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Free Will Theorem
The free will theorem of John H. Conway and Simon B. Kochen states that if we have a free will in the sense that our choices are not a function of the past, then, under specific assumptions drawn from quantum mechanics and relativity, so must some elementary particles. That is, if human experimenters possess a form of free will—defined as the ability to make choices not entirely determined by prior events—then certain elementary particles must also exhibit a corresponding form of indeterminacy. The theorem argues that stochastic processes do not satisfy this definition of "freedom," because random values can, in principle, be pre-determined or embedded in the past (for example, sampled from a pre-existing table). Consequently, the theorem implies that no physical theory relying solely on a combination of deterministic laws and pre-existing randomness can fully account for the observed outcomes of quantum measurements. Conway and Kochen's paper was published in ''Foundations o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John Horton Conway
John Horton Conway (26 December 1937 – 11 April 2020) was an English mathematician. He was active in the theory of finite groups, knot theory, number theory, combinatorial game theory and coding theory. He also made contributions to many branches of recreational mathematics, most notably the invention of the cellular automaton called the Game of Life. Born and raised in Liverpool, Conway spent the first half of his career at the University of Cambridge before moving to the United States, where he held the John von Neumann Professorship at Princeton University for the rest of his career. On 11 April 2020, at age 82, he died of complications from COVID-19. Early life and education Conway was born on 26 December 1937 in Liverpool, the son of Cyril Horton Conway and Agnes Boyce. He became interested in mathematics at a very early age. By the time he was 11, his ambition was to become a mathematician. After leaving sixth form, he studied mathematics at Gonville and Caius Coll ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Causality
Causality is an influence by which one Event (philosophy), event, process, state, or Object (philosophy), object (''a'' ''cause'') contributes to the production of another event, process, state, or object (an ''effect'') where the cause is at least partly responsible for the effect, and the effect is at least partly dependent on the cause. The cause of something may also be described as the reason for the event or process. In general, a process can have multiple causes,Compare: which are also said to be ''causal factors'' for it, and all lie in its past. An effect can in turn be a cause of, or causal factor for, many other effects, which all lie in its future. Some writers have held that causality is metaphysics , metaphysically prior to notions of time and space. Causality is an abstraction that indicates how the world progresses. As such it is a basic concept; it is more apt to be an explanation of other concepts of progression than something to be explained by other more fun ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Counterfactual Definiteness
In quantum mechanics, counterfactual definiteness (CFD) is the ability to speak "meaningfully" of the definiteness of the results of measurements that have not been performed (i.e., the ability to assume the existence of objects, and properties of objects, even when they have not been measured). The term " counterfactual definiteness" is used in discussions of physics calculations, especially those related to the phenomenon called quantum entanglement and those related to the Bell inequalities. In such discussions "meaningfully" means the ability to treat these unmeasured results on an equal footing with measured results in statistical calculations. It is this (sometimes assumed but unstated) aspect of counterfactual definiteness that is of direct relevance to physics and mathematical models of physical systems and not philosophical concerns regarding the meaning of unmeasured results. Overview The subject of counterfactual definiteness receives attention in the study of quantum ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Contextualism
Contextualism, also known as epistemic contextualism, is a family of views in philosophy which emphasize the ''context'' in which an action, utterance, or expression occurs. Proponents of contextualism argue that, in some important respect, the action, utterance, or expression can only be understood relative to that context.Price (2008). Contextualist views hold that philosophically controversial concepts, such as "meaning P", "knowing that P", "having a reason to A", and possibly even "being true" or "being right" only have meaning relative to a specified context. Other philosophers contend that context-dependence leads to complete relativism. In ethics, "contextualist" views are often closely associated with situational ethics, or with moral relativism. Contextualism in architecture is a theory of design where modern building types are harmonized with urban forms usual to a traditional city. In epistemology, contextualism is the treatment of the word 'knows' as context-sens ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Compatibilism
Compatibilism is the belief that free will and determinism are mutually compatible and that it is possible to believe in both without being logically inconsistent. As Steven Weinberg puts it: "I would say that free will is nothing but our conscious experience of deciding what to do, which I know I am experiencing as I write this review, and this experience is not invalidated by the reflection that physical laws made it inevitable that I would want to make these decisions." The opposing belief, that the thesis of determinism is logically incompatible with the classical thesis of free will, is known as "incompatibilism". Compatibilists believe that freedom can be present or absent in situations for reasons that have nothing to do with metaphysics. In other words, that causal determinism does not exclude the truth of possible future outcomes. Because free will is often seen as a necessary prerequisite for moral responsibility, compatibilism is commonly used to support compatibility ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bell's Inequalities
Bell's theorem is a term encompassing a number of closely related results in physics, all of which determine that quantum mechanics is incompatible with local hidden-variable theories, given some basic assumptions about the nature of measurement. The first such result was introduced by John Stewart Bell in 1964, building upon the Einstein–Podolsky–Rosen paradox, which had called attention to the phenomenon of quantum entanglement. In the context of Bell's theorem, "local" refers to the principle of locality, the idea that a particle can only be influenced by its immediate surroundings, and that interactions mediated by physical fields cannot propagate faster than the speed of light. " Hidden variables" are supposed properties of quantum particles that are not included in quantum theory but nevertheless affect the outcome of experiments. In the words of Bell, "If hidden-variable theoryis local it will not agree with quantum mechanics, and if it agrees with quantum mechani ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sheldon Goldstein
Sheldon Goldstein (born October 24, 1947, in Augusta, Georgia) is an American theoretical physicist. He introduced the term " Bohmian mechanics". Biography Goldstein graduated from Yeshiva University with a B.A. in 1969, a B.S. in 1971, and a Ph.D. in physics in 1973. His Ph.D. thesis, supervised by Joel Lebowitz, is entitled ''Ergodic Theory and Infinite Systems'' Since 1977 Goldstein has been a professor at Rutgers University. His research deals with the foundations of quantum mechanics and, especially, theoretical developments of De Broglie–Bohm theory. His collaborators include Joel Lebowitz and Detlef Dürr. In a 1981 paper, Goldstein and Oliver Penrose described a new method of defining nonequilibrium entropy in statistical mechanics. Goldstein contributed the article ''Bohmian Mechanics'' to the ''Stanford Encyclopedia of Philosophy''. For two academic years from 1973 to 1975, Goldstein was at the Institute for Advanced Study. He is a Fellow of the American Association ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bell's Theorem
Bell's theorem is a term encompassing a number of closely related results in physics, all of which determine that quantum mechanics is incompatible with local hidden-variable theories, given some basic assumptions about the nature of measurement. The first such result was introduced by John Stewart Bell in 1964, building upon the Einstein–Podolsky–Rosen paradox, which had called attention to the phenomenon of quantum entanglement. In the context of Bell's theorem, "local" refers to the principle of locality, the idea that a particle can only be influenced by its immediate surroundings, and that interactions mediated by physical fields cannot propagate faster than the speed of light. " Hidden variables" are supposed properties of quantum particles that are not included in quantum theory but nevertheless affect the outcome of experiments. In the words of Bell, "If hidden-variable theoryis local it will not agree with quantum mechanics, and if it agrees with quantum mec ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hidden-variable Theory
In physics, a hidden-variable theory is a Determinism, deterministic model which seeks to explain the probabilistic nature of quantum mechanics by introducing additional, possibly inaccessible, variables. The mathematical formulation of quantum mechanics assumes that the state of a system prior to measurement is quantum indeterminacy, indeterminate; quantitative bounds on this indeterminacy are expressed by the Heisenberg uncertainty principle. Most hidden-variable theories are attempts to avoid this indeterminacy, but possibly at the expense of requiring that Quantum nonlocality, nonlocal interactions be allowed. One notable hidden-variable theory is the de Broglie–Bohm theory. In their 1935 Einstein–Podolsky–Rosen paradox, EPR paper, Albert Einstein, Boris Podolsky, and Nathan Rosen argued that quantum entanglement might imply that quantum mechanics is an incomplete description of reality. John Stewart Bell in 1964, in his Bell's theorem, eponymous theorem proved that co ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kochen–Specker Theorem
In quantum mechanics, the Kochen–Specker (KS) theorem, also known as the Bell–KS 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 Kochen–Specker theorem is a complement to Bell's theorem. While Bell's theorem established nonlocality to be a feature of any hidden-variable theory that recovers the predictions of quantum mechanics, the Kochen–Specker 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-variable theories intended to reproduce the results of quan ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lorentz Covariance
In relativistic physics, Lorentz symmetry or Lorentz invariance, named after the Dutch physicist Hendrik Lorentz, is an equivalence of observation or observational symmetry due to special relativity implying that the laws of physics stay the same for all observers that are moving with respect to one another within an inertial frame. It has also been described as "the feature of nature that says experimental results are independent of the orientation or the boost velocity of the laboratory through space". Lorentz covariance, a related concept, is a property of the underlying spacetime manifold. Lorentz covariance has two distinct, but closely related meanings: # A physical quantity is said to be Lorentz covariant if it transforms under a given representation of the Lorentz group. According to the representation theory of the Lorentz group, these quantities are built out of scalars, four-vectors, four-tensors, and spinors. In particular, a Lorentz covariant scalar (e.g., the s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spacetime
In physics, spacetime, also called the space-time continuum, is a mathematical model that fuses the three dimensions of space and the one dimension of time into a single four-dimensional continuum. Spacetime diagrams are useful in visualizing and understanding relativistic effects, such as how different observers perceive ''where'' and ''when'' events occur. Until the turn of the 20th century, the assumption had been that the three-dimensional geometry of the universe (its description in terms of locations, shapes, distances, and directions) was distinct from time (the measurement of when events occur within the universe). However, space and time took on new meanings with the Lorentz transformation and special theory of relativity. In 1908, Hermann Minkowski presented a geometric interpretation of special relativity that fused time and the three spatial dimensions into a single four-dimensional continuum now known as Minkowski space. This interpretation proved vital t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
