The Limits of Special Relativity

The Special Theory of Relativity and the Theory of the Electron have had an interesting history together. Originally the electron was studied in a non relativistic context and this opened up the interesting possibility that lead to the conclusion that the mass of the electron could be thought of entirely in electromagnetic terms without introducing inertial considerations. However the application of Special Relativity lead to several problems, both for an extended electron and the point electron. These inconsistencies have, contrary to popular belief not been resolved satisfactorily today, even within the context of Quantum Theory. Nevertheless these and subsequent studies bring out the interesting result that Special Relativity breaks down within the Compton scale or when the Compton scale is not neglected. This again runs contrary to an uncritical notion that Special Relativity is valid for point particles.Comment: 13 pages,Te

Causal Cones, Cone Preserving Transformations and Causal Structure in Special and General Theory of Relativity

We present a short review of geometric and algebraic approach to causal cones and describe cone preserving transformations and their relationship with causal structure related to special and general theory of relativity. We describe Lie groups, especially matrix Lie groups, homogeneous and symmetric spaces and causal cones and certain implications of these concepts in special and general theory of relativity related to causal structure and topology of space-time. We compare and contrast the results on causal relations with those in the literature for general space-times and compare these relations with K-causal maps. We also describe causal orientations and their implications for space-time topology and discuss some more topologies on space-time which arise as an application of domain theory.Comment: 16 page

Knot theory and quantum gravity in loop space: a primer

These notes summarize the lectures delivered in the V Mexican School of Particle Physics, at the University of Guanajuato. We give a survey of the application of Ashtekar's variables to the quantization of General Relativity in four dimensions with special emphasis on the application of techniques of analytic knot theory to the loop representation. We discuss the role that the Jones Polynomial plays as a generator of nondegenerate quantum states of the gravitational field.Comment: 44 pages. v2: figures added, also available as PDF at http://www.phys.psu.edu/~pullin/primerfigs.pd

Comparing theories: the dynamics of changing vocabulary. A case-study in relativity theory

There are several first-order logic (FOL) axiomatizations of special relativity theory in the literature, all looking essentially different but claiming to axiomatize the same physical theory. In this paper, we elaborate a comparison, in the framework of mathematical logic, between these FOL theories for special relativity. For this comparison, we use a version of mathematical definability theory in which new entities can also be defined besides new relations over already available entities. In particular, we build an interpretation of the reference-frame oriented theory SpecRel into the observationally oriented Signalling theory of James Ax. This interpretation provides SpecRel with an operational/experimental semantics. Then we make precise, "quantitative" comparisons between these two theories via using the notion of definitional equivalence. This is an application of logic to the philosophy of science and physics in the spirit of Johan van Benthem's work.Comment: 27 pages, 8 figures. To appear in Springer Book series Trends in Logi

General relativity and relativistic astrophysics

Einstein established the theory of general relativity and the corresponding field equation in 1915 and its vacuum solutions were obtained by Schwarzschild and Kerr for, respectively, static and rotating black holes, in 1916 and 1963, respectively. They are, however, still playing an indispensable role, even after 100 years of their original discovery, to explain high energy astrophysical phenomena. Application of the solutions of Einstein's equation to resolve astrophysical phenomena has formed an important branch, namely relativistic astrophysics. I devote this article to enlightening some of the current astrophysical problems based on general relativity. However, there seem to be some issues with regard to explaining certain astrophysical phenomena based on Einstein's theory alone. I show that Einstein's theory and its modified form, both are necessary to explain modern astrophysical processes, in particular, those related to compact objects.Comment: 15 pages including 3 figures and 4 tables; published for a special section in Current Science dedicated to 100 years of general relativity, edited by B. Mukhopadhyay (IISc) and T. P. Singh (TIFR). arXiv admin note: text overlap with arXiv:1603.0013

Special Theory of Relativity without special assumptions and tachyonic motion

The most general form of transformations of spacetime coordinates in Special Theory of Relativity based solely on physical assumptions are described. Only the linearity of spacetime transformations and the constancy of the speed of light are used as assumptions. The application to tachyonic motion is indicated.Comment: 10 page

The Tolman "Antitelephone" Paradox: Its Solution by Tachyon Mechanics

Some recent experiments led to the claim that something can travel faster than light in vacuum. However, such results do not seem to place relativistic causality in jeopardy. Actually, it is possible to solve also the known causal paradoxes, devised for "faster than $c$" motion: even if this is not widely recognized. Here we want to show, in detail and rigorously, how to solve the oldest causal paradox, originally proposed by Tolman, which is the kernel of so many further tachyon paradoxes. The key to the solution is a careful application of {\em tachyon mechanics}, that can be unambiguously derived from special relativity