Showing papers on "Four-force published in 2002"

Lorentz invariance with an invariant energy scale.

Abstract: We propose a modification of special relativity in which a physical energy, which may be the Planck energy, joins the speed of light as an invariant, in spite of a complete relativity of inertial frames and agreement with Einstein's theory at low energies. This is accomplished by a nonlinear modification of the action of the Lorentz group on momentum space, generated by adding a dilatation to each boost in such a way that the Planck energy remains invariant. The associated algebra has unmodified structure constants. We also discuss the resulting modifications of field theory and suggest a modification of the equivalence principle which determines how the new theory is embedded in general relativity.

Gravity: An Introduction to Einstein's General Relativity

Abstract: Einstein's theory of general relativity is a cornerstone of modern physics. It also touches upon a wealth of topics that students find fascinating – black holes, warped spacetime, gravitational waves, and cosmology. Now reissued by Cambridge University Press, this ground-breaking text helped to bring general relativity into the undergraduate curriculum, making it accessible to virtually all physics majors. One of the pioneers of the 'physics-first' approach to the subject, renowned relativist James B. Hartle, recognized that there is typically not enough time in a short introductory course for the traditional, mathematics-first, approach. In this text, he provides a fluent and accessible physics-first introduction to general relativity that begins with the essential physical applications and uses a minimum of new mathematics. This market-leading text is ideal for a one-semester course for undergraduates, with only introductory mechanics as a prerequisite.

Doubly Special Relativity

Abstract: I give a short non-technical review of the results obtained in recent work on "Doubly Special Relativity", the relativistic theories in which the rotation/boost transformations between inertial observers are characterized by two observer-independent scales (the familiar velocity scale, $c$, and a new observer-independent length/momentum scale, naturally identified with the Planck length/momentum). I emphasize the aspects relevant for the search of a solution to the cosmic-ray paradox.

Quantum entropy and special relativity.

Abstract: We consider a single free spin- $\frac{1}{2}$ particle. The reduced density matrix for its spin is not covariant under Lorentz transformations. The spin entropy is not a relativistic scalar and has no invariant meaning.

GPS observables in general relativity

Abstract: I present a complete set of gauge invariant observables, in the context of general relativity coupled with a minimal amount of realistic matter (four particles). These observables have a straightforward and realistic physical interpretation. In fact, the technology to measure them is realized by the Global Positioning System: they are defined by the physical reference system determined by GPS readings. The components of the metric tensor in this physical reference system are gauge invariant quantities and, remarkably, their evolution equations are local.

Modal Interpretations and Relativity

Abstract: A proof is given, at a greater level of generality than previous “no-go” theorems, of the impossibility of formulating a modal interpretation that exhibits “serious” Lorentz invariance at the fundamental level. Particular attention is given to modal interpretations of the type proposed by Bub.

Regge Calculus: A Unique Tool for Numerical Relativity

Abstract: The application of Regge calculus, a lattice formulation of general relativity, is reviewed in the context of numerical relativity. Particular emphasis is placed on problems of current computational interest, and the strengths and weaknesses of the lattice approach are highlighted. Several new and illustrative applications are presented, including initial data for the head on collision of two black holes, and the time evolution of vacuum axisymmetric Brill waves.

Interacting vector fields in relativity without relativity

Abstract: Barbour, Foster and O Murchadha have recently developed a new framework, called here the 3-space approach, for the formulation of classical bosonic dynamics Neither time nor a locally Minkowskian structure of spacetime are presupposed Both arise as emergent features of the world from geodesic-type dynamics on a space of three-dimensional metric–matter configurations In fact gravity, the universal light-cone and Abelian gauge theory minimally coupled to gravity all arise naturally through a single common mechanism It yields relativity—and more—without presupposing relativity This paper completes the recovery of the presently known bosonic sector within the 3-space approach We show, for a rather general ansatz, that 3-vector fields can interact among themselves only as Yang–Mills fields minimally coupled to gravity

Illustrating stability properties of numerical relativity in electrodynamics

Abstract: We show that a reformulation of the Arnowitt-Deser-Misner equations in general relativity, which has dramatically improved the stability properties of numerical implementations, has a direct analogue in classical electrodynamics. We numerically integrate both the original and the revised versions of Maxwell's equations, and show that their distinct numerical behavior reflects the properties found in linearized general relativity. Our results shed further light on the stability properties of general relativity, illustrate them in a very transparent context, and may provide a useful framework for further improvement of numerical schemes.

The Fermat principle in general relativity and applications

Abstract: In this paper we use a general version of Fermat’s principle for light rays in general relativity and a curve shortening method to write the Morse relations for light rays joining an event with a smooth timelike curve in a Lorentzian manifold with boundary The Morse relations are obtained under the most general assumptions and one can apply them to have a mathematical description of the gravitational lens effect in a very general context Moreover, Morse relations can be used to check if existing models are corrected

Charged Static Fluid Spheres in General Relativity

Abstract: The work is concerned with the charged analogue of Bayin's paper (1978) related to Tolman's type astrophysically interesting aspects of stellar structure.

Numerical evolution of axisymmetric, isolated systems in general relativity

Abstract: We describe in this article a new code for evolving axisymmetric isolated systems in general relativity. Such systems are described by asymptotically flat space-times which have the property that they admit a conformal extension. We are working directly in the extended ``conformal'' manifold and solve numerically Friedrich's conformal field equations, which state that Einstein's equations hold in the physical space-time. Because of the compactness of the conformal space-time the entire space-time can be calculated on a finite numerical grid. We describe in detail the numerical scheme, especially the treatment of the axisymmetry and the boundary.

Operational indistinguishabilty of doubly special relativities from special relativity

Abstract: We argue that existing doubly special relativities may not be operationally distinguishable from the special relativity. In the process we point out that some of the phenomenologically motivated modifications of dispersion relations, and arrived conclusions, must be reconsidered. Finally, we reflect on the possible conceptual issues that arise in quest for a theory of spacetime with two invariant scales.

Stability and Instability of the Reissner-Nordstrom Cauchy Horizon and the Problem of Uniqueness in General Relativity

Abstract: This talk describes some recent results [16] regarding the problem of uniqueness in the large (also known as strong cosmic censorship) for the initial value problem in general relativity. In order to isolate the essential analytic features of the problem from the complicated setting of gravitational collapse in which it arises, some familiarity with conformal properties of certain celebrated special solutions of the theory of relativity will have to be developed. This talk is an attempt to present precisely these features to an audience of non-specialists, in a way which will hopefully fully motivate a certain characteristic initial value problem for the spherically-symmetric Einstein-Maxwell-Scalar Field system. The considerations outlined here leading to this particular initial value problem are well known in the physics relativity community, where the problem of uniqueness has been studied heuristically [1, 22] and numerically [2, 3]. In [16], the global behavior of solutions to this IVP, in particular, the issue of uniqueness, is mathematically completely understood. A statement of the relevant Theorems is included in Section 9. Only a sketch of the ideas of the proof is provided here, but the readers may refer to [16] for details.

Scale relativity theory for one-dimensional non-differentiable manifolds

Abstract: We discuss a rigorous foundation of the pure scale relativity theory for a one-dimensional space variable. We define several notions as “representation” of a continuous function, scale law and minimal resolution. We define precisely the meaning of a scale reference system and space reference system for non-differentiable one-dimensional manifolds.

Mathematical Challenges of General Relativity

Abstract: We give an overview of some of the main open problems in General Relativity as well as some new results concerning the bounded L curvature conjecture. Together with Quantum Mechanics, General Relativity provides the conceptual framework of Modern Physics yet, unlike the former, General Relativity has received somewhat less attention from mathematicians. There is, however, no established physical theory, I contend, which has a more impressive mathematical pedigree or a more fertile mathematical ground. Indeed recall that Einstein discovered it in a purely theoretical attempt to find a theory which could reconcile Special Relativity with Newtonian Gravity. The reconciliation required, in a fundamental way, both the language of Riemannian Geometry and the reformulation, by Minkowski, of Special Relativity in the language of a Lorentz metric. Special Relativity itself was born in another grand theoretical effort to reconcile the Galilean invariance of Classical Mechanics with the Lorentzian invariance of the Maxwell equations. Both these physical theories have rich mathematical structures in their own right and have had, and continue to have, an extremely fruitful interaction with the rest of mathematics. It suffices to say, for example, that the theory of differential forms and Hodge theory were greatly influenced by Maxwell’s theory of Electromagnetism while Calculus of Variations and Symplectic Geometry were born from a long and extremely fruitful attempt to unravel the mathematical structure of Classical Mechanics.

Polarizable-Vacuum Approach to General Relativity

Abstract: Topics in general relativity (GR) are routinely treated in terms of tensor formulations in curved spacetime. An alternative approach is presented here, based on treating the vacuum as a polarizable medium. Beyond simply reproducing the standard weak-field predictions of GR, the polarizable vacuum (PV) approach provides additional insight into what is meant by a curved metric. For the strong field case, a divergence of predictions in the two formalisms (GR vs. PV) provides fertile ground for both laboratory and astrophysical tests.

Unphysical Predictions of Some Doubly Special Relativity Theories

Abstract: A kind of doubly special relativity theory proposed by J Magueijo and L Smolin [Phys Rev Lett 88, 190403 (2002)] is analysed It is shown that this theory leads to serious physical difficulties in interpretation of kinematical quantities Moreover, it is argued that statistical mechanics and thermodynamics cannot be resonably formulate within the model proposed in the mentioned paper

Dirac spinors for Doubly Special Relativity

Abstract: We construct a Dirac equation that is consistent with one of the recently-proposed schemes for relativistic transformations with two observer-independent scales (a velocity scale, still naturally identified with the speed-of-light constant, and a length/momentum scale, possibly given by the Planck length/momentum). We exploit the fact that in the energy-momentum sector the transformation laws are governed by a nonlinear realization of the Lorentz group. We find that the nonlinearity, which is due to the introduction of the second observer-independent scale, only induces a mild deformation of the structure of Dirac spinors. After more than 70 years of study [1, 2] the “quantum-gravity problem”, the problem of reconciling/unifying gravity and quantum mechanics, is still unsolved. Even the best developed quantum-gravity theories [3, 4] still lack any observational support [5, 6, 7] and are still affected by serious deficiencies in addressing some of the “conceptual issues” that arise at the interplay between gravity and quantum mechanics. One can conjecture that the lack of observational support might be due to the difficulties of the relevant phenomenology [5, 6, 7] and that the conceptual issues might be eventually settled, but it is also legitimate to take as working assumption that all quantum-gravity theories so far considered are incorrect. At present it is even conceivable that the empasse in the study of the quantum-gravity problem might be due to the inadequacy of some of the key (and apparently most natural) common assumptions of quantum-gravity approaches. One of us recently proposed [9] an alternative path toward quantum gravity based on the possibility that Lorentz symmetry, usually assumed to be unaffected by the interplay between gravity and quantum mechanics, is deformed by the presence of the Planck length Lp (Lp ∼ 10−33cm): “special relativity” would be replaced by a “doubly special relativity”, in which, in addition to the familiar velocity scale c, also a second scale, a length scale λ (momentum scale 1/λ), is introduced as observer-independent feature of the laws of transformation between inertial observers. λ can be naturally (though not necessarily) identified with the Planck length. The fact that in some doubly-special-relativity scenarios the scale 1/λ turns out to set the maximum value of momentum [9, 10, 11] and/or energy [12, 13, 14, 15, 16] attainable by fundamental particles might be a useful tool for quantum-gravity research. In particular, it appears likely that [9, 14] the idea of a doubly special relativity may find applications in the study of certain noncommutative spacetimes. Moreover, while the deformation is soft enough to be consistent with all presently-available data, some of the predictions of doubly-special-relativity scenarios are testable [9, 13, 17] with forthcoming experiments [18], and therefore these theories may prove useful also in the wider picture of quantum-gravity research, as a training camp for the general challenge of setting up experiments capable of reaching sensitivity to very small (Planck-length suppressed) quantum-spacetime effects. Some of these testable predictions, which concern spin-half particles, have been obtained at a rather heuristic level of analysis, since, so far, no DSR formulation of spinors had been presented. We provide here this missing element of DSR theories. We focus on the specific DSR scheme used as illustrative example in the studies [9] that proposed the DSR idea, but our approach appears to be applicable to a wider class of DSR schemes, including the one recently proposed by Maguejio and Smolin in Ref. [12] and the wider class of DSR schemes even more recently considered in Refs. [14, 15]. In fact, in all these DSR schemes the introduction of the second observer-independent scale relies on a nonlinear realization of the Lorentz group: the generators that govern the rules of transformation between inertial observers still Examples of these conceptual issues are the so-called “problem of time” and “backgroundindependence problem” [8]. In presence of an observer-independent length scale the fact that our observations, on photons which inevitably have wavelengths that are much larger than the Planck length, are all consistent with a wavelength-independent speed of photons must be analyzed more cautiously [9]: it is only possible to identify the speed-of-light constant c as the speed of long-wavelength photons. From here onward “DSR” stands for “Doubly Special Relativity”. Indeed, in concurrent work by Ahluwalia and Kirchbach [19] and in work in progress by Magueijo and Smolin [20], completely analogous results are being found concerning Dirac spinors in other DSR schemes.

The Maximum Tension Principle in General Relativity

Abstract: I suggest that classical General Relativity in four spacetime dimensions incorporates a Principal of Maximal Tension and give arguments to show that the value of the maximal tension is $c^4 \over 4 G$. The relation of this principle to other, possibly deeper, maximal principles is discussed, in particular the relation to the tension in string theory. In that case it leads to a purely classical relation between $G$ and the classical string coupling constant $\alpha ^\prime$ and the velocity of light $c$ which does not involve Planck's constant.

Elements of the System Theory of Time

Abstract: In the paper, elements of the system theory of time are presented, mathematical models for time are constructed, and various properties are deduced from the main principles of the system theory of time. This theory is a far-reaching development of the special relativity theory. One of the main principles of the special relativity theory is that two physical systems that are moving relative to each other have different times and it is necessary to use a correspondence between clocks in these systems to coordinate their times. Such correspondence is established by means of electromagnetic signals. In accordance with this principle, it is postulated in the system theory of time that each system has its own time. In some cases, two systems have the same time. In other cases, times of systems are coordinated or correlated. However, there are systems in which times are independent from one another.

K-calculus in 4-dimensional optics

Abstract: 4-dimensional optics is based on the use 4-dimensional movement space, resulting from the consideration of the usual 3-dimensional coordinates complemented by proper time. The paper uses the established K-calculus to make a parallel derivation of special relativity and 4-dimensional optics, allowing a real possibility of comparison between the two theories. The significance of proper time coordinate is given special attention and its definition is made very clear in terms of just send and receive instants of radar pulses. The 4-dimensional optics equivalent to relativistic Lorentz transformations is reviewed. Special relativity and 4-dimensional optics are also compared in terms of Lagrangian definition of worldlines and movement Hamiltonian. The final section of the paper discusses simultaneity through the solution of a two particle head-on collision problem. It is shown that a very simple graphical construction automatically solves energy and momentum conservation when the observer is located at the collision position. A further discussion of the representation for a distant observer further clarifies how simultaneity is accommodated by 4DO.

Conventions in Relativity Theory and Quantum Mechanics

Abstract: The conventionalistic aspects of physical world perception are reviewed with an emphasis on the constancy of the speed of light in relativity theory and the irreversibility of measurements in quantum mechanics. An appendix contains a complete proof of Alexandrov's theorem using mainly methods of affine geometry.