Philosophers
Mortimer Adler Rogers Albritton Alexander of Aphrodisias Samuel Alexander G.E.M.Anscombe Anselm Louise Antony Thomas Aquinas Aristotle David Armstrong Harald Atmanspacher Augustine J.L.Austin A.J.Ayer Alexander Bain Mark Balaguer Jeffrey Barrett William Belsham Henri Bergson Isaiah Berlin Bernard Berofsky Robert Bishop Susanne Bobzien Emil du Bois-Reymond Hilary Bok George Boole Émile Boutroux F.H.Bradley C.D.Broad C.A.Campbell Joseph Keim Campbell 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 Carl Ginet 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 Christine Korsgaard 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 James Martineau Storrs McCall Hugh McCann Colin McGinn Michael McKenna Brian McLaughlin Paul E. Meehl Uwe Meixner Alfred Mele 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 Thomas Reid Charles Renouvier Nicholas Rescher C.W.Rietdijk Richard Rorty Josiah Royce Bertrand Russell Paul Russell Gilbert Ryle Kenneth Sayre 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 Mark Twain 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 Ludwig Wittgenstein Susan Wolf Scientists Michael Arbib Bernard Baars John S. Bell Charles Bennett Ludwig von Bertalanffy Susan Blackmore Margaret Boden David Bohm Niels Bohr Ludwig Boltzmann Emile Borel Max Born Walther Bothe Hans Briegel Leon Brillouin Stephen Brush Henry Thomas Buckle Donald Campbell Anthony Cashmore Eric Chaisson Jean-Pierre Changeux Arthur Holly Compton John Conway John Cramer E. H. Culverwell Charles Darwin Terrence Deacon 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 Joseph Fourier Michael Gazzaniga GianCarlo Ghirardi Nicolas Gisin Paul Glimcher Thomas Gold A.O.Gomes Brian Goodwin Joshua Greene Jacques Hadamard Stuart Hameroff Patrick Haggard Augustin Hamon Sam Harris Martin Heisenberg Werner Heisenberg William Stanley Jevons Pascual Jordan Ruth E. Kastner Simon Kochen Stephen Kosslyn Ladislav Kovàč Rolf Landauer Alfred Landé Pierre-Simon Laplace David Layzer Benjamin Libet Hendrik Lorentz Josef Loschmidt Ernst Mach Henry Margenau James Clerk Maxwell Ernst Mayr Ulrich Mohrhoff Jacques Monod Emmy Noether Wolfgang Pauli Massimo Pauri Roger Penrose Steven Pinker Max Planck Susan Pockett Henri Poincaré Daniel Pollen Ilya Prigogine Hans Primas Adolphe Quételet Jerome Rothstein David Ruelle Erwin Schrödinger Aaron Schurger Claude Shannon Herbert Simon Dean Keith Simonton B. F. Skinner Roger Sperry Henry Stapp Tom Stonier Antoine Suarez Leo Szilard William Thomson (Kelvin) Peter Tse John von Neumann Daniel Wegner Steven Weinberg Paul A. Weiss Norbert Wiener Eugene Wigner E. O. Wilson H. Dieter Zeh Ernst Zermelo Wojciech Zurek |
Schrödinger's Cat
Erwin Schrödinger's intention for his infamous cat-killing box was to discredit certain non-intuitive implications of quantum mechanics, of which his wave mechanics was the second formulation. Schrödinger's wave mechanics is more continuous mathematically, and apparently more deterministic, than Werner Heisenberg's matrix mechanics.
Schrödinger did not like Niels Bohr's idea of "quantum jumps" between Bohr's "stationary states" - the different "energy levels" in an atom. Bohr's "quantum postulate" said that the jumps between discrete states emitted (or absorbed) energy in the amount hν = E_{2} - E_{1}. Bohr did not accept Albert Einstein's 1905 hypothesis that the radiation was a discrete quantum of energy hν. Until well into the 1920's, Bohr (and Max Planck, the inventor of the quantum hypothesis himself) believed radiation was a continuous wave. This was the question of wave-particle duality, which Einstein saw as early as 1909. It was Einstein who originated the suggestion that the superposition of Schrödinger's wave functions implied that two different physical states could exist at the same time. This was a serious interpretational error that plagues the foundation of quantum physics to this day. This error is found frequently in discussions of so-called "entangled" states (see the Einstein-Podolsky-Rosen experiment). Entanglement occurs only for atomic level phenomena and over limited distances that preserve the coherence of two-particle wave functions by isolating the systems (and their eigenfunctions) from interactions with the environment. We never actually "see" or measure any system (whether a microscopic electron or a macroscopic cat) in two distinct states. Quantum mechanics simply predicts a significant probability of the system being found in these different states. And these probability predictions are borne out by the statistics of large numbers of identical experiments.
The Pauli Exclusion Principle says (correctly) that two identical indistinguishable (fermion) particles cannot be in the same place at the same time. Entanglement is often interpreted (incorrectly) as saying that a single particle can be in two places at the same time. Dirac's Principle of Superposition does not say that a particle Einstein wrote to Schrödinger with the idea that the decay of a radioactive nucleus could be arranged to set off a large explosion. Since the moment of decay is unknown, Einstein argued that the superposition of decayed and undecayed nuclear states implies the superposition of an explosion and no explosion. It does not. In both the microscopic and macroscopic cases, quantum mechanics simply estimates the probability amplitudes for the two cases. Many years later, Richard Feynman made Einstein's suggestion into a nuclear explosion! (What is it about some scientists?) Einstein and Schrödinger did not like the fundamental randomness implied by quantum mechanics. They wanted to restore determinism to physics. Indeed Schrödinger's wave equation predicts a perfectly deterministic time evolution of the wave function. But what is evolving deterministically is only abstract probabilities. And these probabilities are confirmed only in the statistics of large numbers of identically prepared experiments. Randomness enters only when a measurement is made and the wave function "collapses" into one of the possible states of the system.
Schrödinger devised a variation in which the random radioactive decay would kill a cat. Observers could not know what happened until the box is opened.
The details of the tasteless experiment include:
This thought experiment is widely misunderstood. It was meant (by both Einstein and Schrödinger) to suggest that quantum mechanics describes the simultaneous (and obviously contradictory) existence of a live and dead cat. Here is the famous diagram with a cat both dead and alive.
What's wrong with this picture?
Quantum mechanics claims only that the time evolution of the Schrödinger wave functions for the probability amplitudes of nuclear decay accurately predict the proportion of nuclear decays that will occur in a given time interval.
(Classical) probabilities (no interference between terms) simply predict the number of live and dead cats that will be observed in a large number of identical experiments.
More specifically, quantum mechanics provides us with the accurate prediction that if this experiment is repeated many times (the SPCA would disapprove), half of the experiments will result in dead cats.
Quantum "probability amplitudes" do allow interference between the possible states of a quantum object, but not between macroscopic objects like live and dead cats Note that this is a problem in epistemology. What knowledge is it that quantum physics provides? If we open the box at the time T when there is a 50% probability of an alpha particle emission, the most a physicist can know is that there is a 50% chance that the radioactive decay will have occurred and the cat will be observed as dead or dying. If the box were opened earlier, say at T/2, there is only a 25% chance that the cat has died. Schrödinger's superposition of live and dead cats would look like this.
If the box were opened later, say at 2T, there is only a 25% chance that the cat is still alive. Quantum mechanics is giving us only statistical information - knowledge about probabilities.
Schrödinger is simply wrong that the mixture of nuclear wave functions that accurately describes decay can be magnified to the macroscopic world to describe a similar mixture of live cat and dead cat wave functions and the simultaneous existence of live and dead cats. The kind of coherent superposition of states needed to describe an atomic system as in a linear combination of states (see Paul Dirac's explanation of superposition using three polarizers) does not describe macroscopic systems. Instead of a linear combination of pure quantum states, with quantum interference between the states, i.e.,
| Cat > = ( 1/√2) | Live > + ( 1/√2) | Dead >,
quantum mechanics tells us only that there is 50% chance of finding the cat in either the live or dead state, i.e.,
Cats = (1/2) Live + (1/2) Dead.
Just as in the quantum case, this probability prediction is confirmed by the statistics of repeated identical experiments, but no interference between these states is seen. What do exist simultaneously in the macroscopic world are genuine alternative possibilities for future events. There is the real possibility of a live or dead cat in any particular experiment. Which one is found is irreducibly random, unpredictable, and a matter of pure chance. Genuine alternative possibilities is what bothered physicists like Einstein, Schrödinger, and Max Planck who wanted a return to deterministic physics. It also bothers determinist and compatibilist philosophers who have what William James calls an "antipathy to chance." Ironically, it was Einstein himself, in 1916, who discovered the existence of irreducible chance, in the elementary interactions of matter and radiation. Until the information comes into existence, the future is indeterministic. Once information is macroscopically encoded, the past is determined.
How does information physics resolve the paradox?
As soon as the alpha particle sets off the avalanche of electrons in the Geiger counter (an irreversible event with a significant entropy increase), new information is created in the world.
For example, a simple pen-chart recorder attached to the Geiger counter could record the time of decay, which a human observer could read at any later time. Notice that, as usual in information creation, the energy expended by a recorder increases the entropy more than the increased information decreases it, thus satisfying the second law of thermodynamics.
Even without a mechanical recorder, the cat's death sets in motion biological processes that constitute an equivalent, if gruesome, recording. When a dead cat is the result, a sophisticated autopsy can provide an approximate time of death, because the cat's body is acting as an event recorder. There never is a superposition (in the sense of the simultaneous existence) of live and dead cats. The paradox points clearly to the Information Philosophy solution to the problem of measurement. Human observers are not required to make measurements. In this case, the cat is the observer. In most physics measurements, the new information is captured by apparatus well before any physicist has a chance to read any dials or pointers that indicate what happened. Indeed, in today's high-energy particle interaction experiments, the data may be captured but not fully analyzed until many days or even months of computer processing establishes what was observed. In this case, the experimental apparatus is the observer. And, in general, the universe is its own observer, able to record (and sometimes preserve) the information created.
The basic assumption made in Schrödinger's cat thought experiments is that the deterministic Schrödinger equation describing a microscopic superposition of decayed and non-decayed radioactive nuclei evolves deterministically into a macroscopic superposition of live and dead cats. But since the essence of a "measurement" is an interaction with another system (quantum or classical) that creates information to be seen (later) by an observer, the interaction between the nucleus and the cat is more than enough to collapse the wave function. Calculating the probabilities for that collapse allows us to estimate the probabilities of live and dead cats. These are probabilities, not probability amplitudes. They do not interfere with one another. After the interaction, they are not in a superposition of states. We always have either a live cat or a dead cat, just as we always observe a complete photon after a polarization measurement and not a superposition of photon states, as P.A.M.Dirac explains so simply and clearly.
According to quantum mechanics the result of this experiment will be that sometimes one will find a whole photon, of energy equal to the energy of the incident photon, on the back side and other times one will find nothing. When one finds a whole photon, it will be polarized perpendicular to the optic axis. One will never find only a part of a photon on the back side. If one repeats the experiment a large number of times, one will find the photon on the back side in a fraction sin^{2}α of the total number of times.
Decoherence and the Lack of Macroscopic Superpositions
Despite the claims of decoherence theorists, microscopic superpositions of quantum states do not allow us to "see" a system in two different states. Quantum mechanics simply predicts a significant probability of the system being found in these different states. Thus it is no surprise that we do not see macroscopic "superpositions of live and dead cats" at the same time. What does exist at any given time is the probabilities of the two states (in the macroscopic world) and the probability amplitude of the two states (which can coherently interfere with one another) in the microscopic world.
Decoherence theorists claim that they explain the "mysterious" non-appearance of macroscopic superpositions of states. But quantum mechanics does not predict such states, despite the popular idea of macroscopic superposition of live and dead cats. |