   #copyright

Wave–particle duality

2007 Schools Wikipedia Selection. Related subjects: General Physics

   In physics and chemistry, wave-particle duality holds that light and
   matter exhibit properties of both waves and of particles. A central
   concept of quantum mechanics, duality represents a way to address the
   inadequacy of conventional concepts like "particle" and "wave" to
   meaningfully describe the behaviour of quantum objects. 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, it is now
   established that all objects have both wave and particle nature (though
   this phenomenon is only detectable on small scales, such as with
   atoms), and that a suitable interpretation of quantum mechanics
   provides the over-arching theory resolving this ostensible paradox.

History

   Thomas Young's sketch of two-slit diffraction of light, 1803.
   Enlarge
   Thomas Young's sketch of two-slit diffraction of light, 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 understood to consist of
   particles called electrons, as demonstrated by J.J. Thomson by his
   research into the work of 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 with this
   viewpoint. The photoelectric effect, as analyzed in 1905 by Albert
   Einstein, demonstrated that light also possessed particle-like
   properties, 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. Quantum mechanics holds that every
   particle in nature, be it a photon, electron or atom, is described by a
   solution to a differential equation, most typically, the Schroedinger
   equation. The solutions to this equation are known as wave functions,
   as they are inherently wave-like in their form. They can diffract and
   interfere, leading to the wave-like phenomena that are observed. Yet
   also, the wave functions are interpreted as describing the probability
   of finding a particle at a given point in space. Thus, if one is
   looking for a particle, one will find one, with a probability density
   given by the square of the magnitude of the wave function.

   One does not observe the wave-like quality of everyday objects because
   the associated wavelengths of people-sized objects are exceedingly
   small.

Huygens and Newton; earliest theories of light

   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 wave-front,
   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.

   Because of Newton's immense intellectual stature, his theory went
   essentially unchallenged for over a century, with Huygens' theories all
   but forgotten. With the discovery of diffraction in the early 19th
   century, the wave theory was revived, and so by the advent of the 20th
   century, a scientific debate over waves vs. particles had already been
   thriving for a very long time.

Fresnel, Maxwell, and Young

   In the early 1800s, the double-slit experiments by Young and Fresnel
   provided evidence for Huygens' 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. 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.

Einstein and photons

   The photoelectric effect. Incoming photons on the left strike a metal
   plate (bottom), and eject electrons, depicted as flying off to the
   right.
   Enlarge
   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 which 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
   them 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
   were knocked free of the metal by incident photons, with each photon
   carrying an amount of energy E that was related to the frequency, ν of
   the light by

          E = h \nu\,

   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

   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, λ (lambda), and momentum, p:

          \lambda = \frac{h}{p}

   This is a generalization of Einstein's equation above since the
   momentum of a photon is given by p = E / c where c is the speed of
   light in vacuum, and λ = c / ν.

   de Broglie's formula was confirmed three years later for electrons
   (which have 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

   Wave-particle duality is often expressed via the Heisenberg uncertainty
   principle, which states, in its most common form, that:

          \Delta x \Delta p \ge \frac{\hbar}{2}

   where

          Δ is a measure of uncertainty or imprecision in the measurement.
          x and p are a particle's position and linear momentum
          respectively.
          \hbar is the reduced Planck's constant (Planck's constant
          divided by 2π).

   However the relationship holds more generally for any two conjugate
   variables, such as time and energy, or angle of rotation and angular
   momentum and follows from the de Broglie hypothesis being applied to
   classical fields. The uncertainty relation implies that the measurement
   of one variable results in the disturbance of its conjugate partner, so
   that the product of their uncertainty is always greater than a certain
   amount.

Wave behaviour of large objects

   Similar experiments have since 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 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 1970's 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. Neutrons are fermions, and thus possess an important
   quality we associate with matter, namely its "rigidness" (due to the
   fact that they obey the Pauli Exclusion Principle). 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 - even deflecting light and
   acting on photons (the Pound-Rebka falling photon experiment), the
   self-interference of the quantum mechanical wave of a massive fermion
   in a gravitational field had never been experimentally confirmed
   before.

   In 1999, the diffraction of C[60] fullerenes by researchers from the
   University of Vienna was reported. Fullerenes are rather large and
   massive objects, having an atomic mass of about 720. The de Broglie
   wavelength is 2.5 picometers, whereas the diameter of the molecule is
   about 1 nanometer, 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. The experimenters have
   assumed the arguments of wave-particle duality and have assumed the
   validity of de Broglie's equation in their argument. In 2003 the Vienna
   group has meanwhile also demonstrated the wave-nature of
   tetraphenylporphyrin - a flat biodye with an extension of about 2 nm
   and a mass of 614 amu. 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
   with a mass of about 1600 amu, 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
   mechanisms .

   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
   Schwarzchild radius, a scale at which current theories of physics may
   break down or need to be replaced by more general ones.

Theoretical sketch and remarks on philosophical inquiry

   Examples ( diffraction, interference, double-slit experiment, phase
   noise in lasers, proton, teleportation, quantum computing, quantum
   cryptography , Bell's theorem, combination with special relativity:
   Klein-Gordon Equation and Dirac equations) for the application of this
   framework have been given above, now the common mathematics behind it
   is discussed.

   The wave and the particle description is made equivalent three steps:
    1. For particles the state of a system is described mathematically by
       the number of particles and their positions; quantum mechanics
       assigns every number and every combination of positions a complex
       number.
    2. For waves the state of a system is described mathematically by the
       field distribution; quantum field theory assigns every field
       distribution (zero everywhere, homogeneous , circular ...) a
       complex number.
    3. It is mathematically proven (see fock space in quantum field
       theory), that both quantum descriptions are equivalent, while the
       classical descriptions are not

   see also: Hilbert space, path integral formulation, Mathematical
   formulation of quantum mechanics

   All complex numbers together make up the ket, which is also called wave
   function. But the name "wave function" is problematic, as it sounds
   that they have more to do with waves than with particles. The time
   evolution of a ket is governed by a partial differential equation
   generically called the Schrödinger equation. The mathematical tools
   learned for classical physics to solve such an equation can still be
   applied: Superposition, eigenfunctions, eigenvalues, FDTD, perturbation
   theory. In other words: "it is a particle and a wave at the same time"
   in reality and in calculations. It has to be admitted that the
   coefficients for the differential equations were derived in a rather
   unsymmetrical way with respect to particles and waves, but it is
   unclear if this is an historical artifact.

   The ket is still interpreted as the probability of finding a system in
   a specific state. Most of the examples allow or even need partial
   measurements followed by a second time evolution of the ket followed by
   more measurements and so on, this is where the philosophical inquiry
   takes place.

Applications

   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.

   Retrieved from "
   http://en.wikipedia.org/wiki/Wave%E2%80%93particle_duality"
   This reference article is mainly selected from the English Wikipedia
   with only minor checks and changes (see www.wikipedia.org for details
   of authors and sources) and is available under the GNU Free
   Documentation License. See also our Disclaimer.
