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Double-slit experiment From Wikipedia, the free encyclopedia

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Same device, one slit open vs. two slits open (Note the 16 fringes.)

The slits; distance between top posts approximately one inch.

Single-slit diffraction pattern

Double-slit diffraction and interference pattern

In the double-slit experiment, light is shone at a solid thin plate that has two slits cut into it. A photographic plate or some other detection screen is set up to record what comes through those slits. One or the other slit may be open, or both may be open.

Normally, when only one slit is open, the pattern on the plate is a diffraction pattern, a fairly narrow central band with dimmer bands parallel to it on each side. When both slits are open, the pattern displayed becomes very much more detailed and at least four times as wide. When two slits are open, probability wave fronts[1] emerge simultaneously from each slit and radiate in concentric circles. When the detector screen is reached, the sum of the two probability wave fronts at each point determines the probability that a photon will be observed at that point. The end result when

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many photons are directed at the screen is a series of bands or "fringes." The interference of probability wave fronts is shown in the graph below.

When two slits are open but something is added to the experiment to allow a determination that a photon has passed through one or the other slit, then the interference pattern disappears and the experimental apparatus yields two simple patterns, one from each slit. (See below.)

However, interference fringes are still obtained even when only one slit is open at any given time, [2] provided that difference in length between the two paths in the interferometer is such that a photon could have travelled through either slit. This is the case even though the photon density in the system is much less than one.

The most baffling part of this experiment comes when only one photon at a time is fired at the barrier with both slits open. The pattern of interference remains the same as can be seen if many photons are emitted one at a time and recorded on the same sheet of photographic film. The clear implication is that something with a wavelike nature passes simultaneously through both slits and interferes with itself — even though there is only one photon present. (The experiment works with electrons, atoms, and even some molecules too.)

"Feynman was fond of saying that all of quantum mechanics can be gleaned from carefully thinking through the implications of this single experiment."[3]

(The following depictions are relatively slow to load.)

• Animation 1 • Animation 2 (zoom in)

Contents

[hide]

• 1 The underpinning of this experiment • 2 Importance to physics • 3 Importance to philosophy • 4 Results observed • 5 Shape of interference fringes • 6 Quantum version of experiment • 7 When observed emission by emission • 8 See also • 9 References

o 9.1 Further reading • 10 External links

[edit] The underpinning of this experiment

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Circles of equal sizes are drawn along an existing wavefront and their tangents are smoothed to form the next predicted wavefront location.

Christiaan Huygens understood the basic idea of how light propagates and how to predict its path through a physical apparatus. He understood a light source to emit a series of waves comparable to the way that water waves spread out from something like a bobber that is jiggled up and down as it floats on the water surface. He said that the way to predict where the next wave front will be found is to generate a series of concentric circles on a sufficiently large number of points on a known wave front and then draw a curve that will pass tangent to all the resulting circles out in front of the known wave front. The diagram given here shows what happens when a flat wave front is extended in this manner, and what happens when a curved wave front is extended in the same way. Augustin Fresnel (1788-1827) based his proof that the wave nature of light does not contradict the observed fact that light propagates in a straight line in homogeneous media on Huygens' work, and also based himself on Huygens' ideas to give a complete account of diffraction and interference phenomena known at his time.[4] See the article Huygens–Fresnel principle for more information.

Note the there are four gaps between crests hitting the screen -- places that will be darker in the resultant diffraction pattern visible to an observer

The second drawing shows what happens when a flat wave front encounters a slit in a wall. Following the same principle elucidated above, it is clear that the new wave front will "bulge out" from the slit and light will be experienced as having diverged around the edges of the slit.

The third drawing shows the explanation for interference based on the classical idea of a single wave front that represents all the light energy emitted by a source at one moment. Since photons diverge beyond the barrier wall, the distance between parts of any pattern they form on the target wall increase as the distance they have to travel increases, a fact that is well known from everyday experience with things like automobile headlights whose beams are not parallel. But decreasing the distance between slits will also increase the distance between fringes (colored bands such as the

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sixteen shown in the second photograph above). Increasing the wavelength will also increase the distance between fringes as long as the slits are wide enough to permit the passage of light of that wavelength. Slits that are very wide in comparison to the frequency of the photons involved (e.g., two ordinary windows in a single wall) will permit light to appear to go "straight through."

J is the distance between fringes. J = Dλ/B "D" = dist. S2 to F, λ = wavelength, B = dist. a to b [5]

When light came to be understood as the result of electrons falling from higher energy orbits to lower energy orbits, the light that is delivered to some surface in any short interval of time came to be understood as ordinarily representing the arrival of very many photons, each with its own wave front. In understanding what actually happens in the two-slit experiment it became important to find out what happens when photons are emitted one by one.[6] When it became possible to perform that experiment, it became apparent that a single photon has its own wave front that passes through both slits, and that the single photon will show up on the detector screen according to the net probability values resulting from the co-incidence of the two probability waves coming by way of the two slits. When a great number of photons are sent through the apparatus one by one and recorded on photographic film, the same interference pattern emerges that had been seen before when many photons were being emitted at the same time. The double-slit experiment was first performed by Taylor in 1909,[7] by reducing the level of incident light until on average only one photon was being transmitted at a time.[8] Note that it is the probabilities of photons appearing at various points along the detection screen that add or cancel. So if there is a cancellation of waves at some point that does not mean that a photon disappears; it means that the probability of a photon's appearing at that point will disappear, and the probability that it will appear somewhere else increases.

[edit] Importance to physics

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Sketch of the layout of a classical optical double-slit experiment Note that lasers are commonly used today and replace the incoherent source of light and the top pinhole.

Although the double-slit experiment is now often referred to in the context of quantum mechanics, it is generally thought to have been first performed by the English scientist Thomas Young in the year 1801 in an attempt to resolve the question of whether light was composed of particles (Newton's "corpuscular" theory), or rather consisted of waves traveling through some ether, just as sound waves travel in air. The interference patterns observed in the experiment seemed to discredit the corpuscular theory, and the wave theory of light remained well accepted until the early 20th century, when evidence began to accumulate which seemed instead to confirm the particle theory of light.[9]

The double-slit experiment, and its variations, then became a classic Gedankenexperiment (thought experiment) for its clarity in expressing the central puzzles of quantum mechanics.

It was shown experimentally in 1972 [10]that in a Young's slit system where only one slit was open at any time, interference was nonetheless observed providing the path difference was such that the detected photon could have come from either slit. The experimental conditions were such that the photon density in the system was much less than unity.

A Young's slit experiments was not performed with anything other than light until 1961, when Claus Jönsson of the University of Tübingen performed it with electrons[11][12], and not until 1974 in the form of "one electron at a time", in a laboratory at the University of Milan, by researchers led by Pier Giorgio Merli, of LAMEL-CNR Bologna.

The results of the 1974 experiment were published and even made into a short film, but did not receive wide attention. The experiment was repeated in 1989 by Tonomura et al at Hitachi in Japan. Their equipment was better, reflecting 15 years of advances in electronics and a dedicated development effort by the Hitachi team. Their methodology was more precise and elegant, and their results agreed with the results of Merli's team. Although Tonomura asserted that the Italian

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experiment had not detected electrons one at a time—a key to demonstrating the wave-particle paradox—single electron detection is clearly visible in the photos and film taken by Merli and his group.[13]

In September 2002, the double-slit experiment of Claus Jönsson was voted "the most beautiful experiment" by readers of Physics World.[14]

[edit] Importance to philosophy

Philosophy is concerned with the nature of ideas about the world (or worlds), how those ideas are grounded, and how to ferret out self-contradictions. The double-slit experiment is of great interest therefore, because it forces philosophers to reevaluate their ideas about such basic concepts as "particles",[15] "waves", "location", "movement from one place to another", etc.

In contrast to the way of conceptualizing the macroscopic world of everyday experience, attempting to describe the motion of a single photon is problematic. As Philipp Frank observes, investigating the motion of single particles through a single slit can obtain a description of the pattern of photon strikes on a target screen. However, "the pattern of fringes for two slits is not the superposition of the two patterns for single slits. Hence, there is no law of motion that would determine the trajectory of a single photon and allow us to derive the observed facts that occur when photons pass two slits."[16] Experience in the micro world of sub-atomic particles forces us to reconceptualize some of our most commonplace ideas.

One of the most striking consequences of the new science is that it is not in agreement with the belief of Laplace that an omniscient entity, knowing the initial positions and velocities of all particles in the universe at one time, could predict their positions at any future time. (To paraphrase Laplace's position, the positions and velocities of all things at any given time depend absolutely on their previous positions and velocities and the absolute laws that govern physical interactions.) Laplace believed that such particles would follow the laws of motion discovered by Newton, but twentieth century physics made it clear that the motions of sub-atomic particles and even some small atoms cannot be predicted by using the laws of Newtonian physics.[17] For instance, most of the orbits for electrons moving around atomic nuclei that are permitted by Newtonian physics are excluded by the new physics. And it is not even clear what the "movement" of a particle such as a photon may be when it is not clear that it "goes through" either one slit or the other, but it is clear that the probability of its arrival at various points on the target screen is a function of its wavelength and of the distance between the slits. Whereas Laplace would expect an omniscient spirit to be able to predict with absolute confidence the arrival of a photon at some specific point on the target screen, it turns out that the particle may arrive at one of a great number of points, but that the percentage of particles that arrive at each of such points is determined by the laws of the new physics.

[edit] Results observed

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Thomas Young's sketch of two-slit diffraction, based on his observations of water waves.[18]

The bright bands observed on the screen happen when the light has interfered constructively—where a crest of a wave meets a crest from another wave. The dark regions show destructive interference—a crest meets a trough. Constructive interference occurs when

where λ is the wavelength of the light, b is the separation of the slits, the distance between A and B in the diagram to the right n is the order of maximum observed (central maximum is n=0), x is the distance between the bands of light and the central maximum (also called fringe distance), and L is the distance from the slits to the screen centerpoint.

This is only an approximation and depends on certain conditions.[19]

It is possible to work out the wavelength of light using this equation and the above apparatus. If b and L are known and x is observed, then λ can be easily calculated.

A detailed treatment of the mathematics of double-slit interference in the context of quantum mechanics is given in the article on Englert-Greenberger duality.

[edit] Shape of interference fringes

The theoretical shapes of the interference fringes observed in Young's double slit experiment are straight lines which is easily proved.

In case two pinholes are used instead of slits, as in the original Young's experiment, hyperbolic fringes are observed.

If the two sources are placed on a line perpendicular to the screen, the shape of the interference fringes is circular as the individual paths travelled by light from the two sources are always equal for a given fringe. This can be done in simpler way by placing a mirror parallel to a screen at a distance and a source of light just above the mirror. (Note the extra phase difference of π due to reflection at the interface of a denser medium)

[edit] Quantum version of experiment

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The wavefronts resulting from two pinholes.

By the 1920s, various other experiments (such as the photoelectric effect) had demonstrated that light interacts with matter only in discrete, "quantum"-sized packets called photons.

If sunlight is replaced with a light source that is capable of producing just one photon at a time, and the screen is sensitive enough to detect a single photon, Young's experiment can, in theory, be performed one photon at a time with identical results.

If either slit is covered, the individual photons hitting the screen, over time, create an ordinary diffraction pattern. But if both slits are left open, the pattern of photons hitting the screen, over time, again becomes a series of light and dark fringes. This result seems to both confirm and contradict the wave theory. If light were not to behave like a wave, there would be no interference pattern. On the other hand, if light were actually a wave then light energy would not arrive in discrete quantities (quanta) and would be spread over more space the farther the detector screen was placed from the screen with the slits in it.

A remarkable result follows from a variation of the double-slit experiment in which detectors are placed in either or both of the two slits in an attempt to determine which slit the photon passes through on its way to the screen. Placing a detector even in just one of the slits will result in the disappearance of the interference pattern. The detection of a photon involves a physical interaction between the photon and the detector of the sort that physically changes the detector. (If nothing changed in the detector, it would not detect anything.) If two photons of the same frequency were emitted at the same time they would be coherent. If they went through two unobstructed slits then they would remain coherent and arriving at the screen at the same time but laterally displaced from each other they would exhibit interference. However, if one or both of them were to encounter a detector time could be required for each to interact with its detector, and then they would most likely fall out of step with each other, that is, they would decohere. They would then arrive at the

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screen at slightly different times and could not interfere because the first to arrive would have already interacted with the screen before the second got there. If only one photon is involved, it must be detected at one or the other detector, and its continued path goes forward only from the slit where it was detected.[20]

The Copenhagen interpretation is a consensus among some of the pioneers in the field of quantum mechanics that it is undesirable to posit anything that goes beyond the mathematical formulae and the kinds of physical apparatus and reactions that enable us to gain some knowledge of what goes on at the atomic scale. One of the mathematical constructs that enables experimenters to very accurately predict certain experimental results is sometimes called a probability wave. In its mathematical form it is analogous to the description of a physical wave, but its "crests" and "troughs" indicate levels of probability for the occurrence of certain phenomena (e.g., a spark of light at a certain point on a detector screen) that can be observed in the macro world of ordinary human experience.

The probability "wave" can be said to "pass through space" because the probability values that one can compute from its mathematical representation are dependent on time. One cannot speak of the location of any particle such as photon between the time it is emitted and the time it is detected simply because in order to say that something is located somewhere at a certain time one has to detect it. The requirement for the eventual appearance of an interference pattern is that particles be emitted, and that there be a screen with at least two slits between the emitter and the detection screen. Experiments observe nothing whatsoever between the time of emission of the particle and its arrival at the detection screen. However, it is essential that both slits be an equal distance from the center line, and that they be within a certain maximum distance of each other that is related to the wavelength of the particle being emitted. If a ray tracing is then made as if a light wave as understood in classical physics is wide enough to encounter both slits and passes through both of them, then that ray tracing will accurately predict the appearance of maxima and minima on the detector screen when many particles pass through the apparatus and gradually "paint" the expected interference pattern.

Note that the existence of any such particle is known only at the point of emission and the point of detection. If by "object A exists" is meant "object A is detected at point x,y,z,t," then this object "exists" only at the point of emission and the point of detection. In between times it is completely out of sensible interaction with the things of our universe, out of sensible interaction with the macro world. What is going on in the apparatus is something that is not known.

It is perhaps not so astounding that one knows nothing about what a light particle is doing between the time it is emitted from the sun and the time it triggers a reaction in one's retina, but the remarkable consequence discovered by this experiment is that anything that one does to try to locate a photon between the emitter and the detection screen will change the results of the experiment in a way that everyday experience would not lead one to expect. If, for instance, any device is used in any way that can determine whether a particle has passed through one slit or the other, the interference pattern formerly produced will then disappear.

Reason, as applied to the events of our ordinary macro experience, tells us that a particle must pass through one slit or the other. The experiment tells us that there must be at least two slits to produce an interference pattern, and that anything that locates the particle before it hits the screen will destroy the interference pattern. Recent experiments have tried to identify which of the two slits a particle is coming out of on its way to the detection screen. Doing so will also prevent interference. Even less in line with the expectations of human scale interactions with nature, if the information

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about which slit a given particle came through is "erased" before a photon has time to interact with the detector screen, interference will be restored. (See Quantum eraser experiment.)

The Copenhagen interpretation is similar to the path integral formulation of quantum mechanics provided by Richard Feynman. (Feynman stresses that his formulation is merely a mathematical description, not an attempt to describe some "real" process that we cannot see.) In the path integral formulation, a particle such as a photon takes every possible path through space-time to get from point A to point B. In the double-slit experiment, point A might be the emitter, and point B the screen upon which the interference pattern appears, and a particle takes every possible path, including paths through both slits at once, to get from A to B. When a detector is placed at one of the slits, the situation changes, and we now have a different point B. Point B is now at the detector, and a new path proceeds from the detector to the screen. In this eventuality there is only empty space between (B =) A' and the new terminus B', no double slit in the way, and so an interference pattern no longer appears.

[edit] When observed emission by emission

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Electron buildup over time

Regardless of whether it is an electron, a proton, or something else existing on what is considered a "quantum" scale, where it will arrive at the screen is highly determinate (in that quantum mechanics predicts accurately the probability that it will arrive at any point on the screen). However, in what sequence members of a series of singly emitted things (e.g., electrons) will arrive is completely unpredictable. The experimental facts are so highly reproducible that there is virtually no argument about them, but the appearance of there being an uncaused event (because of the unpredictability of the sequencing) has aroused a great deal of cognitive dissonance and attempts to account for the sequencing by reference to supposed "additional variables".

For example, when electrons are fired at the target screen in bursts, it is easy to account for the interference pattern that results by assuming that electrons that travel in pairs are interfering with each other because they arrive at the screen at the same time, but when laboratory apparatus was developed that could reliably fire single electrons at the screen, the emergence of an interference pattern suggested that each electron was interfering with itself; and, therefore, in some sense the electron had to be going through both slits. For something that most people continue to imagine to be an unimaginably small particle to be able to interfere with itself would suggest that this "sub-atomic particle" was in two places at once, but that idea is strongly at odds with the truism, "You cannot be in two places at the same time," (see law of noncontradiction). It was easier to conceptualize the electron as a wave than to accept another, more disturbing implication (from the point-of-view of our everyday notions of reality): that quantum objects are able to exist and behave in ways that defy classical interpretation.

When the double-slit experiment is performed one electron at a time with sensitive apparatus the same interference pattern emerges that would be seen if multiple electrons were fired simultaneously as had always been done with the cruder previously available apparatus. So the appearance of an orderly and consistent universe was maintained, albeit one in which everything with atomic dimensions had to be conceived as having some sort of wave nature.

However, when one electron (proton, photon, or whatever) is fired at a time, it also becomes possible to detect the point on the screen at which it arrives—and another result was demonstrated that could not easily be squared with experience of the macro world, the world of everyday experience.

In everyday experience we are accustomed to a seemingly analogous result. If one tests a firearm by locking it in a gun mount and firing several rounds at a target, a scatter pattern of bullet holes will appear in the target. We know from long experience that a poorly made gun firing poorly made ammunition will scatter shots fairly widely. We can learn and understand how flight path deviations are caused; more exacting construction of both firearms and ammunition leads to tighter and tighter patterns of bullet holes. But that is not what happens in the new double-slit experiment.

Returning again to electrons, when electrons are fired one at a time through a double-slit apparatus they do not cluster around two single points directly on lines between the emitter and the two slits, but instead one by one they fill in the same old interference pattern with which we have now become quite familiar. However, they do not arrive at the screen in any predictable order. In other words, knowing where all the previous electrons appeared on the screen and in what order tells us nothing about where the next electron will hit.

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The electrons (and the same applies to photons and to anything of atomic dimensions used) arrive at the screen in an unpredictable and arguably causeless random sequence, and the appearance of a causeless selection event in a highly orderly and predictable formulation of the by now familiar interference pattern has caused many people to try to find additional determinants in the system which, were they to become known, would account for why each impact with the target appears.[21]

Recent studies have revealed that interference is not restricted solely to elementary particles such as protons, neutrons, and electrons. Specifically, it has been shown that large molecular structures like fullerene (C60) also produce interference patterns.[22]

[edit] See also

• Afshar experiment • Elitzur-Vaidman bomb-testing problem • Photon dynamics in the double-slit experiment • Photon polarization • Quantum eraser experiment • Quantum coherence • Delayed choice quantum eraser • Wheeler's delayed choice experiment

[edit] References

1. ^ Greene, The Elegant Universe, p. 109 2. ^ Sillitto R and Wykes, C. 1972, Phys. Lett., An interference experiment with light beams

modulated in anti-phase by an electro-optic shutter, 39A, 333-4 3. ^ Greene, The Elegant Universe, p. 97f 4. ^ Louis de Broglie, The Revolution in Physics, p. 47. 5. ^ Philipp Frank, Philosophy of Science, p. 200f. 6. ^ Louis de Broglie, The Revolution in Physics, p. 178-186 7. ^ Sir Geoffrey Ingram Taylor, "Interference Fringes with Feeble Light", Proc. Cam. phil.

Soc. 15, 114 (1909). 8. ^ Louis de Broglie, The Revolution in Physics, p. 117 9. ^ Albert Einstein, Essays in Science, Philosophical Library (1934), p. 100 10. ^ Sillitto RM & Wykes C, 1972, An interference experiment with light beams modulated in

anti-phase', Physics Letters, 39A, 4, 333-4 11. ^ Jönsson C, Zeitschrift für Physik, 161:454 12. ^ Jönsson C (1974). Electron diffraction at multiple slits. American Journal of Physics, 4:4-

11. 13. ^ See http://physicsworld.com/cws/article/indepth/9745 for more information and

photographs (at the bottom of the article). 14. ^ "The most beautiful experiment". Physics World 2002. 15. ^ Philipp Frank, Philosophy of Science, p. 200 16. ^ Philipp Frank, ""Philosophy of Science, p. 202 17. ^ Philipp Frank, The Philosophy of Science," p. 203 18. ^ Tony Rothman, Everything's Relative and Other Fables in Science and Technology

(Wiley, 2003) 19. ^ For a more complete discussion, with diagrams and photographs, see Arnold L Reimann,

Physics, chapter 38.

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20. ^ Greene, The Elegant Universe, p. 109f 21. ^ Greene, Brian, The Fabric of the Cosmos, 204–213 and throughout 22. ^ Nairz O, Arndt M, and Zeilenger A. Quantum interference experiments with large

molecules. American Journal of Physics, 2003; 71:319-325. http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=AJPIAS000071000004000319000001&idtype=cvips&gifs=yes

[edit] Further reading

• Tipler, Paul (2004). Physics for Scientists and Engineers: Electricity, Magnetism, Light, and Elementary Modern Physics, 5th ed., W. H. Freeman. ISBN 0-7167-0810-8.

• Gribbin, John (1999). Q is for Quantum: Particle Physics from A to Z. Weidenfeld & Nicolson. ISBN 0-7538-0685-1.

• Feynman, Richard P. (1988). QED: The Strange Theory of Light and Matter. Princeton University Press. ISBN 0-691-02417-0.

• Sears, Francis Weston (1949). Optics. Addison Wesley. • Hey, Tony (2003). The New Quantum Universe. Cambridge University Press. ISBN 0-5215-

6457-3. • Frank, Philipp (1957). Philosophy of Science. Prentice-Hall. • Greene, Brian (2000). The Elegant Universe. Vintage. ISBN 0-375-70811-1.

[edit] External links

Wikimedia Commons has media related to: Double-slit experiments

• Simple Derivation of Interference Conditions • The Double Slit Experiment • Double-Slit in Time • Keith Mayes explains the Double Slit Experiment in plain English • Carnegie Mellon department of physics, photo images of Newton's rings • Java demonstration of double slit experiment • Java demonstration of Young's double slit interference • Double-slit experiment animation • Electron Interference movies from the Merli Experiment (Bologna-Italy, 1974) • Freeview video 'Electron Waves Unveil the Microcosmos' A Royal Institution Discourse by

Akira Tonomura provided by the Vega Science Trust • Movie showing single electron events build up to form an interference pattern in the double-

slit experiments. (File size = 3.8 Mb)(Movie Length = 1m 8s) • Hitachi website that provides background on Tonomura video and link to the video • Animated video explaining the double-slit experiment in detail • "Single-particle interference observed for macroscopic objects" • http://www.acoustics.salford.ac.uk/feschools/waves/diffract3.htm Huygens and interference • http://www.strings.ph.qmw.ac.uk/~jmc/sefp/week9.pdf Huygens and interference • Video mashup for Double Slit experiment and Related Topics

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Retrieved from "http://en.wikipedia.org/wiki/Double-slit_experiment" Categories: Foundational quantum physics | Physics experiments | Quantum mechanics | Wave mechanics

Davisson–Germer experiment From Wikipedia, the free encyclopedia

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Quantum mechanics


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[show]Background


[hide]Experiments Double-slit experiment




Popper's experiment

Schrödinger's cat

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16


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In physics, the Davisson–Germer experiment provided a critically important confirmation of the de Broglie hypothesis that particles, such as electrons, could behave as waves. More generally, it helped cement the acceptance of quantum mechanics and of Schrödinger's wave equation.

In 1927 at Bell Labs, Clinton Davisson and Lester Germer fired slow moving electrons at a crystalline nickel target.[1] The angular dependence of the reflected electron intensity was measured, and was determined to have the same diffraction pattern as those predicted by Bragg for X-rays.

This experiment, like Arthur Compton's experiment which gave support to the particle-like nature of light, lent support to de Broglie's hypothesis on the wave-like nature of matter and completed the wave-particle duality hypothesis, which was a fundamental step in quantum theory.

The Davisson-Germer experiment demonstrated the wave nature of the electron, confirming the earlier hypothesis of deBroglie. Putting wave-particle duality on a firm experimental footing, it represented a major step forward in the development of quantum mechanics. The Bragg law for diffraction had been applied to x-ray diffraction, but this was the first application to particle waves.

Davisson and Germer designed and built a vacuum apparatus for the purpose of measuring the energies of electrons scattered from a metal surface. Electrons from a heated filament were accelerated by a voltage and allowed to strike the surface of nickel metal.

The electron beam was directed at the nickel target, which could be rotated to observe angular dependence of the scattered electrons. Their electron detector (called a Faraday box) was mounted on an arc so that it could be rotated to observe electrons at different angles. It was a great surprise to them to find that at certain angles there was a peak in the intensity of the scattered electron beam. This peak indicated wave behavior for the electrons, and could be interpreted by the Bragg law to give values for the lattice spacing in the nickel crystal.

The experimental data above, reproduced above Davisson's article, shows repeated peaks of scattered electron intensity with increasing accelerating voltage. This data was collected at a fixed scattering angle. Using the Bragg law, the deBroglie wavelength expression, and the kinetic energy of the accelerated electrons gives the relationship

In the historical data, an accelerating voltage of 54 volts gave a definite peak at a scattering angle of 50°. The angle theta in the Bragg law corresponding to that scattering angle is 65°, and for that angle the calculated lattice spacing is 0.092 nm. For that lattice spacing and scattering angle, the relationship for wavelength as a function of voltage is empirically

[edit] References

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1. ^ Clinton J. Davisson & Lester H. Germer, "Reflection of electrons by a crystal of nickel", Nature, V119, pp. 558-560 (1927).

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Stern–Gerlach experiment From Wikipedia, the free encyclopedia


Quantum mechanics


Introduction to...


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Popper's experiment

Schrödinger's cat

[show]Formulations

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18


[show]Scientists


In quantum mechanics, the Stern–Gerlach experiment, named after Otto Stern and Walther Gerlach, is a celebrated 1922 experiment on the deflection of particles, often used to illustrate basic principles of quantum mechanics. It can be used to demonstrate that electrons and atoms have intrinsically quantum properties, and how measurement in quantum mechanics affects the system being measured.

Contents

[hide]

• 1 Basic theory and description • 2 Sequential experiments • 3 History • 4 Impact • 5 See also • 6 External links • 7 References

[edit] Basic theory and description

Otto Stern and Walther Gerlach devised an experiment to determine whether particles had any intrinsic angular momentum. In a classical system, such as the earth orbiting the sun, the earth has angular momentum from both its orbit around the sun and the orbit around its axis (its spin). The experiment sought to determine whether individual particles like electrons have any "spin" angular momentum.[dubious – discuss] If the electron is treated like a classical dipole with two halves of charge spinning quickly, it will begin to precess in a magnetic field, because of the torque that the magnetic field exerts on the dipole (see Torque-induced precession).

If the particle travels in a homogeneous magnetic field, the forces exerted on opposite ends of the dipole cancel each other out and the motion of the particle is unaffected. If the experiment is conducted using electrons, an electric field of appropriate magnitude and oriented transverse to the charged particle's path is used to compensate for the tendency of any charged particle to curl in its path through a magnetic field (see cyclotron motion), and the fact that electrons are charged can safely be ignored. The Stern–Gerlach experiment can be conducted using electrically neutral particles and the same conclusion is reached, since it is designed to test angular momentum only, not any electrostatic phenomena.

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Basic elements of the Stern–Gerlach experiment.

If the particle travels through an inhomogeneous magnetic field, then the force on one end of the dipole will be slightly greater than the opposing force on the other end of the dipole. This leads to the particle being deflected in the inhomogeneous magnetic field. The direction in which the particles are deflected is typically called the "z" direction.

If the particles are classical, "spinning" particles, then the distribution of their spin angular momentum vectors is taken to be truly random and each particle would be deflected up or down by a different amount, producing an even distribution on the screen of a detector. Instead, the particles passing through the device are deflected either up or down by a specific amount. This can only mean that spin angular momentum is quantized, i.e. it can only take on discrete values. There is not a continuous distribution of possible angular momenta.

Spin values for fermions.

Electrons are spin-½ particles. These have only two possible spin values, called spin-up and spin-down. The exact value of their spin is +ħ/2 or -ħ/2. If this value arises as a result of the particles rotating the way a planet rotates, then the individual particles would have to be spinning impossibly fast. The speed of rotation would be in excess of the speed of light and thus impossible.[1] Thus, the spin angular momentum has nothing to do with rotation and is a purely quantum mechanical phenomenon. That is why it is sometimes known as the "intrinsic angular momentum."

For electrons, two possible values for spin exist, as well as for the proton and the neutron, which are composite particles made up of three quarks each, which are themselves spin-½ particles. Other particles may have a different number of possible values. Delta baryons (∆++, ∆+, ∆0, ∆−), for example, are spin-3/2 particles and have four possible values for spin angular momentum. Vector mesons, as well as photons, W and Z bosons and gluons are spin-1 particles and have three possible values for spin angular momentum.

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To describe the experiment with spin-½ particles mathematically, it is easiest to use Dirac's bra-ket notation. As the particles pass through the Stern-Gerlach device, they are "being observed." The act of observation in quantum mechanics is equivalent to measuring them. Our observation device is the detector and in this case we can observe one of two possible values, either spin up or spin down. These are described by the angular momentum quantum number j, which can take on one of the two possible allowed values, either +ħ/2 or -ħ/2. The act of observing (measuring) corresponds to the operator Jz. In mathematical terms,

The constants c1 and c2 are complex numbers. The square of their absolute values determines the probability of the state |ψ> being found with one of the two possible values for j. The constants must also be normalized so the probability of finding the wavefunction in one of either state is unity. Here we know that the probability of finding the particle in each state is 0.5. However, this information is not sufficient to determine the values of c1 and c2, because they may in fact be complex numbers. Therefore we only know the absolute values of the constants. These are

[edit] Sequential experiments

If we combine some Stern–Gerlach apparati we can clearly see that they do not act as simple selectors, but alter the states observed (as in light polarization), according to quantum mechanics laws:

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[edit] History

A plaque at the Frankfurt institute commemorating the experiment

The Stern–Gerlach experiment was performed in Frankfurt, Germany in 1922 by Otto Stern and Walther Gerlach. At the time, Stern was an assistant to Max Born at the University of Frankfurt's Institute for Theoretical Physics, and Gerlach was an assistant at the same university's Institute for Experimental Physics.

At the time of the experiment, the most prevalent model for describing the atom was the Bohr model, which described electrons as going around the positively-charged nucleus only in certain discrete atomic orbitals or energy levels. Since the electron was quantized to be only in certain positions in space, the separation into distinct orbits was referred to as space quantization.

[edit] Impact

The Stern–Gerlach experiment had one of the biggest impacts on modern physics:

• In the decade that followed, scientists showed using similar techniques, that the nucleus of some atoms also have quantized angular momentum. It is the interaction of this nuclear angular momentum with the spin of the electron that is responsible for the hyperfine structure of the spectroscopic lines.

• In the thirties, using an extended version of the S–G apparatus, Isidor Rabi and colleagues showed that by using a varying magnetic field, one can force the magnetic momentum to go from one state to the other. The series of experiments culminated in 1937 when they discovered that state transitions could be induced using time varying fields or RF fields. The so called Rabi oscillation is the working mechanism for the Magnetic Resonance Imaging equipment found in hospitals.

• Later Norman F. Ramsey, modified the Rabi apparatus to increase the interaction time with the field. The extreme sensitivity due to frequency of the radiation makes this very useful for keeping accurate time, and is still used today in atomic clocks.

• In the early sixties, Ramsey and Daniel Kleppner used a S–G system to produce a beam of polarized hydrogen as the source of energy for the Hydrogen Maser, which is still one of the most popular atomic clocks.

• The direct observation of the spin is the most direct proof of quantization in quantum mechanics.

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[edit] See also

• Photon polarization


• Stern-Gerlach Experiment Java Applet Animation • Stern-Gerlach Experiment Flash Model • Detailed explanation of the Stern-Gerlach Experiment • "Physics Today" article about the history of the Stern-Gerlach experiment

[edit] References

1. ^ Tomonaga, Sin-itiro (1997). The Story of Spin. University of Chicago Press. ISBN 0-226-80794-0. p. 35

• Friedrich, Bretislav and Herschbach, Dudley. "Stern and Gerlach: How a Bad Cigar Helped Reorient Atomic Physics" Physics Today, December 2003.

Retrieved from "http://en.wikipedia.org/wiki/Stern%E2%80%93Gerlach_experiment" Categories: Articles with disputed statements from September 2007 | Quantum measurement | Foundational quantum physics | Physics experiments | Spintronics

Bell test experiments From Wikipedia, the free encyclopedia


Quantum mechanics


Introduction to...


[show]Background


23





Popper's experiment

Schrödinger's cat

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[show]Equations



[show]Scientists


The Bell test experiments serve to investigate the validity of the entanglement effect in quantum mechanics by using some kind of Bell inequality. John Bell published the first inequality of this kind in his paper "On the Einstein-Podolsky-Rosen Paradox". Bell's Theorem states that a Bell inequality must be obeyed under any local hidden variable theory but can in certain circumstances be violated under quantum mechanics. The term "Bell inequality" can mean any one of a number of inequalities — in practice, in real experiments, the CHSH or CH74 inequality, not the original one derived by John Bell. It places restrictions on the statistical results of experiments on sets of particles that have taken part in an interaction and then separated. A Bell test experiment is one designed to test whether or not the real world obeys a Bell inequality. Such experiments fall into two classes, depending on whether the analysers used have one or two output channels.

Contents

[hide]

• 1 Conduct of optical Bell test experiments o 1.1 A typical CHSH (two-channel) experiment o 1.2 A typical CH74 (single-channel) experiment

• 2 Experimental assumptions • 3 Notable experiments

o 3.1 Freedman and Clauser, 1972 o 3.2 Aspect, 1981-2 o 3.3 Tittel and the Geneva group, 1998

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o 3.4 Weihs' experiment under "strict Einstein locality" conditions o 3.5 Pan et al's experiment on the GHZ state o 3.6 Gröblacher et al (2007) test of Leggett-type non-local realist theories

• 4 Loopholes • 5 See also • 6 References • 7 External links

[edit] Conduct of optical Bell test experiments

In practice most actual experiments have used light, assumed to be emitted in the form of particle-like photons (produced by atomic cascade or spontaneous parametric down conversion), rather than the atoms that Bell originally had in mind. The property of interest is, in the best known experiments, the polarisation direction, though other properties can be used.

[edit] A typical CHSH (two-channel) experiment

Scheme of a "two-channel" Bell test The source S produces pairs of "photons", sent in opposite directions. Each photon encounters a two-channel polariser whose orientation can be set by the experimenter. Emerging signals from each channel are detected and coincidences counted by the coincidence monitor CM.

The diagram shows a typical optical experiment of the two-channel kind for which Alain Aspect set a precedent in 1982 (Aspect, 1982a). Coincidences (simultaneous detections) are recorded, the results being categorised as '++', '+−', '−+' or '−−' and corresponding counts accumulated.

Four separate subexperiments are conducted, corresponding to the four terms E(a, b) in the test statistic S ((2) below). The settings a, a′, b and b′ are generally in practice chosen to be 0, 45°, 22.5° and 67.5° respectively — the "Bell test angles" — these being the ones for which the QM formula gives the greatest violation of the inequality.

For each selected value of a and b, the numbers of coincidences in each category (N++, N--, N+- and N-+) are recorded. The experimental estimate for E(a, b) is then calculated as:

(1) E = (N++ + N-- − N+- − N-+)/(N++ + N-- + N+- + N-+).

Once all four E’s have been estimated, an experimental estimate of the test statistic

(2) S = E(a, b) − E(a, b′) + E(a′, b) + E(a′ b′)

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can be found. If S is numerically greater than 2 it has infringed the CHSH inequality. The experiment is declared to have supported the QM prediction and ruled out all local hidden variable theories.

A strong assumption has had to be made, however, to justify use of expression (2). It has been assumed that the sample of detected pairs is representative of the pairs emitted by the source. That this assumption may not be true comprises the fair sampling loophole.

The derivation of the inequality is given in the CHSH Bell test page.

[edit] A typical CH74 (single-channel) experiment

Setup for a "single-channel" Bell test The source S produces pairs of "photons", sent in opposite directions. Each photon encounters a single channel (e.g. "pile of plates") polariser whose orientation can be set by the experimenter. Emerging signals are detected and coincidences counted by the coincidence monitor CM.

Prior to 1982 all actual Bell tests used "single-channel" polarisers and variations on an inequality designed for this setup. The latter is described in Clauser, Horne, Shimony and Holt's much-cited 1969 article (Clauser, 1969) as being the one suitable for practical use. As with the CHSH test, there are four subexperiments in which each polariser takes one of two possible settings, but in addition there are other subexperiments in which one or other polariser or both are absent. Counts are taken as before and used to estimate the test statistic.

(3) S = (N(a, b) − N(a, b′) + N(a′, b) + N(a′, b′) − N(a′, ∞) − N(∞, b)) / N(∞, ∞),

where the symbol ∞ indicates absence of a polariser.

If S exceeds 0 then the experiment is declared to have infringed Bell's inequality and hence to have "refuted local realism".

The only theoretical assumption (other than Bell's basic ones of the existence of local hidden variables) that has been made in deriving (3) is that when a polariser is inserted the probability of detection of any given photon is never increased: there is "no enhancement". The derivation of this inequality is given in the page on Clauser and Horne's 1974 Bell test.

[edit] Experimental assumptions

In addition to the theoretical assumptions made, there are practical ones. There may, for example, be a number of "accidental coincidences" in addition to those of interest. It is assumed that no bias is introduced by subtracting their estimated number before calculating S, but that this is true is not considered by some to be obvious. There may be synchronisation problems — ambiguity in recognising pairs due to the fact that in practice they will not be detected at exactly the same time.

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Nevertheless, despite all these deficiencies of the actual experiments, one striking fact emerges: the results are, to a very good approximation, what quantum mechanics predicts. If imperfect experiments give us such excellent overlap with quantum predictions, most working quantum physicists would agree with John Bell in expecting that, when a perfect Bell test is done, the Bell inequalities will still be violated. This attitude has led to the emergence of a new sub-field of physics which is now known as quantum information theory. One of the main achievements of this new branch of physics is showing that violation of Bell's inequalities leads to the possibility of a secure information transfer, which utilizes the so-called quantum cryptography (involving entangled states of pairs of particles).

[edit] Notable experiments

Over the past thirty or so years, a great number of Bell test experiments have now been conducted. These experiments have (subject to a few assumptions, considered by most to be reasonable) confirmed quantum theory and shown results that cannot be explained under local hidden variable theories. Advancements in technology have led to significant improvement in efficiencies, as well as a greater variety of methods to test the Bell Theorem. Some of the best known:

[edit] Freedman and Clauser, 1972

This was the first actual Bell test, using Freedman's inequality, a variant on the CH74 inequality.

[edit] Aspect, 1981-2

Aspect and his team at Orsay, Paris, conducted three Bell tests using calcium cascade sources. The first and last used the CH74 inequality. The second was the first application of the CHSH inequality, the third the famous one (originally suggested by John Bell) in which the choice between the two settings on each side was made during the flight of the photons.

[edit] Tittel and the Geneva group, 1998

The Geneva 1998 Bell test experiments showed that distance did not destroy the "entanglement". Light was sent in fibre optic cables over distances of several kilometers before it was analysed. As with almost all Bell tests since about 1985, a "parametric down-conversion" (PDC) source was used.

[edit] Weihs' experiment under "strict Einstein locality" conditions

In 1998 Gregor Weihs and a team at Innsbruck, lead by Anton Zeilinger, conducted an ingenious experiment that closed the "locality" loophole, improving on Aspect's of 1982. The choice of detector was made using a quantum process to ensure that it was random. This test violated the CHSH inequality by over 30 standard deviations, the coincidence curves agreeing with those predicted by quantum theory.

[edit] Pan et al's experiment on the GHZ state

This is the first of new Bell-type experiments on more than two particles; this one uses the so-called GHZ state of three particles; it is reported in Nature (2000)

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[edit] Gröblacher et al (2007) test of Leggett-type non-local realist theories

The authors interpret their results as disfavouring "realism" and hence allow QM to be local but "non-real". However they have actually only ruled out a specific class of non-local theories suggested by Anthony Leggett.[1] [2]

[edit] Loopholes

Main article: Loopholes in Bell test experiments

Though the series of increasingly sophisticated Bell test experiments has convinced the physics community in general that local realism is untenable, there are still critics who point out that the outcome of every single experiment done so far that violates a Bell inequality can, at least theoretically, be explained by faults in the experimental setup, experimental procedure or that the equipment used do not behave as well as it is supposed to. These possibilities are known as "loopholes". The most serious loophole is the detection loophole, which means that particles are not always detected in both wings of the experiment. It is possible to "engineer" quantum correlations (the experimental result) by letting detection be dependent on a combination of local hidden variables and detector setting. Experimenters have repeatedly stated that loophole-free tests can be expected in the near future (García-Patrón, 2004). On the other hand, some researchers point out that it is a logical possibility that quantum physics itself prevents a loophole-free test from ever being implemented (Gill, 2003) (Santos, 2006).

[edit] See also

[edit] References

1. ^ Quantum physics says goodbye to reality 2. ^ An experimental test of non-local realism

• Aspect, 1981: A. Aspect et al., Experimental Tests of Realistic Local Theories via Bell's Theorem, Phys. Rev. Lett. 47, 460 (1981)

• Aspect, 1982a: A. Aspect et al., Experimental Realization of Einstein-Podolsky-Rosen-Bohm Gedankenexperiment: A New Violation of Bell's Inequalities, Phys. Rev. Lett. 49, 91 (1982),

• Aspect, 1982b: A. Aspect et al., Experimental Test of Bell's Inequalities Using Time-Varying Analyzers, Phys. Rev. Lett. 49, 1804 (1982),

• Barrett, 2002 Quantum Nonlocality, Bell Inequalities and the Memory Loophole: quant-ph/0205016 (2002).

• Bell, 1987: J. S. Bell, Speakable and Unspeakable in Quantum Mechanics, (Cambridge University Press 1987)

• Clauser, 1969: J. F. Clauser, M.A. Horne, A. Shimony and R. A. Holt, Proposed experiment to test local hidden-variable theories, Phys. Rev. Lett. 23, 880-884 (1969),

• Clauser, 1974: J. F. Clauser and M. A. Horne, Experimental consequences of objective local theories, Phys. Rev. D 10, 526-35 (1974)

• Freedman, 1972: S. J. Freedman and J. F. Clauser, Experimental test of local hidden-variable theories, Phys. Rev. Lett. 28, 938 (1972)

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• García-Patrón, 2004: R. García-Patrón, J. Fiurácek, N. J. Cerf, J. Wenger, R. Tualle-Brouri, and Ph. Grangier, Proposal for a Loophole-Free Bell Test Using Homodyne Detection, Phys. Rev. Lett. 93, 130409 (2004)

• Gill, 2003: R.D. Gill, Time, Finite Statistics, and Bell's Fifth Position: quant-ph/0301059, Foundations of Probability and Physics - 2, Vaxjo Univ. Press, 2003, 179-206 (2003)

• Kielpinski : D. Kielpinski et al., Recent Results in Trapped-Ion Quantum Computing (2001) • Kwiat, 1999: P.G. Kwiat, et al., Ultrabright source of polarization-entangled photons,

Physical Review A 60 (2), R773-R776 (1999) • Rowe, 2001: M. Rowe et al., Experimental violation of a Bell’s inequality with efficient

detection, Nature 409, 791 (2001) • Santos, 2005: E. Santos, Bell's theorem and the experiments: Increasing empirical support

to local realism: quant-ph/0410193, Studies In History and Philosophy of Modern Physics, 36, 544-565 (2005)

• Tittel, 1997: W. Tittel et al., Experimental demonstration of quantum-correlations over more than 10 kilometers, Phys. Rev. A, 57, 3229 (1997)

• Tittel, 1998: W. Tittel et al., Experimental demonstration of quantum-correlations over more than 10 kilometers, Physical Review A 57, 3229 (1998); Violation of Bell inequalities by photons more than 10 km apart, Physical Review Letters 81, 3563 (1998)

• Weihs, 1998: G. Weihs, et al., Violation of Bell’s inequality under strict Einstein locality conditions, Phys. Rev. Lett. 81, 5039 (1998)


Retrieved from "http://en.wikipedia.org/wiki/Bell_test_experiments" Categories: Quantum measurement

Popper's experiment From Wikipedia, the free encyclopedia


The neutrality of this article is disputed. Please see the discussion on the talk page.(December 2007) Please do not remove this message until the dispute is resolved.

Quantum mechanics


Introduction to...


29

[show]Background






Popper's experiment

Schrödinger's cat

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[show]Scientists


Popper's experiment is an experiment proposed by the 20th century philosopher of science Karl Popper, to test the standard interpretation (the Copenhagen interpretation) of Quantum mechanics.[1][2] Popper's experiment is similar in spirit to the thought experiment of Einstein, Podolsky and Rosen (The EPR paradox). For some reasons, it did not become as well known. Currently, the consensus is that the experiment was based on a flawed premise, and thus its result doesn't constitute a test of quantum mechanics. Nevertheless, the experiment is important from a historical point of view and also exemplifies the pitfalls that one comes across in trying to make sense out of quantum mechanics.

Contents

[hide]

• 1 Background • 2 Popper's proposed experiment • 3 The debate • 4 Realization of Popper's experiment • 5 What is wrong with Popper's proposal?

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• 6 Popper's experiment and faster-than-light signalling • 7 References

[edit] Background

Quantum theory is an astoundingly successful theory when it comes to explaining or predicting physical phenomena. There are various interpretations of quantum mechanics that do not agree with each other. Despite their differences, they are nearly experimentally indistinguishable from each other. The most widely accepted interpretation of quantum mechanics is the Copenhagen interpretation put forward by Niels Bohr. The spirit of the Copenhagen interpretation is that the wavefunction of a system is treated as a composite whole, so disturbing any part of it disturbs the whole wavefunction. This leads to the counter-intuitive result that two well separated, non-interacting systems show a mysterious dependence on each other. Einstein called this spooky action at a distance. Einstein's discomfort with this kind of spooky action is summarized in the famous EPR argument.[3] Karl Popper shared Einstein's discomfort with quantum theory. While the EPR argument involved a thought experiment, Popper proposed a physical experiment to test the Copenhagen interpretation of quantum mechanics.

[edit] Popper's proposed experiment

Popper's proposed experiment consists of a source of particles that can generate pairs of particles traveling to the left and to the right along the x-axis. The momentum along the y-direction of the two particles is entangled in such a way so as to conserve the initial momentum at the source, which is zero. Quantum mechanics allows this kind of entanglement. There are two slits, one each in the paths of the two particles. Behind the slits are semicircular arrays of detectors which can detect the particles after they pass through the slits (see Fig. 1).

Fig.1 Experiment with both slits equally wide. Both the particles should show equal scatter in their momenta.

Popper argued that because the slits localize the particles to a narrow region along the y-axis, from the uncertainty principle they experience large uncertainties in the y-components of their momenta. This larger spread in the momentum will show up as particles being detected even at positions that lie outside the regions where particles would normally reach based on their initial momentum spread.

Popper suggests that we count the particles in coincidence, i.e., we count only those particles behind slit B, whose other member of the pair registers on a counter behind slit A. This would make sure

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that we count only those particles behind slit B, whose partner has gone through slit A. Particles which are not able to pass through slit A are ignored.

We first test the Heisenberg scatter for both the beams of particles going to the right and to the left, by making the two slits A and B wider or narrower. If the slits are narrower, then counters should come into play which are higher up and lower down, seen from the slits. The coming into play of these counters is indicative of the wider scattering angles which go with narrower slit, according to the Heisenberg relations.

Fig.2 Experiment with slit A narrowed, and slit B wide open. Should the two particle show equal scatter in their momenta? If they do not, Popper says, the Copenhagen interpretation is wrong. If they do, it indicates spooky action at a distance, says Popper.

Now we make the slit at A very small and the slit at B very wide. According to the EPR argument, we have measured position "y" for both particles (the one passing through A and the one passing through B) with the precision ∆y, and not just for particle passing through slit A. This is because from the initial entangled EPR state we can calculate the position of the particle 2, once the position of particle 1 is known, with approximately the same precision. We can do this, argues Popper, even though slit B is wide open.

We thus obtain fairly precise "knowledge" about the y position of particle 2 - we have "measured" its y position indirectly. And since it is, according to the Copenhagen interpretation, our knowledge which is described by the theory - and especially by the Heisenberg relations - we should expect that the momentum py of particle 2 scatters as much as that of particle 1, even though the slit A is much narrower than the widely opened slit at B.

Now the scatter can, in principle, be tested with the help of the counters. If the Copenhagen interpretation is correct, then such counters on the far side of slit B that are indicative of a wide scatter (and of a narrow slit) should now count coincidences: counters that did not count any particles before the slit A was narrowed.

To sum up: if the Copenhagen interpretation is correct, then any increase in the precision in the measurement of our mere knowledge of the particles going through slit B should increase their scatter.

Popper was inclined to believe that the test would decide against the Copenhagen interpretation, and this, he argued, would undermine Heisenberg's uncertainty principle. If the test decided in favour of the Copenhagen interpretation, Popper argued, it could be interpreted as indicative of action at a distance.

[edit] The debate

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Many viewed Popper's experiment as a crucial test of quantum mechanics, and there was a debate on what result an actual realization of the experiment would yield.

• In 1985, Sudbery pointed out that the EPR state, which could be written as

, already contained an infinite spread in momenta (tacit in the integral over k), so no further spread could be seen by localizing one particle. [4] [5] Although it pointed to a crucial flaw in Popper's argument, its full implication was not understood.

• Kripps theoretically analyzed Popper's experiment and predicted that narrowing slit A would lead to momentum spread increasing at slit B. Kripps also argued that his result was based just on the formalism of quantum mechanics, without any interpretational problem. Thus, if Popper was challenging anything, he was challenging the central formalism of quantum mechanics. [6]

• In 1987 there came a major objection to Popper's proposal from Collet and Loudon. [7] They pointed out that because the particle pairs originating from the source had a zero total momentum, the source could not have a sharply defined position. They showed that once the uncertainty in the position of the source is taken into account, the blurring introduced washes out the Popper effect. However, it has been demonstrated that a point source is not crucial for Popper's experiment, and a broad spontaneous parametric down cenversion (SPDC) source can be set up to give a strong correlation between two photon pairs.[citation

needed]

• Redhead analyzed Popper's experiment with a broad source and concluded that it could not yield the effect that Popper was seeking. [8] However, it has been demonstrated that if one uses a converging lens with a broad source, the kind of setup Popper was looking for, can be realized.[citation needed]

[edit] Realization of Popper's experiment

Fig.3 Schematic diagram of Kim and Shih's experiment based on a BBO crystal which generates entangled photons. The lens LS helps create a sharp image of slit A on the location of slit B.

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Fig.4 Results of the photon experiment by Kim and Shih, aimed at realizing Popper's proposal. The diffraction pattern in the absence of slit B (red symbols) is much narrower than that in the presence of a real slit (blue symbols).

Popper's experiment was realized in 1999 by Kim and Shih using a SPDC photon source.[9] Interestingly, they did not observe an extra spread in the momentum of particle 2 due to particle 1 passing through a narrow slit. Rather, the momentum spread of particle 2 (observed in coincidence with particle 1 passing through slit A) was narrower than its momentum spread in the initial state. This led to a renewed heated debate, with some even going to the extent of claiming that Kim and Shih's experiment had demonstrated that there is no non-locality in quantum mechanics. [10]

• Short criticized Kim and Shih's experiment, arguing that because of the finite size of the source, the localization of particle 2 is imperfect, which leads to a smaller momentum spread than expected. [11] However, Short's argument implies that if the source were improved, we should see a spread in the momentum of particle 2.

• Sancho carried out a theoretical analysis of Popper's experiment, using the path-integral approach, and found a smililar kind of narrowing in the momentum spread of particle 2, as was observed by Kim and Shih. [12] Although this calculation did not give them any deep insight, it indicated that the experimental result of Kim-Shih agreed with quantum mechanics. It did not say anything about what bearing it has on the Copenhagen interpretation, if any.

[edit] What is wrong with Popper's proposal?

The fundamental flaw in Popper's argument can be seen from the following simple analysis. [13] [14]

The ideal EPR state is written as , where the two labels in the "ket" state represent the positions or momenta of the two particle. This implies perfect correlation, meaning, detecting particle 1 at position x0 will also lead to particle 2 being detected at x0. If particle 1 is measured to have a momentum p0, particle 2 will be detected to have a momentum − p0. The particles in this state have infinte momentum spread, and are infinitely delocalized. However, in real world, correlations are always imperfect. Consider the following entangled state

where σ represents a finite momentum spread, and Ω is a measure of the position spread of the particles. The uncertainties in position and momentum, for the two particles can be written as

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The action of a narrow slit on particle 1 can be thought of as reducing it to a narrow Gaussian state:

. This will reduce the state of particle 2 to

. The momentum uncertainty of particle 2 can now be calculated, and is given by

If we go to the extreme limit of slit A being infinitesimally narrow ( ), the momentum

uncertainty of particle 2 is , which is exactly what the momentum spread was to begin with. In fact, one can show that the momentum spread of particle 2, conditioned

on particle 1 going through slit A, is always less than or equal to (the initial spread), for any value of ε,σ, and Ω. Thus, particle 2 does not acquire any extra momentum spread than what it already had. This is the prediction of standard quantum mechanics.

Thus, the basic premise of Popper's experiment, that the Copenhagen interpretation implies that particle 2 will show an additional momentum spread, is incorrect.

On the other hand, if slit A is gradually narrowed, the momentum spread of particle 2 (conditioned on the detection of particle 1 behind slit A) will show a gradual increase (never beyond the initial spread, of course). This is what quantum mechanics predicts. Popper had said

...if the Copenhagen interpretation is correct, then any increase in the precision in the measurement of our mere knowledge of the particles going through slit B should increase their scatter.

This clearly follows from quantum mechanics, without invoking the Copenhagen interpretation.

[edit] Popper's experiment and faster-than-light signalling

The expected additional momentum scatter which Popper wrongly attributed to the Copenhagen interpretation can be interpreted as allowing faster-than-light communication, which is known to be impossible, even in quantum mechanics. Indeed some authors have criticized Popper's experiment based on this impossibility of superluminal communication in quantum mechanics[15] [16]. Every attempt to use quantum correlations for faster-than-light communication is known to be flawed because of the no cloning theorem in quantum mechanics. One will putatively try to signal 0 and 1 by narrowing the slit, or not narrowing it. However in order to investigate the scattering of each single qubit, one needs to have many identical copies of it. Due to unitarity in quantum mechanics, if one tries to copy a qubit they will produce an entangled "pseudo-copy" that will collapse at the very moment the original qubit is measured. So the result of Popper's experiment cannot be used for faster-than-light communication.

[edit] References

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1. ^ Popper, Karl (1982). Quantum Theory and the Schism in Physics. London: Hutchinson, 27-29.

2. ^ Karl Popper (1985). "Realism in quantum mechanics and a new version of the EPR experiment". Open Questions in Quantum Physics, Eds. G. Tarozzi and A. van der Merwe.

3. ^ A. Einstein, B. Podolsky, and N. Rosen (1935). "Can the quantum mechanical description of physical reality be considered complete?". Phys. Rev. 47: 777-780.

4. ^ A. Sudbery:"Popper's variant of the EPR experiment does not test the Copenhagen interpretation", Phil. Sci.:52:470-476:1985

5. ^ A. Sudbery:"Testing interpretations of quantum mechanics", Microphysical Reality and Quantum Formalism:470-476:1988

6. ^ H. Krips (1984). "Popper, propensities, and the quantum theory". Brit. J. Phil. Sci. 35: 253-274.

7. ^ M. J. Collet, R. Loudon (1987). "Analysis of a proposed crucial test of quantum mechanics". Nature 326: 671-672.

8. ^ M. Redhead (1996). "Popper and the quantum theory". Karl Popper: Philosophy and Problems, edited by A. O'Hear (Cambridge): 163-176.

9. ^ Y.-H. Kim and Y. Shih (1999). "Experimental realization of Popper's experiment: violation of the uncertainty principle?". Found. Phys. 29: 1849-1861.

10. ^ C. S. Unnikrishnan (2002). "Is the quantum mechanical description of physical reality complete? Proposed resolution of the EPR puzzle". Found. Phys. Lett. 15: 1-25.

11. ^ A. J. Short (2001). "Popper's experiment and conditional uncertainty relations". Found. Phys. Lett. 14: 275-284.

12. ^ P. Sancho (2002). "Popper’s Experiment Revisited". Found. Phys. 32: 789-805. 13. ^ T. Qureshi (2005). "Understanding Popper's Experiment". Am. J. Phys. 53: 541-544. 14. ^ T. Qureshi (2005). "On the realization of Popper's Experiment". arXiv:quant-ph/0505158. 15. ^ E. Gerjuoy, A.M. Sessler (2006). "Popper's experiment and communication". Am. J. Phys.

74: 643-648. arXiv:quant-ph/0507121 16. ^ G. Ghirardi, L. Marinatto, F. de Stefano (2007). "A critical analysis of Popper's

experiment". arXiv:quant-ph/0702242

Retrieved from "http://en.wikipedia.org/wiki/Popper%27s_experiment" Categories: Quantum measurement | Philosophy of physics

Schrödinger's cat From Wikipedia, the free encyclopedia


Schrödinger's Cat: A cat, along with a flask containing a poison, is placed in a sealed box shielded

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against environmentally induced quantum decoherence. The flask is shattered, releasing the poison, if a Geiger counter detects radiation. Quantum mechanics seems to suggest that after a while the cat is simultaneously alive and dead, in a quantum superposition of coexisting alive and dead states. Yet when we look in the box we expect to see the cat either alive or dead, not in a mixture of alive and dead.

Schrödinger's cat, often described as a paradox, is a thought experiment devised by Austrian physicist Erwin Schrödinger around 1935. It attempts to illustrate what he saw as the problems of the Copenhagen interpretation of quantum mechanics when it is applied beyond just atomic or subatomic systems.

Quantum mechanics


Introduction to...


[show]Background






Popper's experiment

Schrödinger's cat

[show]Formulations

[show]Equations



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[show]Scientists


The concept of superposition, one of the strangest in quantum mechanics, helped provoke Schrödinger's conjecture. Broadly stated, the superposition is the combination of all the possible positions of a subatomic particle. The Copenhagen interpretation implies that the superposition only undergoes collapse into a definite state at the exact moment of quantum measurement.

Schrödinger's mind-game was meant to criticize the strangeness of this. Influenced by a suggestion of Albert Einstein, Schrödinger extrapolated the concept to a larger scale. He proposed a scenario with a cat in a sealed box, where the cat's life or death was dependent on the state of a subatomic particle. According to Schrödinger, the Copenhagen interpretation implies that the cat remains both alive and dead until the box is opened.

Schrödinger did not wish to promote the idea of dead-and-alive cats as a serious possibility; quite the reverse: the thought experiment serves to illustrate the bizarreness of quantum mechanics and the mathematics necessary to describe quantum states. Several interpretations of quantum mechanics have been put forward in an attempt to resolve the paradox. How they treat it is often used as a way of illustrating and comparing their particular features, strengths and weaknesses.

Contents

[hide]

• 1 The thought experiment • 2 Copenhagen interpretation • 3 Everett's many-worlds interpretation & consistent histories • 4 Ensemble interpretation • 5 Objective collapse theories • 6 Practical applications • 7 Extensions • 8 See also • 9 References • 10 External links

[edit] The thought experiment

Schrödinger wrote:

One can even set up quite ridiculous cases. A cat is penned up in a steel chamber, along with the following device (which must be secured against direct interference by the cat): in a Geiger counter there is a tiny bit of radioactive substance, so small, that perhaps in the course of the hour one of the atoms decays, but also, with equal probability, perhaps none; if it happens, the counter tube discharges and through a relay releases a hammer which shatters a small flask of hydrocyanic acid.

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If one has left this entire system to itself for an hour, one would say that the cat still lives if meanwhile no atom has decayed. The psi-function of the entire system would express this by having in it the living and dead cat (pardon the expression) mixed or smeared out in equal parts. It is typical of these cases that an indeterminacy originally restricted to the atomic domain becomes transformed into macroscopic indeterminacy, which can then be resolved by direct observation. That prevents us from so naively accepting as valid a "blurred model" for representing reality. In itself it would not embody anything unclear or contradictory. There is a difference between a shaky or out-of-focus photograph and a snapshot of clouds and fog banks.[1]

The above text is a translation of two paragraphs from a much larger original article, which appeared in the German magazine Naturwissenschaften ("Natural Sciences") in 1935.[2]

It was intended as a discussion of the EPR article published by Einstein, Podolsky and Rosen in the same year. Apart from introducing the cat, Schrödinger also coined the term "entanglement" (German: Verschränkung) in his article.

Schrödinger's famous thought experiment poses the question: when does a quantum system stop existing as a mixture of states and become one or the other? (More technically, when does the actual quantum state stop being a linear combination of states, each of which resemble different classical states, and instead begin to have a unique classical description?) If the cat survives, it remembers only being alive. But explanations of the EPR experiments that are consistent with standard microscopic quantum mechanics require that macroscopic objects, such as cats and notebooks, do not always have unique classical descriptions. The purpose of the thought experiment is to illustrate this apparent paradox: our intuition says that no observer can be in a mixture of states, yet it seems only cats can be such a mixture. Are cats required to be observers, or does their existence in a single well-defined classical state require another external observer? Each alternative seemed absurd to Albert Einstein, who was impressed by the ability of the thought experiment to highlight these issues; in a letter to Schrödinger dated 1950 he wrote:

You are the only contemporary physicist, besides Laue, who sees that one cannot get around the assumption of reality—if only one is honest. Most of them simply do not see what sort of risky game they are playing with reality—reality as something independent of what is experimentally established. Their interpretation is, however, refuted most elegantly by your system of radioactive atom + amplifier + charge of gun powder + cat in a box, in which the psi-function of the system contains both the cat alive and blown to bits. Nobody really doubts that the presence or absence of the cat is something independent of the act of observation.

Einstein had previously suggested to Schrödinger a similar paradox involving an unstable keg of gunpowder, instead of a cat. Schrödinger had taken the next step of applying quantum mechanics to an entity that may or may not be conscious, to further illustrate the putative incompleteness of quantum mechanics.

[edit] Copenhagen interpretation

Main article: Copenhagen interpretation

In the Copenhagen interpretation of quantum mechanics, a system stops being a superposition of states and becomes either one or the other when an observation takes place. This experiment makes apparent the fact that the nature of measurement, or observation, is not well defined in this

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interpretation. Some interpret the experiment to mean that while the box is closed, the system simultaneously exists in a superposition of the states "decayed nucleus/dead cat" and "undecayed nucleus/living cat", and that only when the box is opened and an observation performed does the wave function collapse into one of the two states. More intuitively, some feel that the "observation" is taken when a particle from the nucleus hits the detector. This line of thinking can be developed into Objective collapse theories. In contrast, the many worlds approach denies that collapse ever occurs.

Steven Weinberg said:

All this familiar story is true, but it leaves out an irony. Bohr's version of quantum mechanics was deeply flawed, but not for the reason Einstein thought. The Copenhagen interpretation describes what happens when an observer makes a measurement, but the observer and the act of measurement are themselves treated classically. This is surely wrong: Physicists and their apparatus must be governed by the same quantum mechanical rules that govern everything else in the universe. But these rules are expressed in terms of a wavefunction (or, more precisely, a state vector) that evolves in a perfectly deterministic way. So where do the probabilistic rules of the Copenhagen interpretation come from? Considerable progress has been made in recent years toward the resolution of the problem, which I cannot go into here. It is enough to say that neither Bohr nor Einstein had focused on the real problem with quantum mechanics. The Copenhagen rules clearly work, so they have to be accepted. But this leaves the task of explaining them by applying the deterministic equation for the evolution of the wavefunction, the Schrödinger equation, to observers and their apparatus.[3]

[edit] Everett's many-worlds interpretation & consistent histories

In the many-worlds interpretation of quantum mechanics, which does not single out observation as a special process, both alive and dead states of the cat persist, but are decoherent from each other. In other words, when the box is opened, that part of the universe containing the observer and cat is split into two separate universes, one containing an observer looking at a box with a dead cat, one containing an observer looking at a box with a live cat.

Since the dead and alive states are decoherent, there is no effective communication or interaction between them. When an observer opens the box, they become entangled with the cat, so observer-states corresponding to the cat being alive and dead are formed, and each can have no interaction with the other. The same mechanism of quantum decoherence is also important for the interpretation in terms of Consistent Histories. Only the "dead cat" or "alive cat" can be a part of a consistent history in this interpretation.

Roger Penrose criticizes this:

"I wish to make it clear that, as it stands this is far from a resolution of the cat paradox. For there is nothing in the formalism of quantum mechanics that demands that a state of consciousness cannot involve the simultaneous perception of a live and a dead cat".[4]

although the mainstream view (without necessarily endorsing many-worlds) is that decoherence is the mechanism that forbids such simultaneous perception.[5][6]

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[edit] Ensemble interpretation

The Ensemble Interpretation states that superpositions are nothing but subensembles of a larger statistical ensemble. That being the case, the state vector would not apply to individual cat experiments, but only to the statistics of many similarly prepared cat experiments. Proponents of this interpretation state that this makes the Schrödinger's cat paradox a trivial non issue.

Taking this interpretation, one forever discards the idea that a single physical system has a mathematical description which corresponds to it in any way.

[edit] Objective collapse theories

According to objective collapse theories, superpositions are destroyed spontaneously (irrespective of external observation) when some objective physical threshold (of time, mass, temperature, irreversibility etc) is reached. Thus, the cat would be expected to have settled into a definite state long before the box is opened. This could loosely be phrased as "the cat observes itself", or "the environment observes the cat".

Objective collapse theories require a modification of standard quantum mechanics, to allow superpositions to be destroyed by the process of time-evolution.

In theory, since each state is determined by the one previous to it, and that from its previous state, ad infinitum, pre-determination for every state would have been achieved instantaneously from the initial "threshold" of the Big Bang. Thus the state of the dead or alive cat is not determined by the observer; it has already been pre-determined from the initial moments of the universe and the ensuing states that have successively led up to the state referenced in this thought experiment.

[edit] Practical applications

The experiment is a purely theoretical one, and the machine proposed is not known to have been constructed. Analogous effects, however, have some practical use in quantum computing and quantum cryptography. It is possible to send light that is in a superposition of states down a fiber optic cable. Placing a wiretap in the middle of the cable which intercepts and retransmits the transmission will collapse the wavefunction (in the Copenhagen interpretation, "perform an observation") and cause the light to fall into one state or another. By performing statistical tests on the light received at the other end of the cable, one can tell whether it remains in the superposition of states or has already been observed and retransmitted. In principle, this allows the development of communication systems that cannot be tapped without the tap being noticed at the other end. This experiment can be argued to illustrate that "observation" in the Copenhagen interpretation has nothing to do with consciousness (unless some version of Panpsychism is true), in that a perfectly unconscious wiretap will cause the statistics at the end of the wire to be different.

In quantum computing, the phrase "cat state" often refers to the special entanglement of qubits

where the qubits are in an equal superposition of all being 0 and all being 1, i.e. + .

[edit] Extensions

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Although discussion of this thought experiment talks about two possible states, in reality there would be a huge number of possible states, since the temperature and degree and state of decomposition of the cat would depend on exactly when and how, as well as if, the mechanism was triggered, as well as the state of the cat prior to death. Prominent physicists have gone so far as to suggest that astronomers observing dark matter in the universe during 1998 may have "reduced its life expectancy" through a Schrödinger's cat scenario.[7][8]

A variant of the Schrödinger's Cat experiment known as the quantum suicide machine has been proposed by cosmologist Max Tegmark. It examines the Schrödinger's Cat experiment from the point of view of the cat, and argues that this may be able to distinguish between the Copenhagen interpretation and many worlds. Another variant on the experiment is Wigner's friend.

[edit] See also

• Measurement problem • Basis function • Double-slit experiment • Interpretations of quantum mechanics • Quantum Zeno effect • Elitzur-Vaidman bomb-tester • Wigner's friend • Quantum suicide • Schrödinger's cat in popular culture • Schroedinbug

[edit] References

1. ^ Schroedinger: "The Present Situation in Quantum Mechanics" 2. ^ Schrödinger, Erwin (November 1935). "Die gegenwärtige Situation in der

Quantenmechanik (The present situation in quantum mechanics)". Naturwissenschaften. 3. ^ Weinberg, Steven (November 2005). "Einstein's Mistakes". Physics Today: 31. 4. ^ Penrose, R. The Road to Reality, p807. 5. ^ Wojciech H. Zurek, Decoherence, einselection, and the quantum origins of the classical,

Reviews of Modern Physics 2003, 75, 715 or [1] 6. ^ Wojciech H. Zurek, Decoherence and the transition from quantum to classical, Physics

Today, 44, pp 36–44 (1991) 7. ^ Highfield, Roger (2007-11-21). Mankind 'shortening the universe's life'. The Daily

Telegraph. Retrieved on 2007-11-25. 8. ^ Chown, Marcus (2007-11-22). Has observing the universe hastened its end?. New

Scientist. Retrieved on 2007-11-25.


Wikimedia Commons has media related to: Schrödinger's cat

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• Erwin Schrödinger, The Present Situation in Quantum Mechanics (Translation) • A Lazy Layman's Guide to Quantum Physics • Quantum Mechanics and Schrodinger's Cat • The many worlds of quantum mechanics • The Straight Dope's Poem of Schroedinger's Cat • The EPR paper • Tears For Fears song lyrics Schrodinger's Cat • A cartoon explantion: :Schrödinger's comic"

Retrieved from "http://en.wikipedia.org/wiki/Schr%C3%B6dinger%27s_cat" Categories: Fundamental physics concepts | Thought experiments | Physical paradoxes | Quantum measurement | Fictional cats

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