arXiv subjects

Ricardo Gallego Torromé

Publications and source records attributed to Ricardo Gallego Torromé.

At least 19 recordsLinked to original sources

arXiv2026

On the notion of kinetic energy in a spacetime of maximal proper acceleration

It is shown in this work that in spacetimes of maximal proper acceleration there are situations where a particle decelerates and simultaneously increases its kinetic energy. To illustrate the effect, a classical $1$-dimensional electric cavity-like scheme is discussed. The gain in kinetic energy by deceleration suggests an equivalence between velocity and acceleration from the energetic point of view. Such an equivalence is stated in a form resembling Born reciprocity principle but formulated in the framework of higher order jet spacetime geometry. We also show the existence in the theory of a dynamical superluminal sector for point particles with positive mass and characterized by superluminal speed and a proper acceleration larger than the maximal proper acceleration. Therefore, the speed of light and the maximal proper acceleration become only {\it separation conditions} at the classical level of the two dynamical sectors.

physics.gen-ph↗

arXiv2026

Spacetimes of maximal proper acceleration and muon mean lifetime

In this paper, it is shown that in spacetimes of maximal proper acceleration, there is a reduction of the mean lifetime of the muon. We consider several candidates for the maximal proper acceleration. For all of them, the induced corrections are small, but for the case when the maximal proper acceleration is identified with the Schwinger's acceleration, the effect is detectable in future muon collider facilities.

gr-qc↗

arXiv2026

Quotient rings and fields of integers from the metric geometry point of view

The theory of Gromov-Hausdorff convergence is applied to sequences of quotient rings of integers, leading to the existence of limit rings as the Gromov-Hausdorff limits. It is also shown that such {\it limit rings} can be endowed with an order relation, although they are not ordered fields. When the construction restricts to quotients $\mathbb{Z}/p\mathbb{Z}$ with $p$ prime, the limits are fields. The relation of those limits with the field of the real numbers $\mathbb{R}$ is discussed, showing that the limit fields are dense in $\mathbb{R}$ but they cannot be identified with $\mathbb{R}$ or with the rational field $\mathbb{Q}$, at least when $\mathbb{R}$ and $\mathbb{Q}$ are endowed with the usual order relations and metric structures, neither they can be identified with the $p$-adic number system. It is also shown that the limit rings and fields have an ordinal larger than the reals and that they are endowed with an Archimedean absolute value function.

math.RA↗

arXiv2026

Foundations for a theory of emergent quantum mechanics and emergent classical gravity

Quantum systems are viewed as emergent systems from the fundamental degrees of freedom. The laws and rules of quantum mechanics are understood as an effective description, valid for the emergent systems and specially useful to handle probabilistic predictions of observables. After introducing the geometric theory of Hamilton-Randers spaces and reformulating it using Hilbert space theory, a Hilbert space structure is constructed from the Hilbert space formulation of the underlying Hamilton-Randers model and associated with the space of wave functions of quantum mechanical systems. We can prove the emergence of the Born rule from ergodic considerations. A geometric mechanism for a natural spontaneous collapse of the quantum states based on the concentration of measure phenomena as it appears in metric geometry is discussed.We show the existence of stable vacua states for the quantized matter Hamiltonian. Another consequence of the concentration of measure is the emergence of a weak equivalence principle for one of the dynamics of the fundamental degrees of freedom. We suggest that the reduction of the quantum state is driven by a gravitational type interaction. Such interaction appears only in the dynamical domain when localization of quantum observables happens, it must be a classical interaction. We discuss the double slit experiment in the context of the framework proposed, the interference phenomena associated with a quantum system in an external gravitational potential, a mechanism explaining non-quantum locality and also provide an argument in favour of an emergent interpretation of every macroscopic time parameter. Entanglement is partially described in the context of Hamilton-Randers theory and how naturally Bell's inequalities should be violated.

math-ph↗

arXiv2025

On the Unruh effect for hyperbolic observers in spacetimes of maximal proper acceleration

In this work, the notion of spacetime of maximal proper acceleration is motivated as a weak form to implement general covariance and a generalized form of Einstein's equivalence principle from a physical point of view and the fundamental geometric and kinematic properties of such spaces are discussed. Thereafter the Unruh temperature formula is generalized to the case of hyperbolic observers in spacetimes of maximal proper acceleration. Such a generalization implies the existence of a maximal value for the Unruh temperature. We discuss this result for an electrodynamic model of point charged particles in a spacetime of maximal proper acceleration. It is shown that according to the model, the maximal Unruh temperature must be of order $4.8\cdot 10^{10}/N$ K for current high acceleration electron laser-plasma acceleration systems, where $N$ is the population of the typical bunch.

gr-qc↗

arXiv2024

On the effect of the maximal proper acceleration in the inertia

The effect of a hypothetical maximal proper acceleration on the mass of a charged particles is investigated in the context of particle accelerators. In particular, it is shown that maximal proper acceleration implies an increase in the kinetic energy of the particle being accelerated with respect to the relativistic energy. Such an increase in kinetic energy leads to a reduction of the luminosity of the bunches with respect to the expected luminosity in the relativistic models of the bunches. This relative loss in luminosity is of the order $10^{-3}$ to $10^{-5}$ for the LHC bunches and can be of order up to $10^{-3}$ for certain laser plasma accelerator facilities. Although the effect is small, it increases with the square of the bunch population.

physics.acc-ph↗

arXiv2024

On the emergence of gravity in a framework of emergent quantum mechanics

In this work we consider the emergent origin of gravity in the framework of Hamilton-Randers theory, a theoretical framework for emergent quantum mechanics. After presenting the essential ingredients of the theory, a derivation of the weak equivalence principle from the first principles of the theory follows. Then it is shown that the Newtonian model of gravity and certain modified gravity models are consistent with Hamilton-Randers theory. One of these models has strong formal resemblance with MOND, providing further ground to think that Hamilton-Randers theory could be a natural theoretical frame for realistic modified gravity models.

physics.gen-ph↗

arXiv2023

Quantum Illumination with Non-Gaussian Three Photons States

It is shown that quantum illumination with three photons non-Gaussian states, where the signal is described by a two photons state and the idler is described by a one photon state, can outperform in sensitivity standard Gaussian quantum illumination in a high noisy background. In particular, there is a reduction in the probability due to an increase in the probability of error exponent by a factor $1/{N_S}$, where $N_S$ is the average number of photons per mode of the signal state.

quant-ph↗

arXiv2023

Enhancement in the mean square range delay accuracy by means of multiple entangled photon states quantum illumination

It has been discussed recently how quantum illumination can be used to increase the accuracy of the value range-delay measurement \cite{Zhuang Shapiro 2022} in the domain of SNR compatible with current radar systems. However, the advantage described in [1] requires of a large integration time. In this work it is argued that multiple entangled photon quantum illumination could help to reduce the integration time when evaluating range-delay. Our analysis is performed in the framework of three entangled photon states discrete quantum illumination protocols. In this setting it is shown explicitly that using a direct generalization of Lloyd's protocol to the case where signal states describe two photons presents interesting advantages: 1. The reduction of the probability of error with respect to Lloyd's quantum illumination, 2. The reduction of the integration time with respect to Lloyd's quantum illumination, 3. The increase in the ultimate in the measurement of the range-delay accuracy.

quant-ph↗

arXiv2022

On the emergent origin of the inertial mass

In the context of a particular framework of emergent quantum mechanics, it is argued the emergent origin of the inertial mass of a physical systems. Two main consequences of the theory are discussed: an emergent interpretation of the law of inertia and a derivation of the energy-time uncertainty relation.

quant-ph↗

arXiv2022

Maximal acceleration and black hole evaporation

We discuss how in certain theories of spacetime admitting a maximal proper acceleration Hawking radiation does not completely evaporate the black hole. The black hole remnant's mass depends on the inverse of the maximal acceleration. Furthermore, as a consequence of a duality between the minimum mass that a Schwarzschild black hole can have in such spacetimes and the maximal acceleration, we show that in certain theories with a maximal acceleration there must be an upper uniform bounds on the value of the force that can be exerted on test particles.

gr-qc↗

arXiv2021

On Penrose's theory of objective gravitationally induced wave function reduction

The formal structure of Penrose's gravitationally induced reduction of the wave function mechanism is analyzed. It is shown that pushing Penrose's argument forward leads to the interpretation of quantum coherence in microscopic systems as an observable signature violation of general covariance. We discuss potential avenues to avoid this conclusion, among them emergent quantum mechanics and super-determinism.

gr-qc↗

arXiv2021

A note on Clifford bundles and certain Finsler type spaces

We study a relation between certain extensions of the Clifford bundle and Finsler type structures that naturally generalize the standard Clifford relation between (pseudo)-Riemannian metric structures and Dirac matrices. We show for flat metrics that there is a triangle map between Finsler structures constructed from an (pseudo)-Riemannian metric and $1$-forms on $M$, the extension of the Clifford bundle and relevant Dirac type operators.

math.DG↗

arXiv2021

General theory of non-reversible local dynamics

A general theory of dynamics is formulated with the aim of its application in emergent quantum mechanics. In such a framework it is argued that the fundamental dynamics of emergent quantum mechanics must be non-reversible.

math-ph↗

arXiv2021

On the interplay between the notions of Randers space and gauge invariance

In this paper we argue that when gauge invariance is taken into consideration, there is no consistent geometric framework of Finsler class that can accommodate Randers type spaces. In this context, an alternative non-Finslerian framework for Randers spacetimes compatible with gauge invariance is introduced.

math-ph↗

arXiv2021

Average of geometric structures in Finsler spaces with Lorentzian signature

Given the class of Finsler spaces with Lorentzian signature $(M,L)$ on a manifold $M$ endowed with a timelike vector field $\mathcal{X}$ satisfying $g_{(x,y)}(\mathcal{X},\mathcal{X})<0$ at any point $(x,y)$ of the slit tangent bundle, a pseudo-Riemannian metric defined on $M$ of signature $n-1$ is associated to the fundamental tensor $g$. Furthermore, an affine, torsion free connection is associated to the Chern connection determined by $L$. The definition of the average connection does not make use of $\mathcal{X}$. Therefore, there is no direct relation between these two averaged objects.

math.DG↗

arXiv2021

Quantum illumination with multiple entangled photons

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

quant-ph↗

arXiv2021

Introduction to quantum radar

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

quant-ph↗