Principle Of Covariance Research Articles

Generalized lift force for complex fluid

Abstract To explain the phenomena in nature, physics are still using many models. In most cases, natural phenomena are simplified assuming that they can be mathematically reduced to relatively simple equations involving continuous and differentiable functions. The reality is much more complex, and these simplifications cannot explain all the aspects of an observation. The paper presents a generalization of the movement of a solid particle in a complex fluid, considering that the fluid particles dynamics occurs on continuous, but non-differentiable curves, a situation much closer to reality. Movement analysis has taken into account the consequences of non-differentiability and of scale covariance principle for continuous but non-differentiable curves. The equation of motion was derived showing that the behavior of the fluid is of viscoelastic or of hysteretic type. The analysis of the lift force was made for both rotational and irrotational movements. The numerical simulation shows that the simultaneous presence of solitons and anti-solitons packages from the force fields specify the transition from a differentiable flow (along the same stream line) to a non-differentiable flow (the jump from one stream line to another). We demonstrated that, in any type of motion (rotational or irrotational), the differentiable part of the velocity field generates circulation, while the non-differentiable part of the same field induces the lift force.

On the Meaning of the Principle of General Covariance

We present a definite formulation of the Principle of General Covariance (GCP) as a Principle of General Relativity with physical content and thus susceptible of verification or contradiction. To that end it is useful to introduce a kind of coordinates, that we call quasi-Minkowskian coordinates (QMC), as an empirical extension of the Minkowskian coordinates employed by the inertial observers in flat space-time to general observers in the curved situations in presence of gravitation. The QMC are operationally defined by some of the operational protocols through which the inertial observers determine their Minkowskian coordinates and may be mathematically characterized in a neighbourhood of the world-line of the corresponding observer. It is taken care of the fact that the set of all the operational protocols which are equivalent to measure a quantity in flat space-time split into inequivalent subsets of operational prescriptions under the presence of a gravitational field or when the observer is not inertial. We deal with the Hole Argument by resorting to the tool of the QMC and show how it is the metric field that supplies the physical meaning of coordinates and individuates point-events in regions of space-time where no other fields exist. Because of that the GCP has also value as a guiding principle supporting Einstein’s appreciation of its heuristic worth in his reply to Kretschmann in 1918.

Batalin-Vilkovisky Formalism in the Functional Approach to Classical Field Theory

We develop the Batalin-Vilkovisky formalism for classical field theory on generic globally hyperbolic spacetimes. A crucial aspect of our treatment is the incorporation of the principle of local covariance which amounts to formulate the theory without reference to a distinguished spacetime. In particular, this allows a homological construction of the Poisson algebra of observables in classical gravity. Our methods heavily rely on the differential geometry of configuration spaces of classical fields.

Covariant description of transformation optics in nonlinear media

The technique of transformation optics (TO) is an elegant method for the design of electromagnetic media with tailored optical properties. In this paper, we focus on the formal structure of TO theory. By using a complete covariant formalism, we present a general transformation law that holds for arbitrary materials including bianisotropic, magneto-optical, nonlinear and moving media. Due to the principle of general covariance, the formalism is applicable to arbitrary space-time coordinate transformations and automatically accounts for magneto-electric coupling terms. The formalism is demonstrated for the calculation of the second harmonic wave generation in a twisted TO concentrator.

Spatially covariant theories of a transverse, traceless graviton: Formalism

General relativity is a generally covariant, locally Lorentz covariant theory of two transverse, traceless graviton degrees of freedom. According to a theorem of Hojman, Kucha\ifmmode \check{r}\else \v{r}\fi{}, and Teitelboim, modifications of general relativity must either introduce new degrees of freedom or violate the principle of local Lorentz covariance. In this paper, we explore modifications of general relativity that retain the same graviton degrees of freedom, and therefore explicitly break Lorentz covariance. Motivated by cosmology, the modifications of interest maintain explicit spatial covariance. In spatially covariant theories of the graviton, the physical Hamiltonian density obeys an analogue of the renormalization group equation which encodes invariance under flow through the space of conformally equivalent spatial metrics. This paper is dedicated to setting up the formalism of our approach and applying it to a realistic class of theories. Forthcoming work will apply the formalism more generally.

The Quaternion Structure of Space-Time and Arrow of Time

In fundamental theories of physics, the dynamical equations all have time inversion invariance. Except for the evolution of some simple system which has realistic inverse processes, but for a slightly more complicated system, the evolution processes are irreversible. This is the problem of arrow of time, which is always warmly debated. In different point of view, we find there may have some conceptual misunderstanding in the controversy: 1) The realization of an inverse process does not mean the time of the system goes backward. 2) The principles of relativity and covariance are the constraints to physical laws, but not constraints to specific solutions. The equations must be covariant, but the solutions are not definitely symmetric. 3) Time is a global property of the universe, which is a measurement of the evolution process of the universe. The internal time of a matter system reflecting its internal evolution speed also takes this cosmic time as a unified background and standard of measurement. 4) The universe has a unified cosmic time T and a cosmic space related to this cosmic time. They are objective and absolute. 5) The eigensolution of a spinor is a critical state losing time concept, which responses the interaction of environment with some uncertainty, then the evolution process of the world is not uniquely determined. 6) The non-uniqueness of the evolution process means that the inverse process is absent. So for a world including spinors, the evolution is essentially irreversible. In this paper, according to the widely accepted principles and direct calculations of transformation, we reveal the misunderstandings in the usual controversy, and then give more natural and reasonable explanations for structure of space-time and arrow of time.

Super-Poincarè algebras, space-times and supergravities (I)

A new formulation of theories of supergravity as theories satisfying a generalized Principle of General Covariance is given. It is a generalization of the superspace formulation of simple 4D-supergravity of Wess and Zumino and it is designed to obtain geometric descriptions for the supergravities that correspond to the super Poincare' algebras of Alekseevsky and Cortes' classification.

Unification of General Relativity with Quantum Field Theory

In the frame of quantum field theory, instead of using the action principle, we deduce the Einstein equation from purely the general covariant principle and the homogeneity of spacetime. The Einstein equation is shown to be the gauge equation to guarantee the local symmetry of spacetime translation. Gravity is an apparent force due to the curvature of spacetime resulted from the conservation of energy-momentum. In the action of quantum field theory, only electroweak-strong interactions should be considered with the curved spacetime metric determined by the Einstein equation.

Local Causal Structures, Hadamard States and the Principle of Local Covariance in Quantum Field Theory

In the framework of the algebraic formulation, we discuss and analyse some new features of the local structure of a real scalar quantum field theory in a strongly causal spacetime. In particular we use the properties of the exponential map to set up a local version of a bulk-to-boundary correspondence. The bulk is a suitable subset of a geodesic neighbourhood of any but fixed point p of the underlying background, while the boundary is a part of the future light cone having p as its own tip. In this regime, we provide a novel notion for the extended *-algebra of Wick polynomials on the said cone and, on the one hand, we prove that it contains the information of the bulk counterpart via an injective *-homomorphism while, on the other hand, we associate to it a distinguished state whose pull-back in the bulk is of Hadamard form. The main advantage of this point of view arises if one uses the universal properties of the exponential map and of the light cone in order to show that, for any two given backgrounds M and M' and for any two subsets of geodesic neighbourhoods of two arbitrary points, it is possible to engineer the above procedure such that the boundary extended algebras are related via a restriction homomorphism. This allows for the pull-back of boundary states in both spacetimes and, thus, to set up a machinery which permits the comparison of expectation values of local field observables in M and M'.

Structure of Lanczos-Lovelock Lagrangians in critical dimensions

The Lanczos-Lovelock models of gravity constitute the most general theories of gravity in D dimensions which satisfy (a) the principle of of equivalence, (b) the principle of general co-variance, and (c) have field equations involving derivatives of the metric tensor only up to second order. The mth order Lanczos-Lovelock Lagrangian is a polynomial of degree m in the curvature tensor. The field equations resulting from it become trivial in the critical dimension $D = 2m$ and the action itself can be written as the integral of an exterior derivative of an expression involving the vierbeins, in the differential form language. While these results are well known, there is some controversy in the literature as to whether the Lanczos-Lovelock Lagrangian itself can be expressed as a total divergence of quantities built only from the metric and its derivatives (without using the vierbeins) in $D = 2m$. We settle this issue by showing that this is indeed possible and provide an algorithm for its construction. In particular, we demonstrate that, in two dimensions, $R \sqrt{-g} = \partial_j R^j$ for a doublet of functions $R^j = (R^0,R^1)$ which depends only on the metric and its first derivatives. We explicitly construct families of such R^j -s in two dimensions. We also address related questions regarding the Gauss-Bonnet Lagrangian in $D = 4$. Finally, we demonstrate the relation between the Chern-Simons form and the mth order Lanczos-Lovelock Lagrangian.

MAKING NONLOCAL REALITY COMPATIBLE WITH RELATIVITY

It is often argued that hypothetic nonlocal reality responsible for nonlocal quantum correlations between entangled particles cannot be consistent with relativity. I review the most frequent arguments of that sort, explain how they can all be circumvented, and present an explicit Bohmian model of nonlocal reality (compatible with quantum phenomena) that fully obeys the principle of relativistic covariance and does not involve a preferred Lorentz frame.

Ternary symmetries and the Lorentz group

We show that the Lorentz and the $SU(3)$ groups can be derived from the covariance principle conserving a $Z_3$-graded three-form on a $Z_3$-graded cubic algebra representing quarks endowed with non-standard commutation laws. The ternary commutation rela

On the question of gauge invariance in physics and Einstein’s covariance principle

On the question of gauge invariance in physics and Einstein’s covariance principle

Lorentz and SU(3) Groups Derived from Cubic Quark Algebra

We show how Lorentz and SU(3) groups can be derived from the covariance principle conserving a Z3-graded three-form on a Z3-graded cubic algebra representing quarks endowed with non-standard commutation laws. This construction suggests that the geometry of space-time can be considered as a manifestation of symmetries of fundamental matter fields.

ENTROPY DENSITY OF SPACE–TIME AND GRAVITY: A CONCEPTUAL SYNTHESIS

I show that combining the principle of equivalence and the principle of general covariance with the known properties of local Rindler horizons, perceived by accelerated observers, leads to the following inescapable conclusion: The field equations describing gravity in any diffeomorphism-invariant theory must have a thermodynamic interpretation. This synthesis of quantum theory, thermodynamics and gravity shows that the gravitational dynamics can be interpreted completely in terms of entropy balance between matter and space–time. This idea has far-reaching implications for the microstructure of space–time and quantum gravity.

Non-relativistic holography and singular black hole

We provide a framework for non-relativistic holography so that a covariant action principle ensuring the Galilean symmetry for dual conformal field theory is given. This framework is based on the Bargmann lift of the Newton–Cartan gravity to the one-dimensional higher Einstein gravity, or reversely, the null-like Kaluza–Klein reduction. We reproduce the previous zero temperature results, and our framework provides a natural explanation about why the holography is co-dimension 2. We then construct the black hole solution dual to the thermal CFT, and find the horizon is curvature singular. However, we are able to derive the sensible thermodynamics for the dual non-relativistic CFT with correct thermodynamical relations. Besides, our construction admits a null Killing vector in the bulk such that the Galilean symmetry is preserved under the holographic RG flow. Finally, we evaluate the viscosity and find it zero if we neglect the back reaction of the singular horizon, otherwise, it could be non-zero.

Spin and rotation

The theoretical aspects of spin-rotation coupling are presented. The approach is based on the general covariance principle. It is shown that the gyrogravitational ratio of the bare spin-1/2 and the spin-1 particles is equal to unity. That is why spin couples with rotation as an ordinary angular momentum. This result is the rigorous substantiation of the cranking model in which spin-rotation coupling is introduced by means of a unitary rotation. To observe the phenomenon, the experiment with hydrogen-like ions in a storage ring is suggested. The degenerated magnetic sub-states of such ion are split if it circulates in a storage ring along a helical trajectory. It is found that the splitting of the 12S1/2, F = 1/2 hyperfine state of the 140Pr58+ and 142Pm60+ ions in the storage ring ESR in Darmstadt is about 4.5 MHz. We argue that such splitting can be experimentally determined by means of the laser-induced quantum beat spectroscopy or the ionic interferometry.

Nonlinear closure relations theory for transport processes in nonequilibrium systems

A decade ago, a macroscopic theory for closure relations has been proposed for systems out of Onsager's region. This theory is referred to as the thermodynamic field theory (TFT). The aim of this work was to determine the nonlinear flux-force relations that respect the thermodynamic theorems for systems far from equilibrium. We propose a formulation of the TFT where one of the basic restrictions, namely, the closed-form solution for the skew-symmetric piece of the transport coefficients, has been removed. In addition, the general covariance principle is replaced by the De Donder-Prigogine thermodynamic covariance principle (TCP). The introduction of TCP requires the application of an appropriate mathematical formalism, which is referred to as the entropy-covariant formalism. By geometrical arguments, we prove the validity of the Glansdorff-Prigogine universal criterion of evolution. A new set of closure equations determining the nonlinear corrections to the linear ("Onsager") transport coefficients is also derived. The geometry of the thermodynamic space is non-Riemannian. However, it tends to be Riemannian for high values of the entropy production. In this limit, we recover the transport equations found by the old theory. Applications of our approach to transport in magnetically confined plasmas, materials submitted to temperature, and electric potential gradients or to unimolecular triangular chemical reactions can be found at references cited herein. Transport processes in tokamak plasmas are of particular interest. In this case, even in the absence of turbulence, the state of the plasma remains close to (but, it is not in) a state of local equilibrium. This prevents the transport relations from being linear.

On the nonlinear continuum mechanics of space and the notion of luminiferous medium

We prove that, when linearized, the governing equations of an incompressible elastic continuum yield Maxwell’s equations as corollaries. Through judicious distinction between the referential and local descriptions, the principle of material invariance is established and shown to be a true covariance principle, unlike the Lorentz covariance, which is valid only for non-deforming frames in rectilinear relative motion. Thus, this paper establishes that electrodynamics can be fully explained if one assumes that it is the manifestation of the internal forces of an underlying elastic material which we term the metacontinuum. The new frame-indifferent formulation of electrodynamics is shown to incorporate the Lorentz force as an integral part of Faraday’s law, rather than as an additional empirical variable. Respectively, if the upper-convected derivative is added in Maxwell’s displacement current it can explain Biot–Savart’s and Oersted–Ampere’s laws. An immediate corollary of the material invariance is the Galilean invariance of the model. The possible detection of the absolute continuum is also discussed. First, the famous experiment of Ives and Stilwell is reexamined with a modified Bohr–Rydberg formula for the emitted frequencies from a moving atom, and it is shown that the results are fully compatible with the presence of an absolute medium. Second, a new interferometry experiment is proposed in which the first-order Doppler effect can be measured, and thus the presence of a medium at rest can be unequivocally established.

Dilaton gravity, Poisson sigma models and loop quantum gravity

Spherically symmetric gravity in Ashtekar variables coupled to Yang–Mills theory in two dimensions and its relation to dilaton gravity and Poisson sigma models are discussed. After introducing its loop quantization, quantum corrections for inverse triad components are shown to provide a consistent deformation without anomalies. The relation to Poisson sigma models provides a covariant action principle of the quantum-corrected theory with effective couplings. Results are also used to provide loop quantizations of spherically symmetric models in arbitrary D spacetime dimensions.