In nonrelativistic quantum mechanics, measurements performed by separate observers are modeled via tensor products. In algebraic quantum field theory, though, local observables corresponding to spacelike separated parties are just required to commute. The problem of determining whether these two definitions of separation lead to the same set of bipartite correlations is known in nonlocality as ...

We consider four-dimensional spacetimes (M,g) which obey the Einstein equations G = T, and admit a global spacelike G1 = R isometry group. By means of dimensional reduction and local analyis on the reduced (2 + 1) spacetime, we obtain a sufficient condition on T which guarantees that (M,g) cannot contain apparent horizons. Given any (3 + 1) spacetime with spacelike translational isometry, the n...

In this paper smooth trajectories are computed in the Lie group SO(2, 1) as a motion planning problem by assigning a Frenet frame to the rigid body system to optimize the cost function of the elastic energy which is spent to track a spacelike curve in Minkowski space. In this case, the derivative of the tangent vector of the spacelike curve at a point s is taken as timelike. A method is propose...

Experiments motivated by Bell’s theorem suggest that information is sometimes transferred over spacelike intervals, and claims have been made that the results of these experiments do have this implication. However, the theoretical basis for such claims is usually taken to be Bell’s Theorem, which shows only that if certain predictions of quantum theory are correct, and certain hidden-variables ...

Introduction. In my note on A 5 curve theorem generalizing the theorem of Carnot, I introduced the notion of curve cross ratio. This extension of the ordinary cross ratio is the simplest situationally invariant (3.4) case of the generalized or hypersurface cross ratio of n + l pairs of hypersurfaces in w-space which is the subject of the following lines. The generalized cross ratio is a t the s...

The main idea of the support vector machine (SVM) classification approach is mapping the data into higher-dimensional linear space where the data can be separated by hyperplane. Based on the Jordan curve theory, a general nonlinear classification method by the use of hypersurface is proposed in this paper. The separating hypersurface is directly used to classify the data according to whether th...