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Quantum mechanics: The mathematical description of the motion and interaction of subatomic particles in terms of quanta, incorporating the idea that particles can also be regarded as waves.





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Double-slit experiment
The double-slit experiment consists of letting light diffract through two slits, which produces
fringes or wave-like interference patterns on a screen. These interference patterns will result in
projected light and dark regions that correspond to where the light waves have constructively
(added) and destructively (subtracted) interfered.

The experiment can also be performed with a beam of electrons or atoms, showing similar
interference patterns; this is taken as evidence of the "wave-particle duality" predicted by
quantum physics. Note, however, that a double-slit experiment can also be performed with water
waves in a ripple tank; the explanation of the observed wave phenomena does not require quantum
mechanics in any way. The phenomenon is quantum mechanical only when quantum particles—such as
atoms, electrons, or photons—manifest as waves.
Although the double-slit experiment is now often referred to in the context of quantum mechanics,
it was originally performed by the English scientist Thomas Young c.1801 in an attempt to resolve
the question of whether light was composed of particles (the "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; although in
this form the experiment was not actually performed with anything other than light until 1961, when
Claus Jonsson of the University of Tubingen 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 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
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.

In September 2002, the double-slit experiment of Claus Jonsson was voted "the most beautiful
experiment" by readers of Physics World.
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 a pattern
with a single peak. 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. On the one hand, the interference pattern confirms that light still
behaves much like a wave, even though we send it one particle at a time. On the other hand, each
time a photon with a certain energy is emitted, the screen detects a photon with the same energy.
Under the Copenhagen Interpretation of quantum theory, an individual photon is seen as passing
through both slits at once, and interfering with itself, producing the interference pattern.

A remarkable result follows from a variation of the double-slit experiment, in which detectors are
placed in each 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, then they would fall out of step with each other, that is, they
would decohere. They would then arrive at the 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.

The Copenhagen interpretation posits the existence of probability waves which describe the
likelihood of finding the particle at a given location. Until the particle is detected at any
location along this probability wave, it effectively exists at every point. Thus, when the particle
could be passing through either of the two slits, it will actually pass through both, and so an
interference pattern results. But if the particle is detected at one of the two slits, then it can
no longer be passing through both - its presence must become manifested at one or the other, and so
no interference pattern appears.

This is similar to the path integral formulation of quantum mechanics provided by Richard Feynman.
(Feynman stresses that this 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 — 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 procedes 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.

Regardless of whether it is an electron, a proton, or something else on that 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) but 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 indicated that each electron was interfering with itself and therefore in some
sense the electron had to be going through both slits. For something that most people continue to
imagine to be an unimaginably small particle to be able to interfere with itself would suggest that
this "sub-atomic particle" was in two places at once, but that idea is strongly at odds with the
truism, "You cannot be two places at once." It was easier to conceptualize the electron as a wave,
and that evasion of awareness of the dual or complementary wave-particle duality may have made the
experiment more palatable for those who otherwise would have been deeply disturbed by it.

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 badly made gun firing badly 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 a single point diametrically opposite the emitter but instead
one by one 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
the last electron appeared on the screen 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 too become known, would account for why each impact with the target appears.

When scientists observed which slit the electrons were passing through, and separately mark the
spot where each strikes the target, the separately tracked electrons behave like bits of matter
instead of a wave of potentials: they create two lines of hits with no interference pattern, just
would be expected if electrons were like tiny marbles.

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