Everything about Double-slit Experiment totally explained
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 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 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, 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's 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."
(The following depictions are relatively slow to load.)
The underpinning of this experiment
Christiaan Huygens understood the basic idea of how light propagates and how to predict its path through a physical apparatus. He understood that a light source emits a series of waves comparable to the way that water waves spread out from something like a bobber that's 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 doesn't 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. See the article
Huygens–Fresnel principle for more information.
The second drawing shows what happens when a flat wave front encounters a slit in a wall. Following the same principle elucidated above, it's 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've to travel increases, a fact that's 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 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 (for example, two ordinary windows in a single wall) will permit light to appear to go "straight through."
When light came to be understood as the result of electrons falling from higher energy orbits to lower energy orbits, the light that's 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.
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, by reducing the level of incident light until on average only one photon was being transmitted at a time. Note that it's the probabilities of photons appearing at various points along the detection screen that add or cancel. So if there's a cancellation of waves at some point that doesn't 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'll appear somewhere else increases.
Importance to physics
Although the double-slit experiment is now often referred to in the context of quantum mechanics, it's 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.
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 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.
As Young's slit experiments wasn't performed with anything other than light until
1961, when
Claus Jönsson of the
University of Tübingen performed it with
electrons, 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 didn't 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 experiment hadn't 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.
In September
2002, the double-slit experiment of Claus Jönsson was voted "the most beautiful experiment" by readers of
Physics World.
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", "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 isn't the superposition of the two patterns for single slits. Hence, there's 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." 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 isn't 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 can't be predicted by using the laws of Newtonian physics. 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 isn't even clear what the "movement" of a particle such as a photon may be when it isn't clear that it "goes through" either one slit or the other, but it's 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.
Results observed
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
» :
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=1),
:
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.
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.
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)
Quantum version of experiment
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's 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 wouldn't 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 wouldn't detect anything.) If two photons of the same frequency were emitted at the same time they'd be
coherent. If they went through two unobstructed slits then they'd remain coherent and arriving at the screen at the same time but laterally displaced from each other they'd 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'd most likely fall out of step with each other, that is, they'd decohere. They would then arrive at the screen at slightly different times and couldn't 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.
The
Copenhagen interpretation is a consensus among some of the pioneers in the field of
quantum mechanics that it's 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's analogous to the description of a physical wave, but its "crests" and "troughs" indicate levels of probability for the occurrence of certain phenomena (for example, 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 can't speak of the location of any particle such as photon between the time it's emitted and the time it's 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's 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's 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's 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 isn't known.
It is perhaps not so astounding that one knows nothing about what a light particle is doing between the time it's 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 wouldn't 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 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 can't 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's 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.
When observed emission by emission
Regardless of whether it's an electron, a proton, or something else existing on what is considered a "quantum" scale,
where it'll arrive at the screen is highly determinate (in that
quantum mechanics predicts accurately the probability that it'll arrive at any point on the screen). However,
in what sequence members of a series of singly emitted things (for example, electrons) will arrive is completely unpredictable. The experimental facts are so highly reproducible that there's 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's 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 can't 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 couldn't easily be squared with experience of the macro world, the world of everyday experience.
In everyday experience we're 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 isn't 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've now become quite familiar. However, they don't 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.
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.
Recent studies have revealed that interference isn't restricted solely to elementary particles such as protons, neutrons, and electrons. Specifically, it has been shown that large molecular structures like
fullerene (C
60) also produce interference patterns.
Simulations
Wolfram's Mathematica
is used to construct a simulation in which the number of quantum particles, the frequency of the particles, and the slit separation can be independently varied.Further Information
Get more info on 'Double-slit Experiment'.
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