Interference of two circular waves  Wavelength (decreasing bottom to top) and Wave centers distance (increasing to the right). Absolute value snapshots of the (realvalued, scalar) wave field. As time progresses, the wave fronts would move outwards from the two centers, but the dark regions (destructive interference) stay fixed. Interference is the addition (superposition) of two or more waves that result in a new wave pattern. Interference may refer to : the physical phenomenon of wave interference, see interference the legal concept of humanitarian interference the interference proceeding of the U.S. patent law interference in baseball the chess tactic of interference of the enemys defence the communications concept where interference is anything which alters, modifies...
Interference of two circular waves, snapshots of absolute value of (real,scalar) wave field for different wave lengths and distances of point sources File links The following pages link to this file: Interference Categories: GFDL images ...
In linear algebra, the principle of superposition states that, for a linear system, a linear combination of solutions to the system is also a solution to the same linear system. ...
Surface waves in water This article is about waves in the most general scientific sense. ...
As most commonly used, the term interference usually refers to the interaction of waves which are correlated or coherent with each other, either because they come from the same source or because they have the same or nearly the same frequency. Coherence is the property of wavelike states that enables them to exhibit interference. ...
For other uses, see Frequency (disambiguation). ...
Two nonmonochromatic waves are only fully coherent with each other if they both have exactly the same range of wavelengths and the same phase differences at each of the constituent wavelengths. Something which is monochromatic has a single color. ...
Coherence is from Latin cohaerere = stick together, to be connected with). ...
For other uses, see Wavelength (disambiguation). ...
This article is about a portion of a periodic process. ...
The total phase difference is derived from the sum of both the path difference and the initial phase difference (if the waves are generated from 2 or more different sources). It can then be concluded whether the waves reaching a point are in phase (constructive interference) or out of phase (destructive interference). Theory
Chromatic interference is seen in sea foam, which is made out of plankton. It is a sample of the naturally occurring interference. The principle of superposition of waves states that the resultant displacement at a point is equal to the vector sum of the displacements of different waves at that point. If a crest of a wave meets a crest of another wave at the same point then the crests interfere constructively and the resultant wave amplitude is greater. If a crest of a wave meets a trough of another wave then they interfere destructively, and the overall amplitude is decreased. This article is about the body of water. ...
Sea foam on the beach Foam on a cappuccino Fireretardant, foamed plastic being used as a temporary dam for firestop mortar in a cable penetration in a pulp and paper mill on Vancouver Island, British Columbia, Canada. ...
This article is about the reallife undersea organisms. ...
A crest is the section of a wave that rises above an undisturbed position. ...
It has been suggested that pulse amplitude be merged into this article or section. ...
Categories: Move to Wiktionary  Stub ...
This form of interference can occur whenever a wave can propagate from a source to a destination by two or more paths of different length. Two or more sources can only be used to produce interference when there is a fixed phase relation between them, but in this case the interference generated is the same as with a single source; see Huygens' principle. Huygens principle (named for Dutch physicist Christiaan Huygens) is a method of analysis applied to problems of wave propagation. ...
Experiments Thomas Young's doubleslit experiment showed interference phenomena where two beams of light which are coherent interfere to produce a pattern. Thomas Young, English scientist Thomas Young (June 13, 1773May 10, 1829) was an English polymath, contributing to the scientific understanding of vision, light, solid mechanics, energy, physiology, and Egyptology. ...
Slit experiment redirects here. ...
The beams of light both have the same wavelength range and at the center of the interference pattern. They have the same phases at each wavelength, as they both come from the same source. This article is about a portion of a periodic process. ...
Constructive and destructive interference
Interference pattern produced with a Michelson interferometer. Bright bands are the result of constructive interference while the dark bands are the result of destructive interference. Consider two waves that are in phase,with amplitudes A_{1} and A_{2}. Their troughs and peaks line up and the resultant wave will have amplitude A = A_{1} + A_{2}. This is known as constructive interference. Image File history File linksMetadata Michelson_Interferometer_Green_Laser_Interference. ...
Image File history File linksMetadata Michelson_Interferometer_Green_Laser_Interference. ...
A Michelson interferometer for use on an optical table. ...
If the two waves are π radians, or 180°, out of phase, then one wave's crests will coincide with another wave's troughs and so will tend to cancel out. The resultant amplitude is A =  A_{1} − A_{2}  . If A_{1} = A_{2}, the resultant amplitude will be zero. This is known as destructive interference. For the musical group, see Radian (band). ...
When two sinusoidal waves superimpose, the resulting waveform depends on the frequency (or wavelength) amplitude and relative phase of the two waves. If the two waves have the same amplitude A and wavelength the resultant waveform will have an amplitude between 0 and 2A depending on whether the two waves are in phase or out of phase. combined waveform 
 wave 1  wave 2 
 Two waves in phase  Two waves 180° out of phase  diagram drawn by Theresa Knott File links The following pages link to this file: Interference Categories: GFDL images ...
General quantum interference Quantum mechanics   Uncertainty principle
 Introduction to... Mathematical formulation of... Image File history File linksMetadata Size of this preview: 397 Ã— 599 pixelsFull resolution (1024 Ã— 1544 pixel, file size: 175 KB, MIME type: image/jpeg)Photographer: Armedblowfish License: BSD Date taken: 2006, sometime during or around May Camera: Film, Nikon N65 Lens: Nikon 2880 mm f/3. ...
Image File history File linksMetadata Size of this preview: 397 Ã— 599 pixelsFull resolution (1024 Ã— 1544 pixel, file size: 175 KB, MIME type: image/jpeg)Photographer: Armedblowfish License: BSD Date taken: 2006, sometime during or around May Camera: Film, Nikon N65 Lens: Nikon 2880 mm f/3. ...
Wikibooks has more about this subject: School science howto In physics and engineering, a ripple tank is a shallow glass tank of water used in schools and colleges to demonstrate the basic properties of waves. ...
For a generally accessible and less technical introduction to the topic, see Introduction to quantum mechanics. ...
In quantum physics, the outcome of even an ideal measurement of a system is not deterministic, but instead is characterized by a probability distribution, and the larger the associated standard deviation is, the more uncertain we might say that that characteristic is for the system. ...
This box: Werner Heisenberg and Erwin SchrÃ¶dinger, founders of Quantum Mechanics. ...
The mathematical formulation of quantum mechanics is the body of mathematical formalisms which permits a rigorous description of quantum mechanics. ...
Fundamental concepts  Quantum state · Wave function Superposition · Entanglement Measurement · Uncertainty Exclusion · Duality Decoherence · Ehrenfest theorem · Tunneling Classical mechanics (commonly confused with Newtonian mechanics, which is a subfield thereof) is used for describing the motion of macroscopic objects, from projectiles to parts of machinery, as well as astronomical objects, such as spacecraft, planets, stars, and galaxies. ...
Braket notation is the standard notation for describing quantum states in the theory of quantum mechanics. ...
The quantum Hamiltonian is the physical state of a system, which may be characterized as a ray in an abstract Hilbert space (or, in the case of ensembles, as a trace class operator with trace 1). ...
Probability densities for the electron at different quantum numbers (l) In quantum mechanics, the quantum state of a system is a set of numbers that fully describe a quantum system. ...
A wave function is a mathematical tool that quantum mechanics uses to describe any physical system. ...
Quantum superposition is the application of the superposition principle to quantum mechanics. ...
It has been suggested that Quantum coherence be merged into this article or section. ...
The framework of quantum mechanics requires a careful definition of measurement, and a thorough discussion of its practical and philosophical implications. ...
In quantum physics, the outcome of even an ideal measurement of a system is not deterministic, but instead is characterized by a probability distribution, and the larger the associated standard deviation is, the more uncertain we might say that that characteristic is for the system. ...
The Pauli exclusion principle is a quantum mechanical principle formulated by Wolfgang Pauli in 1925. ...
This box: In physics and chemistry, waveâ€“particle duality is the concept that all matter exhibits both wavelike and particlelike properties. ...
In quantum mechanics, quantum decoherence is the mechanism by which quantum systems interact with their environments to exhibit probabilistically additive behavior  a feature of classical physics  and give the appearance of wavefunction collapse. ...
The Ehrenfest theorem, named after Paul Ehrenfest, relates the time derivative of the expectation value for a quantum mechanical operator to the commutator of that operator with the Hamiltonian of the system. ...
In quantum mechanics, quantum tunnelling is a micro and nanoscopic phenomenon in which a particle violates principles of classical mechanics by penetrating or passing through a potential barrier or impedance higher than the kinetic energy of the particle. ...
  This box: view • talk • edit  If a system is in state ψ its wavefunction is described in Dirac or braket notation as: Slit experiment redirects here. ...
In quantum mechanics, the Sternâ€“Gerlach experiment, named after Otto Stern and Walther Gerlach, is a celebrated experiment in 1920 on deflection of particles, often used to illustrate basic principles of quantum mechanics. ...
In quantum mechanics, Bells Theorem states that a Bell inequality must be obeyed under any local hidden variable theory but can in certain circumstances be violated under quantum mechanics (QM). ...
Poppers experiment is an experiment proposed by the 20th century philosopher of science Karl Popper, to test the standard interpretation (the Copenhagen interpretation) of Quantum mechanics. ...
SchrÃ¶dingers Cat: When the nucleus (bottom left) decays, the Geiger counter (bottom centre) may sense it and trigger the release of the gas. ...
Heisenbergs form for the equations of motion We have seen that in SchrÃ¶dingers scheme the dynamical variables of the system remain fixed during a period of undisturbed motion. ...
The Heisenberg Picture of quantum mechanics is also known as Matrix mechanics. ...
In quantum mechanics, the Interaction picture (or Dirac picture) is an intermediate between the SchrÃ¶dinger picture and the Heisenberg picture. ...
Matrix mechanics is a formulation of quantum mechanics created by Werner Heisenberg, Max Born, and Pascual Jordan in 1925. ...
This article or section is in need of attention from an expert on the subject. ...
This box: For a nontechnical introduction to the topic, please see Introduction to quantum mechanics. ...
The Pauli equation is a SchrÃ¶dinger equation which handles spin. ...
The KleinGordon equation (KleinFockGordon equation or sometimes KleinGordonFock equation) is the relativistic version of the SchrÃ¶dinger equation. ...
In physics, the Dirac equation is a relativistic quantum mechanical wave equation formulated by British physicist Paul Dirac in 1928 and provides a description of elementary spinÂ½ particles, such as electrons, consistent with both the principles of quantum mechanics and the theory of special relativity. ...
It has been suggested that Quantum mechanics, philosophy and controversy be merged into this article or section. ...
Early twentieth century studies of the physics of very smallscale phenomena led to the Copenhagen interpretation. ...
The Ensemble Interpretation, or Statistical Interpretation of Quantum Mechanics, is an interpretation that can be viewed as a minimalist interpretation. ...
In physics, the hidden variable theory is espoused by a minority of physicists who argue that the statistical nature of quantum mechanics indicates that QM is incomplete. ...
The transactional interpretation of quantum mechanics (TIQM) by Professor John Cramer is an unusual interpretation of quantum mechanics that describes quantum interactions in terms of a standing wave formed by retarded (forward in time) and advanced (backward in time) waves. ...
The manyworlds interpretation or MWI (also known as relative state formulation, theory of the universal wavefunction, manyuniverses interpretation, Oxford interpretation or many worlds), is an interpretation of quantum mechanics that claims to resolve all the paradoxes of quantum theory by allowing every possible outcome to every event to...
In quantum mechanics, the consistent histories approach is intended to give a modern interpretation of quantum mechanics, generalising the conventional Copenhagen interpretation and providing a natural interpretation of quantum cosmology. ...
In mathematical physics and quantum mechanics, quantum logic can be regarded as a kind of propositional logic suitable for understanding the apparent anomalies regarding quantum measurement, most notably those concerning composition of measurement operations of complementary variables. ...
Quantum field theory (QFT) is the quantum theory of fields. ...
Quantum gravity is the field of theoretical physics attempting to unify quantum mechanics, which describes three of the fundamental forces of nature, with general relativity, the theory of the fourth fundamental force: gravity. ...
This page discusses Theories of Everything in physics. ...
Planck redirects here. ...
â€œEinsteinâ€ redirects here. ...
SchrÃ¶dinger in 1933, when he was awarded the Nobel Prize in Physics Bust of SchrÃ¶dinger, in the courtyard arcade of the main building, University of Vienna, Austria. ...
Werner Karl Heisenberg (December 5, 1901 â€“ February 1, 1976) was a celebrated German physicist and Nobel laureate, one of the founders of quantum mechanics and acknowledged to be one of the most important physicists of the twentieth century. ...
Niels Henrik David Bohr (October 7, 1885 â€“ November 18, 1962) was a Danish physicist who made fundamental contributions to understanding atomic structure and quantum mechanics, for which he received the Nobel Prize in Physics in 1922. ...
This article is about the AustrianSwiss physicist. ...
Paul Adrien Maurice Dirac, OM, FRS (IPA: [dÉªrÃ¦k]) (August 8, 1902 â€“ October 20, 1984) was a British theoretical physicist and a founder of the field of quantum physics. ...
Max Born (December 11, 1882 â€“ January 5, 1970) was a German physicist and mathematician. ...
LouisVictorPierreRaymond, 7th duc de Broglie, generally known as Louis de Broglie (August 15, 1892â€“March 19, 1987), was a French physicist and Nobel Prize laureate. ...
For other persons named John Neumann, see John Neumann (disambiguation). ...
This article is about the physicist. ...
David Bohm. ...
Hugh Everett III (November 11, 1930 â€“ July 19, 1982) was an American physicist who first proposed the manyworlds interpretation(MWI) of quantum physics, which he called his relative state formulation. ...
Stephen William Hawking, CH, CBE, FRS, FRSA, (born 8 January 1942) is a British theoretical physicist. ...
This article discusses the concept of a wavefunction as it relates to quantum mechanics. ...
Braket notation is the standard notation for describing quantum states in the theory of quantum mechanics. ...
where the s specify the different quantum "alternatives" available (technically, they form an eigenvector basis) and the ψ_{i} are the probability amplitude coefficients, which are complex numbers. In linear algebra, the eigenvectors (from the German eigen meaning own) of a linear operator are nonzero vectors which, when operated on by the operator, result in a scalar multiple of themselves. ...
In linear algebra, a basis is a set of vectors that, in a linear combination, can represent every vector in a given vector space, and such that no element of the set can be represented as a linear combination of the others. ...
In quantum mechanics, a probability amplitude is a complexvalued function that describes an uncertain or unknown quantity. ...
The complex numbers are an extension of the real numbers, in which all nonconstant polynomials have roots. ...
The probability of observing the system making a transition or quantum leap from state Ψ to a new state Φ is the square of the modulus of the scalar or inner product of the two states: Quantum Leap is a science fiction television series that ran for 97 episodes from March 1989 to May 1993 on NBC. It follows the adventures of Dr. Samuel Beckett (played by Scott Bakula), a brilliant scientist who after researching timetravel, and doing experiments in something he calls The Imaging...
In mathematics, the dot product (also known as the scalar product and the inner product) is a function (·) : V × V → F, where V is a vector space and F its underlying field. ...
In mathematics, an inner product space is a vector space with additional structure, an inner product (also called a scalar product), which allows us to introduce geometrical notions such as angles and lengths of vectors. ...
where (as defined above) and similarly are the coefficients of the final state of the system. * is the complex conjugate so that , etc. In mathematics, the complex conjugate of a complex number is given by changing the sign of the imaginary part. ...
Now let's consider the situation classically and imagine that the system transited from to via an intermediate state . Then we would classically expect the probability of the twostep transition to be the sum of all the possible intermediate steps. So we would have
The classical and quantum derivations for the transition probability differ by the presence, in the quantum case, of the extra terms ; these extra quantum terms represent interference between the different intermediate "alternatives". These are consequently known as the quantum interference terms, or cross terms. This is a purely quantum effect and is a consequence of the nonadditivity of the probabilities of quantum alternatives. The interference terms vanish, via the mechanism of quantum decoherence, if the intermediate state is measured or coupled with the environment^{[1]}^{[2]}. In quantum mechanics, quantum decoherence is the mechanism by which quantum systems interact with their environments to exhibit probabilistically additive behavior  a feature of classical physics  and give the appearance of wavefunction collapse. ...
Examples A conceptually simple case of interference is a small (compared to wavelength) source  say, a small array of regularly spaced small sources (see diffraction grating). To meet Wikipedias quality standards, this article or section may require cleanup. ...
Consider the case of a flat boundary (say, between two media with different or simply a flat mirror), onto which the plane wave is incident at some angle. In this case of continuous distribution of sources, constructive interference will only be in specular direction  the direction at which angle with the normal is exactly the same as the angle of incidence. Thus, this results in the law of reflection which is simply the result of constructive interference of a plane wave on a plane surface. A specular highlight on a rendered sphere. ...
The reflection of sunlight on water Reflection is the abrupt change in direction of a wave front at an interface between two dissimilar media so that the wave front returns into the medium from which it originated. ...
See also In acoustics, a beat is an interference between two sounds of slightly different frequencies, perceived as periodic variations in volume whose rate is the difference between the two frequencies. ...
It has been suggested that Line moirÃ© be merged into this article or section. ...
Interferometry is the applied science of combining two or more input points of a particular data type, such as optical measurements, to form a greater picture based on the combination of the two sources. ...
// Field and linear interferometers FabryPerot Michelson interferometer MachZehnder interferometer Sagnac interferometer Doubleslit interferometer Fouriertransform interferometer Astronomical interferometer / Michelson stellar interferometer Mireau interferometer (also known as a Mireau objective) (microscopy) Multibeam interferometer (microscopy) Watson interferometer (microscopy) Linnik interferometer (microscopy) Diffractiongrating interferometer (white light) GiresTournois...
Coherence is the property of wavelike states that enables them to exhibit interference. ...
In quantum mechanics, quantum decoherence is the mechanism by which quantum systems interact with their environments to exhibit probabilistically additive behavior  a feature of classical physics  and give the appearance of wavefunction collapse. ...
Optical feedback Credit: Profero Graphics Two Screenshots of optical feedback Credit: Profero Graphics Optical feedback is the optical equivalent of acoustic feedback. ...
The intensity pattern formed on a screen by diffraction from a square aperture Diffraction refers to various phenomena associated with wave propagation, such as the bending, spreading and interference of waves passing by an object or aperture that disrupts the wave. ...
There are very few or no other articles that link to this one. ...
Active noise control (ANC) (also known as noise cancellation, active noise reduction (ANR) or antinoise) is a method for reducing unwanted sound. ...
References  ^ Wojciech H. Zurek, Decoherence and the transition from quantum to classical, Physics Today, 44, pp 3644 (1991)
 ^ Wojciech H. Zurek, Decoherence, einselection, and the quantum origins of the classical, Reviews of Modern Physics 2003, 75, 715 or [1]
Wojciech Hubert Zurek is a wellknown physicist, as a Laboratory Fellow at Los Alamos National Laboratory. ...
Wojciech Hubert Zurek is a wellknown physicist, as a Laboratory Fellow at Los Alamos National Laboratory. ...
External links Wikimedia Commons has media related to: Interference Look up Interference in Wiktionary, the free dictionary.  Expressions of position and fringe spacing
 Java demonstration of interference
 Java simulation of interference of water waves 1
 Java simulation of interference of water waves 2
 Flash animations demonstrating interference
Wiktionary (a portmanteau of wiki and dictionary) is a multilingual, Webbased project to create a free content dictionary, available in over 151 languages. ...
