Related papers: On Newtonian frames
A canonical formalism of the rank-three tensor model with the notion of local time is proposed. The consistency of the local time evolution is guaranteed by imposing that local Hamiltonians and the so(N) kinematical symmetry of the tensor…
The existence of time machines, understood as spacetime constructions exhibiting physically realised closed timelike curves (CTCs), would raise fundamental problems with causality and challenge our current understanding of classical and…
The notion of microscopic state of the system at a given moment of time as a point in the phase space as well as a notion of trajectory is widely used in classical mechanics. However, it does not have an immediate physical meaning, since…
We investigate possible explanations of quantum correlations that satisfy the principle of continuity, which states that everything propagates gradually and continuously through space and time. In particular, following [J.D. Bancal et al,…
Dual structures on causal sets called timelets are introduced, being discrete analogs of global time coordinates. Algebraic and geometrical features of the set of timelets on a causal set are studied. A characterization of timelets in terms…
Classical chaos theory rests on the notion of universality, whereby disparate dynamical systems share identical scaling laws. Existing universality classes, however, implicitly assume Markovian dynamics. Here, a logistic map endowed with…
We study in this paper different topos-theoretical approaches to the problem of construction of General Theory of Relativity. In general case the resulting space-time theory will be non-classical, different from that of the usual Einstein…
The coordinate freedom of General Relativity makes it challenging to find mathematically rigorous and physically sound definitions for physical quantities such as the center of mass of an isolated gravitating system. We will argue that a…
Different aspects of relativity, mainly in a canonical formulation, relevant for the question "Is spacetime nothing more than a mathematical space (which describes the evolution in time of the ordinary three-dimensional world) or is it a…
Local realism has been superseded by recent theoretical and experimental developments in quantum physics which show a synchronic connection between the parts. In contrast to the principle of local realism, which is the basis of classical…
We present some modern theories on the structure of spacetime that can be classified as relational theories in the direction of Leibniz's ontology. In order to analyze the nature of spacetime we consider three levels of knowledge…
Causality is one of the fundamental structures of spacetimes, determining the possible behaviour and propagation of physical information. Causal structure can be analysed through the various modal logics it induces. The modal logics for the…
The difficulty of explaining non-local correlations in a fixed causal structure sheds new light on the old debate on whether space and time are to be seen as fundamental. Refraining from assuming space-time as given a priori has a number of…
The classical causal relations between a set of variables, some observed and some latent, can induce both equality constraints (typically conditional independences) as well as inequality constraints (Instrumental and Bell inequalities being…
Flat space-time has not heretofore been thought a suitable locus in which to construct model universes because of the presumed necessity of incorporating gravitation in such models and because of the historical lack of a theory of…
Causal Dynamical Triangulations is a non-perturbative quantum gravity model, defined with a lattice cut-off. The model can be viewed as defined with a proper time but with no reference to any three-dimensional spatial background geometry.…
The so-called ``analogue models of general relativity'' provide a number of specific physical systems, well outside the traditional realm of general relativity, that nevertheless are well-described by the differential geometry of curved…
We show that the random adjacency matrices induced by the chronological relations and i.i.d. samples of two spacetimes coincide in law if and only if the spacetimes in question are smoothly isometric. A similar result holds for weighted…
The fundamental theories of physics are local theories, depending on local interactions of local variables. It is not clear if and how strictly local theories can produce non-local variables that have causal effectiveness. Yet, non-local…
Numerical N-body simulations of large scale structure formation in the universe are based on Newtonian gravity. However, according to our current understanding, the most correct theory of gravity is general relativity. It is therefore…