|
Philosophers
Mortimer Adler Rogers Albritton Alexander of Aphrodisias G.E.M.Anscombe Anselm Thomas Aquinas Aristotle David Armstrong Augustine J.L.Austin A.J.Ayer Alexander Bain Mark Balaguer William Belsham Henri Bergson Isaiah Berlin Bernard Berofsky Susanne Bobzien Emil du Bois-Reymond George Boole Émile Boutroux F.H.Bradley C.D.Broad C.A.Campbell Joseph Keim Campbell Carneades Ernst Cassirer Roderick Chisholm Chrysippus Cicero Randolph Clarke Samuel Clarke Anthony Collins Diodorus Cronus Donald Davidson Democritus Daniel Dennett René Descartes Richard Double Fred Dretske 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 Carl Ginet Nicholas St. John Green H.Paul Grice Ian Hacking Ishtiyaque Haji Stuart Hampshire W.F.R.Hardie R.M.Hare Georg W.F. Hegel Martin Heidegger R.E.Hobart Thomas Hobbes David Hodgson Shadsworth Hodgson Ted Honderich Pamela Huby David Hume Ferenc Huoranszki William James Lord Kames Robert Kane Immanuel Kant Tomis Kapitan William King Christine Korsgaard Keith Lehrer Gottfried Leibniz Leucippus Michael Levin C.I.Lewis David Lewis Peter Lipton John Locke Michael Lockwood John R. Lucas Lucretius James Martineau Hugh McCann Colin McGinn Michael McKenna Paul E. Meehl Alfred Mele John Stuart Mill Dickinson Miller G.E.Moore Thomas Nagel Friedrich Nietzsche 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 H.A.Prichard Hilary Putnam Willard van Orman Quine Frank Ramsey Ayn Rand Thomas Reid Charles Renouvier Nicholas Rescher C.W.Rietdijk Josiah Royce Bertrand Russell Paul Russell Gilbert Ryle T.M.Scanlon Moritz Schlick Arthur Schopenhauer John Searle Wilfrid Sellars Henry Sidgwick Walter Sinnott-Armstrong J.J.C.Smart Saul Smilansky Michael Smith L. Susan Stebbing George F. Stout Galen Strawson Peter Strawson Eleonore Stump Richard Taylor Kevin Timpe 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 Alfred North Whitehead David Widerker David Wiggins Bernard Williams Ludwig Wittgenstein Susan Wolf Scientists Michael Arbib Bernard Baars John S. Bell Charles Bennett Margaret Boden David Bohm Neils Bohr Ludwig Boltzmann Emile Borel Max Born Leon Brillouin Stephen Brush Henry Thomas Buckle Donald Campbell Anthony Cashmore Eric Chaisson Jean-Pierre Changeux Arthur Holly Compton John Conway E. H. Culverwell Charles Darwin Abraham de Moivre Paul Dirac John Eccles Arthur Stanley Eddington Paul Ehrenfest Albert Einstein Richard Feynman Joseph Fourier Michael Gazzaniga GianCarlo Ghirardi Nicolas Gisin Thomas Gold A.O.Gomes Joshua Greene Jacques Hadamard Patrick Haggard Augustin Hamon Sam Harris Martin Heisenberg Werner Heisenberg William Stanley Jevons Pascual Jordan Simon Kochen Stephen Kosslyn Rolf Landauer Alfred Landé Pierre-Simon Laplace David Layzer Benjamin Libet Josef Loschmidt Ernst Mach Henry Margenau James Clerk Maxwell Ernst Mayr Jacques Monod Roger Penrose Steven Pinker Max Planck Henri Poincaré Adolphe Quételet Jerome Rothstein Erwin Schrödinger Claude Shannon Herbert Simon Dean Keith Simonton B. F. Skinner Henry Stapp Antoine Suarez Leo Szilard William Thomson (Kelvin) John von Neumann Daniel Wegner Steven Weinberg Norbert Wiener Eugene Wigner E. O. Wilson Ernst Zermelo |
Werner Heisenberg
In 1925 Max Born, Werner Heisenberg, and Pascual Jordan, formulated their matrix mechanics version of quantum mechanics as a superior formulation of Neils Bohr's old quantum theory. The matrix mechanics confirmed discrete states and "quantum jumps" of electrons between the energy levels, with emission or absorption of photons.
In 1926, Erwin Schrödinger developed wave mechanics as an alternative formulation of quantum mechanics. Schrödinger disliked the abrupt jumps. His wave mechanics was a continuous theory, but it predicted the same energy levels and was otherwise identical in its predictions to the discrete theory.
Within months of the new wave mechanics, Max Born showed that while Schrödinger's wave function evolved over time deterministically, it only predicted the positions and velocities of atomic particles probabilistically.
Heisenberg used Schrödinger's wave functions to calculate the "transition probabilities" for electrons to jump from one energy level to another. Schrödinger's wave mechanics was easier to visualize and much easier to calculate than Heisenberg's own matrix mechanics.
In early 1927, Heisenberg announced his indeterminacy principle limiting our knowledge of the simultaneous position and velocity of atomic particles, and declared that the new quantum theory disproved causality. "We cannot - and here is where the causal law breaks down - explain why a particular atom will decay at one moment and not the next, or what causes it to emit an electron in this direction rather than that." 42
More popularly known as the Uncertainty Principle in quantum mechanics, it states that the exact position and momentum of an atomic particle can only be known within certain (sic) limits. The product of the position error and the momentum error is greater than or equal to Planck's constant h/2π.
ΔpΔx ≥ h/2π (1)
Indeterminacy (Unbestimmtheit) was Heisenberg's original name for his principle. It is a better name than the more popular uncertainty, which connotes lack of knowledge. The Heisenberg principle is an ontological as well as epistemic lack of information.
Causality
Heisenberg was convinced that quantum mechanics had put an end to classical ideas of causality and strict determinism.
In his classic paper introducing the principle of indeterminacy, he concluded with remarks about causailty.
If one assumes that the interpretation of quantum mechanics is already correct in its essential points, it may be permissible to outline briefly its consequences of principle. We have not assumed that quantum theory — in opposition to classical theory — is an essentially statistical theory in the sense that only statistical conclusions can be drawn from precise initial data. The well-known experiments of Geiger and Bothe, for example, speak directly against such an assumption. Rather, in all cases in which relations exist in classical theory between quantities which are really all exactly measurable, the corresponding exact relations also hold in quantum theory (laws of conservation of momentum and energy).But Heisenberg was not convinced that the lack of causality helped with the problem of human freedom. He reportedly said, "We no longer have any sympathy today for the concept of 'free will'." For Teachers
For Scholars
|
