was subject to the causal fiat and was a instrument in the hands of an almighty law which governs the world."Planck looked very closely at the problem of free will, and gave a rough version of the logical opposition between determinism and blind chance in the standard argument against free will. "And here a question arises which seems to set a definite impassable limit to the principle of strict causality, at least in the spiritual sphere. This question is of such urgent human interest that I think it will be well if I treat it here before I come to a close. It is the question of the freedom of the human will. Our own consciousness tells us that our wills are free. And the information which that consciousness directly gives us is the last and highest exercise of our powers of understanding. Let us ask for a moment whether the human will is free or whether it is determined in a strictly causal way. These two alternatives seem definitely to exclude one another. And as the former has obviously to be answered in the affirmative, so the assumption of a law of strict causality operating in the universe seems to be reduced to an absurdity in at least this one instance. In other words, if we assume the law of strict dynamic causality as existing throughout the universe, how can we logically exclude the human will from its operation? Many are the attempts that have been made to solve this dilemma. The purpose which in most cases they have set themselves has been to establish an exact limit beyond which the law of causality does not apply. Recent developments in physical science have come into play here, and the freedom of the human will has been put forward as offering logical grounds for the acceptance of only a statistical causality operative in the physical universe. As I have already stated on other occasions, I do not at all agree with this attitude. If we should accept it, then the logical result would be to reduce the human will to an organ which would be subject to the sway of mere blind chance. In my opinion the question of the human will has nothing whatsoever to do with the opposition between causal and statistical physics. Its importance is of a much more profound character and is entirely independent of any physical or biological hypothesis.In 1925, as the development of quantum mechanics began in earnest, Planck republished a series of articles as the book A Survey of Physical Theory. In an article on "The Nature of Light," Planck describes Einstein's insight in 1905 that led to Einstein's "light-quantum hypothesis." But Planck does not explicitly mention Einstein! When ultra-violet rays fall on a piece of metal in a vacuum, a large number of electrons are shot off from the metal at a high velocity, and since the magnitude of this velocity does not essentially depend on the state of the metal, certainly not on its temperature, it is concluded that the energy of the electrons is not derived from the metal, but from the light rays which fall on the metal. This would not be strange in itself; it would even be assumed that the electro-magnetic energy of light waves, is transformed into the kinetic energy of electronic movements. An apparently insuperable difficulty from the view of Huygens's wave theory is the fact (which was discovered by Philipp Lenard and others), that the velocity of the electrons does not depend on the intensity of the beam, but only on the wavelength, i.e. on the colour of light used. The velocity increases as the wave-length diminishes. If the distance between the metal and the source of light is continuously increased, using, for example, an electric spark as the source of light, the electrons continue to be flung off with the same velocity, in spite of the weakening of the illumination; the only difference is that the number of electrons thrown off per second decreases with the intensity of the light. The difficulty is to state whence the electron obtains its energy, when the distance of the source of light becomes ultimately so great that the intensity of the light almost vanishes, and yet the electrons show no sign of diminution in their velocity. This must evidently be a case of a kind of accumulation of light energy at the spot from which the electron is flung out — an accumulation which is quite contrary to the uniform spreading out in all directions of electro-magnetic energy according to Huygens's wave theory. However, if it is assumed that the light source does not emit its rays uniformly but in impulses, something like an intermittent light, it follows that the energy of such a flash, spreading outwards in all directions in uniform waves, would finally be distributed over the surface of a sphere so large that the metal considered would receive but little of it. It is easy to calculate that under certain circumstances radiation extending for minutes, even hours, would be necessary for the liberation of one electron with the velocity corresponding to the colour of the light, while, in fact, no limiting condition can be determined, for the duration of radiation necessary to produce the effects; the action certainly takes place with great rapidity. Like ultra-violet rays, Röntgen rays and Gamma rays give us the same effect, though, owing to the very much shorter wave-lengths of these rays, the velocities of the liberated electrons are much greater.In the final article. "The Origin and Development of Quantum Theory," which was to be Planck's last writing on quantum theory, as he turned back to classical problems, Planck has a minimum reference to Einstein. as one of many "who made use" of his quantum of action, and still no mention of Einstein's photoelectric effect prediction which Planck described extensively in the previous article. ...the restless, ever-advancing labour of those workers who have made use of the quantum of action in their investigations. The first advance in this work was made by A. Einstein, who proved, on the one hand, that the introduction of the energy quanta, required by the quantum of action, appeared suitable for deriving a simple explanation for a series of remarkable observations of light effects, such as Stokes's rule, emission of electrons, and ionization of gases.
Irreversibility
In 1909, Einstein first suggested that the elementary process of radiation emission may be irreversible.
In 1916, Einstein derived the Planck law of radiation and Bohr's two quantum postulates (stationary states and transitions between states with E = hν). By contrast, Planck's "discovery" of his law was accomplished by trial and error guesses at the mathematical form. Einstein derived it from more basic principles.
Planck did give Einstein more credit in his 1920 Nobel lecture, "The Genesis and Present State of Development of the Quantum Theory". He asked whether the quantum of action was a fictional quantity or would it play a fundamental role in
physics, ... something entirely new, never before heard
of, which seemed called upon to basically revise all our physical
thinking, built as this was ... on the acceptance
of the continuity of all causative connections. He gave the major credit for the second alternative to Einstein:
Experiment has decided for the second alternative. That the decision could be made so soon and so definitely was due not to the proving of the energy distribution law of heat radiation, still less to the special derivation of that law devised by me, but rather should it be attributed to the restless forward thrusting work of those research workers who used the quantum of action to help them in their own investigations and experiments. The first impact in this field was made by A. Einstein who, on the one hand, pointed out that the introduction of the energy quanta, determined by the quantum of action, appeared suitable for obtaining a simple explanation for a series of noteworthy observations during the action of light, such as Stokes' Law, electron emission, and gas ionization, and, on the other hand, derived a formula for the specific heat of a solid body through the identification of the expression for the energy of a system of resonators with that of the energy of a solid body, and this formula expresses, more or less correctly, the changes in specific heat, particularly its reduction with falling temperature. The result was the emergence, in all directions, of a number of problems whose more accurate and extensive elaboration in the course of time brought to light a mass of valuable material...
Matter, Consciousness, Spirit, and Faith
Planck spoke often enough about God and the Church, as well as religions in the plural, to consider him a man of faith. But like Einstein, his faith was in Reason, or a rational spiritual entity behind the empirical facts of matter in motion. The last words of his book The New Science were...
It is only when we have planted our feet on the firm ground which can be won only with the help of the experience of real life, that we have the right to feel secure in surrendering to our belief in a philosophy of the world based upon a faith in the rational ordering of this world.Planck was in some ways a panpsychist, believing that all matter is conscious. I regard consciousness as fundamental. I regard matter as derivative from consciousness. We cannot get behind consciousness. Everything that we talk about, everything that we regard as existing, postulates consciousness.He believed that particles of matter must be held together by a spirit, beyond the laws of quantum physics. One of his most famous quotes, "Mind is the Matrix of Matter," translates Geist (spirit) as mind. The full quote is Als Physiker, der sein ganzes Leben der nüchternen Wissenschaft, der Erforschung der Materie widmete, bin ich sicher von dem Verdacht frei, für einen Schwarmgeist gehalten zu werden. Und so sage ich nach meinen Erforschungen des Atoms dieses: Es gibt keine Materie an sich. Alle Materie entsteht und besteht nur durch eine Kraft, welche die Atomteilchen in Schwingung bringt und sie zum winzigsten Sonnensystem des Alls zusammenhält. Da es im ganzen Weltall aber weder eine intelligente Kraft noch eine ewige Kraft gibt—es ist der Menschheit nicht gelungen, das heißersehnte Perpetuum mobile zu erfinden—so müssen wir hinter dieser Kraft einen bewußten intelligenten Geist annehmen. Dieser Geist ist der Urgrund aller Materie. As a physicist who has devoted his whole life to rational science, to the study of matter, I think I can safely claim to be above any suspicion of irrational exuberance. Having said that, I would like to observe that my research on the atom has shown me that there is no such thing as matter in itself. What we perceive as matter is merely the manifestation of a force that causes the subatomic particles to oscillate and holds them together in the tiniest solar system of the universe. Since there is in the whole universe neither an intelligent force nor an eternal force (mankind, for all its yearnings, has yet to succeed in inventing a perpetual motion machine), we must assume that this force that is active within the atom comes from a conscious and intelligent mind. That mind is the ultimate source of matter.
References
Scientific Autobiography (1947)
Dynamical Laws and Statistical Laws
The Genesis and Present State of Development of the Quantum Theory (Nobel Lecture - 1920)
The Nature of Light
Improvement in Wien Spectrum, October 19, 1900a
Energy Distribution Law, December 14, 1900b
Distribution of Energy in the Normal Spectrum, 1901a
Original Papers in Quantum Physics, with Notes by H. Kangro
The Origin and Development of Quantum Theory (A rewrite of the Nobel Lecture)
Max Planck Biography, by K. A. G. Mendelssohn, from A Physics Anthology, ed. Norman Clarke, 1960
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