Wave–particle Duality
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Wave–particle duality is the concept in
quantum mechanics Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistry, ...
that every
particle In the physical sciences, a particle (or corpuscule in older texts) is a small localized object which can be described by several physical or chemical properties, such as volume, density, or mass. They vary greatly in size or quantity, from ...
or quantum entity may be described as either a particle or a
wave In physics, mathematics, and related fields, a wave is a propagating dynamic disturbance (change from equilibrium) of one or more quantities. Waves can be periodic, in which case those quantities oscillate repeatedly about an equilibrium (res ...
. It expresses the inability of the classical concepts "particle" or "wave" to fully describe the behaviour of quantum-scale objects. As
Albert Einstein Albert Einstein ( ; ; 14 March 1879 – 18 April 1955) was a German-born theoretical physicist, widely acknowledged to be one of the greatest and most influential physicists of all time. Einstein is best known for developing the theory ...
wrote: Through the work of
Max Planck Max Karl Ernst Ludwig Planck (, ; 23 April 1858 – 4 October 1947) was a German theoretical physicist whose discovery of energy quanta won him the Nobel Prize in Physics in 1918. Planck made many substantial contributions to theoretical p ...
,
Albert Einstein Albert Einstein ( ; ; 14 March 1879 – 18 April 1955) was a German-born theoretical physicist, widely acknowledged to be one of the greatest and most influential physicists of all time. Einstein is best known for developing the theory ...
,
Louis de Broglie Louis Victor Pierre Raymond, 7th Duc de Broglie (, also , or ; 15 August 1892 – 19 March 1987) was a French physicist and aristocrat who made groundbreaking contributions to Old quantum theory, quantum theory. In his 1924 PhD thesis, he pos ...
, Arthur Compton,
Niels Bohr Niels Henrik David Bohr (; 7 October 1885 – 18 November 1962) was a Danish physicist who made foundational contributions to understanding atomic structure and quantum theory, for which he received the Nobel Prize in Physics in 1922. B ...
,
Erwin Schrödinger Erwin Rudolf Josef Alexander Schrödinger (, ; ; 12 August 1887 – 4 January 1961), sometimes written as or , was a Nobel Prize-winning Austrian physicist with Irish citizenship who developed a number of fundamental results in quantum theo ...
and many others, current scientific theory holds that all particles exhibit a wave nature and vice versa. This phenomenon has been verified not only for elementary particles, but also for compound particles like
atom Every atom is composed of a nucleus and one or more electrons bound to the nucleus. The nucleus is made of one or more protons and a number of neutrons. Only the most common variety of hydrogen has no neutrons. Every solid, liquid, gas, and ...
s and even molecules. For
macroscopic The macroscopic scale is the length scale on which objects or phenomena are large enough to be visible with the naked eye, without magnifying optical instruments. It is the opposite of microscopic. Overview When applied to physical phenomena a ...
particles, because of their extremely short wavelengths, wave properties usually cannot be detected. Although the use of the wave–particle duality has worked well in physics, the meaning or interpretation has not been satisfactorily resolved; see
interpretations of quantum mechanics An interpretation of quantum mechanics is an attempt to explain how the mathematical theory of quantum mechanics might correspond to experienced reality. Although quantum mechanics has held up to rigorous and extremely precise tests in an extraord ...
. Bohr regarded the "duality
paradox A paradox is a logically self-contradictory statement or a statement that runs contrary to one's expectation. It is a statement that, despite apparently valid reasoning from true premises, leads to a seemingly self-contradictory or a logically u ...
" as a fundamental or metaphysical fact of nature. A given kind of quantum object will exhibit sometimes wave, sometimes particle, character, in respectively different physical settings. He saw such duality as one aspect of the concept of complementarity. Bohr regarded renunciation of the cause-effect relation, or complementarity, of the space-time picture, as essential to the quantum mechanical account.
Werner Heisenberg Werner Karl Heisenberg () (5 December 1901 – 1 February 1976) was a German theoretical physicist and one of the main pioneers of the theory of quantum mechanics. He published his work in 1925 in a breakthrough paper. In the subsequent series ...
considered the question further. He saw the duality as present for all quantic entities, but not quite in the usual quantum mechanical account considered by Bohr. He saw it in what is called
second quantization Second quantization, also referred to as occupation number representation, is a formalism used to describe and analyze quantum many-body systems. In quantum field theory, it is known as canonical quantization, in which the fields (typically as ...
, which generates an entirely new concept of fields that exist in ordinary space-time, causality still being visualizable. Classical field values (e.g. the electric and magnetic field strengths of Maxwell) are replaced by an entirely new kind of field value, as considered in
quantum field theory In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines classical field theory, special relativity, and quantum mechanics. QFT is used in particle physics to construct physical models of subatomic particles and ...
. Turning the reasoning around, ordinary quantum mechanics can be deduced as a specialized consequence of quantum field theory.


History


Classical particle and wave theories of light

Democritus Democritus (; el, Δημόκριτος, ''Dēmókritos'', meaning "chosen of the people"; – ) was an Ancient Greek pre-Socratic philosopher from Abdera, primarily remembered today for his formulation of an atomic theory of the universe. No ...
(5th century BC) argued that all things in the universe, including
light Light or visible light is electromagnetic radiation that can be perceived by the human eye. Visible light is usually defined as having wavelengths in the range of 400–700 nanometres (nm), corresponding to frequencies of 750–420 tera ...
, are composed of indivisible sub-components.
Euclid Euclid (; grc-gre, Wikt:Εὐκλείδης, Εὐκλείδης; BC) was an ancient Greek mathematician active as a geometer and logician. Considered the "father of geometry", he is chiefly known for the ''Euclid's Elements, Elements'' trea ...
(4th–3rd century BC) gives treatises on light propagation, states the principle of shortest trajectory of light, including multiple reflections on mirrors, including spherical, while
Plutarch Plutarch (; grc-gre, Πλούταρχος, ''Ploútarchos''; ; – after AD 119) was a Greek Middle Platonist philosopher, historian, biographer, essayist, and priest at the Temple of Apollo in Delphi. He is known primarily for his ''P ...
(1st–2nd century AD) describes multiple reflections on spherical mirrors discussing the creation of larger or smaller images, real or imaginary, including the case of chirality of the images. At the beginning of the 11th century, the Arabic scientist
Ibn al-Haytham Ḥasan Ibn al-Haytham, Latinized as Alhazen (; full name ; ), was a medieval mathematician, astronomer, and physicist of the Islamic Golden Age from present-day Iraq.For the description of his main fields, see e.g. ("He is one of the pri ...
wrote the first comprehensive ''
Book of Optics The ''Book of Optics'' ( ar, كتاب المناظر, Kitāb al-Manāẓir; la, De Aspectibus or ''Perspectiva''; it, Deli Aspecti) is a seven-volume treatise on optics and other fields of study composed by the medieval Arab scholar Ibn al- ...
'' describing
reflection Reflection or reflexion may refer to: Science and technology * Reflection (physics), a common wave phenomenon ** Specular reflection, reflection from a smooth surface *** Mirror image, a reflection in a mirror or in water ** Signal reflection, in ...
,
refraction In physics, refraction is the redirection of a wave as it passes from one medium to another. The redirection can be caused by the wave's change in speed or by a change in the medium. Refraction of light is the most commonly observed phenomeno ...
, and the operation of a pinhole lens via rays of light traveling from the point of emission to the eye. He asserted that these rays were composed of particles of light. In 1630,
René Descartes René Descartes ( or ; ; Latinized: Renatus Cartesius; 31 March 1596 – 11 February 1650) was a French philosopher, scientist, and mathematician, widely considered a seminal figure in the emergence of modern philosophy and science. Mathem ...
popularized the opposing wave description in his treatise on light,
The World In its most general sense, the term "world" refers to the totality of entities, to the whole of reality or to everything that is. The nature of the world has been conceptualized differently in different fields. Some conceptions see the worl ...
, showing that the behaviour of light could be re-created by modeling wave-like disturbances in a universal medium i.e.
luminiferous aether Luminiferous aether or ether ("luminiferous", meaning "light-bearing") was the postulated medium for the propagation of light. It was invoked to explain the ability of the apparently wave-based light to propagate through empty space (a vacuum), so ...
. Beginning in 1670 and progressing over three decades,
Isaac Newton Sir Isaac Newton (25 December 1642 – 20 March 1726/27) was an English mathematician, physicist, astronomer, alchemist, theologian, and author (described in his time as a "natural philosopher"), widely recognised as one of the grea ...
developed and championed his
corpuscular theory In optics, the corpuscular theory of light states that light is made up of small discrete particles called " corpuscles" (little particles) which travel in a straight line with a finite velocity and possess impetus. This was based on an alternate ...
, arguing that the perfectly straight lines of reflection demonstrated light's particle nature, only particles could travel in such straight lines. He explained refraction by positing that particles of light accelerated laterally upon entering a denser medium. Around the same time, Newton's contemporaries
Robert Hooke Robert Hooke FRS (; 18 July 16353 March 1703) was an English polymath active as a scientist, natural philosopher and architect, who is credited to be one of two scientists to discover microorganisms in 1665 using a compound microscope that ...
and
Christiaan Huygens Christiaan Huygens, Lord of Zeelhem, ( , , ; also spelled Huyghens; la, Hugenius; 14 April 1629 – 8 July 1695) was a Dutch mathematician, physicist, engineer, astronomer, and inventor, who is regarded as one of the greatest scientists of ...
, and later
Augustin-Jean Fresnel Augustin-Jean Fresnel (10 May 1788 – 14 July 1827) was a French civil engineer and physicist whose research in optics led to the almost unanimous acceptance of the wave theory of light, excluding any remnant of Newton's corpuscular th ...
, mathematically refined the wave viewpoint, showing that if light traveled at different speeds in different media, refraction could be easily explained as the medium-dependent propagation of light waves. The resulting Huygens–Fresnel principle was extremely successful at reproducing light's behaviour and was subsequently supported by Thomas Young's discovery of
wave interference In physics, interference is a phenomenon in which two waves combine by adding their displacement together at every single point in space and time, to form a resultant wave of greater, lower, or the same amplitude. Constructive and destructive ...
of light by his
double-slit experiment In modern physics, the double-slit experiment is a demonstration that light and matter can display characteristics of both classically defined waves and particles; moreover, it displays the fundamentally probabilistic nature of quantum mechanics ...
in 1801. The wave view did not immediately displace the ray and particle view, but began to dominate scientific thinking about light in the mid 19th century, since it could explain polarization phenomena that the alternatives could not.
James Clerk Maxwell James Clerk Maxwell (13 June 1831 – 5 November 1879) was a Scottish mathematician and scientist responsible for the classical theory of electromagnetic radiation, which was the first theory to describe electricity, magnetism and ligh ...
discovered that he could apply his previously discovered
Maxwell's equations Maxwell's equations, or Maxwell–Heaviside equations, are a set of coupled partial differential equations that, together with the Lorentz force law, form the foundation of classical electromagnetism, classical optics, and electric circuits. ...
, along with a slight modification to describe self-propagating waves of oscillating electric and magnetic fields. It quickly became apparent that visible light, ultraviolet light, and infrared light were all electromagnetic waves of differing frequency. File:Wave-particle duality.ogv, Animation showing the wave–particle duality with a
double-slit experiment In modern physics, the double-slit experiment is a demonstration that light and matter can display characteristics of both classically defined waves and particles; moreover, it displays the fundamentally probabilistic nature of quantum mechanics ...
and effect of an observer. Increase size to see explanations in the video itself. See also a quiz based on this animation. File:Wave-particle duality.gif, Particle impacts make visible the
interference pattern In physics, interference is a phenomenon in which two waves combine by adding their displacement together at every single point in space and time, to form a resultant wave of greater, lower, or the same amplitude. Constructive and destructive ...
of waves. File:Wavelet.gif, A quantum particle is represented by a
wave packet In physics, a wave packet (or wave train) is a short "burst" or "envelope" of localized wave action that travels as a unit. A wave packet can be analyzed into, or can be synthesized from, an infinite set of component sinusoidal waves of diff ...
. File:Interference of a quantum particle with itself.gif, Interference of a quantum particle with itself.


Black-body radiation and Planck's law

In 1901,
Max Planck Max Karl Ernst Ludwig Planck (, ; 23 April 1858 – 4 October 1947) was a German theoretical physicist whose discovery of energy quanta won him the Nobel Prize in Physics in 1918. Planck made many substantial contributions to theoretical p ...
published an analysis that succeeded in reproducing the observed
spectrum A spectrum (plural ''spectra'' or ''spectrums'') is a condition that is not limited to a specific set of values but can vary, without gaps, across a continuum. The word was first used scientifically in optics to describe the rainbow of colors i ...
of light emitted by a glowing object. To accomplish this, Planck had to make a mathematical assumption of quantized energy of the oscillators, i.e. atoms of the
black body A black body or blackbody is an idealized physical body that absorbs all incident electromagnetic radiation, regardless of frequency or angle of incidence. The name "black body" is given because it absorbs all colors of light. A black body ...
that emit radiation. Einstein later proposed that electromagnetic radiation itself is quantized, not the energy of radiating atoms. Black-body radiation, the emission of electromagnetic energy due to an object's heat, could not be explained from classical arguments alone. The
equipartition theorem In classical statistical mechanics, the equipartition theorem relates the temperature of a system to its average energies. The equipartition theorem is also known as the law of equipartition, equipartition of energy, or simply equipartition. T ...
of classical mechanics, the basis of all classical thermodynamic theories, stated that an object's energy is partitioned equally among the object's vibrational
modes Mode ( la, modus meaning "manner, tune, measure, due measure, rhythm, melody") may refer to: Arts and entertainment * '' MO''D''E (magazine)'', a defunct U.S. women's fashion magazine * ''Mode'' magazine, a fictional fashion magazine which is ...
. But applying the same reasoning to the electromagnetic emission of such a thermal object was not so successful. That thermal objects emit light had been long known. Since light was known to be waves of electromagnetism, physicists hoped to describe this emission via classical laws. This became known as the black body problem. Since the equipartition theorem worked so well in describing the vibrational modes of the thermal object itself, it was natural to assume that it would perform equally well in describing the radiative emission of such objects. But a problem quickly arose if each mode received an equal partition of energy, the short wavelength modes would consume all the energy. This became clear when plotting the
Rayleigh–Jeans law In physics, the Rayleigh–Jeans law is an approximation to the spectral radiance of electromagnetic radiation as a function of wavelength from a black body at a given temperature through classical arguments. For wavelength λ, it is: B_ (T) = \ ...
, which, while correctly predicting the intensity of long wavelength emissions, predicted infinite total energy as the intensity diverges to infinity for short wavelengths. This became known as the
ultraviolet catastrophe The ultraviolet catastrophe, also called the Rayleigh–Jeans catastrophe, was the prediction of late 19th century/early 20th century classical physics that an ideal black body at thermal equilibrium would emit an unbounded quantity of energy ...
. In 1900, Max Planck hypothesized that the frequency of light emitted by the black body depended on the frequency of the oscillator that emitted it, and the energy of these oscillators increased linearly with frequency (according ''E'' = ''hf'' where ''h'' is Planck's constant and ''f'' is the frequency). This was not an unsound proposal considering that macroscopic oscillators operate similarly when studying five
simple harmonic oscillator In mechanics and physics, simple harmonic motion (sometimes abbreviated ) is a special type of periodic motion of a body resulting from a dynamic equilibrium between an inertial force, proportional to the acceleration of the body away from the ...
s of equal amplitude but different frequency, the oscillator with the highest frequency possesses the highest energy (though this relationship is not linear like Planck's). By demanding that high-frequency light must be emitted by an oscillator of equal frequency, and further requiring that this oscillator occupy higher energy than one of a lesser frequency, Planck avoided any catastrophe, giving an equal partition to high-frequency oscillators produced successively fewer oscillators and less emitted light. And as in the
Maxwell–Boltzmann distribution In physics (in particular in statistical mechanics), the Maxwell–Boltzmann distribution, or Maxwell(ian) distribution, is a particular probability distribution named after James Clerk Maxwell and Ludwig Boltzmann. It was first defined and use ...
, the low-frequency, low-energy oscillators were suppressed by the onslaught of thermal jiggling from higher energy oscillators, which necessarily increased their energy and frequency. The most revolutionary aspect of Planck's treatment of the black body is that it inherently relies on an integer number of oscillators in
thermal equilibrium Two physical systems are in thermal equilibrium if there is no net flow of thermal energy between them when they are connected by a path permeable to heat. Thermal equilibrium obeys the zeroth law of thermodynamics. A system is said to be in ...
with the electromagnetic field. These oscillators give their entire energy to the electromagnetic field, creating a quantum of light, as often as they are excited by the electromagnetic field, absorbing a quantum of light and beginning to oscillate at the corresponding frequency. Planck had intentionally created an atomic theory of the black body, but had unintentionally generated an atomic theory of light, where the black body never generates quanta of light at a given frequency with an energy less than ''hf''. However, once realizing that he had quantized the electromagnetic field, he denounced particles of light as a limitation of his approximation, not a property of reality.


Photoelectric effect

While Planck had solved the ultraviolet catastrophe by using atoms and a quantized electromagnetic field, most contemporary physicists agreed that Planck's "light quanta" represented only flaws in his model. A more-complete derivation of black-body radiation would yield a fully continuous and "wave-like" electromagnetic field with no quantization. However, in 1905
Albert Einstein Albert Einstein ( ; ; 14 March 1879 – 18 April 1955) was a German-born theoretical physicist, widely acknowledged to be one of the greatest and most influential physicists of all time. Einstein is best known for developing the theory ...
took Planck's black body model to produce his solution to another outstanding problem of the day: the
photoelectric effect The photoelectric effect is the emission of electrons when electromagnetic radiation, such as light, hits a material. Electrons emitted in this manner are called photoelectrons. The phenomenon is studied in condensed matter physics, and solid st ...
, wherein electrons are emitted from atoms when they absorb energy from light. Since their existence was theorized eight years previously, phenomena had been studied with the electron model in mind in physics laboratories worldwide. In 1902,
Philipp Lenard Philipp Eduard Anton von Lenard (; hu, Lénárd Fülöp Eduárd Antal; 7 June 1862 – 20 May 1947) was a Hungarian-born German physicist and the winner of the Nobel Prize for Physics in 1905 for his work on cathode rays and the discovery of ...
discovered that the energy of these ejected electrons did not depend on the intensity of the incoming light, but instead on its frequency. So if one shines a little low-frequency light upon a metal, a few low energy electrons are ejected. If one now shines a very intense beam of low-frequency light upon the same metal, a whole slew of electrons are ejected; however they possess the same low energy, there are merely more of them. The more light there is, the more electrons are ejected. Whereas in order to get high energy electrons, one must illuminate the metal with high-frequency light. Like blackbody radiation, this was at odds with a theory invoking continuous transfer of energy between radiation and matter. However, it can still be explained using a fully classical description of light, as long as matter is quantum mechanical in nature. If one used Planck's energy quanta, and demanded that electromagnetic radiation at a given frequency could only transfer energy to matter in integer multiples of an energy quantum ''hf'', then the photoelectric effect could be explained very simply. Low-frequency light only ejects low-energy electrons because each electron is excited by the absorption of a single photon. Increasing the intensity of the low-frequency light (increasing the number of photons) only increases the number of excited electrons, not their energy, because the energy of each photon remains low. Only by increasing the frequency of the light, and thus increasing the energy of the photons, can one eject electrons with higher energy. Thus, using Planck's constant ''h'' to determine the energy of the photons based upon their frequency, the energy of ejected electrons should also increase linearly with frequency, the gradient of the line being Planck's constant. These results were not confirmed until 1915, when
Robert Andrews Millikan Robert Andrews Millikan (March 22, 1868 – December 19, 1953) was an American experimental physicist honored with the Nobel Prize for Physics in 1923 for the measurement of the elementary electric charge and for his work on the photoelectric e ...
produced experimental results in perfect accord with Einstein's predictions. While energy of ejected electrons reflected Planck's constant, the existence of photons was not explicitly proven until the discovery of the
photon antibunching Photon antibunching generally refers to a light field with photons more equally spaced than a coherent laser field, a signature being signals at appropriate detectors which are anticorrelated. More specifically, it can refer to sub-Poissonian ph ...
effect. This refers to the observation that once a single emitter (an atom, molecule, solid state emitter, etc.) radiates a detectable light signal, it cannot immediately release a second signal until after the emitter has been re-excited. This leads to a statistically quantifiable time delay between light emissions, so detection of multiple signals becomes increasingly unlikely as the observation time dips under the excited-state lifetime of the emitter. The effect can be demonstrated in an undergraduate-level lab. This phenomenon could only be explained via photons. Einstein's "light quanta" would not be called
photon A photon () is an elementary particle that is a quantum of the electromagnetic field, including electromagnetic radiation such as light and radio waves, and the force carrier for the electromagnetic force. Photons are massless, so they always ...
s until 1925, but even in 1905 they represented the quintessential example of wave–particle duality. Electromagnetic radiation propagates following linear wave equations, but can only be emitted or absorbed as discrete elements, thus acting as a wave and a particle simultaneously.


Einstein's explanation of photoelectric effect

In 1905, Albert Einstein provided an explanation of the photoelectric effect, an experiment that the wave theory of light failed to explain. He did so by postulating the existence of photons, quanta of light energy with particulate qualities. In the
photoelectric effect The photoelectric effect is the emission of electrons when electromagnetic radiation, such as light, hits a material. Electrons emitted in this manner are called photoelectrons. The phenomenon is studied in condensed matter physics, and solid st ...
, it was observed that shining a light on certain metals would lead to an
electric current An electric current is a stream of charged particles, such as electrons or ions, moving through an electrical conductor or space. It is measured as the net rate of flow of electric charge through a surface or into a control volume. The moving pa ...
in a circuit. Presumably, the light was knocking electrons out of the metal, causing current to flow. However, using the case of potassium as an example, it was also observed that while a dim blue light was enough to cause a current, even the strongest, brightest red light available with the technology of the time caused no current at all. According to the classical theory of light and matter, the strength or
amplitude The amplitude of a periodic variable is a measure of its change in a single period (such as time or spatial period). The amplitude of a non-periodic signal is its magnitude compared with a reference value. There are various definitions of amplit ...
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 was not so. Einstein explained this enigma by postulating that electrons can receive energy from an electromagnetic field only in discrete units (quanta or photons): an amount of
energy In physics, energy (from Ancient Greek: ἐνέργεια, ''enérgeia'', “activity”) is the quantitative property that is transferred to a body or to a physical system, recognizable in the performance of work and in the form of heat a ...
''E'' that was related to the
frequency Frequency is the number of occurrences of a repeating event per unit of time. It is also occasionally referred to as ''temporal frequency'' for clarity, and is distinct from ''angular frequency''. Frequency is measured in hertz (Hz) which is eq ...
''f'' of the light by :E = h f\, where ''h'' is Planck's constant (6.626 × 10−34 Js). 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. One photon of light above the threshold frequency could release only one electron; the higher the frequency of a photon, the higher the kinetic energy of the emitted electron, but no amount of light below the threshold frequency could release an electron. To violate this law would require extremely high-intensity lasers that had not yet been invented. Intensity-dependent phenomena have now been studied in detail with such lasers. Einstein was awarded the
Nobel Prize in Physics ) , image = Nobel Prize.png , alt = A golden medallion with an embossed image of a bearded man facing left in profile. To the left of the man is the text "ALFR•" then "NOBEL", and on the right, the text (smaller) "NAT•" then " ...
in 1921 for his discovery of the law of the photoelectric effect.


de Broglie's hypothesis

In 1924,
Louis-Victor de Broglie Louis Victor Pierre Raymond, 7th Duc de Broglie (, also , or ; 15 August 1892 – 19 March 1987) was a French physicist and aristocrat who made groundbreaking contributions to quantum theory. In his 1924 PhD thesis, he postulated the wave na ...
formulated the de Broglie hypothesis, claiming that all matter has a wave-like nature. He related
wavelength In physics, the wavelength is the spatial period of a periodic wave—the distance over which the wave's shape repeats. It is the distance between consecutive corresponding points of the same phase on the wave, such as two adjacent crests, tro ...
and
momentum In Newtonian mechanics, momentum (more specifically linear momentum or translational momentum) is the product of the mass and velocity of an object. It is a vector quantity, possessing a magnitude and a direction. If is an object's mass an ...
: :\lambda = \frac This is a generalization of Einstein's equation above, since the momentum of a photon is given by ''p'' = \tfrac and the wavelength (in a vacuum) by ''λ'' = \tfrac, where ''c'' is the
speed of light The speed of light in vacuum, commonly denoted , is a universal physical constant that is important in many areas of physics. The speed of light is exactly equal to ). According to the special theory of relativity, is the upper limit ...
in vacuum. De Broglie's formula was confirmed three years later for
electron The electron ( or ) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family, and are generally thought to be elementary particles because they have no kn ...
s with the observation of
electron diffraction Electron diffraction refers to the bending of electron beams around atomic structures. This behaviour, typical for waves, is applicable to electrons due to the wave–particle duality stating that electrons behave as both particles and waves. Si ...
, as it had been observed with
X-rays An X-ray, or, much less commonly, X-radiation, is a penetrating form of high-energy electromagnetic radiation. Most X-rays have a wavelength ranging from 10  picometers to 10 nanometers, corresponding to frequencies in the range 30&nbs ...
, in two independent experiments. At the
University of Aberdeen The University of Aberdeen ( sco, University o' 'Aiberdeen; abbreviated as ''Aberd.'' in List of post-nominal letters (United Kingdom), post-nominals; gd, Oilthigh Obar Dheathain) is a public university, public research university in Aberdeen, Sc ...
,
George Paget Thomson Sir George Paget Thomson, FRS (; 3 May 189210 September 1975) was a British physicist and Nobel laureate in physics recognized for his discovery of the wave properties of the electron by electron diffraction. Education and early life Thomso ...
passed a beam of electrons through a thin metal film and observed the predicted interference patterns. At
Bell Labs Nokia Bell Labs, originally named Bell Telephone Laboratories (1925–1984), then AT&T Bell Laboratories (1984–1996) and Bell Labs Innovations (1996–2007), is an American industrial research and scientific development company owned by mult ...
,
Clinton Joseph Davisson Clinton Joseph Davisson (October 22, 1881 – February 1, 1958) was an American physicist who won the 1937 Nobel Prize in Physics for his discovery of electron diffraction in the famous Davisson–Germer experiment. Davisson shared the Nobel Pri ...
and Lester Halbert Germer guided the electron beam through a crystalline grid in their experiment popularly known as
Davisson–Germer experiment The Davisson–Germer experiment was a 1923-27 experiment by Clinton Davisson and Lester Germer at Western Electric (later Bell Labs), in which electrons, scattered by the surface of a crystal of nickel metal, displayed a diffraction pattern. ...
. De Broglie was awarded the
Nobel Prize for Physics ) , image = Nobel Prize.png , alt = A golden medallion with an embossed image of a bearded man facing left in profile. To the left of the man is the text "ALFR•" then "NOBEL", and on the right, the text (smaller) "NAT•" then " ...
in 1929 for his hypothesis. Thomson and Davisson shared the Nobel Prize for Physics in 1937 for their experimental work. De Broglie's proposal also predicts particle interferometry. In particular, single-particle interferometry has become a classic for its clarity in expressing the central puzzles of quantum mechanics. Because it demonstrates the fundamental limitation of the ability of the observer to predict experimental results,
Richard Feynman Richard Phillips Feynman (; May 11, 1918 – February 15, 1988) was an American theoretical physicist, known for his work in the path integral formulation of quantum mechanics, the theory of quantum electrodynamics, the physics of the superflu ...
called it "a phenomenon which is impossible to explain in any
classical way Classical may refer to: European antiquity *Classical antiquity, a period of history from roughly the 7th or 8th century B.C.E. to the 5th century C.E. centered on the Mediterranean Sea *Classical architecture, architecture derived from Greek and ...
, and which has in it the heart of quantum mechanics. In reality, it contains the only mystery f quantum mechanics In 1974, the Italian physicists Pier Giorgio Merli, Gian Franco Missiroli, and Giulio Pozzi performed the first experiment of single particle interferometry using electrons and a biprism (instead of slits), showing that each electron interferes with itself as predicted by quantum theory. In 2018, single particle interference has been first demonstrated for antimatter in th
Positron Laboratory
(L-NESS) o
Rafael Ferragut
in
Como Como (, ; lmo, Còmm, label=Comasco dialect, Comasco , or ; lat, Novum Comum; rm, Com; french: Côme) is a city and ''comune'' in Lombardy, Italy. It is the administrative capital of the Province of Como. Its proximity to Lake Como and ...
(
Italy Italy ( it, Italia ), officially the Italian Republic, ) or the Republic of Italy, is a country in Southern Europe. It is located in the middle of the Mediterranean Sea, and its territory largely coincides with the homonymous geographical re ...
), by a group led by Marco Giammarchi.


Heisenberg's uncertainty principle

In his work on formulating quantum mechanics,
Werner Heisenberg Werner Karl Heisenberg () (5 December 1901 – 1 February 1976) was a German theoretical physicist and one of the main pioneers of the theory of quantum mechanics. He published his work in 1925 in a breakthrough paper. In the subsequent series ...
postulated his uncertainty principle, which states: :\Delta x \, \Delta p \ge \tfrac\hbar where :\Delta here indicates standard deviation, a measure of spread or uncertainty; : and are a particle's position and
linear momentum In Newtonian mechanics, momentum (more specifically linear momentum or translational momentum) is the product of the mass and velocity of an object. It is a vector quantity, possessing a magnitude and a direction. If is an object's mass a ...
respectively. :''\hbar'' is the
reduced Planck's constant The Planck constant, or Planck's constant, is a fundamental physical constant of foundational importance in quantum mechanics. The constant gives the relationship between the energy of a photon and its frequency, and by the mass-energy equivalen ...
(Planck's constant divided by 2\pi). 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. The thought is now, however, that this only partly explains the phenomenon, but that 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 The Copenhagen interpretation is a collection of views about the meaning of quantum mechanics, principally attributed to Niels Bohr and Werner Heisenberg. It is one of the oldest of numerous proposed interpretations of quantum mechanics, as feat ...
first put forward by Bohr and
Heisenberg Werner Karl Heisenberg () (5 December 1901 – 1 February 1976) was a German theoretical physicist and one of the main pioneers of the theory of quantum mechanics. He published his work in 1925 in a breakthrough paper. In the subsequent series ...
, depends even more centrally on the wave nature of a particle. Just as it is nonsensical to discuss the precise location of a wave on a string, particles do not have perfectly precise positions; likewise, just as it is nonsensical to discuss the wavelength of a "pulse" wave traveling down a string, particles do not have perfectly precise momenta that correspond 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–Bohm theory

De Broglie himself had proposed a
pilot wave In theoretical physics, the pilot wave theory, also known as Bohmian mechanics, was the first known example of a hidden-variable theory, presented by Louis de Broglie in 1927. Its more modern version, the de Broglie–Bohm theory, interprets qua ...
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 Quantum theory may refer to: Science *Quantum mechanics, a major field of physics *Old quantum theory, predating modern quantum mechanics * Quantum field theory, an area of quantum mechanics that includes: ** Quantum electrodynamics ** Quantum ...
and
David Bohm David Joseph Bohm (; 20 December 1917 – 27 October 1992) was an American-Brazilian-British scientist who has been described as one of the most significant theoretical physicists of the 20th centuryPeat 1997, pp. 316-317 and who contributed ...
extended de Broglie's model to explicitly include it. In the resulting representation, also called the de Broglie–Bohm theory or Bohmian mechanics, the wave–particle duality vanishes, and explains the wave behaviour as a scattering with wave appearance, because the particle's motion is subject to a guiding equation or
quantum potential The quantum potential or quantum potentiality is a central concept of the de Broglie–Bohm formulation of quantum mechanics, introduced by David Bohm in 1952. Initially presented under the name ''quantum-mechanical potential'', subsequently ''qu ...
. The best illustration of the ''pilot-wave model'' was given by Couder's 2010 "walking droplets" experiments, demonstrating the pilot-wave behaviour in a macroscopic mechanical analog.See this Science Channel production (Season II, Episode VI "How Does The Universe Work?"), presented by Morgan Freeman, https://www.youtube.com/watch?v=W9yWv5dqSKk


Wave nature of large objects

Since the demonstrations of wave-like properties in
photon A photon () is an elementary particle that is a quantum of the electromagnetic field, including electromagnetic radiation such as light and radio waves, and the force carrier for the electromagnetic force. Photons are massless, so they always ...
s and
electron The electron ( or ) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family, and are generally thought to be elementary particles because they have no kn ...
s, similar experiments have been conducted with
neutron The neutron is a subatomic particle, symbol or , which has a neutral (not positive or negative) charge, and a mass slightly greater than that of a proton. Protons and neutrons constitute the nuclei of atoms. Since protons and neutrons beh ...
s and
proton A proton is a stable subatomic particle, symbol , H+, or 1H+ with a positive electric charge of +1 ''e'' elementary charge. Its mass is slightly less than that of a neutron and 1,836 times the mass of an electron (the proton–electron mass ...
s. Among the most famous experiments are those of Estermann and
Otto Stern :''Otto Stern was also the pen name of German women's rights activist Louise Otto-Peters (1819–1895)''. Otto Stern (; 17 February 1888 – 17 August 1969) was a German-American physicist and Nobel laureate in physics. He was the second most n ...
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 physics, gravity () is a fundamental interaction which causes mutual attraction between all things with mass or energy. Gravity is, by far, the weakest of the four fundamental interactions, approximately 1038 times weaker than the stro ...
in relation to wave–particle duality was conducted in the 1970s using the
neutron interferometer In physics, a neutron interferometer is an interferometer capable of diffracting neutrons, allowing the wave-like nature of neutrons, and other related phenomena, to be explored. Interferometry Interferometry inherently depends on the wave na ...
. Neutrons, one of the components of the
atomic nucleus The atomic nucleus is the small, dense region consisting of protons and neutrons at the center of an atom, discovered in 1911 by Ernest Rutherford based on the 1909 Geiger–Marsden gold foil experiment. After the discovery of the neutron i ...
, 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 Tests of general relativity serve to establish observational evidence for the theory of general relativity. The first three tests, proposed by Albert Einstein in 1915, concerned the "anomalous" precession of the perihelion of Mercury, the ben ...
and the Pound–Rebka falling photon experiment), the self-interference of the quantum mechanical wave of a massive
fermion In particle physics, a fermion is a particle that follows Fermi–Dirac statistics. Generally, it has a half-odd-integer spin: spin , spin , etc. In addition, these particles obey the Pauli exclusion principle. Fermions include all quarks an ...
in a gravitational field had never been experimentally confirmed before. In 1999, the diffraction of C60
fullerene A fullerene is an allotrope of carbon whose molecule consists of carbon atoms connected by single and double bonds so as to form a closed or partially closed mesh, with fused rings of five to seven atoms. The molecule may be a hollow sphere, ...
s by researchers from the
University of Vienna The University of Vienna (german: Universität Wien) is a public research university located in Vienna, Austria. It was founded by Duke Rudolph IV in 1365 and is the oldest university in the German-speaking world. With its long and rich histor ...
was reported. Fullerenes are comparatively large and massive objects, having an atomic mass of about 720 u. The
de Broglie wavelength Matter waves are a central part of the theory of quantum mechanics, being an example of wave–particle duality. All matter exhibits wave-like behavior. For example, a beam of electrons can be diffracted just like a beam of light or a water wave ...
of the incident beam was about 2.5  pm, whereas the diameter of the molecule is about 1  nm, about 400 times larger. In 2012, these far-field diffraction experiments could be extended to
phthalocyanine Phthalocyanine () is a large, aromatic, macrocyclic, organic compound with the formula and is of theoretical or specialized interest in chemical dyes and photoelectricity. It is composed of four isoindole units linked by a ring of nitrogen atom ...
molecules and their heavier derivatives, which are composed of 58 and 114 atoms respectively. In these experiments the build-up of such interference patterns could be recorded in real time and with single molecule sensitivity. In 2003, the Vienna group also demonstrated the wave nature of
tetraphenylporphyrin Tetraphenylporphyrin, abbreviated TPP or H2TPP, is a synthetic heterocyclic compound that resembles naturally occurring porphyrins. Porphyrins are dyes and cofactors found in hemoglobin and cytochromes and are related to chlorophyll and vitamin ...
—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 C60F48, a fluorinated
buckyball Buckminsterfullerene is a type of fullerene with the formula C60. It has a cage-like fused-ring structure (truncated icosahedron) made of twenty hexagons and twelve pentagons, and resembles a soccer ball. Each of its 60 carbon atoms is bonded t ...
with a mass of about 1600 u, composed of 108 atoms. Large molecules are already so complex that they give experimental access to some aspects of the quantum-classical interface, i.e., to certain
decoherence Quantum decoherence is the loss of quantum coherence. In quantum mechanics, particles such as electrons are described by a wave function, a mathematical representation of the quantum state of a system; a probabilistic interpretation of the wa ...
mechanisms. In 2011, the interference of molecules as heavy as 6910 u could be demonstrated in a Kapitza–Dirac–Talbot–Lau interferometer. In 2013, the interference of molecules beyond 10,000 u has been demonstrated. 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 The Compton wavelength is a quantum mechanical property of a particle. The Compton wavelength of a particle is equal to the wavelength of a photon whose energy is the same as the rest energy of that particle (see mass–energy equivalence). It was ...
would be smaller than the Planck length and its own
Schwarzschild radius The Schwarzschild radius or the gravitational radius is a physical parameter in the Schwarzschild solution to Einstein's field equations that corresponds to the radius defining the event horizon of a Schwarzschild black hole. It is a characteris ...
, a scale at which current theories of physics may break down or need to be replaced by more general ones. Couder, Fort, ''et al.'' showed that macroscopic oil droplets on a vibrating fluid bath can be used as an analogue model of wave–particle duality; a localized droplet creates periodical wave field around itself. Resonant interaction between the droplet and its own wave field exhibits behaviour analogous to quantum particles: interference in double-slit experiment, unpredictable tunneling (depending in complicated way on practically hidden state of field), orbit quantization (that particle has to 'find a resonance' with field perturbations it creates—after one orbit, its internal phase has to return to the initial state) and
Zeeman effect The Zeeman effect (; ) is the effect of splitting of a spectral line into several components in the presence of a static magnetic field. It is named after the Dutch physicist Pieter Zeeman, who discovered it in 1896 and received a Nobel priz ...
. Note that other single and double slit experiments have shown that wall-droplet interactions rather than diffraction or interference of the pilot wave may be responsible for the observed hydrodynamic patterns, which are different from slit-induced interference patterns exhibited by quantum particles.


Importance

Wave–particle duality is deeply embedded into the foundations of
quantum mechanics Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistry, ...
. In the
formalism Formalism may refer to: * Form (disambiguation) * Formal (disambiguation) * Legal formalism, legal positivist view that the substantive justice of a law is a question for the legislature rather than the judiciary * Formalism (linguistics) * Scie ...
of the theory, all the information about a particle is encoded in its
wave function A wave function in quantum physics is a mathematical description of the quantum state of an isolated quantum system. The wave function is a complex-valued probability amplitude, and the probabilities for the possible results of measurements ...
, a complex-valued function roughly analogous to the amplitude of a wave at each point in space. This function evolves according to
Schrödinger equation The Schrödinger equation is a linear partial differential equation that governs the wave function of a quantum-mechanical system. It is a key result in quantum mechanics, and its discovery was a significant landmark in the development of th ...
. For particles with mass this equation has solutions that follow the form of the wave equation. Propagation of such waves leads to wave-like phenomena such as interference and diffraction. Particles without mass, like photons, have no solutions of the Schrödinger equation. Instead of a particle wave function that localizes mass in space, a photon wave function can be constructed from Einstein kinematics to localize energy in spatial coordinates. The particle-like behaviour is most evident due to phenomena associated with
measurement in quantum mechanics In quantum physics, a measurement is the testing or manipulation of a physical system to yield a numerical result. The predictions that quantum physics makes are in general probabilistic. The mathematical tools for making predictions about what m ...
. Upon measuring the location of the particle, the particle will be forced into a more localized state as given by the uncertainty principle. When viewed through this formalism, the measurement of the wave function will randomly lead to
wave function collapse In quantum mechanics, wave function collapse occurs when a wave function—initially in a quantum superposition, superposition of several eigenstates—reduces to a single eigenstate due to interaction with the external world. This interaction is ...
to a sharply peaked function at some location. For particles with mass, the likelihood of detecting the particle at any particular location is equal to the squared amplitude of the wave function there. The measurement will return a well-defined position, and is subject to
Heisenberg's uncertainty principle In quantum mechanics, the uncertainty principle (also known as Heisenberg's uncertainty principle) is any of a variety of mathematical inequalities asserting a fundamental limit to the accuracy with which the values for certain pairs of physic ...
. Following the development of
quantum field theory In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines classical field theory, special relativity, and quantum mechanics. QFT is used in particle physics to construct physical models of subatomic particles and ...
the ambiguity disappeared. The field permits solutions that follow the wave equation, which are referred to as the wave functions. The term particle is used to label the irreducible representations of the
Lorentz group In physics and mathematics, the Lorentz group is the group of all Lorentz transformations of Minkowski spacetime, the classical and quantum setting for all (non-gravitational) physical phenomena. The Lorentz group is named for the Dutch physicis ...
that are permitted by the field. An interaction as in a
Feynman diagram In theoretical physics, a Feynman diagram is a pictorial representation of the mathematical expressions describing the behavior and interaction of subatomic particles. The scheme is named after American physicist Richard Feynman, who introduc ...
is accepted as a calculationally convenient approximation where the outgoing legs are known to be simplifications of the propagation and the internal lines are for some order in an expansion of the field interaction. Since the field is non-local and quantized, the phenomena that previously were thought of as paradoxes are explained. Within the limits of the wave–particle duality the quantum field theory gives the same results.


Visualization

There are two ways to visualize the wave-particle behaviour: by the standard model and by the de Broglie–Bohm theory. Below is an illustration of wave–particle duality as it relates to de Broglie's hypothesis and Heisenberg's Uncertainty principle, in terms of the position and momentum space wavefunctions for one spinless particle with mass in one dimension. These wavefunctions are
Fourier transform A Fourier transform (FT) is a mathematical transform that decomposes functions into frequency components, which are represented by the output of the transform as a function of frequency. Most commonly functions of time or space are transformed, ...
s of each other. The more localized the position-space wavefunction, the more likely the particle is to be found with the position coordinates in that region, and correspondingly the momentum-space wavefunction is less localized so the possible momentum components the particle could have are more widespread. Conversely, the more localized the momentum-space wavefunction, the more likely the particle is to be found with those values of momentum components in that region, and correspondingly the less localized the position-space wavefunction, so the position coordinates the particle could occupy are more widespread.


Alternative views

Wave–particle duality is an ongoing conundrum in modern physics. Most physicists accept wave–particle duality as the best explanation for a broad range of observed phenomena; however, it is not without controversy. Alternative views are also presented here. These views are not generally accepted by mainstream physics, but serve as a basis for valuable discussion within the community.


Both-particle-and-wave view

The
pilot wave In theoretical physics, the pilot wave theory, also known as Bohmian mechanics, was the first known example of a hidden-variable theory, presented by Louis de Broglie in 1927. Its more modern version, the de Broglie–Bohm theory, interprets qua ...
model, was originally developed by
Louis de Broglie Louis Victor Pierre Raymond, 7th Duc de Broglie (, also , or ; 15 August 1892 – 19 March 1987) was a French physicist and aristocrat who made groundbreaking contributions to Old quantum theory, quantum theory. In his 1924 PhD thesis, he pos ...
and further developed by
David Bohm David Joseph Bohm (; 20 December 1917 – 27 October 1992) was an American-Brazilian-British scientist who has been described as one of the most significant theoretical physicists of the 20th centuryPeat 1997, pp. 316-317 and who contributed ...
into the
hidden variable theory In physics, hidden-variable theories are proposals to provide explanations of quantum mechanical phenomena through the introduction of (possibly unobservable) hypothetical entities. The existence of fundamental indeterminacy for some measurem ...
. The phrase “hidden variable” is misleading since the variable in question is the positions of the particles. Instead of duality, the pilot wave model proposes that both wave and particle are present with the wave guiding the particle in a deterministic fashion. The wave in question is the wavefunction obeying Schrödinger’s equation. Bohm’s formulation is intended to be classical, but it has to incorporate a distinctly non-classical feature: a nonlocal force ("
quantum potential The quantum potential or quantum potentiality is a central concept of the de Broglie–Bohm formulation of quantum mechanics, introduced by David Bohm in 1952. Initially presented under the name ''quantum-mechanical potential'', subsequently ''qu ...
") acting on the particles. Bohm’s original purpose (1952) “was to show that an alternative to the Copenhagen interpretation is at least logically possible. Soon after he set the project aside and did not revive it until he met
Basil Hiley Basil J. Hiley (born 1935), is a British quantum physicist and professor emeritus of the University of London. Long-time colleague of David Bohm, Hiley is known for his work with Bohm on implicate orders and for his work on algebraic descriptio ...
in 1961 when both were at Birbeck College (University of London). Bohm and Hiley then wrote extensively on the theory and it gained a wider audience. This idea is held by a significant minority within the physics community. The
Afshar experiment The Afshar experiment is a variation of the double-slit experiment in quantum mechanics, devised and carried out by Shahriar Afshar while at the private, Boston-based Institute for Radiation-Induced Mass Studies (IRIMS). The results were presente ...
(2007) may suggest that it is possible to simultaneously observe both wave and particle properties of photons. This claim is, however, disputed by other scientists.


Wave-only view

Carver Mead Carver Andress Mead (born May 1, 1934) is an American scientist and engineer. He currently holds the position of Gordon and Betty Moore Professor Emeritus of Engineering and Applied Science at the California Institute of Technology (Caltech), ...
, an American scientist and professor at Caltech, said that the duality can be replaced by a "wave-only" view. In his book ''Collective Electrodynamics: Quantum Foundations of Electromagnetism'' (2000), Mead purports to analyze the behaviour of
electron The electron ( or ) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family, and are generally thought to be elementary particles because they have no kn ...
s and
photon A photon () is an elementary particle that is a quantum of the electromagnetic field, including electromagnetic radiation such as light and radio waves, and the force carrier for the electromagnetic force. Photons are massless, so they always ...
s purely in terms of electron wave functions, and attributes the apparent particle-like behaviour to quantization effects and eigenstates. According to reviewer David Haddon:
Mead has cut the
Gordian knot The Gordian Knot is an Ancient Greek legend of Phrygian Gordium associated with Alexander the Great who is said to have cut the knot in 333 BC. It is often used as a metaphor for an intractable problem (untying an impossibly tangled knot) sol ...
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 player A CD player is an electronic device that plays audio compact discs, which are a digital optical disc data storage format. CD players were first sold to consumers in 1982. CDs typically contain recordings of audio material such as music or audio ...
s, the self-propagating electrical currents of superconductors, and the
Bose–Einstein condensate In condensed matter physics, a Bose–Einstein condensate (BEC) is a state of matter that is typically formed when a gas of bosons at very low densities is cooled to temperatures very close to absolute zero (−273.15 °C or −459.67&n ...
of atoms.
Albert Einstein Albert Einstein ( ; ; 14 March 1879 – 18 April 1955) was a German-born theoretical physicist, widely acknowledged to be one of the greatest and most influential physicists of all time. Einstein is best known for developing the theory ...
, who, in his search for a
Unified Field Theory In physics, a unified field theory (UFT) is a type of field theory that allows all that is usually thought of as fundamental forces and elementary particles to be written in terms of a pair of physical and virtual fields. According to the modern ...
, did not accept wave–particle duality, wrote:
This double nature of radiation (and of material corpuscles) ... has been interpreted by quantum-mechanics in an ingenious and amazingly successful fashion. This interpretation ... appears to me as only a temporary way out...
The
many-worlds interpretation The many-worlds interpretation (MWI) is an interpretation of quantum mechanics that asserts that the universal wavefunction is objectively real, and that there is no wave function collapse. This implies that all possible outcomes of quantum ...
(MWI) is sometimes presented as a waves-only theory, including by its originator,
Hugh Everett Hugh Everett III (; November 11, 1930 – July 19, 1982) was an American physicist who first proposed the many-worlds interpretation (MWI) of quantum physics, which he termed his "relative state" formulation. In contrast to the then-dominant Cope ...
who referred to MWI as "the wave interpretation". The ' of R. Horodecki relates the particle to wave. The hypothesis implies that a massive particle is an intrinsically spatially, as well as temporally extended, wave phenomenon by a nonlinear law. The ' considers collapse and measurement as two independent physical processes. Collapse occurs when two wavepackets spatially overlap and satisfy a mathematical criterion, which depends on the parameters of both wavepackets. It is a contraction to the overlap volume. In a measurement apparatus one of the two wavepackets is one of the atomic clusters, which constitute the apparatus, and the wavepackets collapse to at most the volume of such a cluster. This mimics the action of a point particle.
Hegerfeldt's theorem Hegerfeldt's theorem is a no-go theorem that demonstrates the incompatibility of the existence of localized discrete particles with the combination of the principles of quantum mechanics and special relativity. It has been used to support the conc ...
, which appears to demonstrates the incompatibility of the existence of localized discrete particles with the combination of the principles of quantum mechanics and special relativity, has also been used to support the conclusion that reality must be described solely in terms of field-based formulations.


Particle-only view

Still in the days of the
old quantum theory The old quantum theory is a collection of results from the years 1900–1925 which predate modern quantum mechanics. The theory was never complete or self-consistent, but was rather a set of heuristic corrections to classical mechanics. The theory ...
, a pre-quantum-mechanical version of wave–particle duality was pioneered by William Duane, and developed by others including
Alfred Landé Alfred Landé (13 December 1888 – 30 October 1976) was a German-American physicist known for his contributions to quantum theory. He is responsible for the Landé g-factor and an explanation of the Zeeman effect. Life and achievements Alf ...
. Duane explained diffraction of
x-rays An X-ray, or, much less commonly, X-radiation, is a penetrating form of high-energy electromagnetic radiation. Most X-rays have a wavelength ranging from 10  picometers to 10 nanometers, corresponding to frequencies in the range 30&nbs ...
by a crystal in terms solely of their particle aspect. The deflection of the trajectory of each diffracted photon was explained as due to quantized momentum transfer from the spatially regular structure of the diffracting crystal.


Neither-wave-nor-particle view

It has been argued that there are never exact particles or waves, but only some compromise or intermediate between them. For this reason, in 1928 Arthur Eddington coined the name "''wavicle''" to describe the objects although it is not regularly used today. One consideration is that zero-dimensional mathematical points cannot be observed. Another is that the formal representation of such points, the Dirac delta function is unphysical, because it cannot be normalized. Parallel arguments apply to single-frequency wave states.
Roger Penrose Sir Roger Penrose (born 8 August 1931) is an English mathematician, mathematical physicist, philosopher of science and Nobel Laureate in Physics. He is Emeritus Rouse Ball Professor of Mathematics in the University of Oxford, an emeritus fello ...
states:
Such 'position states' are idealized wavefunctions in the opposite sense from the momentum states. Whereas the momentum states are infinitely spread out, the position states are infinitely concentrated. Neither is normalizable ..


Uses

Although it is difficult to draw a line separating wave–particle duality from the rest of quantum mechanics, it is 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 Neutron diffraction or elastic neutron scattering is the application of neutron scattering to the determination of the atomic and/or magnetic structure of a material. A sample to be examined is placed in a beam of thermal or cold neutrons to o ...
uses neutrons with a wavelength of about 0.1  nm, the typical spacing of atoms in a solid, to determine the structure of solids. * Photos are now able to show this dual nature, which may lead to new ways of examining and recording this behaviour.


See also

*
Afshar experiment The Afshar experiment is a variation of the double-slit experiment in quantum mechanics, devised and carried out by Shahriar Afshar while at the private, Boston-based Institute for Radiation-Induced Mass Studies (IRIMS). The results were presente ...
*
Arago spot Arago may refer to: People * Aragó, a family name of the kings of the Aragonese Crown * Étienne Arago (1802–1892), French journalist, theater director, and politician; brother of Juan, François, and Jacques * François Arago (1786–1853), F ...
* Basic concepts of quantum mechanics *
Complementarity (physics) In physics, complementarity is a conceptual aspect of quantum mechanics that Niels Bohr regarded as an essential feature of the theory. The complementarity principle holds that objects have certain pairs of complementary properties which cannot a ...
*
Einstein's thought experiments A hallmark of Albert Einstein's career was his use of visualized thought experiments (german: Gedankenexperiment) as a fundamental tool for understanding physical issues and for elucidating his concepts to others. Einstein's thought experiments too ...
* Englert–Greenberger–Yasin duality relation *
EPR paradox EPR may refer to: Science and technology * EPR (nuclear reactor), European Pressurised-Water Reactor * EPR paradox (Einstein–Podolsky–Rosen paradox), in physics * Earth potential rise, in electrical engineering * East Pacific Rise, a mid-oc ...
*
Faraday wave Faraday waves, also known as Faraday ripples, named after Michael Faraday (1791–1867), are nonlinear standing waves that appear on liquids enclosed by a vibrating receptacle. When the vibration frequency exceeds a critical value, the flat hydrost ...
*
Hanbury Brown and Twiss effect In physics, the Hanbury Brown and Twiss (HBT) effect is any of a variety of correlation and anti-correlation effects in the intensities received by two detectors from a beam of particles. HBT effects can generally be attributed to the wave–par ...
*
Kapitsa–Dirac effect The Kapitza–Dirac effect is a quantum mechanical effect consisting of the diffraction of matter by a standing wave of light. The effect was first predicted as the diffraction of electrons from a standing wave of light by Paul Dirac and Pyotr K ...
*
Photon polarization Photon polarization is the quantum mechanical description of the classical polarized sinusoidal plane electromagnetic wave. An individual photon can be described as having right or left circular polarization, or a superposition of the two. Equ ...
* Scattering theory *
Wavelet A wavelet is a wave-like oscillation with an amplitude that begins at zero, increases or decreases, and then returns to zero one or more times. Wavelets are termed a "brief oscillation". A taxonomy of wavelets has been established, based on the num ...
* Wheeler's delayed choice experiment


References


External links


Animation, applications and research linked to the wave–particle duality and other basic quantum phenomena
(Université Paris Sud) * * * * E.H. Carlson
''Wave–Particle Duality: Light ''
o
Project PHYSNET
* * {{DEFAULTSORT:Wave Particle Duality Foundational quantum physics Duality theories Dichotomies Articles containing video clips