|
Ensemble Interpretation
The ensemble interpretation of quantum mechanics considers the quantum state description to apply only to an ensemble of similarly prepared systems, rather than supposing that it exhaustively represents an individual physical system. The advocates of the ensemble interpretation of quantum mechanics claim that it is minimalist, making the fewest physical assumptions about the meaning of the standard mathematical formalism. It proposes to take to the fullest extent the statistical interpretation of Max Born, for which he won the Nobel Prize in Physics in 1954. On the face of it, the ensemble interpretation might appear to contradict the doctrine proposed by Niels Bohr, that the wave function describes an individual system or particle, not an ensemble, though he accepted Born's statistical interpretation of quantum mechanics. It is not quite clear exactly what kind of ensemble Bohr intended to exclude, since he did not describe probability in terms of ensembles. The ensemble interpret ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Mechanics
Quantum mechanics is the fundamental physical Scientific theory, theory that describes the behavior of matter and of light; its unusual characteristics typically occur at and below the scale of atoms. Reprinted, Addison-Wesley, 1989, It is the foundation of all quantum physics, which includes quantum chemistry, quantum field theory, quantum technology, and quantum information science. Quantum mechanics can describe many systems that classical physics cannot. Classical physics can describe many aspects of nature at an ordinary (macroscopic and Microscopic scale, (optical) microscopic) scale, but is not sufficient for describing them at very small submicroscopic (atomic and subatomic) scales. Classical mechanics can be derived from quantum mechanics as an approximation that is valid at ordinary scales. Quantum systems have Bound state, bound states that are Quantization (physics), quantized to Discrete mathematics, discrete values of energy, momentum, angular momentum, and ot ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bayes' Theorem
Bayes' theorem (alternatively Bayes' law or Bayes' rule, after Thomas Bayes) gives a mathematical rule for inverting Conditional probability, conditional probabilities, allowing one to find the probability of a cause given its effect. For example, if the risk of developing health problems is known to increase with age, Bayes' theorem allows the risk to someone of a known age to be assessed more accurately by conditioning it relative to their age, rather than assuming that the person is typical of the population as a whole. Based on Bayes' law, both the prevalence of a disease in a given population and the error rate of an infectious disease test must be taken into account to evaluate the meaning of a positive test result and avoid the ''base-rate fallacy''. One of Bayes' theorem's many applications is Bayesian inference, an approach to statistical inference, where it is used to invert the probability of Realization (probability), observations given a model configuration (i.e., th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Aristotle
Aristotle (; 384–322 BC) was an Ancient Greek philosophy, Ancient Greek philosopher and polymath. His writings cover a broad range of subjects spanning the natural sciences, philosophy, linguistics, economics, politics, psychology, and the arts. As the founder of the Peripatetic school of philosophy in the Lyceum (classical), Lyceum in Athens, he began the wider Aristotelianism, Aristotelian tradition that followed, which set the groundwork for the development of modern science. Little is known about Aristotle's life. He was born in the city of Stagira (ancient city), Stagira in northern Greece during the Classical Greece, Classical period. His father, Nicomachus (father of Aristotle), Nicomachus, died when Aristotle was a child, and he was brought up by a guardian. At around eighteen years old, he joined Plato's Platonic Academy, Academy in Athens and remained there until the age of thirty seven (). Shortly after Plato died, Aristotle left Athens and, at the request ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Born Rule
The Born rule is a postulate of quantum mechanics that gives the probability that a measurement of a quantum system will yield a given result. In one commonly used application, it states that the probability density for finding a particle at a given position is proportional to the square of the amplitude of the system's wavefunction at that position. It was formulated and published by German physicist Max Born in July 1926. Details The Born rule states that an observable, measured in a system with normalized wave function , \psi\rang (see Bra–ket notation), corresponds to a self-adjoint operator A whose spectrum is discrete if: * the measured result will be one of the eigenvalues \lambda of A, and * the probability of measuring a given eigenvalue \lambda_i will equal \lang\psi, P_i, \psi\rang, where P_i is the projection onto the eigenspace of A corresponding to \lambda_i. : (In the case where the eigenspace of A corresponding to \lambda_i is one-dimensional and spanned by ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Complex Number
In mathematics, a complex number is an element of a number system that extends the real numbers with a specific element denoted , called the imaginary unit and satisfying the equation i^= -1; every complex number can be expressed in the form a + bi, where and are real numbers. Because no real number satisfies the above equation, was called an imaginary number by René Descartes. For the complex number is called the , and is called the . The set of complex numbers is denoted by either of the symbols \mathbb C or . Despite the historical nomenclature, "imaginary" complex numbers have a mathematical existence as firm as that of the real numbers, and they are fundamental tools in the scientific description of the natural world. Complex numbers allow solutions to all polynomial equations, even those that have no solutions in real numbers. More precisely, the fundamental theorem of algebra asserts that every non-constant polynomial equation with real or complex coefficie ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Paul Adrien Maurice Dirac
Paul Adrien Maurice Dirac ( ; 8 August 1902 – 20 October 1984) was an English mathematician and theoretical physicist who is considered to be one of the founders of quantum mechanics. Dirac laid the foundations for both quantum electrodynamics and quantum field theory. He was the Lucasian Professor of Mathematics at the University of Cambridge and a professor of physics at Florida State University. Dirac shared the 1933 Nobel Prize in Physics with Erwin Schrödinger for "the discovery of new productive forms of atomic theory". Dirac graduated from the University of Bristol with a first class honours Bachelor of Science degree in electrical engineering in 1921, and a first class honours Bachelor of Arts degree in mathematics in 1923. Dirac then graduated from the University of Cambridge with a PhD in physics in 1926, writing the first ever thesis on quantum mechanics. Dirac made fundamental contributions to the early development of both quantum mechanics and quantum electro ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Albert Hibbs
Albert Roach Hibbs (October 19, 1924 – February 24, 2003) was an American mathematician and physicist affiliated with the Jet Propulsion Laboratory (JPL). He was known as "The Voice of JPL" due to his gift for explaining advanced science in simple terms. He helped establish JPL's Space Science Division in 1960 and later served as its first chief. He was the systems designer for Explorer 1, the USA's first satellite, and helped establish the framework for exploration of the Solar System through the 1960s. Hibbs qualified as an astronaut in 1967 and was slated to be a crew member of Apollo 25, but he ultimately did not go to the Moon due to the Apollo program ending after the Apollo 17 mission in 1972. Education Hibbs earned bachelor's degree in physics from the California Institute of Technology (Caltech) in 1945, having attended Caltech under the sponsorship of the US Navy's V-12 program. He then obtained a master's degree in mathematics from the University of Chicago ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Richard Feynman
Richard Phillips Feynman (; May 11, 1918 – February 15, 1988) was an American theoretical physicist. He is best known for his work in the path integral formulation of quantum mechanics, the theory of quantum electrodynamics, the physics of the superfluidity of supercooled liquid helium, and in particle physics, for which he proposed the parton model. For his contributions to the development of quantum electrodynamics, Feynman received the Nobel Prize in Physics in 1965 jointly with Julian Schwinger and Shin'ichirō Tomonaga. Feynman developed a pictorial representation scheme for the mathematical expressions describing the behavior of subatomic particles, which later became known as Feynman diagrams and is widely used. During his lifetime, Feynman became one of the best-known scientists in the world. In a 1999 poll of 130 leading physicists worldwide by the British journal ''Physics World'', he was ranked the seventh-greatest physicist of all time. He assisted in the Manhatt ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Albert Messiah
Albert Messiah (23 September 1921, Nice – 17 April 2013, Paris) was a French physicist. He studied at the Ecole Polytechnique. He spent the Second World War in the Free France forces: he embarked on 22 June 1940 at Saint-Jean-de-Luz for England and participated in the Battle of Dakar with Charles de Gaulle in September 1940. He joined the Free French Forces in Chad, and the 2nd Armored Division in September 1944, and participated in the assault of Hitler's Eagle's nest at Berchtesgaden in 1945. As a French Jew who escaped France to fight in the Free French Army of de Gaulle, he was awarded a grant to study and work at the Institute for Advanced Study in Princeton, New Jersey in the US. The seminars at the Institute were incomprehensible to Messiah who had only a high-school education in physics, and he became depressed to the extent that he considered abandoning his plans to become a physicist. He met Robert Marshak at a meeting of the American Physical Society in Washingt ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wojciech H
Wojciech () is a Polish name, equivalent to Czech Vojtěch , Slovak Vojtech, and German Woitke. The name is formed from two Slavic roots: * ''wój'' (Slavic: ''voj''), a root pertaining to war. It also forms words like ''wojownik'' ("warrior") and ''wojna'' ("war"). * ''ciech'' (from an earlier form, ''tech''), meaning "joy". The resulting combination means "he who enjoys war" or "joyous warrior". Its Polish diminutive forms include ''Wojtek'' , ''Wojtuś'' , ''Wojtas'', ''Wojcio'', ''Wojteczek'', ''Wojcieszek'', ''Wojtaszka'', ''Wojtaszek'', ''Wojan'' (noted already in 1136), ''Wojko'', and variants noted as early as 1400, including ''Woytko'', ''Woythko'', and ''Voytko''. The feminine form is Wojciecha (). Related names in South Slavic languages include ''Vojko'', ''Vojislav'', and ''Vojteh''. The name has been rendered into German in several different variations, including: ''Woitke'', ''Witke'', ''Voitke'', ''Voytke'', ''Woytke'', ''Vogtke'', ''Woytegk'', ''Woytek'', ''Wogtk ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John Archibald Wheeler
John Archibald Wheeler (July 9, 1911April 13, 2008) was an American theoretical physicist. He was largely responsible for reviving interest in general relativity in the United States after World War II. Wheeler also worked with Niels Bohr to explain the basic principles of nuclear fission. Together with Gregory Breit, Wheeler developed the concept of the Breit–Wheeler process. He is best known for popularizing the term "black hole" for objects with gravitational collapse already predicted during the early 20th century, for inventing the terms "quantum foam", "neutron moderator", "wormhole" and "it from bit", and for hypothesizing the "one-electron universe". Stephen Hawking called Wheeler the "hero of the black hole story". At 21, Wheeler earned his doctorate at Johns Hopkins University under the supervision of Karl Herzfeld. He studied under Breit and Bohr on a National Research Council (United States), National Research Council fellowship. In 1939 he collaborated with Bohr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Abner Shimony
Abner Eliezer Shimony (; March 10, 1928 – August 8, 2015) was an American physicist and philosopher. He specialized in quantum theory and philosophy of science. As a physicist, he concentrated on the interaction between relativity theory and quantum mechanics. He authored many works and research on complementarity in quantum entanglement as well as multiparticle quantum interferometry, both relating to quantum coherence. He authored research articles and books on the foundations of quantum mechanics. He received the 1996 Lakatos Prize for his work in philosophy of science. Shimony is also the author of ''Tibaldo and the Hole in the Calendar,'' a 1998 children's book about the calendar reform that has been translated into many languages. Education Shimony was born in Columbus, Ohio. He obtained his BA in Mathematics and Philosophy from Yale University in 1948, and an MA in Philosophy from the University of Chicago in 1950. He obtained his Ph.D. in philosophy from Yale Univers ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
