Showing papers on "Special relativity (alternative formulations) published in 2010"

Extended uncertainty principle and the geometry of (anti)-de sitter space

Abstract: It has been proposed that on (anti)-de Sitter background, the Heisenberg uncertainty principle should be modified by the introduction of a term proportional to the cosmological constant. We show that this modification of the uncertainty principle can be derived straightforwardly from the geometric properties of (anti)-de Sitter spacetime. We also discuss the connection between the so-called extended generalized uncertainty principle and triply special relativity.

Nonlocal modification of Newtonian gravity

Abstract: The Newtonian regime of a recent nonlocal extension of general relativity is investigated. Nonlocality is introduced via a scalar ``constitutive'' kernel in a special case of the translational gauge theory of gravitation, namely, the teleparallel equivalent of general relativity. In this theory, the nonlocal aspect of gravity simulates dark matter. A nonlocal and nonlinear generalization of Poisson's equation of Newtonian gravitation is presented. The implications of nonlocality for the gravitational physics in the solar system are briefly studied.

The classical basis for the κ-Poincaré Hopf algebra and doubly special relativity theories

Abstract: Several issues concerning the quantum κ-Poincare algebra are discussed and reconsidered here. We propose two different formulations of the κ-Poincare quantum algebra. Firstly we present a complete Hopf algebra formula of κ-Poincare in classical Poincare basis. Further by adding one extra generator, which modifies the classical structure of the Poincare algebra, we eliminate nonpolynomial functions in the κ-parameter. Hilbert space representations of such algebras make doubly special relativity (DSR) similar to Stueckelberg's version of (proper-time) relativistic quantum mechanics.

Lorentz contraction, Bell’s spaceships and rigid body motion in special relativity

Abstract: The meaning of Lorentz contraction in special relativity and its connection with Bell's spaceships parable is discussed. The motion of Bell's spaceships is then compared with the accelerated motion of a rigid body. We have tried to write this in a simple form that could be used to correct students' misconceptions due to conflicting earlier treatments.

Quantum Relativity

Abstract: Quantum Relativity is supposed to be a new theory, which locally is a deformation of Special Relativity, and globally it is a background independent theory including the main ideas of General Relativity, with hindsight from Quantum Theory The qubit viewed as a Hopf monopole bundle is considered as a unifying gauge "group" Breaking its chiral symmetry is conjectured to yield gravity as a deformation of electromagnetism It is already a quantum theory in the context of Quantum Information Dynamics as a discrete, background independent theory, unifying classical and quantum physics Based on the above, Quantum Gravity is sketched as an open project

Student experiences of virtual reality: A case study in learning special relativity

Abstract: A teaching package has been developed centered around a relativistic virtual reality. It introduces concepts of special relativity to students in a gamelike environment where users experience the effects of traveling at near light speeds. From this perspective, space and time are significantly different from that experienced in everyday life. We explore how students worked with this environment and how they used this experience in their study of special relativity. Students found the simulation to be a positive learning experience and described the subject area as being less abstract after its use. Students were more capable of correctly answering concept questions relating to special relativity, and a small but measurable improvement was observed in the final exam.

Relativity, gravitation and cosmology

Abstract: 1. Special relativity and spacetime 2. Special relativity and physical laws 3. Geometry and curved spacetime 4. General relativity 5. The Schwarzschild solution and black holes 6. Testing general relativity 7. Cosmological solutions 8. Our Universe Index.

First-Order Logic Investigation of Relativity Theory with an Emphasis on Accelerated Observers

Abstract: This thesis is mainly about extensions of the first-order logic axiomatization of special relativity introduced by Andr\'eka, Madar\'asz and N\'emeti. These extensions include extension to accelerated observers, relativistic dynamics and general relativity; however, its main subject is the extension to accelerated observers (AccRel). One surprising result is that natural extension to accelerated observers is not enough if we want our theory to imply certain experimental facts, such as the twin paradox. Even if we add the whole first-order theory of real numbers to this natural extension, it is still not enough to imply the twin paradox. Nevertheless, that does not mean that this task cannot be carried out within first-order logic since by approximating a second-order logic axiom of real numbers, we introduce a first-order axiom schema that solves the problem. Our theory AccRel nicely fills the gap between special and general relativity theories, and only one natural generalization step is needed to achieve a first-order logic axiomatization of general relativity from it. We also show that AccRel is strong enough to make predictions about the gravitational effect slowing down time. Our general aims are to axiomatize relativity theories within pure first-order logic using simple, comprehensible and transparent basic assumptions (axioms); to prove the surprising predictions (theorems) of relativity theories from a few convincing axioms; to eliminate tacit assumptions from relativity by replacing them with explicit axioms formulated in first-order logic (in the spirit of the first-order logic foundation of mathematics and Tarski's axiomatization of geometry); and to investigate the relationship between the axioms and the theorems.

Space-time and special relativity from causal networks

Abstract: We show how the Minkowskian space-time emerges from a topologically homogeneous causal network, presenting a simple analytical derivation of the Lorentz transformations, with metric as pure event-counting. The derivation holds generally for d=1 space dimension, however, it can be extended to d>1 for special causal networks.

Faster Than Light

Abstract: It is argued that special relativity remains a viable physical theory even when there is permitted signals traveling faster than light.

Teaching physics using virtual reality

Abstract: We present an investigation of game‐like simulations for physics teaching. We report on the effectiveness of the interactive simulation “Real Time Relativity” for learning special relativity. We argue that the simulation not only enhances traditional learning, but also enables new types of learning that challenge the traditional curriculum. The lessons drawn from this work are being applied to the development of a simulation for enhancing the learning of quantum mechanics.

Deformed Special Relativity from Asymptotically Safe Gravity

Abstract: By studying the notion of a fundamentally minimal length scale in asymptotically safe gravity we find that a specific version of deformed special relativity (DSR) naturally arises in this approach. We then consider two thought experiments to examine the interpretation of the scenario and discuss similarities and differences to other approaches to DSR.

Special relativity as a noncommutative geometry: Lessons for deformed special relativity

Abstract: Deformed special relativity (DSR) is obtained by imposing a maximal energy to special relativity and deforming the Lorentz symmetry (more exactly, the Poincar\'e symmetry) to accommodate this requirement. One can apply the same procedure in the context of Galilean relativity by imposing a maximal speed (the speed of light). Effectively, one deforms the Galilean group and this leads to a noncommutative space structure, together with the deformations of composition of speed and conservation of energy momentum. In doing so, one runs into most of the ambiguities that one stumbles onto in the DSR context. However, this time, special relativity is there to tell us what is the underlying physics, in such a way we can understand and interpret these ambiguities. We use these insights to comment on the physics of DSR.

Can quantum theory and special relativity peacefully coexist

Abstract: This white paper aims to identify an open problem in 'Quantum Physics and the Nature of Reality' --namely whether quantum theory and special relativity are formally compatible--, to indicate what the underlying issues are, and put forward ideas about how the problem might be addressed.

Reply to arXiv:1006.2126 by Giovanni Amelino-Camelia et al

Abstract: It was previously shown that models with deformations of special relativity that have an energy-dependent yet observer-independent speed of light suffer from nonlocal effects that are in conflict with observation to very high precision. In a recent preprint it has been claimed that this conclusion is false. This claim was made by writing down expressions for modified Lorentz-transformations the use of which does not reproduce the result. I will show here that the failure to reproduce the result is not a consequence of a novel and improved calculation, but a consequence of repeating the same calculation but making an assumption that is in conflict with the assumptions made to produce the original scenario. I will here explain what the physical meaning of either assumption is and why the original assumption is the physically meaningful one. I will then further explain why even making the differing assumption does not remove but merely shift the problem and why the bound derived by Amelino-Camelia et al is wrong.

On the Finslerian extension of the Schwarzschild metric

Abstract: We provide a Finslerian extension of the Schwarzschild metric based on heuristic arguments. The proposed metric asymptotically approaches not the Minkowski space-time but the Bogoslovsky locally anisotropic space-time which arises naturally as a deformation of very special relativity.

Comments on Nonlocality in Deformed Special Relativity, in reply to arXiv:1004.0664 by Lee Smolin and arXiv:1004.0575 by Jacob et al

Abstract: It was previously shown that models with deformations of special relativity that have an energy-dependent yet observer-independent speed of light suffer from nonlocal effects that are in conflict with observation to very high precision. In a recent paper it has been proposed that these paradoxa arise only in the classical limit and can be prevented by an ad-hoc introduction of a quantum uncertainty that would serve to hide the nonlocality. We will show here that the proposed ansatz for this resolution is inconsistent with observer-independence and, when corrected, is in agreement with the earlier argument that revealed the troublesome nonlocality. We further offer an alternative derivation for the energy-dependent speed of light in the model used.

Republication of: The mechanics of matter particles in general relativity

Abstract: This is an English translation of the first of two papers by Myron Mathisson, first published in German in 1931 and 1937, in which he presented the correct formulation of equations of motion of spinning bodies in general relativity (today known as the Mathisson–Papapetrou equations). The papers have been selected by the Editors of General Relativity and Gravitation for republication in the Golden Oldies series of the journal. This republication is accompanied by an editorial note and Mathisson’s brief biography, both written by Andrzej Trautman.

On the relativity of rotation

Abstract: The question whether rotational motion is relative according to the general theory of relativity is discussed. Einstein’s ambivalence concerning this question is pointed out. In the present article I defend Einstein’s way of thinking on this when he presented the theory in 1916. The significance of the phenomenon of perfect inertial dragging in connection with the relativity of rotational motion is discussed. The necessity of introducing an extended model of the Minkowski spacetime, in which a globally empty space is supplied with a cosmic mass shell with radius equal to its own Schwarzschild radius, in order to extend the principle of relativity to accelerated and rotational motion, is made clear.

Asymptotic approach to special relativity compatible with a relativistic principle

Abstract: We propose a general framework to describe Planckian deviations from special relativity compatible with a relativistic principle. They are introduced as the leading corrections in an asymptotic approach to special relativity going beyond the energy power expansion of effective field theories. We discuss the conditions in which these Planckian effects might be experimentally observable in the near future, together with the nontrivial limits of applicability of this asymptotic approach that such a situation would produce, both at the very high (ultraviolet) and the very low (infrared) energy regimes.

The nonrelativistic limit of the Magueijo-Smolin model of deformed special relativity

Abstract: We study the nonrelativistic limit of the motion of a classical particle and of the corresponding generalized Klein-Gordon and Dirac equations in a model of deformed special relativity, and show that they reproduce nonrelativistic classical and quantum mechanics, respectively, although the rest mass of a particle no longer coincides with its inertial mass. This fact clarifies the meaning of the different definitions of velocity of a particle available in the literature on deformed special relativity. Moreover, the rest masses of particles and antiparticles differ, violating the CPT invariance. This effect is close to observational limits and future experiments may give indications on its effective existence.

Doppler Shift Reveals Light Speed Variation

Abstract: Light speed variation relative to a moving observer occurring according to classical velocity composition is demonstrated using Doppler Shift. This directly contradicts the light speed invariance postulate of special relativity and confirms ether drift.

Comment on arXiv:1007.0718 by Lee Smolin

Abstract: In a recent paper it was suggested a novel interpretation of deformed special relativity. In that new approach, nonlocal effects that had previously been shown to occur and be incompatible with experiment to high precision, are interpreted as coordinate artifacts that do not lead to real physical consequences. It is argued here that if one follows through the consequences of this thought, one finds that the theory one is dealing with needs to be ordinary special relativity to precision even better than the bound on nonlocal effect already requires. Consequently, the new approach cannot be understood as a version of deformed special relativity that circumvents the bound.

Spatial Directions, Anisotropy and Special Relativity

Abstract: The concept of an objective spatial direction in special relativity is investigated and theories assuming light-speed isotropy while accepting the existence of a privileged spatial direction are classified. A natural generalization of the proper time principle is introduced which makes it possible to devise experimental tests of spatial isotropy. Several common misunderstandings in the relativistic literature concerning the role of spatial isotropy are clarified.

The Fundamental Equations of Point, Fluid and Wave Dynamics in the De Sitter-Fantappie-Arcidiacono Projective Relativity Theory

Abstract: A review is presented of the fundamental equations of point, perfect incompressible fluid and wave dynamics in the Fantappie-Arcidiacono theory of projective relativity, also known as "De Sitter relativity". Compared to the original works, some deductions have been simplified and the physical meaning of the equations has been analyzed in greater depth. c

The Adolescence of Relativity: Einstein, Minkowski, and the Philosophy of Space and Time

Abstract: An often repeated account of the genesis of special relativity tells us that relativity theory was to a considerable extent the fruit of an operationalist philosophy of science. Indeed, Einstein’s 1905 paper stresses the importance of rods and clocks for giving concrete physical content to spatial and temporal notions. I argue, however, that it would be a mistake to read too much into this. Einstein’s operationalist remarks should be seen as serving rhetoric purposes rather than as attempts to promulgate a particular philosophical position – in fact, Einstein never came close to operationalism in any of his philosophical writings. By focussing on what could actually be measured with rods and clocks Einstein shed doubt on the empirical status of a number of pre-relativistic concepts, with the intention to persuade his readers that the applicability of these concepts was not obvious. This rhetoric manoeuvre has not always been rightly appreciated in the philosophy of physics. Thus, the influence of operationalist misinterpretations, according to which associated operations strictly define what a concept means, can still be felt in present-day discussions about the conventionality of simultaneity.The standard story continues by pointing out that Minkowski in 1908 supplanted Einstein’s approach with a realist spacetime account that has no room for a foundational role of rods and clocks: relativity theory became a description of a four-dimensional “absolute world.” As it turns out, however, it is not at all clear that Minkowski was proposing a substantivalist position with respect to spacetime. On the contrary, it seems that from a philosophical point of view Minkowski’s general position was not very unlike the one in the back of Einstein’s mind. However, in Minkowski’s formulation of special relativity it becomes more explicit that the content of spatiotemporal concepts relates to considerations about the form of physical laws. If accepted, this position has important consequences for the discussion about the conventionality of simultaneity.