Everything about Wave-particle Duality totally explained
In
physics and
chemistry,
wave–particle duality is the concept that all
matter exhibits both
wave-like and
particle-like properties. A central concept of
quantum mechanics, duality addresses the inadequacy of classical concepts like "particle" and "wave" in fully describing the behaviour of objects. Various
interpretations of quantum mechanics attempt to explain this ostensible
paradox.
The idea of duality is rooted in a debate over the nature of
light and
matter dating back to the 1600s, when competing theories of light were proposed by
Christiaan Huygens and
Isaac Newton. Through the work of
Albert Einstein,
Louis de Broglie and many others, current scientific theory holds that
all particles also have a wave nature. This phenomenon has been verified not only for elementary particles, but also for compound particles like atoms and even molecules. In fact, according to traditional formulations of
non-relativistic quantum mechanics, wave–particle duality applies to all objects, even macroscopic ones; we can't detect wave properties of macroscopic objects due to their small wavelengths.
Richard Feynman emphasized the particle nature of light, stating that it's "very important to know that light behaves like particles, especially for those of you who have gone to school, where you were probably told something about light behaving like waves."
Brief history
At the close of the 19th century, the case for
atomic theory, that matter was made of particulate objects or
atoms, was well established. Electricity, first thought to be a fluid, was now understood to consist of particles called
electrons, as demonstrated by
J.J. Thomson who, led by his research into the work of
Ernest Rutherford, had discovered using
cathode rays that an electrical charge would actually travel across a vacuum from cathode to anode. In brief, it was understood that much of nature was made of particles. At the same time, waves were well understood, together with wave phenomena such as
diffraction and
interference. Light was believed to be a wave, as
Thomas Young's double-slit experiment and effects such as
Fraunhofer diffraction had clearly demonstrated the wave-like nature of light.
But as the 20th century turned, problems had emerged.
Albert Einstein's analysis of the
photoelectric effect in 1905 demonstrated that light also possessed particle-like properties, and this was further confirmed with the discovery of the
Compton effect in 1923. Later on, the
diffraction of electrons would be predicted and experimentally confirmed, thus showing that electrons must have wave-like properties in addition to particle properties.
This confusion over particle versus wave properties was eventually resolved with the advent and establishment of
quantum mechanics in the first half of the 20th century, which ultimately explained wave–particle duality. It provided a single unified theoretical framework for understanding that all matter may have characteristics associated with particles and waves, as explained below. By the very end of the 20th century extremely precise results were obtained
quantifying this duality, in the form of the
Englert-Greenberger duality relation.
Developmental milestones
Huygens and Newton
The earliest comprehensive theory of
light was advanced by
Christiaan Huygens, who proposed a
wave theory of light, and in particular demonstrated how waves might interfere to form a wavefront, propagating in a straight line. However, the theory had difficulties in other matters, and was soon overshadowed by
Isaac Newton's
corpuscular theory of light. That is, Newton proposed that light consisted of small particles, with which he could easily explain the phenomenon of
reflection. With considerably more difficulty, he could also explain
refraction through a
lens, and the splitting of sunlight into a
rainbow by a
prism. Newton's particle viewpoint went essentially unchallenged for over a century.
Young, Fresnel, and Maxwell
In the early 1800s, the
double-slit experiments by
Young and
Fresnel provided
evidence for
Huygens' wave theories: these experiments showed that when light is sent through a grid, a characteristic
interference pattern is observed, very similar to the pattern resulting from the interference of
water waves; the wavelength of light can be computed from such patterns. The wave view didn't immediately displace the ray and particle view, but began to dominate scientific thinking about light in the mid 1800s, since it could explain polarization phenomena that the alternatives could not.
Maxwell, during the late 1800s, explained light as the propagation of
electromagnetic waves according to the
Maxwell equations. These equations were verified by experiment, and Huygens' view became widely accepted.
Planck's formula for black body radiation
In 1901,
Max Planck published an analysis that succeeded in reproducing the observed
spectrum of light emitted by a glowing object. To accomplish this, Planck had to make an ad hoc mathematical assumption of quantized energy of the oscillators (atoms of the blackbody) that emit radiation. It was Einstein who later proposed that it's the electromagnetic radiation itself that's quantized, and not the energy of radiating atoms.
Einstein's explanation of the photoelectric effect
In 1905,
Albert Einstein provided an explanation of the
photoelectric effect, a hitherto troubling experiment that the wave theory of light seemed incapable of explaining. He did so by postulating the existence of
photons,
quanta of light energy with particulate qualities.
In the
photoelectric effect, it was observed that shining a light on certain metals would lead to an
electric current in a
circuit. Presumably, the light was knocking electrons out of the metal, causing current to flow. However, it was also observed that while a dim blue light was enough to cause a current, even the strongest, brightest red light caused no current at all. According to wave theory, the strength or
amplitude of a light wave was in proportion to its brightness: a bright light should have been easily strong enough to create a large current. Yet, oddly, this wasn't so.
Einstein explained this conundrum by
postulating that the electrons can receive energy from electromagnetic field only in discrete portions (quanta that were called
photons): an amount of
energy E that was related to the
frequency,
f of the light by
»
where
h is
Planck's constant (6.626 × 10
-34 J seconds). Only photons of a high-enough frequency, (above a certain
threshold value) could knock an electron free. For example, photons of blue light had sufficient energy to free an electron from the metal, but photons of red light did not. More intense light above the threshold frequency could release more electrons, but no amount of light below the threshold frequency could release an electron.
Einstein was awarded the
Nobel Prize in Physics in 1921 for his theory of the photoelectric effect.
De Broglie's hypothesis
In 1924,
Louis-Victor de Broglie formulated the
de Broglie hypothesis, claiming that
all matter, not just light, has a wave-like nature; he related
wavelength (denoted as
λ), and
momentum (denoted as
p):
»
where
» here indicates
standard deviation, a measure of spread or uncertainty;
x and
p are a particle's position and
linear momentum respectively.
» is the
reduced Planck's constant (Planck's constant divided by 2
).
Heisenberg originally explained this as a consequence of the process of measuring: Measuring position accurately would disturb momentum and vice-versa, offering an example (the "gamma-ray microscope") that depended crucially on the de Broglie hypothesis. It is now understood, however, that this only partly explains the phenomenon: the uncertainty also exists in the particle itself, even before the measurement is made.
In fact, the modern explanation of the uncertainty principle, extending the
Copenhagen interpretation first put forward by
Bohr and
Heisenberg, depends even more centrally on the wave nature of a particle: Just as it's nonsensical to discuss the precise location of a wave on a string, particles don't have perfectly precise positions; likewise, just as it's nonsensical to discuss the wavelength of a "pulse" wave traveling down a string, particles don't have perfectly precise momenta (which corresponds to the inverse of wavelength). Moreover, when position is relatively well defined, the wave is pulse-like and has a very ill-defined wavelength (and thus momentum). And conversely, when momentum (and thus wavelength) is relatively well defined, the wave looks long and sinusoidal, and therefore it has a very ill-defined position.
De Broglie himself had proposed a
pilot wave construct to explain the observed wave–particle duality. In this view, each particle has a well-defined position and momentum, but is guided by a wave function derived from
Schrödinger's equation. The pilot wave theory was initially rejected because it generated non-local effects when applied to systems involving more than one particle. Non-locality, however, soon became established as an integral feature of
quantum theory (see
EPR paradox), and
David Bohm extended de Broglie's model to explicitly include it. In Bohmian mechanics, the wave–particle duality isn't a property of matter itself, but an appearance generated by the particle's motion subject to a guiding equation or quantum potential.
Wave behavior of large objects
Since the demonstrations of wave-like properties in
photons and
electrons, similar experiments have been conducted with
neutrons and
protons. Among the most famous experiments are those of
Estermann and
Otto Stern in 1929. Authors of similar recent experiments with atoms and molecules, described below, claim that these larger particles also act like waves.
A dramatic series of experiments emphasizing the action of
gravity in relation to wave–particle duality were conducted in the 1970s using the
neutron interferometer. Neutrons, one of the components of the
atomic nucleus, provide much of the mass of a nucleus and thus of ordinary matter. In the neutron interferometer, they act as quantum-mechanical waves directly subject to the force of gravity. While the results were not surprising since gravity was known to act on everything, including light (see
tests of general relativity and the
Pound-Rebka falling photon experiment), the self-interference of the quantum mechanical wave of a massive fermion in a gravitational field had never been experimentally confirmed before.
In 1999, the diffraction of C
60 fullerenes by researchers from the
University of Vienna was reported. Fullerenes are comparatively large and massive objects, having an atomic mass of about 720
u. The de Broglie wavelength is 2.5
pm, whereas the diameter of the molecule is about 1
nm, about 400 times larger. As of 2005, this is the largest object for which quantum-mechanical wave-like properties have been directly observed in far-field diffraction.
In 2003 the Vienna group also demonstrated the wave nature of
tetraphenylporphyrin – a flat biodye with an extension of
about 2 nm and a mass of 614 u. For this demonstration they employed a near-field
Talbot Lau interferometer. In the same interferometer they also
found interference fringes for C
60F
48., a fluorinated
buckyball with a mass of about 1600 u, composed of 108 atoms
Whether objects heavier than the
Planck mass (about the weight of a large bacterium) have a de Broglie wavelength is theoretically unclear and experimentally unreachable; above the Planck mass a particle's
Compton wavelength would be smaller than the
Planck length and its own
Schwarzschild radius, a scale at which current theories of physics may break down or need to be replaced by more general ones.
Treatment in modern quantum mechanics
Wave–particle duality is deeply embedded into the foundations of
quantum mechanics, so well that modern practitioners rarely discuss it as such. In the formalism of the theory, all the information about a particle is encoded in its
wave function, a complex function roughly analogous to the amplitude of a wave at each point in space. This function evolves according to a
differential equation (generically called the
Schrödinger equation), and this equation gives rise to wave-like phenomena such as interference and diffraction.
The particle-like behavior is most evident due to phenomena associated with
measurement in quantum mechanics. Upon measuring the location of the particle, the wave-function will randomly "
collapse" to a sharply peaked function at some location, with the likelihood of any particular location equal to the squared amplitude of the wave-function there. The measurement will return a well-defined position, a property traditionally associated with particles.
Although this picture is somewhat simplified (to the
non-relativistic case), it's adequate to capture the essence of current thinking on the phenomena historically called "wave–particle duality". (See also:
Mathematical formulation of quantum mechanics.)
Alternative views
Particle-only view
The
pilot-wave model, originally developed by
Louis de Broglie and further developed by
David Bohm proposes that there's no duality, but rather particles are guided by a pilot wave which will direct them to areas of constructive interference. This idea is supported as an offshoot of
determinism and is held by a signficant minority within the physics community.
At least one physicist considers the “wave-duality” a misnomer, as L. Ballentine,
Quantum Mechanics, A Modern Development, p.4, explains:
When first discovered, particle diffraction was a source of great puzzlement. Are “particles” really “waves”? In the early experiments, the diffraction patterns were detected holistically by means of a photographic plate, which couldn't detect individual particles. As a result, the notion grew that particle and wave properties were mutually incompatible, or complementary, in the sense that different measurement apparatuses would be required to observe them. That idea, however, was only an unfortunate generalization from a technological limitation. Today it's possible to detect the arrival of individual electrons, and to see the diffraction pattern emerge as a statistical pattern made up of many small spots (Tonomura et al., 1989). Evidently, quantum particles are indeed particles, but whose behaviour is very different from classical physics would have us to expect.
Prominent physicist
Richard Feynman wrote:
I want to emphasize that light comes in this form—particles. It is very important to know that light behaves like particles, especially for those of you who have gone to school, where you were probably told something about light behaving like waves. I'm telling you the way it does behave—like particles.
Wave-only view
At least one scientist proposes that the duality can be replaced by a "wave-only" view.
Carver Mead's
Collective Electrodynamics: Quantum Foundations of Electromagnetism (2000) analyzes the behavior of electrons and photons purely in terms of electronic wave functions, and attributes the apparent particle-like behavior to quantization effects and eigenstates. According to reviewer David Haddon:
Mead has cut the Gordian knot of quantum complementarity. He claims that atoms, with their neutrons, protons, and electrons, are not particles at all but pure waves of matter. Mead cites as the gross evidence of the exclusively wave nature of both light and matter the discovery between 1933 and 1996 of ten examples of pure wave phenomena, including the ubiquitous laser of CD players, the self-propagating electrical currents of superconductors, and the Bose–Einstein condensate of atoms.
Applications
Although it's difficult to draw a line separating wave–particle duality from the rest of quantum mechanics, it's nevertheless possible to list some applications of this basic idea.
- Wave–particle duality is exploited in electron microscopy, where the small wavelengths associated with the electron can be used to view objects much smaller than what is visible using visible light.
Similarly, neutron diffraction uses neutrons with a wavelength of about one ångström, the typical spacing of atoms in a solid, to determine the structure of solids.
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