Search Results (106)

The general framework of Entropic Dynamics (ED) is used to construct non-relativistic models of relational Quantum Mechanics from well-known inference principles—probability, entropy and information geometry. Although only partially relational—the absolute structures of simultaneity and Euclidean geometry are still retained—these models provide a useful testing ground for ideas that will prove useful in the context of more realistic relativistic theories. The fact that in ED the positions of particles have definite values, just as in classical mechanics, has allowed us to adapt to the quantum case some intuitions from Barbour and Bertotti’s classical framework. Here, however, we propose a new measure of the mismatch between successive states that is adapted to the information metric and the symplectic structures of the quantum phase space. We make explicit that ED is temporally relational and we construct non-relativistic quantum models that are spatially relational with respect to rigid translations and rotations. The ED approach settles the longstanding question of what form the constraints of a classical theory should take after quantization: the quantum constraints that express relationality are to be imposed on expectation values. To highlight the potential impact of these developments, the non-relativistic quantum model is parametrized into a generally covariant form and we show that the ED approach evades the analogue of what in quantum gravity has been called the problem of time. Full article

The Feynman path integral formalism for non-relativistic quantum mechanics is revisited. A comparison is made with cases of light propagation (Huygens’ principle) and Brownian motion. The difficulties for a physical model applying Feynman’s formalism are pointed out. A reformulation is proposed, where the transition probability of a particle from one space-time point to another one is the sum of probabilities of the possible paths. As an application, Born approximation for scattering is derived within the formalism, which suggests an interpretation involving the stochastic motion of a particle rather than the square of a wavelike amplitude. Full article

Synchronization is a universal phenomenon in driven or coupled self-sustaining oscillators with important applications in a wide range of fields, from physics and engineering to the life sciences. The Adler–Kuramoto equation represents a reduced dynamical model of the inherent phase modulation effects. As a complement to the standard numerical approaches, the analytical solution of the underlying nonlinear dynamics is considered, giving rise to the study of kinematically equivalent elliptical gears. They highlight the cross-disciplinary relevance of mechanical systems in providing a broader and more intuitive understanding of phase modulation effects. The resulting gear model can even be extended to domains beyond classical mechanics, including quasi-relativistic kinematics and analogues of quantum phenomena. Full article

Non-relativistic quantum mechanics was originally formulated to describe particles. Using ideas from the geometric quantization approach, we show how the concept of antiparticles can and should be introduced in the non-relativistic case without appealing to quantum field theory. We discuss this in detail using the example of the one-dimensional harmonic oscillator. Full article

In earlier works, it was demonstrated that Schrödinger’s equation, which includes interactions with electromagnetic fields, can be derived from a fluid dynamic Lagrangian framework. This approach treats the system as a charged potential flow interacting with an electromagnetic field. The emergence of quantum behavior was attributed to the inclusion of Fisher information terms in the classical Lagrangian. This insight suggests that quantum mechanical systems are influenced not just by electromagnetic fields but also by information, which plays a fundamental role in driving quantum dynamics. This methodology was extended to Pauli’s equations by relaxing the constraint of potential flow and employing the Clebsch formalism. Although this approach yielded significant insights, certain terms remained unexplained. Some of these unresolved terms appear to be directly related to aspects of the relativistic Dirac theory. In a recent work, the analysis was revisited within the context of relativistic flows, introducing a novel perspective for deriving the relativistic quantum theory but neglecting the interaction with electromagnetic fields for simplicity. This is rectified in the current work, which shows the implications of the field in the current context. Full article

The pairing of non-relativistic and relativistic Lagrangians within the context of fluid mechanics, advancing methodologies for constructing Poincare-invariant Lagrangians, is explored. Through leveraging symmetries and Noether’s theorem in an inverse framework, three primary cases are investigated: potential flow, barotropic flow expressed in terms of Clebsch variables, and an extended Clebsch Lagrangian incorporating thermodynamic effects. To ensure physical correctness, the eigenvalue relation of the energy–momentum tensor, together with velocity normalisation, are applied as key criteria. The findings confirm that the relativistic Lagrangians successfully reduce to their non-relativistic counterparts in the limit $c\to \infty$. These results demonstrate a systematic approach that enhances the relationship between symmetries and variational formulations, providing the advantage of deriving Lagrangians that unify non-relativistic and relativistic theories. Full article

On October 16th 1843, the prominent Irish mathematician Sir William Rowan Hamilton, in an inspired act of vandalism, carved his famous $i^2=j^2=k^2=ijk=-1$ on the Brougham Bridge in Dublin, thus starting a major clash of ideas with the potential to change the course of history. Quaternions, as he called his invention, were quite useful in describing Newtonian mechanics, and as it turned out later—also quantum and relativistic phenomena, which were yet to be discovered in the next century. However, the scientific community did not embrace this new approach with enthusiasm: there was a battle to be fought and Hamilton failed to make a compelling case probably because he was standing alone at the time. Although Quaternions were soon to find useful applications in geometry and physics (with the works of Clifford, Cayley, Maxwell, Einstein, Pauli, and Dirac), the battle seemed lost a few decades after Hamilton’s death. But, a century later computer algorithms turned the tides, and nowadays we are witnessing a revived interest in the subject, prompted by technology. Full article

In the context of data security, this work aims to present a novel solution that, rather than addressing the topic of endpoint security—which has already garnered significant attention within the international scientific community—offers a different perspective on the subject. In other words, the focus is not on device security but rather on the protection and security of the information contained within those devices. As we will see, the result is a next-generation decentralized infrastructure that simultaneously integrates two cognitive areas: data storage and its protection and security. In this context, an innovative Multiscale Relativistic Quantum (MuReQua) chain is considered to realize a novel decentralized and security solution for storing data. This engine is based on the principles of Quantum Mechanics, stochastic processes, and a new approach of decentralization for data storage focused on information security. The solution is broken down into four main components, considered four levels of security against attackers: (i) defocusing, (ii) fogging, (iii) puzzling, and (iv) crypto agility. The defocusing is realized thanks to a fragmentation of the contents and their distributions on different allocations, while the fogging is a component consisting of a solution of hybrid cyphering. Then, the puzzling is a unit of Information Fusion and Inverse Information Fusion, while the crypto agility component is a frontier component based on Quantum Computing, which gives a stochastic dynamic to the information and, in particular, to its data fragments. The data analytics show a very effective and robust solution, with executions time comparable with cloud technologies, but with a level of security that is a post quantum one. In the end, thanks to a specific application example, going beyond purely technical and technological aspects, this work introduces a new cognitive perspective regarding (i) the distinction between data and information, and (ii) the differentiation between the owner and the custodian of data. Full article

This review article provides the basics and discusses some important applications of thermal field theory, namely, the combination of statistical mechanics and relativistic quantum field theory. In the first part, the fundamentals are covered: the density matrix, the corresponding averages, and the treatment of fields of various spin in a medium. The second part is dedicated to the computation of thermal Green’s function for scalars, vectors, and fermions with path-integral methods. These functions play a crucial role in thermal field theory as explained here. A more applicative part of the review is dedicated to the production of particles in a medium and to phase transitions in field theory, including the process of vacuum decay in a general theory featuring a first-order phase transition. To understand this review, the reader should have good knowledge of non-statistical quantum field theory. Full article

In this work, we present a new theoretical approach to interpreting and reproducing quantum mechanics using trajectory-guided wavelets. Inspired by the 1925 work of Louis de Broglie, we demonstrate that pulses composed of a difference between a delayed wave and an advanced wave (known as antisymmetric waves) are capable of following quantum trajectories predicted by the de Broglie–Bohm theory (also known as Bohmian mechanics). Our theory reproduces the main results of orthodox quantum mechanics and unlike Bohmian theory, is local in the Bell sense. We show that this is linked to the superdeterminism and past–future (anti)symmetry of our theory. Full article

This paper is devoted to the study of stationary trajectories of free particles. From a classical point of view, this appears to be an almost trivial problem: Free particles should follow straight lines as predicted by Newton’s first law, and straight lines are indeed the stationary trajectories of the standard action integrals in the classical theory. In the following, however, a general relativistic approach is studied, and in this situation it is much less evident what action integral should be used. As it turns out, using the traditional Einstein–Hilbert principle gives us stationary states very much in line with the classical theory. But it is suggested that a different action principle, and in fact one which is closer to quantum mechanics, gives stationary states with a much richer structure: Even if these states in a sense can represent particles which obey the first law, they are also inherently rotating. Although we may still be far from understanding how general relativity and quantum mechanics should be united, this may give an interesting clue to why rotation (or rather spin, which is a different but related concept) seems to be the natural state of motion for elementary particles. Full article

The notion of invariance under the Lorentz transformation is fundamental to special relativity and its continuation beyond the speed of light. Theories and solutions with this characteristic are stronger and more powerful than conventional theories or conventional solutions because the Lorentz-invariant approach automatically embodies the conventional approach. We propose a Lorentz-invariant extension of Newton’s second law, which includes both special relativistic mechanics and Schrödinger’s quantum wave theory. Here, we determine new general expressions for energy–momentum, which are Lorentz-invariant. We also examine the Lorentz-invariant power-law energy–momentum expressions, which include Einstein’s energy relation as a particular case. Full article

Previously, it was shown that Schrödinger’s theory can be derived from a potential flow Lagrangian provided a Fisher information term is added. This approach was later expanded to Pauli’s theory of an electron with spin, which required a Clebsch flow Lagrangian with non-zero vorticity. Here, we use the recent relativistic flow Lagrangian to represent Dirac’s theory with the addition of a Lorentz invariant Fisher information term as is required by quantum mechanics. Full article

A consistent theory of quantum entanglement requires that constituent single-particle states belong to the same Hilbert space, the coherent eigenstates of a complete set of operators in a given representation, defined with respect to a shared continuous parameterization. Formulating such eigenstates for a single relativistic particle with spin, and applying them to the description of many-body states, presents well-known challenges. In this paper, we review the covariant theory of relativistic spin and entanglement in a framework first proposed by Stueckelberg and developed by Horwitz, Piron, et al. This approach modifies Wigner’s method by introducing an arbitrary timelike unit vector $n^{\mu }$ and then inducing a representation of $SL(2,C)$, based on $p^{\mu }$ rather than on the spacetime momentum. Generalizing this approach, we construct relativistic spin states on an extended phase space $\{(x^{\mu },p^{\mu }),({\zeta }^{\mu },{\pi }^{\mu })\}$, inducing a representation on the momentum ${\pi }^{\mu }$, thus providing a novel dynamical interpretation of the timelike unit vector $n^{\mu }={\pi }^{\mu }/M$. Studying the unitary representations of the Poincaré group on the extended phase space allows us to define basis quantities for quantum states and develop the gauge invariant electromagnetic Hamiltonian in classical and quantum mechanics. We write plane wave solutions for free particles and construct stable singlet states, and relate these to experiments involving temporal interference, analogous to the spatial interference known from double slit experiments. Full article

The study of spinning systems plays a question of interest in several research branches in physics. It allows the understanding of simple classical mechanical systems but also provides us with tools to investigate a wide range of phenomena, from condensed matter physics to gravitation and cosmology. In this contribution, we review some remarkable theoretical aspects involving the description of spinning quantum systems. We explore the nonrelativistic and relativistic domains and their respective applications in fields such as graphene physics and topological defects in gravitation. Full article