Search Results (23)

We develop an action principle for producing a single-fluid two-constituent system with dissipation in general relativity. The two constituents in the model are particles and entropy. The particle flux creation rate is taken to be zero, while the entropy creation rate is non-zero. Building on previous work, it is demonstrated that a new term (the proper time derivative of the matter space “metric”) is required in the Lagrangian in order to produce terms typically associated with bulk and shear viscosity. Equations of motion, entropy creation rate, and energy–momentum–stress tensor are derived. Using an Onsager approach of identifying thermodynamic “forces” and “fluxes”, a model is produced which delivers the same entropy creation rate as the standard, relativistic Navier–Stokes equations. This result is then contrasted with a model generated in the spirit of the action principle, which takes as its starting point a specific Lagrangian and then produces the equations of motion, entropy creation rate, and energy–momentum–stress tensor. Unlike the equations derived from Onsager reasoning, where the analogs of the bulk and shear viscosity coefficients are prescribed “externally”, we find that the forms of the coefficients in the second example are a direct result of the specified Lagrangian. Furthermore, the coefficients are shown to satisfy evolution equations along the fluid worldline, also a product of the specific Lagrangian. Full article

We construct a fractional Laplacian spinning particle model in an external electromagnetic field that generalizes a standard relativistic spinning particle model without anti-commuting spin variables. The one-dimensional fractional Laplacian in world-line variable $\lambda$ governs the kinetic energy that is non-local in $\lambda$. The interaction between the particle’s charge and the electromagnetic four-potential is non-local in $\lambda$, while the interaction between the particle’s spin tensor and the electromagnetic field is standard. By applying the variational principle, we obtain the equations of motion for particle coordinates. We solve analytically the equations of motion in two particular cases: the constant electric and magnetic field. For more complex field configurations, the equations are, in general, non-local and non-linear. By making the assumption of a much weaker interaction term between the charge and four-potential compared with the interaction between spinning degrees of freedom and the electromagnetic field, we obtain approximate analytical solutions in the case of a quadratic electromagnetic potential. Full article

We briefly present our version of noncommutative analysis over matrix algebras, the algebra of biquaternions ($\mathbb{B}$) in particular. We demonstrate that any $\mathbb{B}$-differentiable function gives rise to a null shear-free congruence (NSFC) on the $\mathbb{B}$-vector space $\mathbb{C}\mathbf{M}$ and on its Minkowski subspace $\mathbf{M}$. Making use of the Kerr–Penrose correspondence between NSFC and twistor functions, we obtain the general solution to the equations of $\mathbb{B}$-differentiability and demonstrate that the source of an NSFC is, generically, a world sheet of a string in $\mathbb{C}\mathbf{M}$. Any singular point, caustic of an NSFC, is located on the complex null cone of a point on the generating string. Further we describe symmetries and associated gauge and spinor fields, with two electromagnetic types among them. A number of familiar and novel examples of NSFC and their singular loci are described. Finally, we describe a conservative algebraic dynamics of a set of identical particles on the “Unique Worldline” and discuss the connections of the theory with the Feynman–Wheeler concept of “One-Electron Universe”. Full article

The field of quantum gravity struggles with several problems related to time, quantum measurement, nonlocality, and realism. To address these issues, this study develops a 4+1 formalism featuring a flat 4D spacetime evolving with a second form of time, $\tau$, worldlines that locally conserve momentum, and a hypersurface representing the present. As a function of $\tau$, worldlines can spatially readjust and influences can travel backward or forward in the time dimension along these worldlines, offering a physical mechanism for retrocausality. Three theoretical models are presented, elucidating how nonlocality in an EPR experiment, the arrival time problem, and superposition in a Mach–Zehnder interferometer can be understood within this 4+1 framework. These results demonstrate that essential quantum phenomena can be reproduced in the 4+1 formalism while upholding the principles of realism, locality, and determinism at a fundamental level. Additionally, there is no measurement or collapse problem, and a natural explanation for the quantum-to-classical transition is obtained. Furthermore, observations of a 4D block universe and of the flow of time can be simultaneously understood. With these properties, the presented 4+1 formalism lays an interesting foundation for a quantum gravity theory based on intuitive principles and compatible with our observation of time. Full article

We develop a new formalism for constructing probabilities associated with the causal ordering of events in quantum theory, where an event is defined as the emergence of a measurement record on a detector. We start with constructing probabilities for the causal ordering events in classical physics, where events are defined in terms of worldline coincidences. Then, we show how these notions generalize to quantum systems, where there exists no fundamental notion of trajectory. The probabilities constructed here are experimentally accessible, at least in principle. Our analysis here clarifies that the existence of quantum orderings of events do not require quantum gravity effects: it is a consequence of the quantum dynamics of matter, and it appears in the presence of a fixed background spacetime. Full article

In 1948, Schwinger developed a local Lorentz-covariant formulation of relativistic quantum electrodynamics in space-time which is fundamentally inconsistent with any delocalized interpretation of quantum mechanics. An interpretation compatible with Schwinger’s theory is presented, which reproduces all of the standard empirical predictions of conventional delocalized quantum theory in configuration space. This is an explicit, unambiguous, and Lorentz-covariant “local hidden variable theory” in space-time, whose existence proves definitively that such theories are possible. This does not conflict with Bell’s theorem because it is a local many-worlds theory. Each physical system is characterized by a wave-field, which is a set of indexed piece-wise single-particle wavefunctions in space-time, each with its own coefficient, along with a memory which contains the separate local Hilbert-space quantum state at each event in space-time. Each single-particle wavefunction of a fundamental system describes the motion of a portion of a conserved fluid in space-time, with the fluid decomposing into many classical point particles, each following a world-line and recording a local memory. Local interactions between two systems take the form of local boundary conditions between the differently indexed pieces of those systems’ wave-fields, with new indexes encoding each orthogonal outcome of the interaction. The general machinery is introduced, including the local mechanisms for entanglement and interference. The experience of collapse, Born rule probability, and environmental decoherence are discussed, and a number of illustrative examples are given. Full article

We present a moving mirror analog of the electron, whose worldline possesses asymptotic constant velocity with corresponding Bogoliubov $\beta$ coefficients that are consistent with finite total emitted energy. Furthermore, the quantum analog model is in agreement with the total energy obtained by integrating the classical Larmor power. Full article

Unifying quantum theory with general relativity is challenging because of several problems related to time and to collapse in quantum measurements. In the double-slit experiment, the questions are how the momentum of the photon is transferred to a specific location on the screen and how the double slit recoils accordingly. This work investigates if these problems can be solved by adding a second time $\tau$, which acts as an external evolution parameter, to standard four-dimensional spacetime. Within the resulting 4+1 formalism, a model for the single-photon double-slit experiment is developed. On the one hand, each spacetime associated to a value of $\tau$ relies on classical worldlines that obey local momentum conservation. On the other hand, these worldlines are allowed to readjust as a function of $\tau$ such that the quantum phenomenon of double-slit interference can be reproduced. The model explains how determinate outcomes are produced and how momentum transfer occurs in a way that satisfies the principles of relativity and local momentum conservation. As a result, the measurement problem and the problem of time evaporate, and an explanation for our experience of the present emerges. Since the presented model succeeds in explaining a key quantum phenomenon with essentially classical worldlines, this is relevant for the field of quantum gravity. Full article

We all have in mind Einstein’s famous thought experiment in the elevator where we observe the free fall of a body, and then the trajectory of a light ray. Here, in addition to the qualitative aspect, the exact calculations are carried out, and the worldlines equations are given. A uniformly accelerated reference frame in rectilinear translation is considered, and it is shown that the trajectories of the particles are semi-ellipses with the center on the event horizon. The frame of reference is non-inertial, the spacetime is flat, and the computations are performed within the framework of special relativity. Some experimental consequences are discussed, especially the experiment with the accelerated Michelson–Morley interferometer is solved, and an experiment, where a new relativistic paradox appears—a particle of matter seems to go faster than light—is described. The differences, compared to the classical case, are important at a large scale and close to the horizon, but they are small in the lift where the interest is above all theoretical. The concepts of metric, coordinated velocity and horizon are discussed, and an analogy with the black hole is made. Full article

Attempts to facilitate and streamline systems architecting have resulted in a great number of reusable principles, practices, mechanisms, frameworks, and tools. Such a practice is the use of architectural viewpoints and views. However, as systems change, these practices should also evolve. The increasing scale and complexity of systems resulting from an ever-growing pool of human needs and breakthroughs may lead, in some cases, to an increased gap between the abstraction activities attempting to capture the whole of a system, and the instantiation activities that produce concrete and detailed descriptions of a system’s architecture. To address this issue, this article introduces a new notion, that of architectural glimpse statements, fundamental questions acting as the building blocks for architectural views and products. This notion can help architects ask the right questions in the right manner to create fundamental statements, the elaboration on which can lead directly to concrete architectural products. Working on top of standardized and common approaches, the article introduces a language for the creation of architectural glimpse statements using the 5W1H maxim. Based on this language, a tool and guidelines are also provided to facilitate the usage of glimpses. Finally, the overall methodology is demonstrated in two case studies. Full article

The recent Planck Legacy 2018 release confirmed the existence of an enhanced lensing amplitude in the cosmic microwave background (CMB) power spectra. Notably, this amplitude is higher than that estimated by the lambda cold dark matter model, which prefers a positively curved early Universe with a confidence level greater than 99%. In this study, the pre-existing curvature is incorporated to extend the field equations where the space-time worldlines are utilised to model the evolution of the Universe with reference to the scale factor of the early Universe and its radius of curvature upon the emission of the CMB. The worldlines reveal both positive and negative solutions, implying that matter and antimatter of early Universe plasma evolved in opposite directions as distinct Universe sides during a first decelerating phase. The worldlines then indicate a second accelerated phase in reverse directions, whereby both sides free-fall towards each other under gravitational acceleration. The simulation of the predicted conformal curvature evolution demonstrates the fast orbital speed of the outer stars owing to external fields exerted on galaxies as they travel through conformally curved space-time. Finally, the worldlines predict an eventual time-reversal phase comprising rapid spatial contraction that culminates in a Big Crunch, signalling a cyclic Universe. These findings reveal that the early Universe’s plasma could be separated and evolved into distinct sides of the Universe that collectively and geometrically inducing its evolution, physically explaining the effects attributed to dark energy and dark matter. Full article

The vorticity of world-lines of observers associated with the rotation of a massive body was reported by Lense and Thirring more than a century ago. In their example, the frame-dragging effect induced by the vorticity is directly (explicitly) related to the rotation of the source. However, in many other cases, it is not so, and the origin of vorticity remains obscure and difficult to identify. Accordingly, in order to unravel this issue, and looking for the ultimate origin of vorticity associated to frame-dragging, we analyze in this manuscript very different scenarios where the frame-dragging effect is present. Specifically, we consider general vacuum stationary spacetimes, general electro-vacuum spacetimes, radiating electro-vacuum spacetimes, and Bondi–Sachs radiating spacetimes. We identify the physical quantities present in all these cases, which determine the vorticity and may legitimately be considered as responsible for the frame-dragging. Doing so, we provide a comprehensive, physical picture of frame-dragging. Some observational consequences of our results are discussed. Full article

We propose a field theory for the local metric in Stueckelberg–Horwitz–Piron (SHP) general relativity, a framework in which the evolution of classical four-dimensional (4D) worldlines $x^{\mu }\left(\tau \right)$ ($\mu =0,1,2,3$) is parameterized by an external time $\tau$. Combining insights from SHP electrodynamics and the ADM formalism in general relativity, we generalize the notion of a 4D spacetime $\mathcal{M}$ to a formal manifold ${\mathcal{M}}_5=\mathcal{M}\times R$, representing an admixture of geometry (the diffeomorphism invariance of $\mathcal{M}$) and dynamics (the system evolution of $\mathcal{M}\left(\tau \right)$ with the monotonic advance of $\tau \in R$). Strategically breaking the formal 5D symmetry of a metric $g_{\alpha \beta }(x,\tau )$ ($\alpha ,\beta =0,1,2,3,5$) posed on ${\mathcal{M}}_5$, we obtain ten unconstrained Einstein equations for the $\tau$-evolution of the 4D metric ${\gamma }_{\mu \nu }(x,\tau )$ and five constraints that are to be satisfied by the initial conditions. The resulting theory differs from five-dimensional (5D) gravitation, much as SHP U(1) gauge theory differs from 5D electrodynamics. Full article

Private and permissioned blockchains are conceptualized and mostly assembled for fulfilling corporations’ demands and needs in the context of their own premises. This paper presents a complete and sophisticated end-to-end permissioned blockchain application for governance and management of musical rights endorsed by smart contract development. In a music industry use case, this disclosed solution monitors and regulates conflicting musical rights of diverse entities under a popular permissioned distributed ledger technology network. The proposed implementation couples various and distinct business domains across the music industry organizations and non-profit blockchain associations. Full article

We discuss a covariant relativistic Boltzmann equation which describes the evolution of a system of particles in spacetime evolving with a universal invariant parameter $\tau$ . The observed time t of Einstein and Maxwell, in the presence of interaction, is not necessarily a monotonic function of $\tau$ . If $t\left(\tau \right)$ increases with $\tau$ , the worldline may be associated with a normal particle, but if it is decreasing in $\tau$ , it is observed in the laboratory as an antiparticle. This paper discusses the implications for entropy evolution in this relativistic framework. It is shown that if an ensemble of particles and antiparticles, converge in a region of pair annihilation, the entropy of the antiparticle beam may decreaase in time. Full article