Related papers: On Applications of Campbell's Embedding Theorem

We revisit the Riemann-Cartan geometry in the context of recent higher-dimensional theories of spacetime. After introducing the concept of torsion in a modern geometrical language we present some results that represent extensions of…

In this chapter we discuss the Einstein Podolsky Rosen theorem and its strong relation with Bell's theorem. The central role played by the concept of beable introduced by Bell is emphasized. In particular we stress that beables involved in…

Let k be a field. This paper investigates the embedding dimension and codimension of Noetherian local rings arising as localizations of tensor products of k-algebras. We use results and techniques from prime spectra and dimension theory to…

A recent article of Colbeck and Renner tackled the problem whether entanglements may be explained by combined models of local and non-local hidden variables. To the difference from previous works they considered models in which each pair of…

Bell's theorem proves that quantum theory is inconsistent with local physical models. It has propelled research in the foundations of quantum theory and quantum information science. As a fundamental feature of quantum theory, it impacts…

The embedding theorem of Roelcke and Dierolf for the completions of four standard uniform structures on topological groups and their quotients holds more generally for spaces of uniform measures. The natural mappings between the four spaces…

Franson showed that Aspect's experiment to test Bell's inequality did not rule out local realistic theories with delayed determinism. A class of local, deterministic discrete mathematical models with delayed determinism is described that…

The real cohomology of the space of imbeddings of S^1 into R^n, n>3, is studied by using configuration space integrals. Nontrivial classes are explicitly constructed. As a by-product, we prove the nontriviality of certain cycles of…

Here it is shown that the simplest description of Bell's experiment according to the canon of von Neumann's theory of measurement explicitly assumes the (Quantum Mechanics-language equivalent of the classical) condition of Locality. This…

We study local structure of the moduli space of compact Einstein metrics with respect to the boundary conformal metric and mean curvature. In dimension three, we confirm M. Anderson's conjecture in a strong sense, showing that the map from…

Large collections of high-dimensional data have become nearly ubiquitous across many academic fields and application domains, ranging from biology to the humanities. Since working directly with high-dimensional data poses challenges, the…

Bell's 1964 theorem, which states that the predictions of quantum theory cannot be accounted for by any local theory, represents one of the most profound developments in the foundations of physics. In the last two decades, Bell's theorem…

Bell's theorem, stating that quantum predictions are incompatible with a local hidden variable description, is a cornerstone of quantum theory and at the center of many quantum information processing protocols. Over the years, different…

Leggett formulated an inequality which seems to generalize the Bell theorem to non-local hidden variable theories. Leggett inequality is violated by quantum mechanics, as was confirmed by experiment. However, a careful analysis reveals that…

The mathematical theory of isometric embedding is applied to study the notion of quasilocal mass in general relativity. In particular, I shall report some recent progress of quasilocal mass with reference to a cosmological spacetime, such…

The celebrated Takens' embedding theorem concerns embedding an attractor of a dynamical system in a Euclidean space of appropriate dimension through a generic delay-observation map. The embedding also establishes a topological conjugacy. In…

We introduce a class of special geometries associated to the choice of a differential graded algebra contained in \Lambda R^n. We generalize some known embedding results, that effectively characterize the real analytic Riemannian manifolds…

Usually the 'hidden variables' of Bell's theorem are supposed to describe the pair of Bell particles. Here a semantic shift is proposed, namely to attach the hidden variables to a stochastic medium or field in which the particles move. It…

Listing has recently extended results of Kozameh, Newman and Tod for four-dimensional spacetimes and presented a set of necessary and sufficient conditions for a metric to be locally conformally equivalent to an Einstein metric in all…

In this article we show how one can use the local models of integrable Hamiltonian systems near critical points to prove a localization theorem for certain singular loci of integrables semi-toric systems for dimension greater than 4.