From Wikipedia, the free encyclopedia
Wave–particle duality is the concept that every
elementary particle or
quantic entity may be partly described in terms not only of
particles, but also of
waves. It expresses the inability of the
classical concepts "particle" or "wave" to fully describe the behavior of
quantum-scale objects. As
Albert Einstein wrote: "
It
seems as though we must use sometimes the one theory and sometimes the
other, while at times we may use either. We are faced with a new kind of
difficulty. We have two contradictory pictures of reality; separately
neither of them fully explains the phenomena of light, but together they
do."
^{[1]}
Through the work of
Max Planck, Einstein,
Louis de Broglie,
Arthur Compton,
Niels Bohr and many others, current scientific theory holds that all particles also have a wave nature (and vice versa).
^{[2]}
This phenomenon has been verified not only for elementary particles,
but also for compound particles like atoms and even molecules. For
macroscopic particles, because of their extremely short wavelengths, wave properties usually cannot be detected.
^{[3]}
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.
Niels Bohr regarded the "duality
paradox"
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.
^{[4]} Bohr regarded renunciation of the cause-effect relation, or
complementarity, of the space-time picture, as essential to the quantum
mechanical account.
^{[5]}
Werner Heisenberg
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,
which generates an entirely new concept of fields which 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. Turning the reasoning around, ordinary quantum mechanics can be deduced as a specialized consequence of quantum field theory.
^{[6]}^{[7]}
Brief history of wave and particle viewpoints
Democritus—the original
atomist—argued
that all things in the universe, including light, are composed of
indivisible sub-components (light being some form of solar atom).
^{[8]} At the beginning of the 11th Century, the Arabic scientist
Alhazen wrote the first comprehensive
treatise on optics;
describing refraction, reflection, 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 popularized and accredited the opposing wave description in his
treatise on light,
showing that the behavior of light could be re-created by modeling
wave-like disturbances in a universal medium ("plenum"). Beginning in
1670 and progressing over three decades,
Isaac Newton developed and championed his
corpuscular hypothesis, 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 and
Christiaan Huygens—and later
Augustin-Jean Fresnel—mathematically
refined the wave viewpoint, showing that if light traveled at different
speeds in different media (such as water and air),
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 behavior and was subsequently supported by
Thomas Young's 1803 discovery of
double-slit interference.
^{[9]}^{[10]}
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.
^{[11]}
Thomas Young's sketch of two-slit diffraction of waves, 1803
James Clerk Maxwell discovered that he could apply
his equations for electromagnetism,
which had been previously discovered, along with a slight modification
to describe self-propagating waves of oscillating electric and magnetic
fields. When the propagation speed of these electromagnetic waves was
calculated, the
speed of light
fell out. It quickly became apparent that visible light, ultraviolet
light, and infrared light (phenomena thought previously to be unrelated)
were all electromagnetic waves of differing frequency. The wave theory
had prevailed—or at least it seemed to.
While the 19th century had seen the success of the wave theory at describing light, it had also witnessed the rise of the
atomic theory at describing matter.
Antoine Lavoisier deduced the law of
conservation of mass and categorized many new chemical elements and compounds; and
Joseph Louis Proust advanced chemistry towards the atom by showing that elements combined in
definite proportions. This led
John Dalton to propose that elements were invisible sub components;
Amedeo Avogadro
discovered diatomic gases and completed the basic atomic theory,
allowing the correct molecular formulae of most known compounds—as well
as the correct weights of atoms—to be deduced and categorized in a
consistent manner.
Dimitri Mendeleev saw an order in
recurring chemical properties, and created a
table presenting the elements in unprecedented order and symmetry.
Animation showing the wave-particle duality with a double slit
experiment and effect of an observer. Increase size to see explanations
in the video itself.
Particle impacts make visible the interference pattern of waves.
A quantum particle is represented by a wave packet.
Interference of a quantum particle with itself.
Click images for animations.
Turn of the 20th century and the paradigm shift
Particles of electricity
At
the close of the 19th century, the reductionism of atomic theory began
to advance into the atom itself; determining, through physics, the
nature of the atom and the operation of chemical reactions. Electricity,
first thought to be a fluid, was now understood to consist of particles
called
electrons. This was first demonstrated by
J. J. Thomson in 1897 when, using a
cathode ray tube,
he found that an electrical charge would travel across a vacuum (which
would possess infinite resistance in classical theory). Since the vacuum
offered no medium for an electric fluid to travel, this discovery could
only be explained via a particle carrying a negative charge and moving
through the vacuum. This
electron flew in the face of classical
electrodynamics, which had successfully treated electricity as a fluid
for many years (leading to the invention of
batteries,
electric motors,
dynamos, and
arc lamps).
More importantly, the intimate relation between electric charge and
electromagnetism had been well documented following the discoveries of
Michael Faraday and
James Clerk Maxwell. Since electromagnetism was
known to be a wave generated by a changing electric or magnetic
field (a continuous, wave-like entity itself) an atomic/particle description of electricity and charge was a
non sequitur. Furthermore, classical electrodynamics was not the only classical theory rendered incomplete.
Radiation quantization
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
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
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.
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
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.
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 to
his constant h,
where E = hν). This was not an unsound proposal considering that
macroscopic oscillators operate similarly: when studying five
simple harmonic oscillators
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,
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 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
hν. 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 illuminated
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 took Planck's black body model to produce his solution to another outstanding problem of the day: the
photoelectric effect,
wherein electrons are emitted from atoms when they absorb energy from
light. Since their discovery eight years previously, electrons had been
studied in physics laboratories worldwide.
In 1902
Philipp Lenard 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.
^{[12]}
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
hν, 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,
who had previously determined the charge of the electron, produced
experimental results in perfect accord with Einstein's predictions.
While the energy of ejected electrons reflected Planck's constant, the
existence of photons was not explicitly proven until the discovery of
the
photon antibunching effect, of which a modern experiment can be performed in undergraduate-level labs.
^{[13]}
This phenomenon could only be explained via photons, and not through
any semi-classical theory (which could alternatively explain the
photoelectric effect). When Einstein received his
Nobel Prize in 1921, it was not for his more difficult and mathematically laborious
special and
general relativity, but for the simple, yet totally revolutionary, suggestion of quantized light. Einstein's "light quanta" would not be called
photons
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 the photoelectric effect
The photoelectric effect. Incoming photons on the left strike a metal
plate (bottom), and eject electrons, depicted as flying off to the
right.
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, 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
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 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
- $E=hf\,$
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. 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 (using technology available at the time) below the threshold
frequency could release an electron. To "violate" this law would require
extremely high-intensity lasers which had not yet been invented.
Intensity-dependent phenomena have now been studied in detail with such
lasers.
^{[14]}
Einstein was awarded the
Nobel Prize in Physics in 1921 for his discovery of the law of the photoelectric effect.
De Broglie's wavelength
Propagation of
de Broglie waves in 1d—real part of the
complex amplitude is blue, imaginary part is green. The probability (shown as the colour
opacity) of finding the particle at a given point
x is spread out like a waveform; there is no definite position of the particle. As the amplitude increases above zero the
curvature decreases, so the amplitude decreases again, and vice versa—the result is an alternating amplitude: a wave. Top:
Plane wave. Bottom:
Wave packet.
In 1924,
Louis-Victor de Broglie formulated the
de Broglie hypothesis, claiming that
all matter,
^{[15]}^{[16]} not just light, has a wave-like nature; he related
wavelength (denoted as
λ), and
momentum (denoted as
p):
- $\lambda ={\frac {h}{p}}$
This is a generalization of Einstein's equation above, since the momentum of a photon is given by
p =
${\tfrac {E}{c}}$ and the wavelength (in a vacuum) by
λ =
${\tfrac {c}{f}}$, where
c is the
speed of light in vacuum.
De Broglie's formula was confirmed three years later for
electrons (which differ from photons in having a
rest mass) with the observation of
electron diffraction in two independent experiments. At the
University of Aberdeen,
George Paget Thomson passed a beam of electrons through a thin metal film and observed the predicted interference patterns. At
Bell Labs,
Clinton Joseph Davisson and
Lester Halbert Germer guided their beam through a crystalline grid.
De Broglie was awarded the
Nobel Prize for Physics in 1929 for his hypothesis. Thomson and Davisson shared the Nobel Prize for Physics in 1937 for their experimental work.
Heisenberg's uncertainty principle
In his work on formulating quantum mechanics,
Werner Heisenberg postulated his
uncertainty principle, which states:
- $\Delta x\Delta p\geq {\frac {\hbar }{2}}$
where
- $\Delta$ here indicates standard deviation, a measure of spread or uncertainty;
- x and p are a particle's position and linear momentum respectively.
- $\hbar$ is the reduced Planck's constant (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 first put forward by
Bohr and
Heisenberg,
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 (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–Bohm theory
Couder experiments,^{[17]} "materializing" the pilot wave model.
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 the resulting representation, also called the
de Broglie–Bohm theory or Bohmian mechanics,
^{[18]}
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.
"This
idea seems to me so natural and simple, to resolve the wave-particle
dilemma in such a clear and ordinary way, that it is a great mystery to
me that it was so generally ignored",
^{[19]} J.S.Bell.
The best illustration of the
pilot-wave model was given by Couder's 2010 "walking droplets" experiments,
^{[20]} demonstrating the pilot-wave behaviour in a macroscopic mechanical analog.
^{[17]}
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.
^{[21]}
Authors of similar recent experiments with atoms and molecules,
described below, claim that these larger particles also act like waves. A
wave is basically a group of particles which moves in a particular form
of motion, i.e. to and fro. If we break that flow by an object it will
convert into radiants.
A dramatic series of experiments emphasizing the action of
gravity in relation to wave–particle duality was conducted in the 1970s using the
neutron interferometer.
^{[22]} 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.
^{[23]} Fullerenes are comparatively large and massive objects, having an atomic mass of about 720
u. The
de Broglie wavelength 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 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.
^{[24]}^{[25]}
In 2003, the Vienna group also demonstrated the wave nature of
tetraphenylporphyrin^{[26]}—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.
^{[27]}^{[28]} In the same interferometer they also found interference fringes for C
_{60}F
_{48.}, a fluorinated
buckyball with a mass of about 1600 u, composed of 108 atoms.
^{[26]}
Large molecules are already so complex that they give experimental
access to some aspects of the quantum-classical interface, i.e., to
certain
decoherence mechanisms.
^{[29]}^{[30]} In 2011, the interference of molecules as heavy as 6910 u could be demonstrated in a Kapitza–Dirac–Talbot–Lau interferometer.
^{[31]} In 2013, the interference of molecules beyond 10,000 u has been demonstrated.
^{[32]}
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.
^{[33]}
Recently Couder, Fort,
et al. showed
^{[34]}
that we can use macroscopic oil droplets on a vibrating surface as a
model of wave–particle duality—localized droplet creates periodical
waves around and interaction with them leads to quantum-like phenomena:
interference in double-slit experiment,
^{[35]} unpredictable tunneling
^{[36]} (depending in complicated way on practically hidden state of field), orbit quantization
^{[37]}
(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.
^{[38]}
Treatment in modern quantum mechanics
Wave–particle duality is deeply embedded into the foundations of
quantum mechanics. In the
formalism of the theory, all the information about a particle is encoded in its
wave function,
a complex-valued 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). 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 so have
another wave.
The particle-like behavior is most evident due to phenomena associated with
measurement in quantum mechanics.
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 "
collapse", or rather "
decohere",
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, (subject to
uncertainty),
a property traditionally associated with particles. It is important to
note that a measurement is only a particular type of interaction where
some data is recorded and the measured quantity is forced into a
particular
eigenstate. The act of measurement is therefore not fundamentally different from any other interaction.
Following the development of
quantum field theory
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 that are permitted by the field. An interaction as in a
Feynman diagram
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
which 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", described below; and by the
Broglie–Bohm model, where no duality is perceived.
Below is an illustration of wave–particle duality as it relates to De
Broglie's hypothesis and Heisenberg's uncertainty principle (above), in
terms of the
position and momentum space wavefunctions for one spinless particle with mass in one dimension. These wavefunctions are
Fourier transforms 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.
Position x and momentum p wavefunctions corresponding to
quantum particles. The colour opacity (%) of the particles corresponds
to the probability density of finding the particle with position x or momentum component p.
Top: If wavelength λ is unknown, so are momentum p, wave-vector k and energy E (de Broglie relations). As the particle is more localized in position space, Δx is smaller than for Δp_{x}.
Bottom: If λ is known, so are p, k, and E. As the particle is more localized in momentum space, Δp is smaller than for Δx.
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 model, originally developed by
Louis de Broglie and further developed by
David Bohm into the
hidden variable theory
proposes that there is no duality, but rather a system exhibits both
particle properties and wave properties simultaneously, and particles
are guided, in a
deterministic fashion, by the pilot wave (or its "
quantum potential") which will direct them to areas of
constructive interference in preference to areas of
destructive interference. This idea is held by a significant minority within the physics community.
^{[39]}
At least one physicist considers the "wave-duality" as not being an incomprehensible mystery. L.E. 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 could not 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 is 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.
The
Afshar experiment^{[40]}
(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.
^{[41]}^{[42]}^{[43]}^{[44]}
Wave-only view
At least one scientist proposes that the duality can be replaced by a "wave-only" view. In his book
Collective Electrodynamics: Quantum Foundations of Electromagnetism (2000),
Carver Mead
purports to analyze the behavior of electrons and photons purely in
terms of electron wave functions, and attributes the apparent
particle-like behavior to quantization effects and eigenstates.
According to reviewer David Haddon:
^{[45]}
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.
Albert Einstein, who, in his search for a
Unified Field Theory, did not accept wave-particle duality, wrote:
^{[46]}
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 (MWI) is sometimes presented as a waves-only theory, including by its originator,
Hugh Everett who referred to MWI as "the wave interpretation".
^{[47]}
The
Three Wave Hypothesis of R. Horodecki relates the particle to wave.
^{[48]}^{[49]}
The hypothesis implies that a massive particle is an intrinsically
spatially as well as temporally extended wave phenomenon by a nonlinear
law.
Particle-only view
Still in the days of the
old quantum theory, a pre-quantum-mechanical version of wave–particle duality was pioneered by
William Duane,
^{[50]} and developed by others including
Alfred Landé.
^{[51]} Duane explained diffraction of
x-rays
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.
^{[52]}
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^{[53]} 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 pure wave states.
Roger Penrose states:
^{[54]}
"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 [...]."
Relational approach to wave–particle duality
Relational quantum mechanics
is developed which regards the detection event as establishing a
relationship between the quantized field and the detector. The inherent
ambiguity associated with applying Heisenberg's uncertainty principle
and thus wave–particle duality is subsequently avoided.
^{[55]}
Applications
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 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.^{[56]}