Showing papers on "Special relativity (alternative formulations) published in 2002"

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.

Physical instances of noncommuting coordinates

Abstract: Noncommuting spatial coordinates and fields can be realized in actual physical situations. Plane wave solutions to noncommuting photodynamics exhibit violaton of Lorentz invariance (special relativity).

Theorems on Existence and Global Dynamics for the Einstein Equations.

Abstract: This article is a guide to theorems on existence and global dynamics of solutions of the Einstein equations. It draws attention to open questions in the field. The local-in-time Cauchy problem, which is relatively well understood, is surveyed. Global results for solutions with various types of symmetry are discussed. A selection of results from Newtonian theory and special relativity that offer useful comparisons is presented. Treatments of global results in the case of small data and results on constructing spacetimes with prescribed singularity structure are given. A conjectural picture of the asymptotic behaviour of general cosmological solutions of the Einstein equations is built up. Some miscellaneous topics connected with the main theme are collected in a separate section.

On peaceful coexistence: is the collapse postulate incompatible with relativity?

Abstract: In this paper, it is argued that the prima facie conflict between special relativity and the quantum-mechanical collapse postulate is only apparent, and that the seemingly incompatible accounts of entangled systems undergoing collapse yielded by different reference frames can be regarded as no more than differing accounts of the same processes and events. Attention to the transformation properties of quantum-mechanical states undergoing unitary, non-collapse evolution points the way to a treatment of collapse evolution consistent with the demands of relativity.

Doubly Special Relativity versus $\kappa$-deformation of relativistic kinematics

Abstract: We argue that recently proposed by Amelino-Camelia et all [1,2] so-called doubly special relativity (DSR), with deformed boost transformations identical with the formulae for $\kappa$-deformed kinematics in bicrossproduct basis is a classical special relativity in nonlinear disguise. The choice of symmetric composition law for deformed fourmomenta as advocated in [1, 2] implies that DSR is obtained by considering nonlinear fourmomenta basis of classical Poincar\'{e} algebra and it does not lead to noncommutative space-time. We also show how to construct large two classes of doubly special relativity theories - generalizing the choice in [1,2] and the one presented by Magueijo and Smolin [3]. The older version of deformed relativistic kinematics, differing essentially from classical theory in the coalgebra sector and leading to noncommutative $\kappa$-deformed Minkowski space is provided by quantum $\kappa$-deformation of Poincar\'e symmetries.

The Challenge of Changing Deeply Held Student Beliefs about the Relativity of Simultaneity.

Abstract: Previous research indicates that after standard instruction, students at all levels often construct a conceptual framework in which the ideas of absolute simultaneity and the relativity of simultaneity co-exist. We describe the development and assessment of instructional materials intended to improve student understanding of the concept of time in special relativity, the relativity of simultaneity, and the role of observers in inertial reference frames. Results from pretests and post-tests are presented to demonstrate the effect of the curriculum in helping students deepen their understanding of these topics. Excerpts from taped interviews and classroom interactions help illustrate the intense cognitive conflict that students encounter as they are led to confront the incompatibility of their deeply held beliefs about simultaneity with the results of special relativity.

Special Relativity and Motions Faster than Light

Abstract: Introduction Light and relativity Imaginary paradoxes The velocities' play Superluminal motions Slow light and fast light Tachyons and tachyon-like objects The speed of light as a fundamental constant of Nature

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.

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.

Kinematical test theories for special relativity: a comparison

Abstract: A comparison of certain kinematical test theories for Special Relativity including the Robertson and Mansouri–Sext test theories is presented and the accuracy of the experimental results testing Special Relativity are expressed in terms of the parameters appearing in these test theories. The theoretical results are applied to the most precise experimental results obtained recently for the isotropy of light propagation and the constancy of the speed of light.

Thomas rotation: a Lorentz matrix approach

Abstract: The composition of two pure Lorentz transformations (boosts) parametrized by non-parallel velocities is equivalent to a boost combined with a pure spatial rotation - the Thomas rotation. Thirty years elapsed from Thomas's 1926 calculation for the precessional application until an explicit result for the Thomas rotation angle appropriate to two finite boost velocities appeared in the literature. Over the years there have been a number of papers that have produced results by various methods for the Thomas rotation angle but none by direct Lorentz matrix methods. This paper repairs that deficiency by presentation of an explicit Lorentz matrix proof of sufficient conciseness to show that the much-vaunted complexity of the direct approach has been considerably overstated. The demonstration fills a gap at a fundamental level in the development of the basics of special relativity.

A simple solution of the twin paradox also shows anomalous behaviour of rigidly connected distant clocks

Abstract: Although it has even been experimentally confirmed that the twin who travels away and comes back will age less, a conceptually very convincing theoretical treatment of the problem is still awaited. This paper presents a very simple solution of the twin paradox based on special relativity which proves from the viewpoint of the traveller twin also that he or she ages less. But with that, an anomalous behaviour of rigidly connected distant clocks is also observed.

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.

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.

On Stages, Worms, and Relativity

Abstract: Four–dimensionalism, or perdurantism, the view that temporally extended objects persist through time by having (spatio-)temporal parts or stages, includes two varieties, the worm theory and the stage theory. According to the worm theory, perduring objects are four–dimensional wholes occupying determinate regions of space–time and having temporal parts, or stages, each of them confined to a particular time. The stage theorist, however, claims, not that perduring objects have stages, but that the fundamental entities of the perdurantist ontology are stages. I argue that considerations of special relativity favor the worm theory over the stage theory.

Ten arguments for the essence of special relativity

Abstract: In searching for the essence of special relativity, we have been gradually accumulating ten arguments focusing on one fundamental postulate based on quantum mechanicsA particle is always not pure It always contain two contradictory fields, $\phi(\vec{x},t)$ and $\chi(\vec{x},t)$,which are coupled together with the symmetry $\phi(-\vec{x},-t)\longrightarrow\chi(\vec{x},t)$ and $\chi(-\vec{x},-t)\longrightarrow\phi(\vec{x},t)$

A Note on the correspondence between Qubit Quantum Operations and Special Relativity

Abstract: We exploit a well-known isomorphism between complex hermitian $2\times 2$ matrices and $\mathbb{R}^4$, which yields a convenient real vector representation of qubit states. Because these do not need to be normalized we find that they map onto a Minkowskian future cone in $\mathbb{E}^{1,3}$, whose vertical cross-sections are nothing but Bloch spheres. Pure states are represented by light-like vectors, unitary operations correspond to special orthogonal transforms about the axis of the cone, positive operations correspond to pure Lorentz boosts. We formalize the equivalence between the generalized measurement formalism on qubit states and the Lorentz transformations of special relativity, or more precisely elements of the restricted Lorentz group together with future-directed null boosts. The note ends with a discussion of the equivalence and some of its possible consequences.

Gravitation and the Local Symmetry Group of Space-Time

Abstract: According to general relativity, the interaction of a matter field with gravitation requires the simultaneous introduction of a tetrad field, which is a field related to translations, and a spin connection, which is a field assuming values in the Lie algebra of the Lorentz group. These two fields, however, are not independent. By analyzing the constraint between them, it is concluded that the relevant local symmetry group behind general relativity is provided by the Lorentz group. Furthermore, it is shown that the minimal coupling prescription obtained from the Lorentz covariant derivative coincides exactly with the usual coupling prescription of general relativity. Instead of the tetrad, therefore, the spin connection is to be considered as the fundamental field representing gravitation.

The physical meaning of synchronization and simultaneity in Special Relativity

Abstract: Based on two previous papers, the physical meaning of synchronization and simultaneity as is presented in Einstein's Special Relativity paper of 1905 is reconsidered We follow Einstein's argumentation to introduce a criterium of synchronization and for the same arguments we arrive at a different criterium for synchronization From that we conclude that simultaneity is absolute