Related papers: Spacelike distance from discrete causal order

Processes with an indefinite causal structure may violate a causal inequality, which quantifies quantum correlations that arise from a lack of causal order. In this paper, we show that when the inequalities are analysed with a…

We use causality to derive a number of simple and universal constraints on dispersion relations, which describe the location of singularities of retarded two-point functions in relativistic quantum field theories. We prove that all causal…

Combining gravity with quantum theory is still work in progress. On the one hand, classical gravity, is the geometry of space-time determined by the energy-momentum tensor of matter and the resulting nonlinear equations; on the other hand,…

In the light of some recent results, it is argued that usual concepts of causality and locality are approximations valid at scales greater than the Compton wavelength and corresponding time scales. It follows that the "spooky" non-locality…

In the first part of the paper, we define an approximated Brunn-Minkowski inequality which generalizes the classical one for length spaces. Our new definition based only on distance properties allows us also to deal with discrete spaces.…

In this paper, based on the local comparison principle in [12], we study the local behavior of the difference of two spacelike graphs in a neighborhood of a second contact point. Then we apply it to the constant mean curvature equation in…

The idea that events obey a definite causal order is deeply rooted in our understanding of the world and at the basis of the very notion of time. But where does causal order come from, and is it a necessary property of nature? We address…

The first goal of this paper is to show that discreteness, locality, and relativistic covariance can peacefully coexist if the ordinary spacetime (OST) is replaced with phase spacetime (PST) as a geometric background of a Poisson process,…

Spatial and temporal quantum correlations can be unified in the framework of the pseudo-density operators, and quantum causality between the involved events in an experiment is encoded in the corresponding pseudo-density operator. We study…

Theories with a curved momentum space, which became recently of interest in the quantum-gravity literature, can in general violate many apparently robust aspects of our current description of the laws of physics, including relativistic…

A subset of a metric space is a k-distance set if there are exactly k non-zero distances occuring between points. We conjecture that a k-distance set in a d-dimensional Banach space (or Minkowski space), contains at most (k+1)^d points,…

We develop a new description of the much-studied $\kappa$-Minkowski noncommutative spacetime, centered on representing on a single Hilbert space not only the $\kappa$-Minkowski coordinates, but also the associated differential calculus and…

The necessity of rejecting the numerical model of geometrical extension is postulated on the basis of the idea of identity of space-time and physical vacuum. An attempt is made to define space-time not via the concept of manifold, but via…

We take causality and uniqueness of events observation as our driving forces. They are built in in the way we define distinct observers, which then require a finite time to communicate between each other. This unavoidably leads to the…

We propose, for dimension d, a discrete Lorentz invariant operator on scalar fields that approximates the Minkowski spacetime scalar d'Alembertian. For each dimension, this gives rise to a scalar curvature estimator for causal sets, and…

We investigate the limitations of length measurements by accelerated observers in Minkowski spacetime brought about via the hypothesis of locality, namely, the assumption that an accelerated observer at each instant is equivalent to an…

We develop causality theory for upper semi-continuous distributions of cones over manifolds generalizing results from mathematical relativity in two directions: non-round cones and non-regular differentiability assumptions. We prove the…

Quantum theories of gravity are generally expected to have some degree of non-locality, with familiar local physics emerging only in a particular limit. Perturbative quantum gravity around backgrounds with isometries and compact Cauchy…

The existence of a minimal observable length has long been suggested, in quantum gravity, as well as in string theory. In this context a generalized uncertainty relation has been derived which quantum theoretically describes the minimal…

We evaluate the spectral dimension in causal set quantum gravity by simulating random walks on causal sets. In contrast to other approaches to quantum gravity, we find an increasing spectral dimension at small scales. This observation can…