Boundary of a boundary principle and geometric structure of field theories

We formulate the boundary of a boundary principle, review its applications in electrodynamics, Yang-Mills theory, and general relativity and translate its basic ideas into geometric language. In each of these three theories the density of the source lets itself be constructed-we discover-out of the curvature associated with the field as a Cartan-like moment of this curvature.     

Derivation of O(3) Electrodynamics from the Irreducible Representations of the Einstein Group

By considering the irreducible representations of the Einstein group (the Lie group of general relativity), Sachs [1] has shown that the electromagnetic field tensor can be developed in terms of a metric q , which is a set of four quaternion-valued components of four-vector. Using this method, it is shown that the electromagnetic field vanishes [1] in flat spacetime, and that electromagnetism in general is a non-Abelian field theory. In this paper the non-Abelian component of the field tensor is developed to show the presence of the B ⁽³⁾ field of the O(3) electrodynamics, and the basic structure of O(3) electrodynamics is shown to be a sub-structure of general relativity as developed by Sachs. The extensive empirical evidence for both theories is summarized.     

Framework for possible unification of quantum and relativity theories

We put forward a framework, inspired by recent axiomatic and operational approaches to generalized quantum theories, wherein we investigate the possibility of unifying quantum and relativity theories. The framework concentrates on a detailed analysis of a general construction of reality that can be used in both quantum and relativity theories. By means of this construction of reality we clarify some well-known conceptual problems that stand in the way of a conceptual unification of quantum and relativity theories on a more profound physical level than the purely mathematical algebraic level on which unification attempts are generally investigated. More specifically we concentrate on the problem of what is physical reality in quantum and relativity theories.     

Dimensions and units in electrodynamics

We sketch the foundations of classical electrodynamics, in particular the transition that took place when Einstein, in 1915, succeeded to formulate general relativity. In 1916 Einstein demonstrated that, with a choice of suitable variables for the electromagnetic field, it is possible to put Maxwells equation into a form that is covariant under general coordinate transformations. This unfolded, by basic contributions of Kottler, Cartan, van Dantzig, Schouten & Dorgelo, Toupin & Truesdell, and Post, to what one may call premetric classical electrodynamics. This framework will be described shortly. An analysis is given of the physical dimensions involved in electrodynamics and subsequently the question of units addressed. It will be pointed out that these results are untouched by the generalization of classical to quantum electrodynamics (QED). We compare critically our results with those of L.B. Okun which he had presented at a recent conference.     

Revised Robertson's test theory of special relativity: Space-time structure and dynamics

The experimental testing of the Lorentz transformations is based on a family of sets of coordinate transformations that do not comply in general with the principle of equivalence of the inertial frames. The Lorentz and Galilean sets of transformations are the only member sets of the family that satisfy this principle. In the neighborhood of regular points of space-time, all members in the family are assumed to comply with local homogeneity of space-time and isotropy of space in at least one free-falling elevator, to be denoted as Robertson'sab initio rest frame [H. P. Robertson,Rev. Mod. Phys. 21, 378 (1949)].Without any further assumptions, it is shown that Robertson's rest frame becomes a preferred frame for all member sets of the Robertson family except for, again, Galilean and Einstein's relativities. If one now assumes the validity of Maxwell-Lorentz electrodynamics in the preferred frame, a different electrodynamics spontaneously emerges for each set of transformations. The flat space-time of relativity retains its relevance, which permits an obvious generalization, in a Robertson context, of Dirac's theory of the electron and Einstein's gravitation. The family of theories thus obtained constitutes a covering theory of relativistic physics.A technique is developed to move back and forth between Einstein's relativity and the different members of the family of theories. It permits great simplifications in the analysis of relativistic experiments with relevant Robertson's subfamilies. It is shown how to adapt the Clifford algebra version of standard physics for use with the covering theory and, in particular, with the covering Dirac theory.Part of this work was done at the Department of Physics, Utah State University, Logan, Utah 84322.     

Energy and momentum from the Palatini formalism

I derive from the Palatini formalism, in which metric and affinity are varied independently, an energy-momentum complex qualitatively different in form from the usual energy-momentum representations of general relativity. A similar procedure can be carried out for electrodynamics, illuminating by analogy the structure of the gravitational Lagrangian. The new energy density vanishes for all static vacuum solutions of the Einstein equations, and the radiated energy from an isolated system in an asymptotically flat space in general diverges. These facts suggest that the formalism could be used to express Mach's principle.     

Mapping nonlinear gravity into General Relativity with nonlinear electrodynamics

We show that families of nonlinear gravity theories formulated in a metric-affine approach and coupled to a nonlinear theory of electrodynamics can be mapped into general relativity (GR) coupled to another nonlinear theory of electrodynamics. This allows to generate solutions of the former from those of the latter using purely algebraic transformations. This correspondence is explicitly illustrated with the Eddington-inspired Born–Infeld theory of gravity, for which we consider a family of nonlinear electrodynamics and show that, under the map, preserve their algebraic structure. For the particular case of Maxwell electrodynamics coupled to Born–Infeld gravity we find, via this correspondence, a Born–Infeld-type nonlinear electrodynamics on the GR side. Solving the spherically symmetric electrovacuum case for the latter, we show how the map provides directly the right solutions for the former. This procedure opens a new door to explore astrophysical and cosmological scenarios in nonlinear gravity theories by exploiting the full power of the analytical and numerical methods developed within the framework of GR.     

Simple Derivation of Minimum Length, Minimum Dipole Moment and Lack of Space–Time Continuity

The principle of maximum power makes it possible to summarize special relativity, quantum theory and general relativity in one fundamental limit principle each. Special relativity contains an upper limit to speed; following Bohr, quantum theory is based on a lower limit to action; recently, a maximum power given by c ⁵/4G was shown to be equivalent to the full field equations of general relativity. Taken together, these three fundamental principles imply a limit value for every physical observable, from acceleration to size. The new, precise limit values differ from the usual Planck values by numerical prefactors of order unity. Among others, minimum length and time intervals appear. The limits imply that elementary particles are not point-like and suggest a lower limit on electric dipole values. The minimum intervals also imply that the non-continuity of space–time is an inevitable result of the unification of quantum theory and relativity, independently of the approach used. PACS numbers: 04.20.Cv; 13.40.Em; 04.60.-m.     

Protational monopoles,non-Riemannian geometry,and quasars

In pursuing analogies between gravitation and electrodynamics, the question occurs as to the possible existence of a gravitational analog of the (hypothetical) magnetic monopole. This entity cannot exist in standard general relativity, but could in a theory which makes use of non-Riemannian geometry. A theory involving such “protational monopoles” is formulated here, and comments are made on the possible relevance of such a theory for the spectral shifts and energy releases in such objects as quasars. But it is also pointed out that the quantization of mass necessitated by protational monopoles casts doubts upon their existence.     

Some physical implications of a new relativistic boundary condition

It is shown that a new boundary condition in general relativity can be interpreted as a condition on the rate of spinning in a model for the gravitational field of an isolated body embedded in Trautman's expanding universe of spinning particles. The new condition is also shown to be independent of the usual O'Brien-Synge conditions in the sense that it is not an identity following from them.The validity of the delta function technique employed in deriving the above new boundary condition is investigated in a non-relativistic framework. The technique is shown to yield familiar non-relativistic results as well as a new one which involves rate-of-strain and pressure-gradient in the case of an adiabatic flow such as in a compressible fluid with an isentropic equation.On leave of absence from the Department of Mathematics, University of Ghana, Legon, Accra, Ghana.     

Derivation of O(3) Electrodynamics from the Einstein–Sachs Theory of General Relativity

General relativity is reduced to O(3) electrodynamics by consideration of the irreducible representations of the Einstein group and through a particular choice of basis. The photon is shown always to possess a scalar curvature R, and so the origin of quantization is found in general relativity.     

Reference systems and gravitation

It is shown how the formalism of the tetrad theory of gravitation used by Treder (1967a, b, 1970) follows from the more general fibre bundle formalism. This is of interest in the study of the relations between tetrad theories and the general theory of relativity. In particular, the breaking of the principle of general relativity and the interpretation of tetrad fields as reference systems are considered in greater detail.     

A unification scheme for the Einstein and Maxwell theories

A unification scheme for the Einstein and Maxwell theories is developed within a Riemann-Cartan geometry. The electromagnetic field is introduced at the level of the connection and it is, in fact, coded in the torsion. Within our framework, the unification of the massless spin-one and spin-two fields requires the inclusion of a massless spin-zero field, whose introduction may give rise to a non-constant gravitational coupling. However, for the case of dust-filled homogeneous and isotropic universe the result is essentially the same as the one supplied by general relativity.     

相对性原理及其对自然界定律的协变性要求--机械能守恒定律协变性疑难的解答

阐明狭义相对性原理的准确含义,批出它并不要求自然界每条定律都单独协变,但要求每条定律至少属于一个协变集合,给出最小协变集的求法。表明机械能守恒定律满足狭义相对性原理及其对自然界定律的协变性要求,还指出一切社会科学定律也都满足狭义相对性原理。     

Universal boundary reflection amplitudes

For all affine Toda field theories we propose a new type of generic boundary bootstrap equations, which can be viewed as a very specific combination of elementary boundary bootstrap equations. These equations allow to construct general solutions for the boundary reflection amplitudes, which are valid for theories related to all simple Lie algebras, that is simply laced and non-simply laced. We provide a detailed study of these solutions for concrete Lie algebras in various representations. The boundary bootstrap equations relating different types of exited boundary states are not automatically solved by our expressions.     

Quantum Gauge General Relativity

Based on gauge principle, a new model on quantum gravity is proposed in the frame work of quantum gauge theory of gravity. The model has local gravitational gauge symmetry, and the field equation of the gravitational gauge field is just the famous Einstein‘s field equation. Because of this reason, this model is called quantum gauge general relativity, which is the consistent unification of quantum theory and general relativity. The model proposed in this paper is a perturbatively renormalizable quantum gravity, which is one of the most important advantage of the quantum gauge general relativity proposed in this paper. Another important advantage of the quantum gauge general relativity is that it can explain both classical tests of gravity and quantum effects of gravitational interactions, such as gravitational phase effects found in COW experiments and gravitational shielding effects found in Podkletnov experiments.     

Gyro precession and mach's principle

The precession of a gyroscope is calculated in a nonrelativistic theory due to Harbour which satisfies Mach's principle. It is shown that the theory predicts both the geodetic and motional precession of general relativity to within factors of order 1. The significance of the gyro experiment is discussed from the point of view of metric theories of gravity and this is contrasted with its significance from the point of view of Mach's principle.     

An elementary notion of gauge equivalence

An elementary notion of gauge equivalence is introduced that does not require any Lagrangian or Hamiltonian apparatus. It is shown that in the special case of theories, such as general relativity, whose symmetries can be identified with spacetime diffeomorphisms this elementary notion has many of the same features as the usual notion. In particular, it performs well in the presence of asymptotic boundary conditions.