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Kochen–Specker Theorem
In quantum mechanics, the Kochen–Specker (KS) theorem, also known as the Bell–Kochen–Specker theorem, is a "no-go" theorem proved by John S. Bell in 1966 and by Simon B. Kochen and Ernst Specker in 1967. It places certain constraints on the permissible types of hidden-variable theories, which try to explain the predictions of quantum mechanics in a context-independent way. The version of the theorem proved by Kochen and Specker also gave an explicit example for this constraint in terms of a finite number of state vectors. The theorem is a complement to Bell's theorem (to be distinguished from the (Bell–)Kochen–Specker theorem of this article). While Bell's theorem established nonlocality to be a feature of any hidden variable theory that recovers the predictions of quantum mechanics, the KS theorem established contextuality to be an inevitable feature of such theories. The theorem proves that there is a contradiction between two basic assumptions of the hidden-vari ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Mechanics
Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistry, quantum field theory, quantum technology, and quantum information science. Classical physics, the collection of theories that existed before the advent of quantum mechanics, describes many aspects of nature at an ordinary (macroscopic) scale, but is not sufficient for describing them at small (atomic and subatomic) scales. Most theories in classical physics can be derived from quantum mechanics as an approximation valid at large (macroscopic) scale. Quantum mechanics differs from classical physics in that energy, momentum, angular momentum, and other quantities of a bound system are restricted to discrete values ( quantization); objects have characteristics of both particles and waves (wave–particle duality); and there are limits to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
David Bohm
David Joseph Bohm (; 20 December 1917 – 27 October 1992) was an American-Brazilian-British scientist who has been described as one of the most significant theoretical physicists of the 20th centuryPeat 1997, pp. 316-317 and who contributed unorthodox ideas to quantum theory, neuropsychology and the philosophy of mind. Among his many contributions to physics is his causal and deterministic interpretation of quantum theory, now known as De Broglie–Bohm theory. Bohm advanced the view that quantum physics meant that the old Cartesian model of reality—that there are two kinds of substance, the mental and the physical, that somehow interact—was too limited. To complement it, he developed a mathematical and physical theory of "implicate" and "explicate" order.David Bohm: ''Wholeness and the Implicate Order'', Routledge, 1980 (). He also believed that the brain, at the cellular level, works according to the mathematics of some quantum effects, and postulated that thought is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Indeterminacy
Quantum indeterminacy is the apparent ''necessary'' incompleteness in the description of a physical system, that has become one of the characteristics of the standard description of quantum physics. Prior to quantum physics, it was thought that :(a) a physical system had a determinate state which uniquely determined all the values of its measurable properties, and :(b) conversely, the values of its measurable properties uniquely determined the state. Quantum indeterminacy can be quantitatively characterized by a probability distribution on the set of outcomes of measurements of an observable. The distribution is uniquely determined by the system state, and moreover quantum mechanics provides a recipe for calculating this probability distribution. Indeterminacy in measurement was not an innovation of quantum mechanics, since it had been established early on by experimentalists that errors in measurement may lead to indeterminate outcomes. By the later half of the 18th century, m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Foundations
Quantum foundations is a discipline of science that seeks to understand the most counter-intuitive aspects of quantum theory, reformulate it and even propose new generalizations thereof. Contrary to other physical theories, such as general relativity, the defining axioms of quantum theory are quite ad hoc, with no obvious physical intuition. While they lead to the right experimental predictions, they do not come with a mental picture of the world where they fit. There exist different approaches to resolve this conceptual gap: * First, one can put quantum physics in contraposition with classical physics: by identifying scenarios, such as Bell experiments, where quantum theory radically deviates from classical predictions, one hopes to gain physical insights on the structure of quantum physics. * Second, one can attempt to find a re-derivation of the quantum formalism in terms of operational axioms. * Third, one can search for a full correspondence between the mathematical elements ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Louis De Broglie
Louis Victor Pierre Raymond, 7th Duc de Broglie (, also , or ; 15 August 1892 – 19 March 1987) was a French physicist and aristocrat who made groundbreaking contributions to quantum theory. In his 1924 PhD thesis, he postulated the wave nature of electrons and suggested that all matter has wave properties. This concept is known as the de Broglie hypothesis, an example of wave–particle duality, and forms a central part of the theory of quantum mechanics. De Broglie won the Nobel Prize for Physics in 1929, after the wave-like behaviour of matter was first experimentally demonstrated in 1927. The 1925 pilot-wave model, and the wave-like behaviour of particles discovered by de Broglie was used by Erwin Schrödinger in his formulation of wave mechanics.Antony Valentini: ''On the Pilot-Wave Theory of Classical, Quantum and Subquantum Physics'', Ph.D. Thesis, ISAS, Trieste 1992 The pilot-wave model and interpretation was then abandoned, in favor of the quantum formalism, unt ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Interpretation Of Quantum Mechanics
An interpretation of quantum mechanics is an attempt to explain how the mathematical theory of quantum mechanics might correspond to experienced reality. Although quantum mechanics has held up to rigorous and extremely precise tests in an extraordinarily broad range of experiments, there exist a number of contending schools of thought over their interpretation. These views on interpretation differ on such fundamental questions as whether quantum mechanics is deterministic or stochastic, which elements of quantum mechanics can be considered real, and what the nature of measurement is, among other matters. Despite nearly a century of debate and experiment, no consensus has been reached among physicists and philosophers of physics concerning which interpretation best "represents" reality. History The definition of quantum theorists' terms, such as ''wave function'' and ''matrix mechanics'', progressed through many stages. For instance, Erwin Schrödinger originally viewed the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Homomorphism
In algebra, a homomorphism is a structure-preserving map between two algebraic structures of the same type (such as two groups, two rings, or two vector spaces). The word ''homomorphism'' comes from the Ancient Greek language: () meaning "same" and () meaning "form" or "shape". However, the word was apparently introduced to mathematics due to a (mis)translation of German meaning "similar" to meaning "same". The term "homomorphism" appeared as early as 1892, when it was attributed to the German mathematician Felix Klein (1849–1925). Homomorphisms of vector spaces are also called linear maps, and their study is the subject of linear algebra. The concept of homomorphism has been generalized, under the name of morphism, to many other structures that either do not have an underlying set, or are not algebraic. This generalization is the starting point of category theory. A homomorphism may also be an isomorphism, an endomorphism, an automorphism, etc. (see below). Each of th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
CHSH Inequality
In physics, the CHSH inequality can be used in the proof of Bell's theorem, which states that certain consequences of entanglement in quantum mechanics can not be reproduced by local hidden-variable theories. Experimental verification of the inequality being violated is seen as confirmation that nature cannot be described by such theories. CHSH stands for John Clauser, Michael Horne, Abner Shimony, and Richard Holt, who described it in a much-cited paper published in 1969. They derived the CHSH inequality, which, as with John Stewart Bell's original inequality, is a constraint on the statistical occurrence of "coincidences" in a Bell test which is necessarily true if there exist underlying local hidden variables, an assumption that is sometimes termed local realism. It is in fact the case that the inequality is routinely violated by modern experiments in quantum mechanics. Statement The usual form of the CHSH inequality is where ''a'' and ''a''′ are detector setti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Conditional Probability
In probability theory, conditional probability is a measure of the probability of an event occurring, given that another event (by assumption, presumption, assertion or evidence) has already occurred. This particular method relies on event B occurring with some sort of relationship with another event A. In this event, the event B can be analyzed by a conditional probability with respect to A. If the event of interest is and the event is known or assumed to have occurred, "the conditional probability of given ", or "the probability of under the condition ", is usually written as or occasionally . This can also be understood as the fraction of probability B that intersects with A: P(A \mid B) = \frac. For example, the probability that any given person has a cough on any given day may be only 5%. But if we know or assume that the person is sick, then they are much more likely to be coughing. For example, the conditional probability that someone unwell (sick) is coughing might be ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Joint Probability Distribution
Given two random variables that are defined on the same probability space, the joint probability distribution is the corresponding probability distribution on all possible pairs of outputs. The joint distribution can just as well be considered for any given number of random variables. The joint distribution encodes the marginal distributions, i.e. the distributions of each of the individual random variables. It also encodes the conditional probability distributions, which deal with how the outputs of one random variable are distributed when given information on the outputs of the other random variable(s). In the formal mathematical setup of measure theory, the joint distribution is given by the pushforward measure, by the map obtained by pairing together the given random variables, of the sample space's probability measure. In the case of real-valued random variables, the joint distribution, as a particular multivariate distribution, may be expressed by a multivariate cumulativ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Asher Peres
Asher Peres ( he, אשר פרס; January 30, 1934 – January 1, 2005) was an Israeli physicist. He is well known for his work relating quantum mechanics and information theory. He helped to develop the Peres–Horodecki criterion for quantum entanglement, as well as the concept of quantum teleportation, and collaborated with others on quantum information and special relativity. He also introduced the Peres metric and researched the Hamilton–Jacobi–Einstein equation in general relativity. With Mario Feingold, he published work in quantum chaos that is known to mathematicians as the Feingold–Peres conjecture and to physicists as the Feingold–Peres theory. Life According to his autobiography, he was born ''Aristide Pressman'' in Beaulieu-sur-Dordogne in France, where his father, a Polish electrical engineer, had found work laying down power lines. He was given the name ''Aristide'' at birth, because the name his parents wanted, ''Asher'', the name of his maternal ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
David Mermin
Nathaniel David Mermin (; born 30 March 1935) is a solid-state physicist at Cornell University best known for the eponymous Mermin–Wagner theorem, his application of the term " boojum" to superfluidity, his textbook with Neil Ashcroft on solid-state physics, and for contributions to the foundations of quantum mechanics and quantum information science. Education and career Mermin was born in 1935 in New Haven, Connecticut. He obtained a bachelor's degree in mathematics from Harvard University in 1956, graduating ''summa cum laude.'' He remained at Harvard for his graduate studies, earning a PhD in physics in 1961. After holding postdoctoral positions at the University of Birmingham and the University of California, San Diego, he joined the Cornell University faculty in 1964. He became a Cornell professor emeritus in 2006. Early in his career, Mermin worked in statistical physics and condensed-matter physics, including the study of matter at low temperatures, the behavior of e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
