Hidden Variables and Nonlocality in Quantum Mechanics
... in spite of David Bohm’s successful construction of such a theory and John S. Bell’s strong arguments in favor of the idea. Many are convinced either that it is impossible to interpret quantum theory in this way, or that such an interpretation would actually be irrelevant. There are essentially two ...
... in spite of David Bohm’s successful construction of such a theory and John S. Bell’s strong arguments in favor of the idea. Many are convinced either that it is impossible to interpret quantum theory in this way, or that such an interpretation would actually be irrelevant. There are essentially two ...
Equivariant rigidity of Menger compacta and the Hilbert
... Theorem 1 [Hilbert’s fifth problem] Let G be a topological group which is locally Euclidean. Then G is isomorphic to a Lie group. The above theorem was proved by Gleason [9, Theorem 3.1] and by Montgomery and Zippin [20, Theorem A] in 1952. The theorem and the mathematical tools developed in the cou ...
... Theorem 1 [Hilbert’s fifth problem] Let G be a topological group which is locally Euclidean. Then G is isomorphic to a Lie group. The above theorem was proved by Gleason [9, Theorem 3.1] and by Montgomery and Zippin [20, Theorem A] in 1952. The theorem and the mathematical tools developed in the cou ...
Mathematics via Symmetry - Philsci
... force. None of the partner particles have yet been discovered, but because they are mandated by the symmetries that is what scientists are looking for. Symmetry, as we have described it, is only part of the story. In numerous cases the laws of physics actually violate a symmetry law and break into d ...
... force. None of the partner particles have yet been discovered, but because they are mandated by the symmetries that is what scientists are looking for. Symmetry, as we have described it, is only part of the story. In numerous cases the laws of physics actually violate a symmetry law and break into d ...
An anti-realist account of the application of mathematics
... Second, independently of the concerns surrounding platonism, the model-theoretic account of consequence faces a serious limitation. It does not apply to classical set theory, in particular to a set theory such as Zermelo–Fraenkel with the axiom of choice (ZFC). After all, to use the model-theoretic ...
... Second, independently of the concerns surrounding platonism, the model-theoretic account of consequence faces a serious limitation. It does not apply to classical set theory, in particular to a set theory such as Zermelo–Fraenkel with the axiom of choice (ZFC). After all, to use the model-theoretic ...
A Selective History of the Stone-von Neumann Theorem
... The first observation to make is that (1) has no solutions if H is finite-dimensional and ~ 6= 0, since the trace of any commutator must vanish, but Tr(−i~) = −i~ dim H does not. But (1) also has no solutions with either P or Q bounded. 8 (P and Q play symmetrical roles, since interchanging them amo ...
... The first observation to make is that (1) has no solutions if H is finite-dimensional and ~ 6= 0, since the trace of any commutator must vanish, but Tr(−i~) = −i~ dim H does not. But (1) also has no solutions with either P or Q bounded. 8 (P and Q play symmetrical roles, since interchanging them amo ...
On a class of transformation groups
... Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at . http://www.jstor.org/action/showPublisher?publisherCode=jhup. . Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or p ...
... Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at . http://www.jstor.org/action/showPublisher?publisherCode=jhup. . Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or p ...
THE C∗-ALGEBRAIC FORMALISM OF QUANTUM MECHANICS
... determine why these results are not in agreement with experimental observation. Once it is determined why this characterization of states and observables is not compatible with our physical world, we take these results about observables and states from classical mechanics, and modify them just sligh ...
... determine why these results are not in agreement with experimental observation. Once it is determined why this characterization of states and observables is not compatible with our physical world, we take these results about observables and states from classical mechanics, and modify them just sligh ...
J. von Neumann`s views on mathematical and axiomatic physics
... formalism. It is difficult to understand such a theory if these two things, the formalism and its physical interpretation, are not kept sharply apart. This separation should be performed here as clearly as possible although, corresponding to the current status of the theory, we do not want yet to es ...
... formalism. It is difficult to understand such a theory if these two things, the formalism and its physical interpretation, are not kept sharply apart. This separation should be performed here as clearly as possible although, corresponding to the current status of the theory, we do not want yet to es ...
Dilations, Poduct Systems and Weak Dilations∗
... unitary. The inner product on the tensor product is hx ¯ y, x0 ¯ y 0 i = y, hx, x0 iy 0 . For a detailed introduction to Hilbert modules (adapted to our needs) we refer to Skeide [Ske01a], for a quick reference (without proofs) to Bhat and Skeide [BS00]. Formally, product systems appear as a general ...
... unitary. The inner product on the tensor product is hx ¯ y, x0 ¯ y 0 i = y, hx, x0 iy 0 . For a detailed introduction to Hilbert modules (adapted to our needs) we refer to Skeide [Ske01a], for a quick reference (without proofs) to Bhat and Skeide [BS00]. Formally, product systems appear as a general ...
PROPERTIES OF FINITE-DIMENSIONAL GROUPS Topological
... When M is an n-dimensional manifold and G is compact, effective, and has locally connected orbits, Zippin and the author have shown that G must be a Lie group [12]. This result is related to the fact that a pointwise periodic homeomorphism of a manifold must be periodic, that is, if every point has ...
... When M is an n-dimensional manifold and G is compact, effective, and has locally connected orbits, Zippin and the author have shown that G must be a Lie group [12]. This result is related to the fact that a pointwise periodic homeomorphism of a manifold must be periodic, that is, if every point has ...
abstracts - Istituto Nazionale di Fisica Nucleare
... branch of natural sciences and of theoretical physics was a subject of discussion since Hilbert (who was a pursuer of Descartes and a precursor of Bourbaki) and Poincaré (the founder of modern mathematics, topology, chaos theory and dynamical systems). I will speak essentially about some examples, s ...
... branch of natural sciences and of theoretical physics was a subject of discussion since Hilbert (who was a pursuer of Descartes and a precursor of Bourbaki) and Poincaré (the founder of modern mathematics, topology, chaos theory and dynamical systems). I will speak essentially about some examples, s ...
Derivation of the Born Rule from Operational Assumptions
... Whence the Born rule? It is fundamental to quantum mechanics; it is the essential link between probability and a formalism which is otherwise deterministic; it encapsulates the measurement postulates. Gleason’s theorem [4] is mathematically informative, but its premises are too strong to have any di ...
... Whence the Born rule? It is fundamental to quantum mechanics; it is the essential link between probability and a formalism which is otherwise deterministic; it encapsulates the measurement postulates. Gleason’s theorem [4] is mathematically informative, but its premises are too strong to have any di ...
A TOUR THROUGH MATHEMATICAL LOGIC
... The word “tour” in the title of this book also deserves some explanation. For one thing, I chose this word to emphasize that it is not a textbook in the strict sense. To be sure, it has many of the features of a textbook, including exercises. But it is less structured, more freeflowing, than a stand ...
... The word “tour” in the title of this book also deserves some explanation. For one thing, I chose this word to emphasize that it is not a textbook in the strict sense. To be sure, it has many of the features of a textbook, including exercises. But it is less structured, more freeflowing, than a stand ...
k-ordered
... A graph is said to be k-cyclable if given any set of k vertices, there is a cycle that contains the k vertices. (introduced in 1967) It is well known that being 2-connected is equivalent to being 2-cyclable,and that in general being k-connected implies k-cyclable. Also, a hamiltonian graph is one t ...
... A graph is said to be k-cyclable if given any set of k vertices, there is a cycle that contains the k vertices. (introduced in 1967) It is well known that being 2-connected is equivalent to being 2-cyclable,and that in general being k-connected implies k-cyclable. Also, a hamiltonian graph is one t ...
Special Volume on Orthogonal Polynomials and Mathematical Physics
... Special Volume on Orthogonal Polynomials and Mathematical Physics This special volume of ETNA contains twelve selected papers presented at the Sixth International Workshop on Orthogonal Polynomials, held at Universidad Carlos III de Madrid in July 5–8, 2004. The workshop was organized by Francisco M ...
... Special Volume on Orthogonal Polynomials and Mathematical Physics This special volume of ETNA contains twelve selected papers presented at the Sixth International Workshop on Orthogonal Polynomials, held at Universidad Carlos III de Madrid in July 5–8, 2004. The workshop was organized by Francisco M ...
Operator Theory - UNL Math Department
... For someone with a bit of scientific/technical knowledge I usually say something like: One of the big ideas of 20th c science was quantum mechanics, and the key thing quantum mechanics found was that there's a fundamental limit to how well you can measure some things. And that's different from just ...
... For someone with a bit of scientific/technical knowledge I usually say something like: One of the big ideas of 20th c science was quantum mechanics, and the key thing quantum mechanics found was that there's a fundamental limit to how well you can measure some things. And that's different from just ...
poster
... with a single question: how can we count the number of solutions to an equation? This lecture will describe some of the remarkable answers mathematicians have found to this question, and how, in recent years, the fundamentals of algebraic topology have been re-thought in order to come to grips with ...
... with a single question: how can we count the number of solutions to an equation? This lecture will describe some of the remarkable answers mathematicians have found to this question, and how, in recent years, the fundamentals of algebraic topology have been re-thought in order to come to grips with ...
Andrew M. Gleason
Andrew Mattei Gleason (November 4, 1921 – October 17, 2008) was an American mathematician whoas a young World War II naval officer broke German and Japanese military codes, then over the succeeding sixty years made fundamental contributions to widely varied areas of mathematics,including the solution of Hilbert's fifth problem, and was a leader in reform and innovation in mathematics teaching at all levels.Gleason's theorem in quantum logic and the Greenwood–Gleason graph, an important example in Ramsey theory, are named for him.Gleason's entire academic career was at Harvard, from which he retired in 1992. His numerous academic and scholarly leadership posts included chairmanship of the Harvard Mathematics Department and Harvard Society of Fellows, and presidency of the American Mathematical Society.He continued to advise the United States government on cryptographic security, and the Commonwealth of Massachusetts on mathematics education for children, almost until the end of his life.Gleason won the Newcomb Cleveland Prize in 1952 and the Gung–Hu Distinguished Service Award of the American Mathematical Society in 1996. He was a member of the National Academy of Sciences and of the American Philosophical Society, and held the Hollis Chair of Mathematics and Natural Philosophy at Harvard.He was fond of saying that mathematical proofs ""really aren't there to convince you that something is true—they're there to show you why it is true.""The Notices of the American Mathematical Society called him ""one of the quiet giants of twentieth-century mathematics, the consummate professor dedicated to scholarship, teaching, and service in equal measure.""