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 Belsham Henri Bergson George Berkeley Isaiah Berlin Richard J. Bernstein Bernard Berofsky Robert Bishop Max Black Susanne Bobzien Emil du BoisReymond 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 Heraclitus 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 C. Lloyd Morgan John Locke Michael Lockwood E. Jonathan Lowe John R. Lucas Lucretius Alasdair MacIntyre 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 Thomas Nagel Otto Neurath Friedrich Nietzsche John Norton P.H.NowellSmith Robert Nozick William of Ockham Timothy O'Connor Parmenides David F. 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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 Walter Baade 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 JeanPierre Changeux Arthur Holly Compton John Conway John Cramer E. P. Culverwell Charles Darwin Richard Dawkins Terrence Deacon Lüder Deecke 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 Philipp Frank 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 JohnDylan Haynes Donald Hebb Martin Heisenberg Werner Heisenberg John Herschel Art Hobson Jesper Hoffmeyer E. T. Jaynes William Stanley Jevons Roman Jakobson Pascual Jordan Ruth E. Kastner Stuart Kauffman Martin J. Klein Simon Kochen Hans Kornhuber Stephen Kosslyn Ladislav Kovàč Rolf Landauer Alfred Landé PierreSimon Laplace David Layzer Benjamin Libet Seth Lloyd Hendrik Lorentz Josef Loschmidt Ernst Mach Donald MacKay Henry Margenau James Clerk Maxwell Ernst Mayr John McCarthy Ulrich Mohrhoff Jacques Monod Emmy Noether Abraham Pais 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 John Stachel Henry Stapp Tom Stonier Antoine Suarez Leo Szilard Max Tegmark William Thomson (Kelvin) Peter Tse Vlatko Vedral 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 Konrad Zuse Fritz Zwicky Presentations Biosemiotics Free Will Mental Causation James Symposium 
The TwoSlit Experiment and "One Mystery" of Quantum Mechanics
Richard Feynman said that the twoslit experiment contains the "one mystery" of quantum mechanics.
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'. We will show that the (one) mystery of quantum mechanics is how mere "probabilities" can causally control (statistically) the positions of material particles  how immaterial information can affect the material world. This remains a deep metaphysical mystery. The twoslit experiment was until recent years for the most part a thought experiment, since it is difficult to build an inexpensive demonstration, but its predictions have been verified in many ways since the 1960's, primarily with electrons. Recently, extremely sensitive CCDs used in photography have been used to collect singlephoton events, establishing experimentally everything that Albert Einstein imagined, merely by thinking about it, as early as 1905. Light at the yellow dot slowly disappears as the second slit opens! Adding light causes some light to disappear. The twoslit experiment demonstrates better than any other experiment that a quantum wave function is a probability amplitude that can interfere with itself, producing places where the probability (the square of the absolute value of the complex probability amplitude) of finding a quantum particle is actually zero. Perhaps the most nonintuitive aspect of the twoslit experiment is when we first note the pattern of light on the screen with just one slit open, then open the second slit  admitting more light into the experiment, but observe that some places on the screen where there was visible light, have now gone dark! And this happens even when we are admitting only one particle of light at a time. Light waves are often compared to water waves, as are quantum probability waves, but this latter is a serious error. Water waves and light waves (as well as sound waves) contain something substantial like matter or energy. But quantum waves are just abstract information  mathematical possibilities.
Young's 1802 drawing of wave interference
Water waves in a pond Dr. Quantum and the twoslit experiment The twoslit experiment also demonstrates the famous "collapse" of the wave function or "reduction" of the wave packet, which show an inherent probabilistic element in quantum mechanics that is irreducibly ontological and nothing like the epistemological indeterminacy (human ignorance) in classical statistical physics. Note that the probability amplitude is pure information. It is neither matter nor energy. When a wave function "collapses" or "goes through both slits" in this dazzling experiment, nothing material is traveling faster than the speed of light or going through both slits. We argue that the particle of matter or energy always goes through just one slit, although the popular Copenhagen interpretation of physics claims we cannot know the particle path, that a path does not even exist until we make a measurement, that the particle may be in more than one place at the same time, and other similar nonsense that deeply bothered Einstein as he hoped for an "objective reality." For example, a large number of panpsychists, some philosophers, some scientists, believe that the mind of a conscious observer is needed to cause the collapse of the wave function. There is something similar in the EinsteinPodolskyRosen thought experiments, where measurement of one particle transmits nothing physical (matter or energy) to the other "entangled" particle. We shall show that it is conservation of angular momentum or of spin that makes the state of the coherently entangled second particle determinate, however far away it might be. In the twoslit experiment, just as in the Dirac Three Polarizers experiment, the critical case to consider is just one photon or electron at a time in the experiment. With one particle at a time (whether photon or electron), the quantum object is mistakenly described as interfering with itself, when interference is never seen in a single event. It only shows up in the statistics of large numbers of experiments. Indeed, even in the oneslit case, interference fringes are visible when large numbers of particles are present, although this is rarely described in the context of quantum mysteries.
It is the fundamental relation between a particle and the associated wave that controls its probable locations that raises the "local reality" question first seen in 1905 and described in 1909 by Albert Einstein. Thirty years later, the EPR paper and Erwin Schrödinger's insights into the wave function of two entangled particles, first convinced physicists that there was a deep problem . It was not for another thirty years that John Stewart Bell in 1964 imagined an experimental test that could confirm or deny quantum mechanics. Ironically, the goal of Bell's "theorem" was to invalidate the nonintuitive aspects of quantum mechanics and restore Einstein's hope for a more deterministic picture of an "objective reality" at, or perhaps even underlying below, the microscopic level of quantum physics. At about the same time, in his famous Lectures on Physics at Cal Tech and the Messenger Lectures at Cornell, Richard Feynman described the twoslit experiment as demonstrating what he claimed is the "only mystery" of quantum mechanics. We can thus begin the discussion of the twoslit experiment with a section from Feynman's sixth Messenger lecture entitled "Probability and Uncertainty." We provide the complete video and text of the lecture on this page, and a version starting with Feynman's provocative statement that "no one understands quantum mechanics" below.
How, Feynman asks, can the particle go through both slits? We will see that the thing that goes through both slits is only immaterial information  the probability amplitude wave function. The particle always goes through a single slit. A particle cannot be divided and in two places at the same time. It is the wave function that interferes with itself. And the highly localized particle can not be identified with the wave widely distributed in space and determined by the boundary conditions of the measuring apparatus. The immaterial wave function exerts an causal influence over the particles, one that we can jusitifiably call "mysterious." It results in the statistics of many experiments agreeing with the quantum mechanical predictions with increasing accuracy as we increase the number of identical experiments. It is this "influence," no ordinary "force," that is Feynman's "only mystery" in quantum mechanics. Let's look first at the oneslit case. We prepare a slit that is about the same size as the wavelength of the light in order to see the Fraunhofer diffraction effect most clearly. Parallel waves from a distant source fall on the slit from below. The diagram shows that the wave from the left edge of the slit interferes with the one from the right edge. If the slit width is d and the photon wavelength is λ, at an angle α ≈ λ/2d there will be destructive interference. At an angle α ≈ λ/d, there is constructive interference (which shows up as the fan out of lightening patterns in the interfering waves in the illustration).
The height of the function or curve on the top of the diagram is proportional to the number of photons falling along the screen. At first they are individual pixels in a CCD or grains in a photographic plate, but over time and very large numbers of photons they appear as the continuous gradients of light in the band below (we represent this intensity as the height of the function).
Now what happens if we add a second slit? Perhaps we should start by showing what happens if we run the experiment with the first slit open for a time, and then with the second slit open for an equal time. In this case, the height of the intensity curve is the sum of the curves for the individual slits.
But that is not the intensity curve we get when the two slits are open at the same time! Instead, we see many new interference fringes with much narrower width angles α ≈ λ/D, where D is the distance between the two slits. Note that the overall envelope of the curve is similar to that of one big slit of width D. And also note many more lightening fanouts in the overlapping waves.
Remembering that the doubleslit interference appears even if only one particle at a time is incident on the two slits, we see why many say that the particle interferes with itself. But it is the wave function alone that is interfering with itself. Whichever slit the particle goes through, the interference pattern is what it is because the two slits are open.
Why interference patterns show up when both slits are open, even when particles go through just one slit, though we cannot know which slit or we lose the interference
Now let's see what happens if we animate the opening and closing of the righthand slit.
Collapse of the Wave Function
But how do we interpret the notion of the "collapse" of the wave function? At the moments just before a particle is detected at the CCD or photographic plate, there is a finite nonzero probability that the photon could be detected anywhere that the modulus (complex conjugate squared) of the probability amplitude wave function has a nonzero value. If our experiment were physically very large (and it is indeed large compared to the atomic scale), we can say that the finite probability of detecting (potentially measuring) the particle at position x_{1} on the screen "collapses" (goes to zero) and reappears as part of the unit probability (certainty) that the particle is at x_{2}, where it is actually measured. Since the collapse to zero of the probability at x_{1} is instantaneous with the measurement at x_{2}, critics of quantum theory like to say that something traveled faster than the speed of light. This is most clear in the nonlocality and entanglement aspects of the EinsteinPodolskyRosen experiment. But the sum of all the probabilities of measuring anywhere on the screen is not a physical quantity, it is only immaterial information that "collapses" to a point.
Here is what happens to the probability amplitude wave function (the blue waves) when the particle is detected at the screen (either a photographic plate or CCD) in the second interference fringe to the right (red spot). The probability simply disappears instantly.
Animation of a wave function collapsing  click to restart
History
The first suggestion of two possible directions through a slit, one of which disappears ("collapses?") when the other is realized (implying a mysterious "nonlocal" correlation between the directions), was made by Albert Einstein at the 1927 Solvay conference on "Electrons and Photons." Niels Bohr remembered the occasion with a somewhat confusing description.
Here is his 1949 recollection:
At the general discussion in Como, we all missed the presence of Einstein, but soon after, in October 1927, I had the opportunity to meet him in Brussels at the Fifth Physical Conference of the Solvay Institute, which was devoted to the theme "Electrons and Photons." Although Bohr seems to have missed Einstein's point completely, Werner Heisenberg at least came to explain it well. In his 1930 lectures at the University of Chicago, Heisenberg presented a critique of both particle and wave pictures, including a new example of nonlocality that Einstein had apparently developed since 1927. It includes Einstein's concern about "actionatadistance" that might violate his principle of relativity, and anticipates the EinsteinPodolskyRosen paradox. Heisenberg wrote: In relation to these considerations, one other idealized experiment (due to Einstein) may be considered. We imagine a photon which is represented by a wave packet built up out of Maxwell waves. It will thus have a certain spatial extension and also a certain range of frequency. By reflection at a semitransparent mirror, it is possible to decompose it into two parts, a reflected and a transmitted packet. There is then a definite probability for finding the photon either in one part or in the other part of the divided wave packet. After a sufficient time the two parts will be separated by any distance desired; now if an experiment yields the result that the photon is, say, in the reflected part of the packet, then the probability of finding the photon in the other part of the packet immediately becomes zero. The experiment at the position of the reflected packet thus exerts a kind of action (reduction of the wave packet) at the distant point occupied by the transmitted packet, and one sees that this action is propagated with a velocity greater than that of light. However, it is also obvious that this kind of action can never be utilized for the transmission of signals so that it is not in conflict with the postulates of the theory of relativity. Clearly the "kind of action (reduction of the wave packet)" described by Heisenberg is the same "mysterious" influence that the wave function has over the places that the particle will be found statistically in a large number of experiments, including our canonical "mystery," the twoslit experiment. Apart from the statistical information in the wave function, quantum mechanics gives us only vague and uncertain information about any individual particle. This is the true source of Heisenberg's uncertainty principle. It is the reason that Einstein correctly describes quantum mechanics as "incomplete." Quantum mechanics does not prove that the particle actually has no position at each instant and a path that conserves its momentum, spin, and other conserved properties. In Einstein's view of "objective reality," the particle has those properties, even if quantum mechanics prevents us from knowing them  without a measurement that destroys their interference capabilities or "decoheres" them.
Some Other Animations of the TwoSlit Experiment
None of these animations, viewed many millions of times, can explain why a particle entering one slit when both are open exhibits the properties of waves characteristic of two open slits. It remains Feynman's "one mystery" of quantum mechanics.
PBS Digital Studios
Veritasium
Veritasium
Dr Quantum
WaveParticle Duality Animation
One good thing in this animation is that it initially shows only particles firing at the slits. This is important historically because Isaac Newton thought that light was a stream of particles traveling along a light ray. He solved many problems in optics by tracing light rays through lenses. But without a clear verbal explanation it is hard to follow. For Teachers
For Scholars
