In this work, a version of Fermat's principle for causal curves with the same energy in time orientable Finsler spacetimes is proved. We calculate secondvariation {\it arrival functional} along geodesic terms index form associated spacetime Lagrangian. Then character critical points functional investigated and Morse theorem context presented.

After a brief introduction to the notion of quantum entanglement and correlations, several schemes for radar based upon illumination others protocols are discussed. We review different concepts that have been introduced overcome inherent difficulties in implementation generation and/or detection sensing RADAR applications. Our is an up-to date critical presentation state art, with emphasis case by assessment feasibility concepts. also aim accessible non-experts field. Hence appendixes...

A geometric framework for metrics of maximal acceleration which is applicable to large proper accelerations discussed, including a theory connections associated with the geometry acceleration. In such framework, it shown that uniform bound on implies certain bilinear combinations Riemannian curvature components in domain spacetime where finite.

Using the Finsler structure living in phase space associated to tangent bundle of configuration manifold, deterministic models at Planck scale are obtained. The Hamiltonian functions constructed directly from geometric data and some assumptions concerning time inversion symmetry. existence a maximal acceleration speed is proved for Finslerian models. We investigate spontaneous symmetry breaking orthogonal SO(6N) system. This break implies nonvalidity argument used obtain Bell’s inequalities...

In this work, a theoretical generalization of Lloyd's quantum illumination to signal beams described by two entangled photon states is developed. It shown that the new protocol offers method find range target, reduces size required time-bandwidth product have same noise ratio than in illumination, has lower probability false positive and resilient against also potentially losses. However, generation three for posses technical problem its practical implementation not fully addressed. Recent...

Motivated by obtaining a consistent mathematical description for the radiation reaction of point charged particles in linear classical electrodynamics, theory generalized higher order tensors and differential forms is introduced. The generalization some fundamental notions geometry presented. In particular, cohomology integration theories are developed, including Cartan calculus, de Rham version Thom's isomorphism theorem. We consider detail special type associated with bounded maximal...

The notion of singular generalized Finsler spacetime and Berwald are introduced their relevance for the description classical gravity discussed. A method to construct examples such spacetimes is sketched. applied at two different levels generality. First, a class flat, obtained. Then in an attempt further generalization, non-flat presented associated Einstein field equations In this context, argument favour small value cosmological constant given. physical significance models briefly...

In a recent paper (arXiv:1412.6000) general mechanism for emergence of cosmological space-time geometry from quantum gravity setting was devised and departure standard dispersion relations elementary particle were predicted. We elaborate here on this approach extending the results obtained in that showing generically such framework will not lead to higher order modified matter sector. Furthermore, we shall discuss possible phenomenological constraints scenarios have be by nowadays classical...

We argue that in a framework for emergent quantum mechanics, the weak equivalence principle is consequence of concentration measure large-dimensional spaces [Formula: see text]-Lipshitz functions. Furthermore, as and properties we assume fundamental dynamics, it argued gravity must be classical, interaction.

General relativity is incomplete because it cannot describe quantum effects of space-time. The complete theory gravity not yet known and to date no observational evidence exists that space-time quantized. However, in most approaches the manifold general only an effective limit that, among other things like higher curvature terms, should receive corrections stemming from defects. We here develop a modification describes local defects solve Friedmann equations. From this, we obtain...

A model for the dynamics of a classical point charged particle interacting with higher order jet fields is introduced. In this model, described by an implicit ordinary second differential equation. Such equation free run-away and pre-accelerated solutions Dirac's type. The theory Lorentz invariant, compatible first law Newton Larmor's power radiation formula. Few implications new in phenomenology non-neutral plasmas considered.

A geometric theory for spacetimes whose world lines associated with physical particles have an upper bound the proper acceleration is developed. After some fundamental remarks on requirements that classical dynamics point should hold, notion of a generalized metric and maximal are introduced. perturbative approach to metrics discussed we show how it provides consistent where Lorentzian corresponds limit when goes infinity. Then several kinematical properties investigated, including...

Maximal accelerations are related to the existence of a minimal time for given physical system. Such can be either an intrinsic timescale system or connected quantum gravity induced ultraviolet cutoff. In this paper, we pedagogically introduce four major formulations kinematics accounting maximal acceleration. Some phenomenological repercussions offered as hints future investigations.

Given a Finsler space (M,F) on manifold M, the averaging method associates to Finslerian geometric objects affine objects} living $M$. In particular, Riemannian metric is associated fundamental tensor $g$ and an affine, torsion free connection Chern-Rund connection. As illustration of technique, generalization Gauss-Bonnet theorem Berwald surfaces using average presented. The parallel transport curvature endomorphisms are obtained. holonomy group for discussed. New local isometric invariants...

Using a geometric averaging procedure applied to non-affine linear connection, we prove that for narrow one particle distribution function and in the ultra-relativistic limit, bunch of point charged particles can be described by Charged Cold Fluid Model, without additional hypothesis on moments.

In this paper we consider classical electrodynamic theories with maximal acceleration and some of their phenomenological consequences for laser-plasma acceleration. It is shown that in a recently proposed higher order jet theory electrodynamics, the effective reachable by consistent bunch point charged particles being accelerated wakefield damped bunches containing large number particles. We argue such prediction falsifiable. case Born-Infeld kinematics, phenomenology provides an upper bound...

Quantum systems are viewed as emergent from the fundamental degrees of freedom. The laws and rules quantum mechanics understood an effective description, valid for specially useful to handle probabilistic predictions observables. After introducing geometric theory Hamilton-Randers spaces reformulating it using Hilbert space theory, a structure is constructed formulation underlying model associated with wave functions mechanical systems. We can prove emergence Born rule ergodic...