Double-slit experiment - Knowledge (XXG)

1241: 2642:(measuring device) and the object being observed (physically interacted with), not any absolute property possessed by the object. In the case of an electron, if it is initially "observed" at a particular slit, then the observer–particle (photon–electron) interaction includes information about the electron's position. This partially constrains the particle's eventual location at the screen. If it is "observed" (measured with a photon) not at a particular slit but rather at the screen, then there is no "which path" information as part of the interaction, so the electron's "observed" position on the screen is determined strictly by its probability function. This makes the resulting pattern on the screen the same as if each individual electron had passed through both slits. 1486:. If one sets polarizers before each slit with their axes orthogonal to each other, the interference pattern will be eliminated. The polarizers can be considered as introducing which-path information to each beam. Introducing a third polarizer in front of the detector with an axis of 45° relative to the other polarizers "erases" this information, allowing the interference pattern to reappear. This can also be accounted for by considering the light to be a classical wave, and also when using circular polarizers and single photons. Implementations of the polarizers using 1419:

probability zero. It is interesting to consider what would happen if the photon were definitely in either of paths between the beam splitters. This can be accomplished by blocking one of the paths, or equivalently by detecting the presence of a photon there. In both cases there will be no interference between the paths anymore, and both photodetectors will be hit with probability 1/2. From this we can conclude that the photon does not take one path or another after the first beam splitter, but rather that it is in a genuine quantum superposition of the two paths.

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physicists who played an important role in the establishment of quantum mechanics, and who were collaborators of Bohr's at his Institute or took part in the discussions during the crucial years. On closer inspection, one sees quite easily that these ideas are divergent in detail and that in particular the views of Bohr, the spiritual leader of the school, form a separate entity which can now be understood only by a thorough study of as many as possible of the relevant publications by Bohr himself.

1463: 1230: 1021:, producing bright and dark bands on the screen – a result that would not be expected if light consisted of classical particles. However, the light is always found to be absorbed at the screen at discrete points, as individual particles (not waves); the interference pattern appears via the varying density of these particle hits on the screen. Furthermore, versions of the experiment that include detectors at the slits find that each detected 1633:, changing it from transparent to reflective for around 200 femtoseconds long where a subsequent probe laser beam hitting the ITO screen would then see this temporary change in optical properties as a slit in time and two of them as a double slit with a phase difference adding up destructively or constructively on each frequency component resulting in an interference pattern. Similar results have been obtained classically on water waves. 1650: 1564:

vacuum. The interference pattern between the two electron waves could then be observed. In 2017, researchers performed the double-slit experiment using light-induced field electron emitters. With this technique, emission sites can be optically selected on a scale of ten nanometers. By selectively deactivating (closing) one of the two emissions (slits), researchers were able to show that the interference pattern disappeared.

8096: 8070: 2602:, and others. The term "Copenhagen interpretation" was apparently coined by Heisenberg during the 1950s to refer to ideas developed in the 1925–1927 period, glossing over his disagreements with Bohr. Consequently, there is no definitive historical statement of what the interpretation entails. Features common across versions of the Copenhagen interpretation include the idea that quantum mechanics is intrinsically 1077: 1110: 2194: 2622:

probability distribution. The particles are discrete and identical; many are needed to build up the full interference pattern. The results from some of the which-way experiments are described as observations of complementarity: modifying the experiment to monitor the slit suppresses the interference pattern. Other which-way experiments make no mention of complementarity in their analysis.

59: 8132: 2730: 45: 8156: 1658: 8108: 8144: 1513:. Weak measurement followed by post-selection did not allow simultaneous position and momentum measurements for each individual particle, but rather allowed measurement of the average trajectory of the particles that arrived at different positions. In other words, the experimenters were creating a statistical map of the full trajectory landscape. 8120: 2678:

slit de Broglie-Bohm trajectories were first calculated by Chris Dewdney while working with Chris Philippidis and Basil Hiley at Birkbeck College (London). The de Broglie-Bohm theory produces the same statistical results as standard quantum mechanics, but dispenses with many of its conceptual difficulties by adding complexity through an

2618:. A particular experiment can demonstrate particle behavior (passing through a definite slit) or wave behavior (interference), but not both at the same time. Copenhagen-type interpretations hold that quantum descriptions are objective, in that they are independent of physicists' personal beliefs and other arbitrary mental factors. 1440:), technically feasible realizations of this experiment were not proposed until the 1970s. (Naive implementations of the textbook thought experiment are not possible because photons cannot be detected without absorbing the photon.) Currently, multiple experiments have been performed illustrating various aspects of complementarity. 2677:

states that particles also have precise locations at all times, and that their velocities are defined by the wave-function. So while a single particle will travel through one particular slit in the double-slit experiment, the so-called "pilot wave" that influences it will travel through both. The two

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argues that the way to understand the double-slit experiment is that in each universe the particle travels through a specific slit, but its motion is affected by the interference with particles in other universes. This creates the observable fringes. David Wallace, another advocate of the many-worlds

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have been developed that can recreate various aspects of quantum mechanical systems, including single-particle interference through a double-slit. A silicone oil droplet, bouncing along the surface of a liquid, self-propels via resonant interactions with its own wave field. The droplet gently sloshes

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In a highly publicized experiment in 2012, researchers claimed to have identified the path each particle had taken without any adverse effects at all on the interference pattern generated by the particles. In order to do this, they used a setup such that particles coming to the screen were not from a

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An important version of this experiment involves single particle detection. Illuminating the double-slit with a low intensity results in single particles being detected as white dots on the screen. Remarkably, however, an interference pattern emerges when these particles are allowed to build up one

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particles, and these particles were fired in a straight line through a slit and allowed to strike a screen on the other side, we would expect to see a pattern corresponding to the size and shape of the slit. However, when this "single-slit experiment" is actually performed, the pattern on the screen

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The experiment belongs to a general class of "double path" experiments, in which a wave is split into two separate waves (the wave is typically made of many photons and better referred to as a wave front, not to be confused with the wave properties of the individual photon) that later combine into a

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Frabboni, Stefano; Gabrielli, Alessandro; Carlo Gazzadi, Gian; Giorgi, Filippo; Matteucci, Giorgio; Pozzi, Giulio; Cesari, Nicola Semprini; Villa, Mauro; Zoccoli, Antonio (May 2012). "The Young-Feynman two-slits experiment with single electrons: Build-up of the interference pattern and arrival-time

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equation, which implies that as the plane of observation gets closer to the plane in which the slits are located, the diffraction patterns associated with each slit decrease in size, so that the area in which interference occurs is reduced, and may vanish altogether when there is no overlap in the

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The Mach–Zehnder interferometer can be seen as a simplified version of the double-slit experiment. Instead of propagating through free space after the two slits, and hitting any position in an extended screen, in the interferometer the photons can only propagate via two paths, and hit two discrete

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If one illuminates two parallel slits, the light from the two slits again interferes. Here the interference is a more pronounced pattern with a series of alternating light and dark bands. The width of the bands is a property of the frequency of the illuminating light. (See the bottom photograph to

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Numerical simulation of the double-slit experiment with electrons. Figure on the left: evolution (from left to right) of the intensity of the electron beam at the exit of the slits (left) up to the detection screen located 10 cm after the slits (right). The higher the intensity, the more the

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Where d is the distance between the two slits. When the two waves are in phase, i.e. the path difference is equal to an integral number of wavelengths, the summed amplitude, and therefore the summed intensity is maximum, and when they are in anti-phase, i.e. the path difference is equal to half a

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In the double-slit experiment, the two slits are illuminated by the quasi-monochromatic light of a single laser. If the width of the slits is small enough (much less than the wavelength of the laser light), the slits diffract the light into cylindrical waves. These two cylindrical wavefronts are

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In 2002, an electron field emission source was used to demonstrate the double-slit experiment. In this experiment, a coherent electron wave was emitted from two closely located emission sites on the needle apex, which acted as double slits, splitting the wave into two coherent electron waves in a

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In 2012, Stefano Frabboni and co-workers sent single electrons onto nanofabricated slits (about 100 nm wide) and, by detecting the transmitted electrons with a single-electron detector, they could show the build-up of a double-slit interference pattern. Many related experiments involving the

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performed a related experiment using single electrons from a coherent source and a biprism beam splitter, showing the statistical nature of the buildup of the interference pattern, as predicted by quantum theory. In 2002, the single-electron version of the experiment was voted "the most beautiful

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The results from the most basic double slit experiment, the observation of an interference pattern, is explained by wave interference from the two paths to the screen from each of the two slits. The single-particle results show that the waves are probability amplitudes which square to produce a

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It was shown experimentally in 1972 that in a double-slit system where only one slit was open at any time, interference was nonetheless observed provided the path difference was such that the detected photon could have come from either slit. The experimental conditions were such that the photon

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In 2005, E. R. Eliel presented an experimental and theoretical study of the optical transmission of a thin metal screen perforated by two subwavelength slits, separated by many optical wavelengths. The total intensity of the far-field double-slit pattern is shown to be reduced or enhanced as a

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in which the light is spread out. The smaller the slit, the greater the angle of spread. The top portion of the image shows the central portion of the pattern formed when a red laser illuminates a slit and, if one looks carefully, two faint side bands. More bands can be seen with a more highly

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Copenhagen interpretation as a unified and consistent logical structure. Terms such as "Copenhagen interpretation" or "Copenhagen school" are based on the history of the development of quantum mechanics; they form a simplified and often convenient way of referring to the ideas of a number of

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A photon emitted by the laser hits the first beam splitter and is then in a superposition between the two possible paths. In the second beam splitter these paths interfere, causing the photon to hit the photodetector on the right with probability one, and the photodetector on the bottom with

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superimposed, and the amplitude, and therefore the intensity, at any point in the combined wavefronts depends on both the magnitude and the phase of the two wavefronts. The difference in phase between the two waves is determined by the difference in the distance travelled by the two waves.

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Behaviors mimicked via this hydrodynamic pilot-wave system include quantum single particle diffraction, tunneling, quantized orbits, orbital level splitting, spin, and multimodal statistics. It is also possible to infer uncertainty relations and exclusion principles. Videos are available

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While there is no doubt that Young's demonstration of optical interference, using sunlight, pinholes and cards, played a vital part in the acceptance of the wave theory of light, there is some question as to whether he ever actually performed a double-slit interference experiment.

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Feynman was fond of saying that all of quantum mechanics can be gleaned from carefully thinking through the implications of this single experiment. He also proposed (as a thought experiment) that if detectors were placed before each slit, the interference pattern would disappear.

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However, more complicated systems that involve two or more particles in superposition are not amenable to such a simple, classically intuitive explanation. Accordingly, no hydrodynamic analog of entanglement has been developed. Nevertheless, optical analogs are possible.

5601:-dimensional configuration space or 'phase space'. It is difficult to visualize a reality comprising imaginary functions in an abstract, multi-dimensional space. No difficulty arises, however, if the imaginary functions are not to be given a real interpretation.") 1642: 1602:, causes it to exhibit behaviors previously thought to be peculiar to elementary particles – including behaviors customarily taken as evidence that elementary particles are spread through space like waves, without any specific location, until they are measured. 1059:

The double-slit experiment (and its variations) has become a classic for its clarity in expressing the central puzzles of quantum mechanics. Because it demonstrates the fundamental limitation of the ability of the observer to predict experimental results,

1579:, using new instruments that allowed control of the transmission of the two slits and the monitoring of single-electron detection events. Electrons were fired by an electron gun and passed through one or two slits of 62 nm wide × 4 μm tall. 1246:

Experimental electron double slit diffraction pattern. Across the middle of the image at the top, the intensity alternates from high to low, showing interference in the signal from the two slits. Bottom: movie of the pattern being built up dot-by-dot.

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An experiment performed in 1987 produced results that demonstrated that partial information could be obtained regarding which path a particle had taken without destroying the interference altogether. This "wave-particle trade-off" takes form of an

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of quantum mechanics provided by Feynman. The path integral formulation replaces the classical notion of a single, unique trajectory for a system, with a sum over all possible trajectories. The trajectories are added together by using

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In 1999, a quantum interference experiment (using a diffraction grating, rather than two slits) was successfully performed with buckyball molecules (each of which comprises 60 carbon atoms). A buckyball is large enough (diameter about

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principle that photons can behave as either particles or waves, but cannot be observed as both at the same time. Despite the importance of this thought experiment in the history of quantum mechanics (for example, see the discussion on

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It seems that light passes through one slit or the other in the form of photons if we set up an experiment to detect which slit the photon passes, but passes through both slits in the form of a wave if we perform an interference

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demonstrated that under different circumstances, light can behave as if it is composed of discrete particles. These seemingly contradictory discoveries made it necessary to go beyond classical physics and take into account the

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beam, illuminates a plate pierced by two parallel slits, and the light passing through the slits is observed on a screen behind the plate. The wave nature of light causes the light waves passing through the two slits to

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The experiment can be done with entities much larger than electrons and photons, although it becomes more difficult as size increases. The largest entities for which the double-slit experiment has been performed were

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in 1909, by reducing the level of incident light until photon emission/absorption events were mostly non-overlapping. A slit interference experiment was not performed with anything other than light until 1961, when

1040:, are found to exhibit the same behavior when fired towards a double slit. Additionally, the detection of individual discrete impacts is observed to be inherently probabilistic, which is inexplicable using 1265:

of detecting the particle at a specific place on the screen giving a statistical interference pattern. This phenomenon has been shown to occur with photons, electrons, atoms, and even some molecules: with

1121:(1773–1829) first demonstrated this phenomenon, it indicated that light consists of waves, as the distribution of brightness can be explained by the alternately additive and subtractive interference of 7236:

Movie showing single electron events build up to form an interference pattern in double-slit experiments. Several versions with and without narration (File size = 3.6 to 10.4 MB) (Movie Length = 1m 8s)

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In 2013, a quantum interference experiment (using diffraction gratings, rather than two slits) was successfully performed with molecules that each comprised 810 atoms (whose total mass was over 10,000

1084:(the faint spots on either side of the main band) forms due to the nonzero width of the slit. This diffraction pattern is also seen in the double-slit image, but with many smaller interference fringes. 2320: 1825: 3314:...if in a double-slit experiment, the detectors which register outcoming photons are placed immediately behind the diaphragm with two slits: A photon is registered in one detector, not in both... 1998: 3460:

Yaakov Y. Fein; Philipp Geyer; Patrick Zwick; Filip Kiałka; Sebastian Pedalino; Marcel Mayor; Stefan Gerlich; Markus Arndt (September 2019). "Quantum superposition of molecules beyond 25 kDa".

4701:"However, the 'wave-particle trade-off is now expressed in terms of an inequality, known as Englert-Greenberger duality or simply wave-particle duality relation". See also ref 24 in this work. 1261:, which states that all matter exhibits both wave and particle properties: The particle is measured as a single pulse at a single position, while the modulus squared of the wave describes the 1431:

predicts that if particle detectors are positioned at the slits, showing through which slit a photon goes, the interference pattern will disappear. This which-way experiment illustrates the

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and his research student Alexander Reid demonstrated that electrons show the same behavior, which was later extended to atoms and molecules. Thomas Young's experiment with light was part of

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interpretation, writes that in the familiar setup of the double-slit experiment the two paths are not sufficiently separated for a description in terms of parallel universes to make sense.

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observed by the double-slit experiment. Feynman stressed that his formulation is merely a mathematical description, not an attempt to describe a real process that we can measure.

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A simulation that runs in Mathematica Player, in which the number of quantum particles, the frequency of the particles, and the slit separation can be independently varied

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the liquid with every bounce. At the same time, ripples from past bounces affect its course. The droplet's interaction with its own ripples, which form what is known as a

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point-like source, but from a source with two intensity maxima. However, commentators such as Svensson have pointed out that there is in fact no conflict between the

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to the action along each path. The differences in the cumulative action along the different paths (and thus the relative phases of the contributions) produces the

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demonstrate that extracting "which path" information after a particle passes through the slits can seem to retroactively alter its previous behavior at the slits.

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Camilleri, K.; Schlosshauer, M. (2015). "Niels Bohr as Philosopher of Experiment: Does Decoherence Theory Challenge Bohr's Doctrine of Classical Concepts?".

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Arndt, Markus; Nairz, Olaf; Vos-Andreae, Julian; Keller, Claudia; Van Der Zouw, Gerbrand; Zeilinger, Anton (1999). "Wave–particle duality of C60 molecules".

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is one such model; it states that each point on a wavefront generates a secondary wavelet, and that the disturbance at any subsequent point can be found by

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Mermin, N. David (1 January 2017). "Why QBism Is Not the Copenhagen Interpretation and What John Bell Might Have Thought of It". In Bertlmann, Reinhold;

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demonstrate that particles do not form the interference pattern if one detects which slit they pass through. These results demonstrate the principle of

1696:), the phase difference can be found using the geometry shown in the figure below right. The path difference between two waves travelling at an angle 3037:

Eibenberger, Sandra; et al. (2013). "Matter-wave interference with particles selected from a molecular library with masses exceeding 10000 amu".

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Bartell, L. (1980). "Complementarity in the double-slit experiment: On simple realizable systems for observing intermediate particle-wave behavior".

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color is light blue – Figure in the center: impacts of the electrons observed on the screen – Figure on the right: intensity of the electrons in the

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experiments demonstrate that wave behavior can be restored by erasing or otherwise making permanently unavailable the "which path" information.

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approximation (on the screen). Numerical data from Claus Jönsson's experiment (1961). Photons, atoms and molecules follow a similar evolution.

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A diagram of Wheeler's delayed choice experiment, showing the principle of determining the path of the photon after it passes through the slit

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performed it with coherent electron beams and multiple slits. In 1974, the Italian physicists Pier Giorgio Merli, Gian Franco Missiroli, and

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Sillitto, R.M.; Wykes, Catherine (1972). "An interference experiment with light beams modulated in anti-phase by an electro-optic shutter".

1522: 1125:. Young's experiment, performed in the early 1800s, played a crucial role in the understanding of the wave theory of light, vanquishing the 7591: 6404:(February 2015). "Does it Make Sense to Speak of Self-Locating Uncertainty in the Universal Wave Function? Remarks on Sebens and Carroll". 6191: 2565: 581: 7241:

Freeview video 'Electron Waves Unveil the Microcosmos' A Royal Institution Discourse by Akira Tonomura provided by the Vega Science Trust

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Yanagisawa, Hirofumi; Ciappina, Marcelo; Hafner, Christian; Schötz, Johannes; Osterwalder, Jürg; Kling, Matthias F. (4 October 2017).

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100 trajectories guided by the wave function. In De Broglie-Bohm's theory, a particle is represented, at any time, by a wave function

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coherent interference have been performed; they are the basis of modern electron diffraction, microscopy and high resolution imaging.

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Nairz, Olaf; Brezger, Björn; Arndt, Markus; Zeilinger, Anton (2001). "Diffraction of Complex Molecules by Structures Made of Light".

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function represents the fine structure, and the coarser structure represents diffraction by the individual slits as described by the

1378:) in 2011, and with molecules of up to 2000 atoms in 2019. In addition interference patterns built up from single particles, up to 4 7337: 7300: 6282: 6200: 4151: 3793: 2165:

function in this equation, and the second figure shows the combined intensity of the light diffracted from the two slits, where the

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photodetectors. This makes it possible to describe it via simple linear algebra in dimension 2, rather than differential equations.

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wavelength, one and a half wavelengths, etc., then the two waves cancel and the summed intensity is zero. This effect is known as

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Oshima, C.; Mastuda, K.; Kona, T.; Mogami, Y.; Komaki, M.; Murata, Y.; Yamashita, T.; Kuzumaki, T.; Horiike, Y. (4 January 2002).

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as well as other complicated combinations of de Broglie and Compton waves. To date there is no evidence that these are useful.

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This is illustrated in the figure above, where the first pattern is the diffraction pattern of a single slit, given by the

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Svensson, Bengt E. Y. (2013). "Pedagogical Review of Quantum Measurement Theory with an Emphasis on Weak Measurements".

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Website with the movie and other information from the first single electron experiment by Merli, Missiroli, and Pozzi.

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Niels Bohr and the Development of Physics: Essays Dedicated to Niels Bohr on the Occasion of his Seventieth Birthday

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P. Mittelstaedt; A. Prieur; R. Schieder (1987). "Unsharp particle-wave duality in a photon split-beam experiment".

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Chiao, R. Y.; P. G. Kwiat; Steinberg, A. M. (1995). "Quantum non-locality in two-photon experiments at Berkeley".

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provides a detailed treatment of the mathematics of double-slit interference in the context of quantum mechanics.

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Sala, S.; Ariga, A.; Ereditato, A.; Ferragut, R.; Giammarchi, M.; Leone, M.; Pistillo, C.; Scampoli, P. (2019).

2638:, observations such as those in the double-slit experiment result specifically from the interaction between the 1080:

Same double-slit assembly (0.7 mm between slits); in top image, one slit is closed. In the single-slit image, a

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passes through one slit (as would a classical particle), and not through both slits (as would a wave). However,

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In 1967, Pfleegor and Mandel demonstrated two-source interference using two separate lasers as light sources.

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Near-field intensity distribution patterns for plasmonic slits with equal widths (A) and non-equal widths (B).

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demonstrates that light and matter can satisfy the seemingly incongruous classical definitions for both waves

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Merli, P G; Missiroli, G F; Pozzi, G (1976). "On the statistical aspect of electron interference phenomena".

2564:, the double-slit experiment is often used to highlight the differences and similarities between the various 8186: 8033: 7619: 7581: 7545: 5004: 2832: 2686: 2558: 2532: 2325: 2128:{\displaystyle {\begin{aligned}I(\theta )&\propto \cos ^{2}\left~\mathrm {sinc} ^{2}\left\end{aligned}}} 1670: 891: 609: 567: 517: 465: 231: 3604:

Jönsson, Claus (1 August 1961). "Elektroneninterferenzen an mehreren künstlich hergestellten Feinspalten".

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the contributions of the individual wavelets at that point. This summation needs to take into account the

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C.S. Peirce (July 1879). "Note on the Progress of Experiments for Comparing a Wave-length with a Meter".

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a position (center of mass). This is a kind of augmented reality compared to the standard interpretation.

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Mukhopadhyay, P. (1986). "A correlation between the compton wavelength and the de Broglie wavelength".

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D.M. Greenberger and A. Yasin, "Simultaneous wave and particle knowledge in a neutron interferometer",

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relating the visibility of the interference pattern and the distinguishability of the which-way paths.

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A laboratory double-slit assembly; distance between top posts is approximately 2.5 cm (one inch).

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Philippidis, C.; Dewdney, C.; Hiley, B. J. (1979). "Quantum interference and the quantum potential".

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Physics for Scientists and Engineers: Electricity, Magnetism, Light, and Elementary Modern Physics

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Bacot, Vincent; Labousse, Matthieu; Eddi, Antonin; Fink, Mathias; Fort, Emmanuel (November 2016).

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Through Two Doors at Once: The Elegant Experiment That Captures the Enigma of Our Quantum Reality

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Through Two Doors at Once: The Elegant Experiment That Captures the Enigma of Our Quantum Reality

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Steeds, John; Merli, Pier Giorgio; Pozzi, Giulio; Missiroli, GianFranco; Tonomura, Akira (2003).

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A simple do-it-at-home illustration of the quantum eraser phenomenon was given in an article in

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Since that time a number of related experiments have been published, with a little controversy.

5048: 3810: 3549: 3543: 3414::Quantum Mechanics p.1-1 "There is one lucky break, however— electrons behave just like light". 2197:

One of an infinite number of equally likely paths used in the Feynman path integral (see also:

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particles. This ambiguity is considered evidence for the fundamentally probabilistic nature of

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The Elegant Universe: Super Strings, Hidden Dimensions, and the Quest for the Ultimate Theory

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Each path is considered equally likely, and thus contributes the same amount. However, the

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In 2023, an experiment was reported recreating an interference pattern in time by shining a

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explains the pattern as being the result of the interference of light waves from the slit.

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Photons or matter (like electrons) produce an interference pattern when two slits are used

6150: 6075: 5571: 5546: 5527: 5154: 4362: 4149: 3789: 3021: 1133:, which had been the accepted model of light propagation in the 17th and 18th centuries. 64:

Light from a green laser passing through two slits 0.4 mm wide and 0.1 mm apart

7142: 6938: 6895: 6852: 6766: 6558: 6427: 6371: 6233: 5946: 5811: 5753: 5698: 5628: 5589:. New York: Oxford University Press. pp. 76. ("The wavefunction of a system containing 5562: 5492: 5436: 5428: 5383: 5375: 5304: 5235: 5170: 5115: 5064: 5017: 4962: 4900: 4788: 4733: 4625: 4590: 4555: 4378: 4321: 4267: 4209: 4121: 4026: 4018: 3951: 3750: 3711: 3668: 3617: 3505:

first proposed the use of this effect as an artifact-independent reference standard for

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The probability distribution of the outcome is the normalized square of the norm of the

27:

Physics experiment, showing light and matter can be modelled by both waves and particles

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Frabboni, Stefano; Gazzadi, Gian Carlo; Grillo, Vincenzo; Pozzi, Giulio (1 July 2015).

5976: 5645: 5612: 5511: 5476: 5287:; Alkemade, P.F.A.; Blok, H.; Hooft, G.W.; Lenstra, D.; Eliel, E.R. (7 February 2005). 5260: 5209: 4338: 4305: 3968: 3935: 3767: 3734: 3443: 2198: 1476: 901: 861: 841: 811: 791: 741: 707: 557: 547: 340: 72: 17: 6696: 5352:

Bach, Roger; et al. (March 2013). "Controlled double-slit electron diffraction".

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Donati, O; Missiroli, G F; Pozzi, G (1973). "An Experiment on Electron Interference".

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of a light field can be measured—this is proportional to the square of the amplitude.

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Pfleegor, R. L.; Mandel, L. (July 1967). "Interference of Independent Photon Beams".

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In 1991, Carnal and Mlynek performed the classic Young's double slit experiment with

1179: 961: 956: 886: 856: 826: 697: 643: 370: 345: 135: 6925:

Elbaz, Claude (1985). "On de Broglie waves and Compton waves of massive particles".

6582: 6469: 6387: 5962: 5901: 5722: 5338: 4796: 4516: 4233: 3826: 1641: 8124: 8095: 7792: 7405: 7400: 7198: 7111: 6315: 6257: 5139: 3862: 3539: 3086: 3004: 1521: 1173: 1130: 951: 946: 881: 866: 831: 325: 5391: 5312: 5178: 4217: 4042: 2916:"Electron diffraction chez Thomson: early responses to quantum physics in Britain" 2735:

Trajectories of particles in De Broglie–Bohm theory in the double-slit experiment.

1987:

equation is needed to determine the intensity of the diffracted light as follows:

6727: 5613:"Classical hypercorrelation and wave-optics analogy of quantum superdense coding" 3138: 1665:

Much of the behaviour of light can be modelled using classical wave theory. The

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which would alter the properties of the electrons within the material due to the

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Hitachi website that provides background on Tonomura video and link to the video

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Li, Pengyun; Sun, Yifan; Yang, Zhenwei; Song, Xinbing; Zhang, Xiangdong (2016).

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Quantum and Semiclassical Optics: Journal of the European Optical Society Part B

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If the viewing distance is large compared with the separation of the slits (the

1630: 1109: 1099: 916: 871: 806: 761: 123: 6681:"Testing the limits of quantum mechanics: motivation, state of play, prospects" 6028:. The Frontiers Collection. Springer International Publishing. pp. 83–93. 5819: 5761: 5243: 4984: 4598: 2875:"The Bakerian lecture. Experiments and calculation relative to physical optics" 2708:

More complex variants of this type of approach have appeared, for instance the

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World in the Balance: The historic quest for an absolute system of measurement

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Davisson, C. J (1928). "The diffraction of electrons by a crystal of nickel".

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Bach, Roger; Pope, Damian; Liou, Sy-Hwang; Batelaan, Herman (13 March 2013).

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In 2018, single particle interference was demonstrated for antimatter in the

223:{\displaystyle i\hbar {\frac {d}{dt}}|\Psi \rangle ={\hat {H}}|\Psi \rangle } 91:

in 1801, as a demonstration of the wave behavior of visible light. In 1927,

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Jenkins FA and White HE, Fundamentals of Optics, 1967, McGraw Hill, New York

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of this contribution at any given point along the path is determined by the

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Zeilinger, A. (1999). "Experiment and the foundations of quantum physics".

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Jönsson, Claus (1 January 1974). "Electron Diffraction at Multiple Slits".

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Longhurst RS, Physical and Geometrical Optics, 1967, 2nd Edition, Longmans

4923:"Interference of Independent Photon Beams: The Pfleegor-Mandel Experiment" 6362: 6216:

Scully, Marian O.; Englert, Berthold-Georg; Walther, Herbert (May 1991).

5897: 5049:"Young's Double-Slit Experiment with Atoms: A Simple Atom Interferometer" 5000:"Young's Double-Slit Experiment with Atoms: A Simple Atom Interferometer" 4779: 4200: 3321:

Introduction to Quantum Mechanics: Schrödinger Equation and Path Integral

2599: 1049: 776: 6133: 5445: 4696: 4672: 4459:"Complementarity and the Copenhagen Interpretation of Quantum Mechanics" 2729: 44: 6809: 6566: 6379: 4820:"Disentangling the wave–particle duality in the double-slit experiment" 4633: 4486:"Quantum Mechanics 1925–1927: Triumph of the Copenhagen Interpretation" 4329: 3625: 3070: 2673:

An alternative to the standard understanding of quantum mechanics, the

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Two slits are illuminated by a plane wave, showing the path difference.

1657: 1192: 7282: 6657: 5706: 5636: 5321: 5289:"Plasmon-Assisted Two-Slit Transmission: Young's Experiment Revisited" 4275: 4129: 3888:. North Holland personal library (3rd ed.). Amsterdam: Elsevier. 3676: 2332:, to get the probability distribution for the position of a particle: 6241: 5547:"Probabilities and trajectories in a classical wave–particle duality" 3735:"The Merli–Missiroli–Pozzi Two-Slit Electron-Interference Experiment" 3506: 2987: 2962: 1556:, nearly half a million times larger than a proton) to be seen in an 1022: 7292: 5528:"Have We Been Interpreting Quantum Mechanics Wrong This Whole Time?" 4148:(Introduction, subscription needed for full text, quoted in full in 3719: 1575:

performed the double-slit experiment with electrons as described by

103:

long before the development of quantum mechanics and the concept of

8119: 7271:: Yves Couder . Explains Wave/Particle Duality via Silicon Droplets 6622:(Fall 2021 ed.), Metaphysics Research Lab, Stanford University 5937: 5689: 5226: 122:

single wave. Changes in the path-lengths of both waves result in a

6418: 6034: 5366: 5123: 4854: 4009: 3053: 3032: 3030: 1656: 1648: 1640: 1548:

helium atoms passing through micrometer-scale slits in gold foil.

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The Road to Reality: A Complete Guide to the Laws of the Universe

4059:

The Fabric of the Cosmos: Space, Time, and the Texture of Reality

2535:, over all paths from the point of origin to the final point, of 2536: 1509:

performed in this variant of the double-slit experiment and the

1200: 7296: 7258:"Single-particle interference observed for macroscopic objects" 4146:

New Scientist: Quantum wonders: Corpuscles and buckyballs, 2010

3211:

Feynman, Richard P.; Robert B. Leighton; Matthew Sands (1965).

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called it "a phenomenon which is impossible to explain in any

5155:"Young's Interference of Electrons in Field Emission Patterns" 1406:

exhibit wave-like interference and particle-like detection at

1159:

A low-intensity double-slit experiment was first performed by

5673:"Time reversal and holography with spacetime transformations" 1586:). The record was raised to 2000 atoms (25,000 amu) in 2019. 1423:"Which-way" experiments and the principle of complementarity 1052:

that each comprised 2000 atoms (whose total mass was 25,000

114:

was correct, and his experiment is sometimes referred to as

6753:

Horodecki, R. (1981). "De broglie wave and its dual wave".

5876:(2nd ed.). Princeton University Press. pp. 2–16. 3455: 3453: 4521:

15th UK and European Meeting on the Foundations of Physics

2522:{\displaystyle \iiint _{\text{all space}}p(x,y,z,t)\,dV=1} 6796:

Horodecki, R. (1983). "Superluminal singular dual wave".

2879:

Philosophical Transactions of the Royal Society of London

2324:

All these contributions are then added together, and the

3286:

Leon Lederman; Christopher T. Hill (27 September 2011).

2315:{\displaystyle A_{\text{path}}(x,y,z,t)=e^{iS(x,y,z,t)}} 1958:

For example, if two slits are separated by 0.5 mm (

1820:{\displaystyle ~d\theta _{n}=n\lambda ,~n=0,1,2,\ldots } 1645:

Two-slit diffraction pattern with an incident plane wave

4249:"Quantum interference experiments with large molecules" 3936:"First demonstration of antimatter wave interferometry" 2650:

As with Copenhagen, there are multiple variants of the

1964:), and are illuminated with a 0.6 μm wavelength laser ( 1568:

function of the wavelength of the incident light beam.

7283:

Java demonstration of Young's double slit interference

6839:

Das, S.N. (1984). "De Broglie wave and Compton wave".

6603:. Metaphysics Research Lab, Stanford University. 2017. 5283:

Schouten, H.F.; Kuzmin, N.; Dubois, G.; Visser, T.D.;

30:"Slit experiment" redirects here. For other uses, see 8084: 4409:"Entangled photons show interference and bilocation." 2465: 2338: 2231: 1996: 1905: 1852: 1758: 1709: 161: 8026: 7978: 7811: 7743: 7677: 7590: 7554: 7508: 7373: 7330: 5924:

Studies in History and Philosophy of Modern Physics

3849:distribution using a fast-readout pixel detector". 1974:), the spacing of the fringes will be 1.2 mm. 7089: 7066: 3811:"The double-slit experiment with single electrons" 3585:(1909). "Interference Fringes with Feeble Light". 2616:except according to the results of its measurement 2521: 2441: 2314: 2127: 1947: 1879: 1834:of the light. The angular spacing of the fringes, 1819: 1749:. The interference fringe maxima occur at angles 1733: 1653:Photo of the double-slit interference of sunlight. 222: 6470:"Many-Worlds Interpretation of Quantum Mechanics" 4515:Boscá Díaz-Pintado, María C. (29–31 March 2007). 4363:"Quantum superposition of molecules beyond 25kDa" 4306:"Quantum interference of large organic molecules" 3384:. UK: Cambridge University Press. pp. 9–10. 3140:History of the Principle of Interference of Light 3022:Physicists Smash Record For Wave–Particle Duality 87:. This type of experiment was first performed by 6524:. Oxford: Oxford University Press. p. 382. 5910:. Metaphysics Research Lab, Stanford University. 5902:"Copenhagen Interpretation of Quantum Mechanics" 5736:Rodríguez-Fortuño, Francisco J. (3 April 2023). 4673:"The uncertainty relations in quantum mechanics" 2705:have criticized it for not adding anything new. 4835: 4833: 4492:. American Institute of Physics. Archived from 3348:Niels Bohr and Complementarity: An Introduction 3167:Lederman, Leon M.; Christopher T. Hill (2011). 1983:is appreciable compared to the wavelength, the 7116:Q is for Quantum: Particle Physics from A to Z 6195:. Kluwer Academic Publishers. pp. 36–39. 6082:. Princeton University Press. pp. 41–54. 5796:"Light waves squeezed through 'slits in time'" 4711: 4709: 2920:The British Journal for the History of Science 2632:relational interpretation of quantum mechanics 2586:is a collection of views about the meaning of 2205:The double-slit experiment can illustrate the 1606:illustrating various features of this system. 7308: 5597:position coordinates and is a function in a 3 4728:. Vol. 296, no. 5. pp. 90–95. 4141: 4139: 3993:"Controlled double-slit electron diffraction" 3515:, as referenced by Crease, Robert P. (2011). 3292:. Prometheus Books, Publishers. p. 109. 1880:{\displaystyle \theta _{f}\approx \lambda /d} 1734:{\displaystyle d\sin \theta \approx d\theta } 1382:photons can also show interference patterns. 989: 8: 7263:Pilot-Wave Hydrodynamics: Supplemental Video 6350:International Journal of Theoretical Physics 4760: 4758: 4407:Hessmo, B., M. W. Mitchell, and P. Walther. 4304:Stefan Gerlich; et al. (5 April 2011). 3016: 3014: 2963:"Diffraction of Cathode Rays by a Thin Film" 1541:density in the system was much less than 1. 1490:photon pairs have no classical explanation. 1452:Delayed choice and quantum eraser variations 1249:Click on the thumbnail to enlarge the movie. 217: 191: 7019:QED: The Strange Theory of Light and Matter 5738:"An optical double-slit experiment in time" 5403: 5401: 4426:Introduction to Quantum Information Science 2685:While the model is in many ways similar to 1948:{\displaystyle ~w=z\theta _{f}=z\lambda /d} 1088:If light consisted strictly of ordinary or 1008:In the basic version of this experiment, a 7315: 7301: 7293: 6218:"Quantum optical tests of complementarity" 5587:The Quantum Story: A History in 40 Moments 4361:Yaakov Fein; et al. (December 2019). 3173:. US: Prometheus Books. pp. 102–111. 3162: 3160: 2682:quantum potential to guide the particles. 2606:, with probabilities calculated using the 1282:) in 2001, with 2 molecules of 430 atoms ( 996: 982: 140: 6417: 6361: 6078:(1999). "The Copenhagen Interpretation". 6033: 5981:The Logical Analysis of Quantum Mechanics 5936: 5688: 5644: 5570: 5510: 5500: 5444: 5365: 5320: 5259: 5225: 4853: 4778: 4337: 4247:Nairz, O; Arndt, M; Zeilinger, A (2003). 4199: 4008: 3967: 3766: 3206: 3204: 3202: 3200: 3198: 3196: 3194: 3192: 3190: 3052: 2986: 2890: 2506: 2470: 2464: 2433: 2392: 2382: 2337: 2276: 2236: 2230: 2093: 2083: 2069: 2037: 2024: 1997: 1995: 1937: 1922: 1904: 1890:The spacing of the fringes at a distance 1869: 1857: 1851: 1769: 1757: 1708: 209: 198: 197: 183: 168: 160: 6640:Heisenberg, W. (1956). Pauli, W (ed.). " 6348:(1996). "Relational Quantum Mechanics". 6277:. North Holland, John Wiley & Sons. 6145: 6143: 6112:(1953). "Strife about Complementarity". 2192: 8091: 7046:French, A.P.; Taylor, Edwin F. (1978). 6620:The Stanford Encyclopedia of Philosophy 6601:The Stanford Encyclopedia of Philosophy 6155:The Interpretation of Quantum Mechanics 3214:The Feynman Lectures on Physics, Vol. 3 2865: 2693:. Many authors such as nobel laureates 2451:As is always the case when calculating 1207:), by a group led by Marco Giammarchi. 165: 148: 107:. He believed it demonstrated that the 1216:Interference from individual particles 6979:. London: Weidenfeld & Nicolson. 5794:Castelvecchi, Davide (3 April 2023). 5789: 5787: 5666: 5664: 5551:Journal of Physics: Conference Series 3381:Quantum Physics: Illusion Or Reality? 1681:of the individual wavelets. Only the 1438:Einstein's version of this experiment 1036:Other atomic-scale entities, such as 7: 6685:Journal of Physics: Condensed Matter 6192:Quantum Theory: Concepts and Methods 4517:"Updating the wave–particle duality" 3324:. US: World Scientific. p. 14. 3256:The Internet Encyclopedia of Science 3217:. Addison-Wesley. pp. 1.1–1.8. 2566:interpretations of quantum mechanics 1471:Wheeler's delayed-choice experiments 1154:Englert–Greenberger duality relation 1136:However, the later discovery of the 6499:. London: Penguin. pp. 40–53. 6479:Stanford Encyclopedia of Philosophy 5907:Stanford Encyclopedia of Philosophy 5437:10.1146/annurev-fluid-010814-014506 4998:Carnal, O.; Mlynek, J. (May 1991). 3911:High-resolution electron microscopy 3110:. New York, NY: Pi Press. pp. 3040:Physical Chemistry Chemical Physics 1607: 7048:An Introduction to Quantum Physics 6977:Quantum: A Guide for the Perplexed 5873:Quantum Field Theory in a Nutshell 5526:Natalie Wolchover (30 June 2014). 3548:. New York: W.W. Norton. pp. 3444:10.1002/j.1538-7305.1928.tb00342.x 2079: 2076: 2073: 2070: 528:Sum-over-histories (path integral) 214: 188: 144:Part of a series of articles about 25: 5456:from the original on 21 June 2015 4742:10.1038/scientificamerican0507-90 4722:"A do-it-yourself quantum eraser" 4465:. Dept. of Physics, U. of Toronto 3519:. New York: W.W. Norton. p. 317. 3318:Müller-Kirsten, H. J. W. (2006). 2961:Thomson, G. P.; Reid, A. (1927). 2553:Interpretations of the experiment 1637:Classical wave-optics formulation 8154: 8142: 8130: 8118: 8106: 8094: 8069: 8068: 7195:Double slit interference lecture 6003:here is no point in looking for 5417:Annual Review of Fluid Mechanics 4818:Francis, Matthew (21 May 2012). 4062:. Random House LLC. p. 90. 3351:. US: Springer. pp. 75–76. 3107:The Last Man Who Knew Everything 2803:Dual-polarization interferometry 2756: 2740: 2728: 1511:Heisenberg uncertainty principle 1239: 1228: 57: 43: 32:Slit experiment (disambiguation) 7173:(5th ed.). W. H. Freeman. 6080:Understanding Quantum Mechanics 5047:Carnal, O.; Mlynek, J. (1991). 3790:"The most beautiful experiment" 3407:The Feynman Lectures on Physics 2838:Young's interference experiment 1590:Hydrodynamic pilot wave analogs 134:, which splits the beam with a 8018:Relativistic quantum mechanics 7160:Sears, Francis Weston (1949). 7137:. Cambridge University Press. 7022:. Princeton University Press. 6316:10.1016/j.ultramic.2015.03.006 6157:. Princeton University Press. 5572:10.1088/1742-6596/361/1/012001 5477:"Quantum mechanics writ large" 3863:10.1016/j.ultramic.2012.03.017 2503: 2479: 2423: 2399: 2366: 2342: 2307: 2283: 2266: 2242: 2010: 2004: 1968:), then at a distance of 1 m ( 1617:Double-slit experiment on time 1573:University of Nebraska–Lincoln 1221:by one (see the image below). 1113:Young's drawing of diffraction 1026: 678:Relativistic quantum mechanics 210: 203: 184: 1: 7996:Quantum statistical mechanics 7773:Quantum differential calculus 7695:Delayed-choice quantum eraser 7478:Symmetry in quantum mechanics 7118:. Weidenfeld & Nicolson. 6618:, in Zalta, Edward N. (ed.), 5904:. In Zalta, Edward N. (ed.). 5545:Couder, Y.; Fort, E. (2012). 5384:10.1088/1367-2630/15/3/033018 5313:10.1103/physrevlett.94.053901 5179:10.1103/PhysRevLett.88.038301 4218:10.1103/physrevlett.87.160401 4027:10.1088/1367-2630/15/3/033018 4003:(3). IOP Publishing: 033018. 3431:Bell System Technical Journal 3258:. The Worlds of David Darling 2793:Delayed-choice quantum eraser 2176:Similar calculations for the 1458:Delayed-choice quantum eraser 718:Quantum statistical mechanics 8177:Foundational quantum physics 7016:Feynman, Richard P. (1988). 6947:10.1016/0375-9601(85)90379-2 6904:10.1016/0375-9601(86)90200-8 6861:10.1016/0375-9601(84)90291-3 6775:10.1016/0375-9601(81)90571-5 4971:10.1016/0375-9601(72)91015-8 4168:Wave Particle Duality of C60 2848:Hydrodynamic quantum analogs 2590:, stemming from the work of 2180:can be made by applying the 1625:pulse at a screen coated in 1571:In 2012, researchers at the 1211:Variations of the experiment 7798:Quantum stochastic calculus 7788:Quantum measurement problem 7710:Mach–Zehnder interferometer 7225:Single particle experiments 6697:10.1088/0953-8984/14/15/201 6614:Goldstein, Sheldon (2021), 6044:10.1007/978-3-319-38987-5_4 5955:10.1016/j.shpsb.2015.01.005 5073:10.1103/PhysRevLett.66.2689 5026:10.1103/PhysRevLett.66.2689 4428:. Oxford University Press. 4256:American Journal of Physics 4110:American Journal of Physics 4083:Ananthaswamy, Anil (2018). 3909:Spence, John C. H. (2017). 3700:American Journal of Physics 3657:American Journal of Physics 3583:Sir Geoffrey, Ingram Taylor 3513:American Journal of Science 3378:Rae, Alastair I.M. (2004). 3345:Plotnitsky, Arkady (2012). 2808:Elitzur–Vaidman bomb tester 2455:, the results must then be 1896:from the slits is given by 1404:Mach–Zehnder interferometer 1394:Mach–Zehnder interferometer 1388:Mach-Zehnder interferometer 1127:corpuscular theory of light 688:Quantum information science 132:Mach–Zehnder interferometer 8203: 5820:10.1038/d41586-023-00968-4 5762:10.1038/s41567-023-02026-2 5410:"Pilot-wave hydrodynamics" 5244:10.1038/s41598-017-12832-3 4599:10.1103/RevModPhys.71.S288 3425:Davisson–Germer experiment 2666: 2652:many-worlds interpretation 2646:Many-worlds interpretation 2575: 1977:If the width of the slits 1497: 1455: 1391: 1177:experiment" by readers of 29: 8064: 7858:Quantum complexity theory 7836:Quantum cellular automata 7541:Path integral formulation 6436:10.1007/s10701-014-9862-5 6114:Science Progress (1933– ) 5475:Bush, John W. M. (2010). 4797:10.1088/1355-5111/7/3/006 4579:Reviews of Modern Physics 4387:10.1038/s41567-019-0663-9 4154:25 September 2017 at the 3827:10.1088/2058-7058/16/5/24 3759:10.1007/s00016-011-0079-0 3482:10.1038/s41567-019-0663-9 3289:Quantum Physics for Poets 3170:Quantum Physics for Poets 3104:Robinson, Andrew (2006). 2932:10.1017/S0007087410000026 2788:Complementarity (physics) 2626:Relational interpretation 2584:Copenhagen interpretation 2578:Copenhagen interpretation 2572:Copenhagen interpretation 2207:path integral formulation 2189:Path-integral formulation 2185:two diffracted patterns. 1667:Huygens–Fresnel principle 1608:(See the External links.) 130:. Another version is the 7925:Quantum machine learning 7905:Quantum key distribution 7895:Quantum image processing 7885:Quantum error correction 7735:Wheeler's delayed choice 7212:Huygens and interference 7135:The New Quantum Universe 7092:The Fabric of the Cosmos 6798:Lettere al Nuovo Cimento 6271:Messiah, Albert (1966). 4909:10.1103/PhysRev.159.1084 4564:10.1103/PhysRevD.21.1698 4457:Harrison, David (2002). 4411:CERN Courier (2004): 11. 3572:Feynman, 1965, chapter 3 3143:. Springer. p. 65. 3137:Kipnis, Naum S. (1991). 1199:) of Rafael Ferragut in 723:Quantum machine learning 476:Wheeler's delayed-choice 7841:Quantum finite automata 7217:28 October 2007 at the 7037:Frank, Philipp (1957). 6726:Penrose, Roger (2004). 6522:The Emergent Multiverse 6520:Wallace, David (2012). 6493:Deutsch, David (1998). 5502:10.1073/pnas.1012399107 5159:Physical Review Letters 5053:Physical Review Letters 5005:Physical Review Letters 4985:""To a light particle"" 4864:10.12743/quanta.v2i1.12 4484:Cassidy, David (2008). 4087:. Penguin. p. 63. 3252:"Wave–Particle Duality" 2914:Navarro, Jaume (2010). 2610:, and the principle of 2328:of the final result is 1408:single-photon detectors 433:Leggett–Garg inequality 18:Double slit diffraction 7945:Quantum neural network 7206:Interactive animations 7088:Greene, Brian (2005). 7065:Greene, Brian (2000). 6406:Foundations of Physics 6088:10.2307/j.ctv173f2pm.9 5593:particles depends on 3 5408:Bush, John WM (2015). 5354:New Journal of Physics 4614:Foundations of Physics 4056:Greene, Brian (2007). 3997:New Journal of Physics 3960:10.1126/sciadv.aav7610 3884:Cowley, J. M. (1995). 3739:Physics in Perspective 3606:Zeitschrift für Physik 3503:Charles Sanders Peirce 2892:10.1098/rstl.1804.0001 2873:Young, Thomas (1804). 2798:Diffraction from slits 2675:De Broglie–Bohm theory 2669:de Broglie–Bohm theory 2663:De Broglie–Bohm theory 2523: 2443: 2316: 2212:functional integration 2202: 2158:≠ 0, and sinc(0) = 1. 2129: 1985:Fraunhofer diffraction 1949: 1881: 1821: 1735: 1662: 1654: 1646: 1627:indium tin oxide (ITO) 1534: 1526: 1467: 1411: 1257:This demonstrates the 1170:University of Tübingen 1114: 1085: 224: 77:double-slit experiment 7970:Quantum teleportation 7498:Wave–particle duality 7169:Tipler, Paul (2004). 7039:Philosophy of Science 6679:Leggett, A J (2002). 6496:The Fabric of Reality 6026:Quantum Speakables II 5585:Baggott, Jim (2011). 4310:Nature Communications 4173:31 March 2012 at the 3792:. Physics World 2002 3276:Feynman, 1965, p. 1.7 3237:Feynman, 1965, p. 1.5 2813:N-slit interferometer 2710:three wave hypothesis 2699:Anthony James Leggett 2524: 2444: 2317: 2196: 2130: 1950: 1882: 1822: 1736: 1660: 1652: 1644: 1532: 1524: 1465: 1401: 1259:wave–particle duality 1197:Politecnico di Milano 1112: 1079: 1031:wave–particle duality 1010:coherent light source 418:Elitzur–Vaidman 408:Davisson–Germer 225: 105:wave–particle duality 8001:Quantum field theory 7930:Quantum metamaterial 7875:Quantum cryptography 7605:Consistent histories 7277:Computer simulations 7269:Through the Wormhole 7069:The Elegant Universe 3587:Prof. Cam. Phil. Soc 2783:Aharonov-Bohm effect 2722:Bohmian trajectories 2691:quantum field theory 2687:Schrödinger equation 2634:, first proposed by 2547:interference pattern 2463: 2336: 2229: 1994: 1903: 1850: 1756: 1707: 1595:Hydrodynamic analogs 1268:buckminsterfullerene 1138:photoelectric effect 683:Quantum field theory 595:Consistent histories 232:Schrödinger equation 159: 128:interference pattern 112:wave theory of light 97:George Paget Thomson 8182:Physics experiments 7986:Quantum fluctuation 7955:Quantum programming 7915:Quantum logic gates 7900:Quantum information 7880:Quantum electronics 7355:Classical mechanics 7252:Hydrodynamic analog 7143:2003nqu..book.....H 6939:1985PhLA..109....7E 6896:1986PhLA..114..179M 6853:1984PhLA..102..338D 6767:1981PhLA...87...95H 6616:"Bohmian Mechanics" 6597:"Bohmian Mechanics" 6559:1979NCimB..52...15P 6428:2015FoPh...45..211K 6372:1996IJTP...35.1637R 6234:1991Natur.351..111S 5947:2015SHPMP..49...73C 5812:2023Natur.616..230C 5754:2023NatPh..19..929R 5699:2016NatPh..12..972B 5629:2015NatSR...518574L 5563:2012JPhCS.361a2001C 5493:2010PNAS..10717455B 5487:(41): 17455–17456. 5429:2015AnRFM..47..269B 5376:2013NJPh...15c3018B 5305:2005PhRvL..94e3901S 5236:2017NatSR...712661Y 5171:2002PhRvL..88c8301O 5116:1999Natur.401..680A 5065:1991PhRvL..66.2689C 5018:1991PhRvL..66.2689C 4963:1972PhLA...39..333S 4901:1967PhRv..159.1084P 4789:1995QuSOp...7..259C 4734:2007SciAm.296e..90H 4726:Scientific American 4626:1987FoPh...17..891M 4591:1999RvMPS..71..288Z 4556:1980PhRvD..21.1698B 4379:2019NatPh..15.1242F 4322:2011NatCo...2..263G 4268:2003AmJPh..71..319N 4210:2001PhRvL..87p0401N 4122:1973AmJPh..41..639D 4019:2013NJPh...15c3018B 3952:2019SciA....5.7610S 3886:Diffraction physics 3796:24 May 2021 at the 3751:2012PhP....14..178R 3712:1976AmJPh..44..306M 3669:1974AmJPh..42....4J 3618:1961ZPhy..161..454J 3474:2019NatPh..15.1242F 3063:2013PCCP...1514696E 3047:(35): 14696–14700. 2979:1927Natur.119Q.890T 2843:Measurement problem 2823:Photon polarization 2182:Fresnel diffraction 2142:is defined as sinc( 1558:electron microscope 1484:Scientific American 1193:Positron Laboratory 1098:refined apparatus. 1095:diffraction pattern 1082:diffraction pattern 1042:classical mechanics 471:Stern–Gerlach 268:Classical mechanics 109:Christiaan Huygens' 95:and, independently 93:Davisson and Germer 8039:in popular culture 7821:Quantum algorithms 7669:Von Neumann–Wigner 7649:Objective collapse 7360:Old quantum theory 7133:Hey, Tony (2003). 7001:. Dutton/Penguin. 6995:Ananthaswamy, Anil 6810:10.1007/bf02817964 6567:10.1007/bf02743566 6547:Il Nuovo Cimento B 6380:10.1007/BF02302261 5983:. Pergamon Press. 5617:Scientific Reports 5214:Scientific Reports 4634:10.1007/BF00734319 4496:on 14 January 2016 4330:10.1038/ncomms1263 3626:10.1007/BF01342460 3071:10.1039/C3CP51500A 2562:thought experiment 2519: 2439: 2312: 2203: 2125: 2123: 1945: 1877: 1817: 1731: 1663: 1655: 1647: 1535: 1527: 1468: 1429:thought experiment 1412: 1115: 1086: 659:Von Neumann–Wigner 639:Objective-collapse 438:Mach–Zehnder 428:Leggett inequality 423:Franck–Hertz 273:Old quantum theory 220: 118:or Young's slits. 116:Young's experiment 8082: 8081: 8056:Quantum mysticism 8034:Schrödinger's cat 7965:Quantum simulator 7935:Quantum metrology 7863:Quantum computing 7826:Quantum amplifier 7803:Quantum spacetime 7768:Quantum cosmology 7758:Quantum chemistry 7473:Scattering theory 7421:Zero-point energy 7416:Degenerate levels 7324:Quantum mechanics 7180:978-0-7167-0810-0 7164:. Addison Wesley. 7152:978-0-521-56457-1 7125:978-0-7538-0685-2 7103:978-0-375-72720-7 7080:978-0-375-70811-4 7057:978-0-393-09106-9 7029:978-0-691-02417-2 7008:978-1-101-98609-7 6986:978-0-297-84305-4 6927:Physics Letters A 6884:Physics Letters A 6841:Physics Letters A 6755:Physics Letters A 6739:978-0-224-04447-9 6691:(15): R415–R451. 6658:10.1063/1.3060063 6531:978-0-19-954696-1 6506:978-0-14-014690-5 6468:(5 August 2021). 6274:Quantum Mechanics 6228:(6322): 111–116. 6164:978-0-691-03669-4 6053:978-3-319-38985-1 5990:978-0-08-017158-6 5883:978-0-691-14034-6 5707:10.1038/nphys3810 5637:10.1038/srep18574 5110:(6754): 680–682. 5059:(21): 2689–2692. 5012:(21): 2689–2694. 4951:Physics Letters A 4929:on 3 January 2011 4544:Physical Review D 4490:Werner Heisenberg 4435:978-0-19-921570-6 4373:(12): 1242–1245. 4276:10.1119/1.1531580 4130:10.1119/1.1987321 4094:978-1-101-98611-0 4069:978-0-307-42853-0 3920:978-0-19-879583-4 3895:978-0-444-82218-5 3677:10.1119/1.1987592 3559:978-0-393-04688-5 3525:978-0-393-07298-3 3468:(12): 1242–1245. 3391:978-1-139-45527-5 3358:978-1-4614-4517-3 3299:978-1-61614-281-0 3224:978-0-201-02118-9 3180:978-1-61614-281-0 3150:978-0-8176-2316-6 3121:978-0-13-134304-7 2853:Pilot wave theory 2833:Schrödinger's cat 2828:Quantum coherence 2714:Ryszard Horodecki 2695:Werner Heisenberg 2630:According to the 2596:Werner Heisenberg 2588:quantum mechanics 2559:Schrödinger's cat 2473: 2385: 2239: 2115: 2067: 2059: 1908: 1789: 1761: 1584:atomic mass units 1507:weak measurements 1145:nature of light. 1054:atomic mass units 1006: 1005: 713:Scattering theory 693:Quantum computing 466:Schrödinger's cat 398:Bell's inequality 206: 181: 150:Quantum mechanics 101:classical physics 85:quantum mechanics 16:(Redirected from 8194: 8159: 8158: 8157: 8147: 8146: 8145: 8135: 8134: 8133: 8123: 8122: 8111: 8110: 8109: 8099: 8098: 8090: 8072: 8071: 7783:Quantum geometry 7778:Quantum dynamics 7635:Superdeterminism 7531:Matrix mechanics 7386:Bra–ket notation 7317: 7310: 7303: 7294: 7184: 7165: 7156: 7129: 7107: 7095: 7084: 7072: 7061: 7042: 7041:. 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London: Cape. 6723: 6717: 6716: 6676: 6670: 6669: 6637: 6631: 6630: 6629: 6627: 6611: 6605: 6604: 6593: 6587: 6586: 6542: 6536: 6535: 6517: 6511: 6510: 6490: 6484: 6483: 6474:Zalta, Edward N. 6462: 6456: 6455: 6421: 6398: 6392: 6391: 6365: 6363:quant-ph/9609002 6356:(8): 1637–1678. 6342: 6336: 6335: 6295: 6289: 6288: 6268: 6262: 6261: 6242:10.1038/351111a0 6213: 6207: 6206: 6183: 6177: 6176: 6147: 6138: 6137: 6120:(163): 393–410. 6106: 6100: 6099: 6072: 6066: 6065: 6037: 6022:Zeilinger, Anton 6017: 6011: 6010: 5973: 5967: 5966: 5940: 5918: 5912: 5911: 5894: 5888: 5887: 5864: 5858: 5855: 5849: 5846: 5840: 5839: 5791: 5782: 5781: 5733: 5727: 5726: 5692: 5668: 5659: 5658: 5648: 5608: 5602: 5583: 5577: 5576: 5574: 5542: 5536: 5535: 5523: 5517: 5516: 5514: 5504: 5472: 5466: 5465: 5463: 5461: 5455: 5448: 5414: 5405: 5396: 5395: 5369: 5349: 5343: 5342: 5324: 5280: 5274: 5273: 5263: 5229: 5205: 5199: 5198: 5150: 5144: 5143: 5099: 5093: 5091: 5089: 5087: 5044: 5038: 5037: 4995: 4989: 4988: 4981: 4975: 4974: 4946: 4940: 4938: 4936: 4934: 4925:. 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Rev. Lett 5282: 5281: 5277: 5207: 5206: 5202: 5152: 5151: 5147: 5101: 5100: 5096: 5085: 5083: 5046: 5045: 5041: 4997: 4996: 4992: 4983: 4982: 4978: 4948: 4947: 4943: 4932: 4930: 4921: 4920: 4916: 4888:Physical Review 4884: 4883: 4879: 4839: 4838: 4831: 4817: 4816: 4812: 4764: 4763: 4756: 4746: 4744: 4715: 4714: 4707: 4677:Current Science 4670: 4669: 4665: 4661:, 391–4 (1988). 4656:Physics Letters 4653: 4649: 4611: 4610: 4606: 4576: 4575: 4571: 4541: 4540: 4536: 4526: 4524: 4514: 4513: 4509: 4499: 4497: 4483: 4482: 4478: 4468: 4466: 4456: 4455: 4451: 4436: 4420: 4419: 4415: 4406: 4402: 4360: 4359: 4355: 4303: 4302: 4298: 4288: 4286: 4282: 4251: 4246: 4245: 4241: 4188:Phys. Rev. Lett 4185: 4184: 4180: 4175:Wayback Machine 4166: 4162: 4156:Wayback Machine 4144: 4137: 4107: 4106: 4102: 4095: 4082: 4081: 4077: 4070: 4055: 4054: 4050: 3990: 3989: 3985: 3946:(5): eaav7610. 3933: 3932: 3928: 3921: 3908: 3907: 3903: 3896: 3883: 3882: 3878: 3851:Ultramicroscopy 3847: 3846: 3842: 3808: 3807: 3803: 3798:Wayback Machine 3788: 3784: 3732: 3731: 3727: 3720:10.1119/1.10184 3697: 3696: 3692: 3654: 3653: 3649: 3603: 3602: 3598: 3581: 3580: 3576: 3571: 3567: 3560: 3538: 3537: 3533: 3501: 3497: 3459: 3458: 3451: 3427: 3422: 3418: 3403: 3399: 3392: 3377: 3370: 3366: 3359: 3344: 3343: 3339: 3332: 3331:978-981-2566911 3317: 3311: 3307: 3300: 3285: 3284: 3280: 3275: 3271: 3261: 3259: 3246: 3245: 3241: 3236: 3232: 3225: 3210: 3209: 3188: 3181: 3166: 3165: 3158: 3151: 3136: 3135: 3131: 3122: 3103: 3098: 3094: 3036: 3035: 3028: 3019: 3012: 2960: 2959: 2955: 2913: 2912: 2908: 2872: 2871: 2867: 2862: 2857: 2778: 2773: 2772: 2771: 2770: 2769: 2761: 2753: 2752: 2745: 2737: 2736: 2733: 2724: 2723: 2671: 2665: 2648: 2628: 2612:complementarity 2604:indeterministic 2580: 2574: 2555: 2466: 2461: 2460: 2388: 2378: 2377: 2373: 2372: 2334: 2333: 2272: 2232: 2227: 2226: 2191: 2170: 2166: 2162: 2122: 2121: 2095: 2089: 2068: 2039: 2033: 2020: 2013: 1992: 1991: 1978: 1969: 1965: 1959: 1918: 1901: 1900: 1891: 1853: 1848: 1847: 1841: 1835: 1830:where λ is the 1765: 1754: 1753: 1705: 1704: 1697: 1677:as well as the 1639: 1619: 1592: 1577:Richard Feynman 1519: 1502: 1496: 1460: 1454: 1433:complementarity 1425: 1396: 1390: 1374: 1371: 1370: 1369: 1365: 1362: 1361: 1360: 1356: 1353: 1352: 1351: 1347: 1344: 1343: 1342: 1338: 1335: 1334: 1333: 1329: 1326: 1325: 1324: 1322: 1317: 1314: 1313: 1312: 1308: 1305: 1304: 1303: 1299: 1296: 1295: 1294: 1290: 1287: 1286: 1285: 1283: 1278: 1275: 1274: 1273: 1271: 1255: 1254: 1253: 1252: 1251: 1244: 1235: 1234: 1233: 1218: 1213: 1074: 1062:Richard Feynman 1002: 973: 972: 971: 736: 728: 727: 673: 672:Advanced topics 665: 664: 663: 615:Hidden-variable 605:de Broglie–Bohm 584: 582:Interpretations 574: 573: 572: 542: 534: 533: 532: 490: 482: 481: 480: 447: 403:CHSH inequality 392: 384: 383: 382: 311:Complementarity 305: 297: 296: 295: 263: 234: 173: 157: 156: 69: 68: 67: 66: 65: 62: 53: 52: 51: 48: 35: 28: 23: 22: 15: 12: 11: 5: 8200: 8198: 8190: 8189: 8187:Wave mechanics 8184: 8179: 8169: 8168: 8164: 8163: 8151: 8139: 8127: 8115: 8103: 8080: 8079: 8077: 8076: 8065: 8062: 8061: 8059: 8058: 8053: 8048: 8043: 8042: 8041: 8030: 8028: 8024: 8023: 8021: 8020: 8015: 8010: 8009: 8008: 7998: 7993: 7991:Casimir effect 7988: 7982: 7980: 7976: 7975: 7973: 7972: 7967: 7962: 7957: 7952: 7950:Quantum optics 7947: 7942: 7937: 7932: 7927: 7922: 7917: 7912: 7907: 7902: 7897: 7892: 7887: 7882: 7877: 7872: 7871: 7870: 7860: 7855: 7850: 7845: 7844: 7843: 7833: 7828: 7823: 7817: 7815: 7809: 7808: 7806: 7805: 7800: 7795: 7790: 7785: 7780: 7775: 7770: 7765: 7760: 7755: 7749: 7747: 7741: 7740: 7738: 7737: 7732: 7727: 7725:Quantum eraser 7722: 7717: 7712: 7707: 7702: 7697: 7692: 7687: 7681: 7679: 7675: 7674: 7672: 7671: 7666: 7661: 7656: 7651: 7646: 7641: 7640: 7639: 7638: 7637: 7622: 7617: 7612: 7607: 7602: 7596: 7594: 7588: 7587: 7585: 7584: 7579: 7574: 7569: 7564: 7558: 7556: 7552: 7551: 7549: 7548: 7543: 7538: 7533: 7528: 7523: 7518: 7512: 7510: 7506: 7505: 7503: 7502: 7501: 7500: 7495: 7485: 7480: 7475: 7470: 7465: 7460: 7455: 7450: 7445: 7440: 7435: 7430: 7425: 7424: 7423: 7418: 7413: 7408: 7398: 7396:Density matrix 7393: 7388: 7383: 7377: 7375: 7371: 7370: 7368: 7367: 7362: 7357: 7352: 7351: 7350: 7340: 7334: 7332: 7328: 7327: 7322: 7320: 7319: 7312: 7305: 7297: 7291: 7290: 7285: 7278: 7275: 7274: 7273: 7265: 7260: 7253: 7250: 7249: 7248: 7243: 7238: 7233: 7226: 7223: 7222: 7221: 7207: 7204: 7203: 7202: 7190: 7189:External links 7187: 7186: 7185: 7179: 7166: 7157: 7151: 7130: 7124: 7108: 7102: 7085: 7079: 7062: 7056: 7043: 7034: 7028: 7013: 7007: 6991: 6985: 6967: 6964: 6961: 6960: 6917: 6890:(4): 179–182. 6874: 6847:(8): 338–339. 6831: 6788: 6745: 6738: 6718: 6671: 6632: 6606: 6588: 6537: 6530: 6512: 6505: 6485: 6457: 6412:(2): 211–217. 6393: 6346:Rovelli, Carlo 6337: 6290: 6283: 6263: 6208: 6201: 6178: 6163: 6139: 6101: 6067: 6052: 6012: 5989: 5968: 5913: 5889: 5882: 5859: 5850: 5841: 5783: 5748:(7): 929–930. 5742:Nature Physics 5728: 5677:Nature Physics 5660: 5603: 5578: 5537: 5518: 5467: 5423:(1): 269–292. 5397: 5344: 5275: 5200: 5145: 5094: 5039: 4990: 4976: 4957:(4): 333–334. 4941: 4914: 4877: 4829: 4810: 4773:(3): 259–278. 4754: 4705: 4683:(2): 203–218. 4663: 4647: 4620:(9): 891–903. 4604: 4569: 4534: 4507: 4476: 4449: 4434: 4422:Vedral, Vlatko 4413: 4400: 4367:Nature Physics 4353: 4296: 4285:on 4 June 2015 4262:(4): 319–325. 4239: 4194:(16): 160401. 4178: 4160: 4135: 4116:(5): 639–644. 4100: 4093: 4075: 4068: 4048: 3983: 3926: 3919: 3901: 3894: 3876: 3840: 3801: 3782: 3745:(2): 178–194. 3725: 3706:(3): 306–307. 3690: 3647: 3612:(4): 454–474. 3596: 3574: 3565: 3558: 3531: 3529: 3528: 3495: 3462:Nature Physics 3449: 3416: 3397: 3390: 3364: 3357: 3337: 3330: 3305: 3298: 3278: 3269: 3248:Darling, David 3239: 3230: 3223: 3186: 3179: 3156: 3149: 3129: 3127: 3126: 3120: 3092: 3026: 3010: 2953: 2926:(2): 245–275. 2906: 2864: 2863: 2861: 2858: 2856: 2855: 2850: 2845: 2840: 2835: 2830: 2825: 2820: 2815: 2810: 2805: 2800: 2795: 2790: 2785: 2779: 2777: 2774: 2762: 2755: 2754: 2746: 2739: 2738: 2734: 2727: 2726: 2725: 2721: 2720: 2719: 2718: 2667:Main article: 2664: 2661: 2647: 2644: 2627: 2624: 2576:Main article: 2573: 2570: 2554: 2551: 2543:proportionally 2518: 2515: 2512: 2509: 2505: 2502: 2499: 2496: 2493: 2490: 2487: 2484: 2481: 2478: 2469: 2436: 2431: 2425: 2422: 2419: 2416: 2413: 2410: 2407: 2404: 2401: 2398: 2395: 2391: 2381: 2376: 2371: 2368: 2365: 2362: 2359: 2356: 2353: 2350: 2347: 2344: 2341: 2309: 2306: 2303: 2300: 2297: 2294: 2291: 2288: 2285: 2282: 2279: 2275: 2271: 2268: 2265: 2262: 2259: 2256: 2253: 2250: 2247: 2244: 2235: 2199:Wiener process 2190: 2187: 2136: 2135: 2119: 2114: 2110: 2107: 2104: 2101: 2098: 2092: 2086: 2081: 2078: 2075: 2072: 2063: 2058: 2054: 2051: 2048: 2045: 2042: 2036: 2032: 2027: 2023: 2019: 2016: 2014: 2012: 2009: 2006: 2003: 2000: 1999: 1956: 1955: 1944: 1940: 1936: 1933: 1930: 1925: 1921: 1917: 1914: 1911: 1888: 1887: 1876: 1872: 1868: 1865: 1860: 1856: 1843:, is given by 1837: 1828: 1827: 1816: 1813: 1810: 1807: 1804: 1801: 1798: 1795: 1792: 1786: 1783: 1780: 1777: 1772: 1768: 1764: 1742: 1741: 1730: 1727: 1724: 1721: 1718: 1715: 1712: 1638: 1635: 1618: 1615: 1591: 1588: 1518: 1515: 1498:Main article: 1495: 1492: 1477:Quantum eraser 1456:Main article: 1453: 1450: 1424: 1421: 1392:Main article: 1389: 1386: 1372: 1363: 1354: 1345: 1336: 1327: 1315: 1306: 1297: 1288: 1276: 1245: 1238: 1237: 1236: 1227: 1226: 1225: 1224: 1223: 1217: 1214: 1212: 1209: 1073: 1070: 1004: 1003: 1001: 1000: 993: 986: 978: 975: 974: 970: 969: 964: 959: 954: 949: 944: 939: 934: 929: 924: 919: 914: 909: 904: 899: 894: 889: 884: 879: 874: 869: 864: 859: 854: 849: 844: 839: 834: 829: 824: 819: 814: 809: 804: 799: 794: 789: 784: 779: 774: 769: 764: 759: 754: 749: 744: 738: 737: 734: 733: 730: 729: 726: 725: 720: 715: 710: 708:Density matrix 705: 700: 695: 690: 685: 680: 674: 671: 670: 667: 666: 662: 661: 656: 651: 646: 641: 636: 631: 630: 629: 628: 627: 612: 607: 602: 597: 592: 586: 585: 580: 579: 576: 575: 571: 570: 565: 560: 555: 550: 544: 543: 540: 539: 536: 535: 531: 530: 525: 520: 515: 510: 505: 499: 498: 497: 491: 488: 487: 484: 483: 479: 478: 473: 468: 462: 461: 460: 459: 458: 456:Delayed-choice 451:Quantum eraser 446: 445: 440: 435: 430: 425: 420: 415: 410: 405: 400: 394: 393: 390: 389: 386: 385: 381: 380: 379: 378: 368: 363: 358: 353: 348: 343: 341:Quantum number 338: 333: 328: 323: 318: 313: 307: 306: 303: 302: 299: 298: 294: 293: 288: 282: 281: 280: 275: 270: 264: 261: 260: 257: 256: 255: 254: 249: 244: 236: 235: 230: 219: 216: 212: 205: 202: 196: 193: 190: 186: 179: 176: 172: 167: 164: 153: 152: 146: 145: 126:, creating an 82: 73:modern physics 63: 56: 55: 54: 49: 42: 41: 40: 39: 38: 26: 24: 14: 13: 10: 9: 6: 4: 3: 2: 8199: 8188: 8185: 8183: 8180: 8178: 8175: 8174: 8172: 8162: 8152: 8150: 8140: 8138: 8128: 8126: 8121: 8116: 8114: 8104: 8102: 8097: 8092: 8088: 8075: 8067: 8066: 8063: 8057: 8054: 8052: 8049: 8047: 8044: 8040: 8037: 8036: 8035: 8032: 8031: 8029: 8025: 8019: 8016: 8014: 8011: 8007: 8004: 8003: 8002: 7999: 7997: 7994: 7992: 7989: 7987: 7984: 7983: 7981: 7977: 7971: 7968: 7966: 7963: 7961: 7958: 7956: 7953: 7951: 7948: 7946: 7943: 7941: 7938: 7936: 7933: 7931: 7928: 7926: 7923: 7921: 7918: 7916: 7913: 7911: 7910:Quantum logic 7908: 7906: 7903: 7901: 7898: 7896: 7893: 7891: 7888: 7886: 7883: 7881: 7878: 7876: 7873: 7869: 7866: 7865: 7864: 7861: 7859: 7856: 7854: 7851: 7849: 7846: 7842: 7839: 7838: 7837: 7834: 7832: 7829: 7827: 7824: 7822: 7819: 7818: 7816: 7814: 7810: 7804: 7801: 7799: 7796: 7794: 7791: 7789: 7786: 7784: 7781: 7779: 7776: 7774: 7771: 7769: 7766: 7764: 7763:Quantum chaos 7761: 7759: 7756: 7754: 7751: 7750: 7748: 7746: 7742: 7736: 7733: 7731: 7730:Stern–Gerlach 7728: 7726: 7723: 7721: 7718: 7716: 7713: 7711: 7708: 7706: 7703: 7701: 7698: 7696: 7693: 7691: 7688: 7686: 7683: 7682: 7680: 7676: 7670: 7667: 7665: 7664:Transactional 7662: 7660: 7657: 7655: 7654:Quantum logic 7652: 7650: 7647: 7645: 7642: 7636: 7633: 7632: 7631: 7628: 7627: 7626: 7623: 7621: 7618: 7616: 7613: 7611: 7608: 7606: 7603: 7601: 7598: 7597: 7595: 7593: 7589: 7583: 7580: 7578: 7575: 7573: 7570: 7568: 7565: 7563: 7560: 7559: 7557: 7553: 7547: 7544: 7542: 7539: 7537: 7534: 7532: 7529: 7527: 7524: 7522: 7519: 7517: 7514: 7513: 7511: 7507: 7499: 7496: 7494: 7491: 7490: 7489: 7488:Wave function 7486: 7484: 7481: 7479: 7476: 7474: 7471: 7469: 7466: 7464: 7463:Superposition 7461: 7459: 7458:Quantum state 7456: 7454: 7451: 7449: 7446: 7444: 7441: 7439: 7436: 7434: 7431: 7429: 7426: 7422: 7419: 7417: 7414: 7412: 7411:Excited state 7409: 7407: 7404: 7403: 7402: 7399: 7397: 7394: 7392: 7389: 7387: 7384: 7382: 7379: 7378: 7376: 7372: 7366: 7363: 7361: 7358: 7356: 7353: 7349: 7346: 7345: 7344: 7341: 7339: 7336: 7335: 7333: 7329: 7325: 7318: 7313: 7311: 7306: 7304: 7299: 7298: 7295: 7289: 7286: 7284: 7281: 7280: 7276: 7272: 7270: 7266: 7264: 7261: 7259: 7256: 7255: 7251: 7247: 7244: 7242: 7239: 7237: 7234: 7232: 7229: 7228: 7224: 7220: 7216: 7213: 7210: 7209: 7205: 7200: 7196: 7193: 7192: 7188: 7182: 7176: 7172: 7167: 7163: 7158: 7154: 7148: 7144: 7140: 7136: 7131: 7127: 7121: 7117: 7113: 7112:Gribbin, John 7109: 7105: 7099: 7094: 7093: 7086: 7082: 7076: 7071: 7070: 7063: 7059: 7053: 7049: 7044: 7040: 7035: 7031: 7025: 7021: 7020: 7014: 7010: 7004: 7000: 6996: 6992: 6988: 6982: 6978: 6974: 6970: 6969: 6965: 6956: 6952: 6948: 6944: 6940: 6936: 6932: 6928: 6921: 6918: 6913: 6909: 6905: 6901: 6897: 6893: 6889: 6885: 6878: 6875: 6870: 6866: 6862: 6858: 6854: 6850: 6846: 6842: 6835: 6832: 6827: 6823: 6819: 6815: 6811: 6807: 6803: 6799: 6792: 6789: 6784: 6780: 6776: 6772: 6768: 6764: 6760: 6756: 6749: 6746: 6741: 6735: 6731: 6730: 6722: 6719: 6714: 6710: 6706: 6702: 6698: 6694: 6690: 6686: 6682: 6675: 6672: 6667: 6663: 6659: 6655: 6651: 6647: 6646:Physics Today 6643: 6636: 6633: 6621: 6617: 6610: 6607: 6602: 6598: 6592: 6589: 6584: 6580: 6576: 6572: 6568: 6564: 6560: 6556: 6552: 6548: 6541: 6538: 6533: 6527: 6523: 6516: 6513: 6508: 6502: 6498: 6497: 6489: 6486: 6481: 6480: 6475: 6471: 6467: 6461: 6458: 6453: 6449: 6445: 6441: 6437: 6433: 6429: 6425: 6420: 6415: 6411: 6407: 6403: 6397: 6394: 6389: 6385: 6381: 6377: 6373: 6369: 6364: 6359: 6355: 6351: 6347: 6341: 6338: 6333: 6329: 6325: 6321: 6317: 6313: 6309: 6305: 6301: 6294: 6291: 6286: 6284:0-486-40924-4 6280: 6276: 6275: 6267: 6264: 6259: 6255: 6251: 6247: 6243: 6239: 6235: 6231: 6227: 6223: 6219: 6212: 6209: 6204: 6202:0-7923-2549-4 6198: 6194: 6193: 6188: 6182: 6179: 6174: 6170: 6166: 6160: 6156: 6152: 6146: 6144: 6140: 6135: 6131: 6127: 6123: 6119: 6115: 6111: 6110:Rosenfeld, L. 6105: 6102: 6097: 6093: 6089: 6085: 6081: 6077: 6076:Omnès, Roland 6071: 6068: 6063: 6059: 6055: 6049: 6045: 6041: 6036: 6031: 6027: 6023: 6016: 6013: 6009: 6006: 6000: 5996: 5992: 5986: 5982: 5978: 5972: 5969: 5964: 5960: 5956: 5952: 5948: 5944: 5939: 5934: 5930: 5926: 5925: 5917: 5914: 5909: 5908: 5903: 5899: 5893: 5890: 5885: 5879: 5875: 5874: 5869: 5863: 5860: 5854: 5851: 5845: 5842: 5837: 5833: 5829: 5825: 5821: 5817: 5813: 5809: 5806:(7956): 230. 5805: 5801: 5797: 5790: 5788: 5784: 5779: 5775: 5771: 5767: 5763: 5759: 5755: 5751: 5747: 5743: 5739: 5732: 5729: 5724: 5720: 5716: 5712: 5708: 5704: 5700: 5696: 5691: 5686: 5682: 5678: 5674: 5667: 5665: 5661: 5656: 5652: 5647: 5642: 5638: 5634: 5630: 5626: 5622: 5618: 5614: 5607: 5604: 5600: 5596: 5592: 5588: 5582: 5579: 5573: 5568: 5564: 5560: 5557:(1): 012001. 5556: 5552: 5548: 5541: 5538: 5533: 5529: 5522: 5519: 5513: 5508: 5503: 5498: 5494: 5490: 5486: 5482: 5478: 5471: 5468: 5452: 5447: 5442: 5438: 5434: 5430: 5426: 5422: 5418: 5411: 5404: 5402: 5398: 5393: 5389: 5385: 5381: 5377: 5373: 5368: 5363: 5360:(3): 033018. 5359: 5355: 5348: 5345: 5340: 5336: 5332: 5328: 5323: 5318: 5314: 5310: 5306: 5302: 5299:(5): 053901. 5298: 5294: 5290: 5286: 5279: 5276: 5271: 5267: 5262: 5257: 5253: 5249: 5245: 5241: 5237: 5233: 5228: 5223: 5219: 5215: 5211: 5204: 5201: 5196: 5192: 5188: 5184: 5180: 5176: 5172: 5168: 5165:(3): 038301. 5164: 5160: 5156: 5149: 5146: 5141: 5137: 5133: 5129: 5125: 5124:10.1038/44348 5121: 5117: 5113: 5109: 5105: 5098: 5095: 5082: 5078: 5074: 5070: 5066: 5062: 5058: 5054: 5050: 5043: 5040: 5035: 5031: 5027: 5023: 5019: 5015: 5011: 5007: 5006: 5001: 4994: 4991: 4986: 4980: 4977: 4972: 4968: 4964: 4960: 4956: 4952: 4945: 4942: 4928: 4924: 4918: 4915: 4910: 4906: 4902: 4898: 4894: 4890: 4889: 4881: 4878: 4873: 4869: 4865: 4861: 4856: 4851: 4847: 4843: 4836: 4834: 4830: 4825: 4821: 4814: 4811: 4806: 4802: 4798: 4794: 4790: 4786: 4781: 4776: 4772: 4768: 4761: 4759: 4755: 4743: 4739: 4735: 4731: 4727: 4723: 4719: 4716:Hillmer, R.; 4712: 4710: 4706: 4702: 4698: 4694: 4690: 4686: 4682: 4678: 4674: 4667: 4664: 4660: 4657: 4651: 4648: 4643: 4639: 4635: 4631: 4627: 4623: 4619: 4615: 4608: 4605: 4600: 4596: 4592: 4588: 4584: 4580: 4573: 4570: 4565: 4561: 4557: 4553: 4549: 4545: 4538: 4535: 4522: 4518: 4511: 4508: 4495: 4491: 4487: 4480: 4477: 4464: 4460: 4453: 4450: 4445: 4441: 4437: 4431: 4427: 4423: 4417: 4414: 4410: 4404: 4401: 4396: 4392: 4388: 4384: 4380: 4376: 4372: 4368: 4364: 4357: 4354: 4349: 4345: 4340: 4335: 4331: 4327: 4323: 4319: 4315: 4311: 4307: 4300: 4297: 4281: 4277: 4273: 4269: 4265: 4261: 4257: 4250: 4243: 4240: 4235: 4231: 4227: 4223: 4219: 4215: 4211: 4207: 4202: 4197: 4193: 4189: 4182: 4179: 4176: 4172: 4169: 4164: 4161: 4157: 4153: 4150: 4147: 4142: 4140: 4136: 4131: 4127: 4123: 4119: 4115: 4111: 4104: 4101: 4096: 4090: 4086: 4079: 4076: 4071: 4065: 4061: 4060: 4052: 4049: 4044: 4040: 4036: 4032: 4028: 4024: 4020: 4016: 4011: 4006: 4002: 3998: 3994: 3987: 3984: 3979: 3975: 3970: 3965: 3961: 3957: 3953: 3949: 3945: 3941: 3937: 3930: 3927: 3922: 3916: 3912: 3905: 3902: 3897: 3891: 3887: 3880: 3877: 3872: 3868: 3864: 3860: 3856: 3852: 3844: 3841: 3836: 3832: 3828: 3824: 3820: 3816: 3815:Physics World 3812: 3805: 3802: 3799: 3795: 3791: 3786: 3783: 3778: 3774: 3769: 3764: 3760: 3756: 3752: 3748: 3744: 3740: 3736: 3729: 3726: 3721: 3717: 3713: 3709: 3705: 3701: 3694: 3691: 3686: 3682: 3678: 3674: 3670: 3666: 3662: 3658: 3651: 3648: 3643: 3639: 3635: 3631: 3627: 3623: 3619: 3615: 3611: 3608:(in German). 3607: 3600: 3597: 3592: 3588: 3584: 3578: 3575: 3569: 3566: 3561: 3555: 3551: 3547: 3546: 3541: 3540:Greene, Brian 3535: 3532: 3526: 3522: 3518: 3514: 3510: 3509: 3508: 3504: 3499: 3496: 3491: 3487: 3483: 3479: 3475: 3471: 3467: 3463: 3456: 3454: 3450: 3445: 3441: 3437: 3433: 3432: 3426: 3420: 3417: 3413: 3409: 3408: 3401: 3398: 3393: 3387: 3383: 3382: 3375: 3368: 3365: 3360: 3354: 3350: 3349: 3341: 3338: 3333: 3327: 3323: 3322: 3315: 3309: 3306: 3301: 3295: 3291: 3290: 3282: 3279: 3273: 3270: 3257: 3253: 3249: 3243: 3240: 3234: 3231: 3226: 3220: 3216: 3215: 3207: 3205: 3203: 3201: 3199: 3197: 3195: 3193: 3191: 3187: 3182: 3176: 3172: 3171: 3163: 3161: 3157: 3152: 3146: 3142: 3141: 3133: 3130: 3123: 3117: 3113: 3109: 3108: 3102: 3101: 3096: 3093: 3088: 3084: 3080: 3076: 3072: 3068: 3064: 3060: 3055: 3050: 3046: 3042: 3041: 3033: 3031: 3027: 3023: 3017: 3015: 3011: 3006: 3002: 2998: 2994: 2989: 2984: 2980: 2976: 2973:(3007): 890. 2972: 2968: 2964: 2957: 2954: 2949: 2945: 2941: 2937: 2933: 2929: 2925: 2921: 2917: 2910: 2907: 2902: 2898: 2893: 2888: 2884: 2880: 2876: 2869: 2866: 2859: 2854: 2851: 2849: 2846: 2844: 2841: 2839: 2836: 2834: 2831: 2829: 2826: 2824: 2821: 2819: 2816: 2814: 2811: 2809: 2806: 2804: 2801: 2799: 2796: 2794: 2791: 2789: 2786: 2784: 2781: 2780: 2775: 2767: 2759: 2750: 2743: 2731: 2717: 2715: 2711: 2706: 2704: 2703:Roger Penrose 2700: 2696: 2692: 2688: 2683: 2681: 2676: 2670: 2662: 2660: 2657: 2656:David Deutsch 2653: 2645: 2643: 2641: 2637: 2636:Carlo Rovelli 2633: 2625: 2623: 2619: 2617: 2613: 2609: 2605: 2601: 2597: 2593: 2589: 2585: 2579: 2571: 2569: 2567: 2563: 2560: 2552: 2550: 2548: 2544: 2541: 2538: 2534: 2533:superposition 2529: 2516: 2513: 2510: 2507: 2500: 2497: 2494: 2491: 2488: 2485: 2482: 2476: 2467: 2459:by imposing: 2458: 2454: 2449: 2434: 2429: 2420: 2417: 2414: 2411: 2408: 2405: 2402: 2396: 2393: 2389: 2379: 2374: 2369: 2363: 2360: 2357: 2354: 2351: 2348: 2345: 2339: 2331: 2327: 2322: 2304: 2301: 2298: 2295: 2292: 2289: 2286: 2280: 2277: 2273: 2269: 2263: 2260: 2257: 2254: 2251: 2248: 2245: 2233: 2224: 2220: 2215: 2213: 2208: 2200: 2195: 2188: 2186: 2183: 2179: 2174: 2159: 2157: 2153: 2149: 2145: 2141: 2140:sinc function 2117: 2112: 2108: 2105: 2102: 2099: 2096: 2090: 2084: 2061: 2056: 2052: 2049: 2046: 2043: 2040: 2034: 2030: 2025: 2021: 2017: 2015: 2007: 2001: 1990: 1989: 1988: 1986: 1981: 1975: 1972: 1962: 1942: 1938: 1934: 1931: 1928: 1923: 1919: 1915: 1912: 1909: 1899: 1898: 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1103: 1101: 1096: 1091: 1083: 1078: 1071: 1069: 1067: 1066:classical way 1063: 1057: 1055: 1051: 1045: 1043: 1039: 1034: 1032: 1028: 1024: 1020: 1015: 1011: 999: 994: 992: 987: 985: 980: 979: 977: 976: 968: 965: 963: 960: 958: 955: 953: 950: 948: 945: 943: 940: 938: 935: 933: 930: 928: 925: 923: 920: 918: 915: 913: 910: 908: 905: 903: 900: 898: 895: 893: 890: 888: 885: 883: 880: 878: 875: 873: 870: 868: 865: 863: 860: 858: 855: 853: 850: 848: 845: 843: 840: 838: 835: 833: 830: 828: 825: 823: 820: 818: 815: 813: 810: 808: 805: 803: 800: 798: 795: 793: 790: 788: 785: 783: 780: 778: 775: 773: 770: 768: 765: 763: 760: 758: 755: 753: 750: 748: 745: 743: 740: 739: 732: 731: 724: 721: 719: 716: 714: 711: 709: 706: 704: 701: 699: 698:Quantum chaos 696: 694: 691: 689: 686: 684: 681: 679: 676: 675: 669: 668: 660: 657: 655: 654:Transactional 652: 650: 647: 645: 644:Quantum logic 642: 640: 637: 635: 632: 626: 623: 622: 621: 618: 617: 616: 613: 611: 608: 606: 603: 601: 598: 596: 593: 591: 588: 587: 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7406:Ground state 7401:Energy level 7374:Fundamentals 7338:Introduction 7268: 7199:Walter Lewin 7170: 7161: 7134: 7115: 7091: 7068: 7047: 7038: 7018: 6998: 6976: 6933:(1–2): 7–8. 6930: 6926: 6920: 6887: 6883: 6877: 6844: 6840: 6834: 6801: 6797: 6791: 6761:(3): 95–97. 6758: 6754: 6748: 6728: 6721: 6688: 6684: 6674: 6649: 6645: 6641: 6635: 6624:, retrieved 6619: 6609: 6600: 6591: 6553:(1): 15–28. 6550: 6546: 6540: 6521: 6515: 6495: 6488: 6477: 6466:Vaidman, Lev 6460: 6409: 6405: 6402:Kent, Adrian 6396: 6353: 6349: 6340: 6307: 6303: 6293: 6273: 6266: 6225: 6221: 6211: 6190: 6187:Peres, Asher 6181: 6154: 6117: 6113: 6104: 6079: 6070: 6025: 6015: 6004: 6002: 5980: 5971: 5928: 5922: 5916: 5905: 5892: 5872: 5868:Zee, Anthony 5862: 5853: 5844: 5803: 5799: 5745: 5741: 5731: 5680: 5676: 5620: 5616: 5606: 5598: 5594: 5590: 5586: 5581: 5554: 5550: 5540: 5531: 5521: 5484: 5480: 5470: 5458:. 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Leeds, UK 3663:(1): 4–11. 3374:experiment. 2818:Matter wave 2540:propagating 2453:probability 1631:Kerr effect 1263:probability 1100:Diffraction 942:von Neumann 927:Schrödinger 703:EPR paradox 634:Many-worlds 568:Schrödinger 523:Schrödinger 518:Phase-space 508:Interaction 413:Double-slit 391:Experiments 366:Uncertainty 336:Nonlocality 331:Measurement 316:Decoherence 286:Hamiltonian 124:phase shift 8171:Categories 7979:Extensions 7813:Technology 7659:Relational 7610:Copenhagen 7521:Heisenberg 7468:Tunnelling 7331:Background 7050:. Norton. 5938:1502.06547 5690:1510.01277 5322:1887/71482 5227:1710.02216 4747:11 January 3438:: 90–105. 3262:18 October 2860:References 2592:Niels Bohr 2457:normalized 2178:near field 2173:function. 2138:where the 1832:wavelength 1623:pump laser 1600:pilot wave 1546:metastable 1446:inequality 1123:wavefronts 937:Sommerfeld 852:Heisenberg 847:Gutzwiller 787:de Broglie 735:Scientists 649:Relational 600:Copenhagen 503:Heisenberg 361:Tunnelling 262:Background 8113:Astronomy 7685:Bell test 7555:Equations 7381:Born rule 6955:0375-9601 6912:0375-9601 6869:0375-9601 6826:120784358 6818:1827-613X 6783:0375-9601 6713:250911999 6705:0953-8984 6666:0031-9228 6652:(8): 12. 6626:14 August 6575:1826-9877 6452:118471198 6444:0015-9018 6419:1408.1944 6324:0304-3991 6310:: 49–56. 6250:0028-0836 6173:439453957 6151:Omnès, R. 6126:0036-8504 6096:203390914 6062:118458259 6035:1409.2454 5999:799397091 5931:: 73–83. 5898:Faye, Jan 5836:257922697 5778:257945438 5770:1745-2481 5715:1745-2481 5623:: 18574. 5367:1210.6243 5252:2045-2322 5187:0031-9007 4872:119242577 4855:1202.5148 4805:118987962 4718:Kwiat, P. 4689:0011-3891 4642:122856271 4444:442351498 4395:203638258 4035:1367-2630 4010:1210.6243 3871:0304-3991 3857:: 73–76. 3835:0953-8585 3685:0002-9505 3642:121659705 3634:0044-3328 3527:. p. 203. 3490:203638258 3404:Feynman, 3054:1310.8343 2997:0028-0836 2948:171025814 2940:0007-0874 2901:110408369 2766:far field 2608:Born rule 2557:Like the 2472:all space 2468:∭ 2384:all paths 2380:∫ 2370:∝ 2326:magnitude 2113:λ 2109:θ 2106:⁡ 2097:π 2057:λ 2053:θ 2050:⁡ 2041:π 2031:⁡ 2018:∝ 2008:θ 1935:λ 1920:θ 1867:λ 1864:≈ 1855:θ 1815:… 1782:λ 1767:θ 1729:θ 1723:≈ 1720:θ 1717:⁡ 1694:far field 1683:intensity 1679:amplitude 1552:0.7 1488:entangled 1380:entangled 1195:(L-NESS, 1090:classical 1050:molecules 1038:electrons 1019:interfere 967:Zeilinger 812:Ehrenfest 541:Equations 218:⟩ 215:Ψ 204:^ 192:⟩ 189:Ψ 166:ℏ 8074:Category 7868:Timeline 7620:Ensemble 7600:Bayesian 7493:Collapse 7365:Glossary 7348:Timeline 7215:Archived 7114:(1999). 6997:(2018). 6975:(2003). 6583:53575967 6388:16325959 6332:25799917 6189:(1995). 6153:(1994). 6134:43414997 6024:(eds.). 5979:(1973). 5963:27697360 5900:(2019). 5870:(2010). 5828:37012471 5723:53536274 5655:26689679 5451:Archived 5339:19197175 5331:15783641 5285:Gbur, G. 5270:28978914 5195:11801091 5132:18494170 5086:20 March 5081:10043591 5034:10043591 4720:(2007). 4697:24103129 4424:(2006). 4348:21468015 4234:21547361 4226:11690188 4171:Archived 4152:Archived 3978:31058223 3794:Archived 3777:26525832 3542:(1999). 3250:(2007). 3079:23900710 2885:: 1–16. 2776:See also 2701:and Sir 2640:observer 2600:Max Born 2146:) = sin( 1072:Overview 892:Millikan 817:Einstein 802:Davisson 757:Blackett 742:Aharonov 610:Ensemble 590:Bayesian 495:Overview 376:Collapse 356:Symmetry 247:Glossary 8101:Science 8087:Portals 8027:Related 8006:History 7745:Science 7577:Rydberg 7343:History 7139:Bibcode 6935:Bibcode 6892:Bibcode 6849:Bibcode 6763:Bibcode 6555:Bibcode 6476:(ed.). 6424:Bibcode 6368:Bibcode 6258:4311842 6230:Bibcode 5943:Bibcode 5808:Bibcode 5750:Bibcode 5695:Bibcode 5646:4686973 5625:Bibcode 5559:Bibcode 5512:2955131 5489:Bibcode 5460:21 June 5425:Bibcode 5372:Bibcode 5301:Bibcode 5261:5627254 5232:Bibcode 5167:Bibcode 5140:4424892 5112:Bibcode 5061:Bibcode 5014:Bibcode 4959:Bibcode 4933:16 June 4897:Bibcode 4785:Bibcode 4730:Bibcode 4622:Bibcode 4587:Bibcode 4552:Bibcode 4527:21 June 4500:21 June 4469:21 June 4463:UPSCALE 4375:Bibcode 4339:3104521 4318:Bibcode 4316:: 263. 4264:Bibcode 4206:Bibcode 4118:Bibcode 4015:Bibcode 3969:6499593 3948:Bibcode 3768:4617474 3747:Bibcode 3708:Bibcode 3665:Bibcode 3614:Bibcode 3470:Bibcode 3112:123–124 3087:3944699 3059:Bibcode 3005:4122313 2975:Bibcode 2330:squared 1671:summing 1168:of the 1143:quantum 932:Simmons 922:Rydberg 887:Moseley 867:Kramers 857:Hilbert 842:Glauber 837:Feynman 822:Everett 792:Compton 563:Rydberg 252:History 7720:Popper 7201:of MIT 7177: 7162:Optics 7149: 7122: 7100: 7077: 7054: 7026: 7005: 6983: 6953: 6910: 6867: 6824: 6816: 6781: 6736: 6711: 6703: 6664: 6581: 6573: 6528: 6503: 6450: 6442: 6386: 6330: 6322: 6281: 6256: 6248: 6222:Nature 6199: 6171: 6161: 6132: 6124: 6094: 6060: 6050: 5997: 5987: 5961: 5880: 5834: 5826: 5800:Nature 5776: 5768: 5721: 5713: 5653: 5643: 5509: 5392:832961 5390: 5337: 5329: 5268: 5258: 5250: 5193: 5185: 5138: 5130: 5104:Nature 5079: 5032: 4870: 4842:Quanta 4803: 4695: 4687: 4640: 4442: 4432: 4393: 4346: 4336: 4289:4 June 4232: 4224: 4091: 4066: 4043:832961 4041: 4033: 3976: 3966: 3917: 3892: 3869: 3833: 3775: 3765: 3683: 3640: 3632: 3593:: 114. 3556: 3550:97–109 3523: 3507:length 3488: 3388: 3355: 3328: 3296: 3221: 3177: 3147: 3118: 3085: 3077: 3003: 2995: 2967:Nature 2946: 2938: 2899: 2697:, Sir 2680:ad hoc 2223:action 2066: 1907: 1788: 1760: 1023:photon 962:Zeeman 957:Wigner 907:Planck 877:Landau 862:Jordan 513:Matrix 443:Popper 75:, the 8125:Stars 7630:Local 7572:Pauli 7562:Dirac 6822:S2CID 6709:S2CID 6579:S2CID 6472:. In 6448:S2CID 6414:arXiv 6384:S2CID 6358:arXiv 6254:S2CID 6130:JSTOR 6092:S2CID 6058:S2CID 6030:arXiv 5959:S2CID 5933:arXiv 5832:S2CID 5774:S2CID 5719:S2CID 5685:arXiv 5532:Wired 5454:(PDF) 5413:(PDF) 5388:S2CID 5362:arXiv 5335:S2CID 5222:arXiv 5136:S2CID 4868:S2CID 4850:arXiv 4801:S2CID 4775:arXiv 4693:JSTOR 4659:A 128 4638:S2CID 4391:S2CID 4283:(PDF) 4252:(PDF) 4230:S2CID 4196:arXiv 4039:S2CID 4005:arXiv 3638:S2CID 3486:S2CID 3423:See: 3083:S2CID 3049:arXiv 3001:S2CID 2944:S2CID 2897:S2CID 2537:waves 2219:phase 1675:phase 1205:Italy 1117:When 1093:is a 1014:laser 917:Raman 902:Pauli 897:Onnes 832:Fermi 807:Debye 797:Dirac 762:Bloch 752:Bethe 620:Local 558:Pauli 548:Dirac 346:State 7175:ISBN 7147:ISBN 7120:ISBN 7098:ISBN 7075:ISBN 7052:ISBN 7024:ISBN 7003:ISBN 6981:ISBN 6951:ISSN 6908:ISSN 6865:ISSN 6814:ISSN 6779:ISSN 6734:ISBN 6701:ISSN 6662:ISSN 6628:2023 6571:ISSN 6526:ISBN 6501:ISBN 6440:ISSN 6328:PMID 6320:ISSN 6279:ISBN 6246:ISSN 6197:ISBN 6169:OCLC 6159:ISBN 6122:ISSN 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