(Redirected from Wave-particle duality)In
physics and
chemistry, 'wave–particle duality' is a conceptualization that all objects in our universe exhibit properties of both
waves (such as
interference) and of
particles (such as
quantization of some of their properties). A central concept of
quantum mechanics, duality addresses the inadequacy of classical concepts like "particle" and "wave" in fully describing the behaviour of quantum objects. Various
interpretations of quantum mechanics attempt to explain this ostensible
paradox.
The idea of duality is rooted in a debate over the nature of
light and
matter dating back to the 1600s, when competing theories of light were proposed by
Christiaan Huygens and
Isaac Newton. Through the work of
Albert Einstein,
Louis de Broglie and many others, current scientific theory holds that ''all'' particles also have a wave nature.
[1] This phenomenon has been verified not only for elementary particles, but also for compound particles like atoms and even molecules. In fact, according to standard quantum mechanics, wave–particle duality applies to all objects, even macroscopic ones; the reason we can't detect wave properties of macroscopic objects is their small wavelength.
[2]
Brief history
Thomas Young's sketch of two-slit diffraction of waves, 1803.
At the close of the 19th century, the case for
atomic theory, that matter was made of particulate objects or
atoms, was well established. Electricity, first thought to be a fluid, was now understood to consist of particles called
electrons, as demonstrated by
J.J. Thomson by his research into the work of
Ernest Rutherford, who had investigated using
cathode rays that an electrical charge would actually travel across a vacuum from cathode to anode. In brief, it was understood that much of nature was made of particles. At the same time, waves were well understood, together with wave phenomena such as
diffraction and
interference. Light was believed to be a wave, as
Thomas Young's double-slit experiment and effects such as
Fraunhofer diffraction had clearly demonstrated the wave-like nature of light.
But as the 20th century turned, problems had emerged.
Albert Einstein's analysis of the
photoelectric effect in 1905 demonstrated that light also possessed particle-like properties, and this was further confirmed with the discovery of the
Compton effect in 1923. Later on, the
diffraction of electrons would be predicted and experimentally confirmed, thus showing that electrons must have wave-like properties in addition to particle properties.
This confusion over particle versus wave properties was eventually resolved with the advent and establishment of
quantum mechanics in the first half of the 20th century, which ultimately explained wave–particle duality. It provided a single unified theoretical framework for understanding that all matter may have characteristics associated with particles and waves, as explained below.
Developmental milestones
Huygens and Newton
The earliest comprehensive theory of
light was advanced by
Christiaan Huygens, who proposed a
wave theory of light, and in particular demonstrated how waves might interfere to form a wavefront, propagating in a straight line. However, the theory had difficulties in other matters, and was soon overshadowed by
Isaac Newton's
corpuscular theory of light. That is, Newton proposed that light consisted of small particles, with which he could easily explain the phenomenon of
reflection. With considerably more difficulty, he could also explain
refraction through a
lens, and the splitting of sunlight into a
rainbow by a
prism. Newton's particle viewpoint went essentially unchallenged for over a century.
[3]
Young, Fresnel, and Maxwell
In the early 1800s, the
double-slit experiments by
Young and
Fresnel provided
evidence for
Huygens' wave theories: these experiments showed that when light is sent through a
grid, a characteristic
interference pattern is
observed, very similar to the pattern resulting from the interference of
water waves; the wavelength of light can be
computed from such patterns. The wave view did not immediately displace the ray and particle view, but began to dominate scientific thinking about light in the mid 1800s, since it could explain polarization phenomena that the alternatives could not.
Maxwell, during the late-1800s, explained light as the propagation of
electromagnetic waves with the
Maxwell equations. These equations were verified by experiment, and Huygens' view became widely accepted.
Planck's formula for black body radiation
Main articles: Planck's law of black body radiation
In 1901,
Max Planck published an analysis that succeeded in reproducing the observed
spectrum of light emitted by a glowing object. To accomplish this, Planck had to make an ad hoc mathematical assumption of quantized energy of the oscillators (atoms of the blackbody) that emit radiation. It was Einstein who later proposed that it is the electromagnetic radiation itself that is quantized, and not the energy of radiating atoms.
Einstein's explanation of the photoelectric effect
Main articles: Photoelectric effect
In 1905,
Albert Einstein provided an explanation of the
photoelectric effect, a hitherto troubling experiment that the wave theory of light seemed incapable of explaining. He did so by postulating the existence of
photons,
quanta of light energy with particulate
qualities.
In the
photoelectric effect, it was observed that shining a light on certain metals would lead to an
electric current in a
circuit. Presumably, the light was knocking electrons out of the metal, causing current to flow. However, it was also observed that while a dim blue light was enough to cause a current, even the strongest, brightest red light caused no current at all. According to wave theory, the strength or
amplitude of a light wave was in proportion to its brightness: a bright light should have been easily strong enough to create a large current. Yet, oddly, this 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
:
where ''h'' is
Planck's constant (6.626 x 10
-34 J seconds). Only photons of a high-enough frequency, (above a certain ''threshold'' value) could knock an electron free. For example, photons of blue light had sufficient energy to free an electron from the metal, but photons of red light did not. More intense light above the threshold frequency could release more electrons, but no amount of light below the threshold frequency could release an electron.
Einstein was awarded the
Nobel Prize in Physics in 1921 for his theory of the photoelectric effect.
de Broglie's hypothesis
Main articles: de Broglie hypothesis
In 1924,
Louis-Victor de Broglie formulated the
de Broglie hypothesis, claiming that ''all'' matter, not just light, has a wave-like nature; he related
wavelength (denoted as ''
λ''), and
momentum (denoted as ''p''):
:
This is a generalization of Einstein's
equation above, since the momentum of a photon is given by ''p''=''E''/''c'' and the wavelength by ''λ''=''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
Main articles: Heisenberg uncertainty principle
In his work on formulating quantum mechanics,
Werner Heisenberg postulated his
uncertainty principle, which states:
:
where
:
here indicates
standard deviation, a measure of spread or uncertainty;
:'x' and 'p' are a particle's position and
linear momentum respectively.
:''
'' is the
reduced Planck's constant (Planck's constant divided by 2
).
Heisenberg originally explained this as a consequence of the process of measuring: Measuring position accurately would disturb momentum and vice-versa, offering an example (the "gamma-ray microscope") that depended crucially on the de Broglie hypothesis. It is now understood, however, that this only partly explains the phenomenon: the uncertainty also exists in the particle itself, even before the measurement is made.
In fact, the modern explanation of the uncertainty principle, extending the
Copenhagen Interpretation first put forward by
Bohr and
Heisenberg, depends even more centrally on the wave nature of a particle: Just as it 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 himself had proposed a
pilot wave construct to explain the observed wave–particle duality. In this view, each particle has a well-defined position and momentum, but is guided by a wave function derived from
Schrödinger's equation. The pilot wave theory was initially rejected because it generated non-local effects when applied to systems involving more than one particle. Non-locality, however, soon became established as an integral feature of
Quantum Theory (see
EPR paradox), and
David Bohm extended de Broglie's model to explicitly include it. In Bohmian mechanics
[4], the wave–particle duality is not a property of matter itself, but an appearance generated by the particle's motion subject to a guiding equation or quantum potential.
Wave behavior of large objects
Since the demonstrations of wave-like properties in
photons and
electrons, similar experiments have been conducted with
neutrons and
protons. Among the most famous experiments are those of
Estermann and
Otto Stern in 1929. Authors of similar recent experiments with atoms and molecules, described below, claim that these larger particles also act like waves.
A dramatic series of experiments emphasizing the action of
gravity in relation to wave–particle duality were conducted in the 1970s using the
neutron interferometer.
Neutrons, one of the components of the
atomic nucleus, provide much of the mass of a nucleus and thus of ordinary matter. In the neutron interferometer, they act as quantum-mechanical waves directly subject to the force of
gravity. While the results were not surprising since gravity was known to act on everything, including light (see
tests of general relativity and the
Pound-Rebka falling photon experiment), the self-interference of the quantum mechanical wave of a massive fermion in a gravitational field had never been experimentally confirmed before.
In 1999, the diffraction of C
60 fullerenes by researchers from the
University of Vienna was reported.
[5] Fullerenes are comparatively large and massive objects, having an atomic mass of about 720u. The de Broglie wavelength is 2.5
pm, whereas the diameter of the molecule is about 1
nm, i.e. about 400 times larger.
As of 2005, this is the largest object for which quantum-mechanical wave-like properties have been directly observed in far-field diffraction.
In 2003 the Vienna group also demonstrated the wave nature of
tetraphenylporphyrin[6] – a flat biodye with an extension of
about 2 nm and a mass of 614u. For this demonstration they employed a near-field
Talbot Lau interferometer.
[7][8] In the same interferometer they also
found interference fringes for C
60F
48., a fluorinated
buckyball with a mass of about 1600u, composed of 108 atoms
6 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.
[9][10]
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.
[11]
Treatment in modern quantum mechanics
Wave–particle duality is deeply embedded into the foundations of
quantum mechanics, so well that modern practitioners rarely discuss it as such. In the formalism of the theory, all the information about a particle is encoded in its ''wave function'', a
complex function roughly analogous to the height of a wave at each point in space. This function evolves according to a
differential equation (generically called the
Schrödinger equation), and this equation gives rise to wave-like phenomena such as interference and diffraction.
The particle-like behavior is most evident due to phenomena associated with
measurement in quantum mechanics. Upon measuring the location of the particle, the wave-function will randomly "
collapse" to a sharply peaked function at some location, with the likelihood of any particular location equal to the squared amplitude of the wave-function there. The measurement will return a well-defined position, a property traditionally associated with particles.
Although this picture is somewhat simplified (to the
non-relativistic case), it is adequate to capture the essence of current thinking on the phenomena historically called "wave–particle duality". (See also:
Mathematical formulation of quantum mechanics.)
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 one
angstrom, the typical spacing of atoms in a solid, to determine the structure of solids.
See also
★
Afshar experiment
★
Arago spot
★
Hanbury-Brown and Twiss effect
★
Photon polarization
★
Scattering theory
★
Dark Matter
References
1. Quantum Mechanics: An Introduction, Walter Greiner, , , Springer, 2001,
2. Quantum Physics of Atoms, Molecules, Solids, Nuclei, and Particles, R. Eisberg and R. Resnick, , , John Wiley & Sons, 1985, ISBN 047187373X
3. "light", The Columbia Encyclopedia, Sixth Edition. 2001-05.
4. Bohmian Mechanics, ''Stanford Encyclopedia of Philosophy.''
5. Wave–particle duality of C60, , Markus, Arndt, Nature, 1999
6. The wave nature of biomolecules and fluorofullerenes, , Lucia, Hackermüller, Phys. Rev. Lett., 2003
7. Talbot von Lau interefometry with cold slow potassium atoms., , John F., Clauser, Phys. Rev. A, 1994
8. Matter-wave interferometer for large molecules, , Björn, Brezger, Phys. Rev. Lett., 2002
9. Observation of Collisional Decoherence in Interferometry, , Klaus, Hornberger, Phys. Rev. Lett., 2003
10. Decoherence of matter waves by thermal emission of radiation, , Lucia, Hackermüller, Nature, 2004
11. Peter Gabriel Bergmann, ''The Riddle of Gravitation'', Courier Dover Publications, 1993 ISBN 0486273784 online
External links
★
Quantum mechanics: Myths and facts H. Nikolic
★
College Physics Young & Geller
★
Light as a Particle B. Crowell
★ E.H. Carlson,
''Wave–Particle Duality: Light '' on
Project PHYSNET
★
Wave–Particle Duality R. Nave
★
Interferometry and decoherence experiments with large molecules Markus Arndt
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