In modern physics, the double-slit experiment is a demonstration that light and matter can display characteristics of both classically defined waves and particles. This type of experiment was first performed, using light, by Thomas Young in 1801, as a demonstration of the wave behavior of light. At that time it was thought that light consisted of either particles. With the beginning of modern physics, about a hundred years it was realized that light could in fact show behavior characteristic of waves and particles. In 1927, Davisson and Germer demonstrated that electrons show the same behavior, extended to atoms and molecules. Thomas Young's experiment with light was part of classical physics well before quantum mechanics, the concept of wave-particle duality, he believed it demonstrated that the wave theory of light was correct, his experiment is sometimes referred to as Young's experiment or Young's slits. The experiment belongs to a general class of "double path" experiments, in which a wave is split into two separate waves that combine into a single wave.
Changes in the path lengths of both waves result in a phase shift, creating an interference pattern. Another version is the Mach -- Zehnder interferometer. In the basic version of this experiment, a coherent light source, such as a laser beam, illuminates a plate pierced by two parallel slits, the light passing through the slits is observed on a screen behind the plate; the wave nature of light causes the light waves passing through the two slits to interfere, producing bright and dark bands on the screen – a result that would not be expected if light consisted of classical particles. However, the light is always found to be absorbed at the screen at discrete points, as individual particles. Furthermore, versions of the experiment that include detectors at the slits find that each detected photon passes through one slit, not through both slits. However, such experiments demonstrate that particles do not form the interference pattern if one detects which slit they pass through; these results demonstrate the principle of wave–particle duality.
Other atomic-scale entities, such as electrons, are found to exhibit the same behavior when fired towards a double slit. Additionally, the detection of individual discrete impacts is observed to be inherently probabilistic, inexplicable using classical mechanics; the experiment can be done with entities much larger than electrons and photons, although it becomes more difficult as size increases. The largest entities for which the double-slit experiment has been performed were molecules that each comprised 810 atoms; the double-slit experiment has become a classic thought experiment, 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 called it "a phenomenon, impossible to explain in any classical way, which has in it the heart of quantum mechanics. In reality, it contains the only mystery." If light consisted of ordinary or classical particles, these particles were fired in a straight line through a slit and allowed to strike a screen on the other side, we would expect to see a pattern corresponding to the size and shape of the slit.
However, when this "single-slit experiment" is performed, the pattern on the screen is a diffraction pattern in which the light is spread out. The smaller the slit, the greater the angle of spread; the top portion of the image shows the central portion of the pattern formed when a red laser illuminates a slit and, if one looks two faint side bands. More bands can be seen with a more refined apparatus. Diffraction explains the pattern as being the result of the interference of light waves from the slit. If one illuminates two parallel slits, the light from the two slits again interferes. Here the interference is a more pronounced pattern with a series of alternating light and dark bands; the width of the bands is a property of the frequency of the illuminating light. When Thomas Young first demonstrated this phenomenon, it indicated that light consists of waves, as the distribution of brightness can be explained by the alternately additive and subtractive interference of wavefronts. Young's experiment, performed in the early 1800s, played a vital part in the acceptance of the wave theory of light, vanquishing the corpuscular theory of light proposed by Isaac Newton, the accepted model of light propagation in the 17th and 18th centuries.
However, the discovery of the photoelectric effect demonstrated that under different circumstances, light can behave as if it is composed of discrete particles. These contradictory discoveries made it necessary to go beyond classical physics and take the quantum nature of light into account. Feynman was fond of saying that all of quantum mechanics can be gleaned from thinking through the implications of this single experiment, he proposed that if detectors were placed before each slit, the interference pattern would disappear. The Englert–Greenberger duality relation provides a detailed treatment of the mathematics of double-slit interference in the context of quantum mechanics. A low-intensity double-slit experiment was first performed by G. I. Taylor in 1909, by reducing t
Patamanta is a small town in Bolivia. Patamanta is the second largest town in the district Pucarani in the province of Los Andes and is located on the right bank of an inlet to Lake Titicaca; the village is located at an altitude of 3962m on the Bolivian Altiplano, 25 kilometers southeast of Lake Titicaca. Patamanta is the second largest town in the district Pucarani in the province of Los Andes and is located on the right bank of an inlet to Lake Titicaca; the village is located at an altitude of 3962 m on the Bolivian Altiplano, 25 kilometers southeast of Lake Titicaca. Patamanta lies on the Bolivian plateau between the Andean mountain ranges of the Cordillera Occidental in the west and the Cordillera Central in the east; the region has a pronounced daytime climate in which the average temperature fluctuations are more evident during the day than during the course of the year. The annual average temperature of the region is 9 °C, the average monthly values fluctuate only between 6 °C in July and 10 °C in November and December.
The annual precipitation is about 600 mm, the monthly precipitation is between less than 15 mm in the months of June to August and between 100 and 120 mm from December to February. Patamanta is located 37 kilometers northwest of La Paz, the capital of the department of the same name. La Paz leading highway Ruta 2 through El Alto and Villa Vilaque in a northwesterly direction to Patamanta and from there via Batallas and Huarina to Copacabana on Lake Titicaca. Towards the west, a dirt road branches off one kilometer north of Patamanta, which leads to the provincial capital Pucarani, ten kilometers away; the population of the place has increased by a quarter in the past two decades: Due to the historical population development, the region has a high proportion of Aymara population, in the Municipio Pucarani 96.7 percent of the population speak the Aymara language. Reliefkarte der Region La Paz 1:250.000 Municipio Pucarani - Übersichtskarten Nr. 21201 Municipio Pucarani - Detailkarte und Bevölkerungsdaten Departamento La Paz - Sozialdaten der Municipios
The Music Scene is a television series aired by ABC as part of its Fall 1969 lineup, in the Monday, 7:30 to 8:15 timeslot featuring rock and pop music. The show had many hosts, with comedian David Steinberg the most frequently-appearing one. Many huge names of the era, including James Brown, Stills, Nash & Young, Three Dog Night, Tom Jones on the initial program, Janis Joplin, Bobby Sherman, The Miracles, Sly & the Family Stone, Isaac Hayes, Stevie Wonder, Bo Diddley and Mama Cass Elliot, among many others, appearing on subsequent shows. Existing promos used to sell this show to ABC affiliates featured the improvisational group The Committee, which featured actor Howard Hesseman, as well as the Rolling Stones; the promos implied. However, The Committee never appeared on the show, neither did the Rolling Stones. Despite the level of talent presented, this show did not fare well in Nielsen ratings. Advertisers of the era were more interested in shows achieving a mass audience rather than one of younger people who were deemed as having less disposable income than the then-coveted middle aged, middle income viewers that most network programming targeted.
The program was cancelled mid-season. Two DVDs of highlights from the show have been released; this program and the show that followed it, The New People, are rare examples of U. S. network television programming designed to run for 45 minutes. The Music Scene on IMDb The Music Scene at TV.com
Paul Kenneth Peterson was a lawyer, insurance broker and Republican politician who served as mayor of Minneapolis from 1957 to 1961. Peterson was born in Minneapolis, Minnesota in 1915, he attended the University after graduating worked as an insurance salesman. During World War II, he served in Air Combat Intelligence with the United States Navy. After the war, Peterson became involved in politics after working with Governor Luther Youngdahl. Peterson ran for the Minnesota House of Representatives as a Republican and won, serving four terms from January 7, 1947 to January 3, 1955. While serving in the legislature, Peterson earned a law degree from the William Mitchell College of Law. From 1950 to 1953, he chaired the Minnesota Republican Party. After leaving the legislature, Peterson ran for mayor of Minneapolis, he won and served two terms from 1957 to 1961. His mayoralty focused on developing the city's core and demolishing slum neighborhoods such as the Gateway District. In 1960 he unsuccessfully ran for a seat in the United States Senate.
In 1961, Peterson lost his bid for reelection to Democratic challenger Arthur Naftalin. In 1963, he ran for mayor again, again lost to Naftalin. Peterson entered private law practice, but served on a number of city and state boards and commissions, as an administrative law judge for Hennepin County, Minnesota from 1974 to 1985. Peterson was killed in an automobile accident in Minneapolis on December 31, 1990
Wallace Woodworth was a wealthy businessman and rancher in Los Angeles County, California, in the 19th century. He was a member of the governing bodies of both Los Angeles County, he helped organize the city's first gas company. Woodworth was born in Johnstown, Ohio, on July 28, 1832, he came to Los Angeles County in 1853 and lived with his uncle, Isaac Williams, on the Chino Ranch, of which the young man became manager. He grew wealthy in selling cattle. Woodworth married Carrie, a granddaughter of Antonio Maria Lugo, they had six children, including an oldest son named Joseph and a younger one named Wallace J. Daughters were Hazel and Mamie, he died September 13, 1882, in his home on San Pedro Street of what his physicians called an "affection of the heart." Interment was in Los Angeles. Upon moving to Los Angeles in 1858, Woodworth bought the interest of James D. Brady in a furniture business co-owned by William H. Perry. In 1867 the Woodworth and Perry partnership organized a gas company, which brought the first gas lights to the city.
Others in the venture, capitalized with $36,000, were John Goller and George J. Clark. In 1872, S. H. Mott became a partner and the firm disposed of the furniture business and became "one of the largest and wealthiest" lumber yards in Los Angeles. Woodworth, a Democrat, was elected to the Los Angeles Common Council, the governing body of the city, in 1859, 1860 and 1864, to the Los Angeles County Board of Supervisors in 1867, serving until 1871. In late 1860 in his role as Council President, Woodworth served as acting mayor for two weeks as a result of the death of Mayor Henry Mellis. Woodworth is remembered with a large burial vault at Evergreen Cemetery, designed by A. C. Thompson, a leading memorialist of his time. Upon his death, Woodworth left an estate estimated at $350,000 to $450,000, half to his wife and half to their six children. Access to the Los Angeles Times links may require the use of a library card
The Sérsic profile is a mathematical function that describes how the intensity I of a galaxy varies with distance R from its center. It is a generalization of de Vaucouleurs' law. José Luis Sérsic first published his law in 1963; the Sérsic profile has the form ln I = ln I 0 − k R 1 / n, where I 0 is the intensity at R = 0. The parameter n, called the "Sérsic index," controls the degree of curvature of the profile; the smaller the value of n, the less centrally concentrated the profile is and the shallower the logarithmic slope at small radii is: d ln I d ln R = − R 1 / n. Today, it is more common to write this function in terms of the half-light radius, Re, the intensity at that radius, Ie, such that I = I e e x p, where b is 2n-1/3, it can be shown that b n satisfies γ = 1 2 Γ, where Γ and γ are the Gamma function and lower incomplete Gamma function. Many related expressions, in terms of the surface brightness exist. Most galaxies are fit by Sérsic profiles with indices in the range 1/2 < n < 10.
The best-fit value of n correlates with galaxy size and luminosity, such that bigger and brighter galaxies tend to be fit with larger n. Setting n = 4 gives the de Vaucouleurs profile: I ∝ e − b R 1 / 4, a rough approximation of ordinary elliptical galaxies. Setting n = 1 gives the exponential profile: I ∝ e − b R, a good approximation of spiral galaxy disks and a rough approximation of dwarf elliptical galaxies; the correlation of Sérsic index with galaxy morphology is sometimes used in automated schemes to determine the Hubble type of distant galaxies. Sérsic indices have been shown to correlate with the mass of the supermassive black hole at the centers of the galaxies. Sérsic profiles can be used to describe dark matter halos, where the Sérsic index correlates with halo mass; the brightest elliptical galaxies have low-density cores that are not well described by Sérsic's law. The core-Sérsic family of models was introduced to describe such galaxies. Core-Sérsic models have an additional set of parameters.
Dwarf elliptical galaxies and bulges have point-like nuclei that are not well described by Sérsic's law. These galaxies are fit by a Sérsic model with an added central component representing the nucleus; the Einasto profile is mathematically identical to the Sérsic profile, except that I is replaced by ρ, the volume density, R is replaced by r, the internal distance from the center. Elliptical galaxies Bulges Stellar systems following the R exp 1/m luminosity law A comprehensive paper that derives many properties of Sérsic models. A Concise Reference to Sérsic R1/n Quantities, Including Concentration, Profile Slopes, Petrosian Indices, Kron Magnitudes