Related papers: A revised de Broglie relation in discrete space-ti…
We present and prove the version of Marstrand's theorem for discrete metric space. We provide explicit estimates of the quotient of upper and lower densities of measures on this space.
Following the usual definition of $\lambda$-symmetries of differential equations, we introduce the analogous concept for difference equations and apply it to some examples.
Some sharp discrete inequalities in normed linear spaces are obtained. New reverses of the generalised triangle inequality are also given.
In this paper I explain the relation between the need for observers in de Sitter space and the spontaneous breakdown of time-reversal symmetry.
We discuss discrete Morrey spaces and their generalizations, and we prove necessary and sufficient conditions for the inclusion property among these spaces through an estimate for the characteristic sequences.
It was recently proposed that deformations of the relativistic symmetry, as those considered in Deformed Special Relativity (DSR), can be seen as the outcome of a measurement theory in the presence of non-negligible (albeit small) quantum…
We investigate the space of simplices in Euclidean Space
In recent years, the picture of discrete space time has been studied in the context of stochastic theory. There are a number of ramifications, which are briefly examined. We argue that the causality of physiics has its roots in the…
In the present work, metrics which lead to projected closed orbits are found by comparing the relativistic differential equation of orbits with the corresponding classical differential equation. Physical and geometrical properties of these…
An overview is given of recent developments in the field of Dirac equations generalized to curved space-times. An illustrative discussion is provided. We conclude with a variation of Dirac's large-number hypothesis which relates a number of…
Using an elementary example based on two simple harmonic oscillators, we show how a relational time may be defined that leads to an approximate Schrodinger dynamics for subsystems, with corrections leading to an intrinsic decoherence in the…
The Bose-Marletto-Vedral experiment tests a non-relativistic quantum effect due to a gravitational interaction. It has received attention because it may soon be within observational reach in the lab. We observe here that: (i) in…
Within a Liouville approach to non-critical string theory, we argue for a non-trivial commutation relation between space and time observables, leading to a non-zero space-time uncertainty relation $\delta x \delta t > 0$, which vanishes in…
It is argued that de Sitter space-times might be solutions of entangled relativity once the quantum trace anomaly from matter fields in curved space-times is taken into account. This hypothesis would be an elegant solution to the…
Dynamical systems with long delay feedback can exhibit complicated temporal phenomena, which once re-organized in a two-dimensional space are reminiscent of spatio-temporal behavior. In this framework, normal forms description have been…
This paper begins with a theoretical explanation of why spacetime is discrete. The derivation shows that there exists an elementary length which is essentially Planck's length. We then show how the existence of this length affects time…
In a previous work [arXiv:2211.02945] we made an attempt to set up a discrete octonionic Stokes' formula. Due to an algebraic property that we have not considered in that attempt, the formula however turned out to involve an associator term…
A space spectrum of density perturbation In the Universe with nontrivial topology of space-time is shown to become discrete.
The dispersion relation of de Sitter special relativity is obtained in a simple and compact form, which is formally similar to the dispersion relation of ordinary special relativity. It is manifestly invariant under change of scale of mass,…
The Hamiltonian formulation of modified dispersion relations (MDRs) allows for their implementation on generic curved spacetimes. In turn it is possible to derive phenomenological effects. I will present how to construct the kappa-Poincare…