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1
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.)
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Animation 1
Animation 2 (zoom in)
Contents
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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
3
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
5
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
8
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
11
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 "subatomic 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
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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, 4:411.
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.
13
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=AJPIAS00007100000
4000319000001&idtype=cvips&gifs=yes
[edit] Further reading
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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 0-52156457-3.
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
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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 doubleslit 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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Categories: Foundational quantum physics | Physics experiments | Quantum mechanics | Wave
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Davisson–Germer experiment
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Quantum mechanics
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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
16
1. ^ Clinton J. Davisson & Lester H. Germer, "Reflection of electrons by a crystal of nickel",
Nature, V119, pp. 558-560 (1927).
This quantum mechanics-related article is a stub. You can help Wikipedia by expanding it.
Retrieved from "http://en.wikipedia.org/wiki/Davisson%E2%80%93Germer_experiment"
Categories: Quantum physics stubs | Foundational quantum physics | Physics experiments
Stern–Gerlach experiment
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17
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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.
18
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 spindown. 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 (Δ++, Δ+, Δ0, Δ−), 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.
19
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:
20
[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.
21
[edit] See also

Photon polarization
[edit] External links
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
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 0-22680794-0. 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
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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]
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
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
23
o
o
o
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3.4 Weihs' experiment under "strict Einstein locality" conditions
3.5 Pan et al's experiment on the GHZ state
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 particlelike 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′)
24
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.
25
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 downconversion" (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)
26
[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
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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-RosenBohm 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 TimeVarying Analyzers, Phys. Rev. Lett. 49, 1804 (1982),
Barrett, 2002 Quantum Nonlocality, Bell Inequalities and the Memory Loophole: quantph/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 hiddenvariable theories, Phys. Rev. Lett. 28, 938 (1972)
27
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García-Patrón, 2004: R. García-Patrón, J. Fiurácek, N. J. Cerf, J. Wenger, R. TualleBrouri, 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)
[edit] External links
Retrieved from "http://en.wikipedia.org/wiki/Bell_test_experiments"
Categories: Quantum measurement
Popper's experiment
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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
Uncertainty principle
Introduction to...
Mathematical formulation of...
28
[show]Background
[show]Fundamental concepts
[hide]Experiments
Double-slit experiment
Davisson–Germer experiment
Stern–Gerlach experiment
Bell's inequality experiment
Popper's experiment
Schrödinger's cat
[show]Formulations
[show]Equations
[show]Interpretations
[show]Advanced topics
[show]Scientists
This box: view • talk • edit
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]
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1 Background
2 Popper's proposed experiment
3 The debate
4 Realization of Popper's experiment
5 What is wrong with Popper's proposal?
29
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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, noninteracting 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
30
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 Δy, 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
31
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.
32
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
33
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
34
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
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Schrödinger's Cat: A cat, along with a flask containing a poison, is placed in a sealed box shielded
35
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
Uncertainty principle
Introduction to...
Mathematical formulation of...
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Davisson–Germer experiment
Stern–Gerlach experiment
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Popper's experiment
Schrödinger's cat
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[show]Advanced topics
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[show]Scientists
This box: view • talk • edit
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]
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

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

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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.
37
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
38
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 observerstates 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]
39
[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
40
.
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

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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.
[edit] External links
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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