Special relativity (alternative formulations)

About: Special relativity (alternative formulations) is a research topic. Over the lifetime, 3102 publications have been published within this topic receiving 55015 citations.

General relativistic dynamics: extending einstein's legacy throughout the universe

Abstract: This book brings Einstein's general relativity into action in new ways at scales ranging from the tiny Planck scale to the scale of immense galactic clusters. It presents the case that Einstein's theory of gravity can describe the observed dynamics of galaxies without invoking the unknown “dark matter” required in models based on Newtonian gravity.Drawing on the author's experience as a lecturer and on his own research, the book covers the essentials of Einstein's special and general relativity at a level accessible to undergraduate students. The early chapters provide a compact introduction to relativity for readers who have little or no background in the subject. Hermann Bondi's very transparent approach to special relativity is expanded to resolve the “twin paradox” using only elementary mathematics. In later chapters, general relativity is used to extend the concept of the Planck scale, to address the role of the cosmological term and to analyze the concept of “time machines”.

Testing Lorentz symmetry of special relativity by means of the Virgo or Ligo set-up, through the differential measure of the two orthogonal beams time-of-flight

Abstract: A novel experiment to test special relativity via Lorentz symmetry has become factible thanks to three recent technological achievements: huge Michelson-like set-up with arms 3 km long (Virgo) and 4 km (Ligo) with beam paths respectively reaching 120 km and 200 km through multiple reflections, ultrashort laser pulses of 10-15 s and ultrafast detectors of 10-12 s resolution. The alliance of these three elements would allow checking the equality of the time-of-flight of the two orthogonal beams with a resolution high enough to allow prospecting in a novel way the equivalency of inertial system postulated in special relativity. In effect, for a beam path length of 120 or 200 km and a net drift velocity of earth of 370 km/s relative to the cosmic microwave background CMB), a classical analysis predicts a time-of-flight difference of the order of 10 ns between the two orthogonal beams, while relativity infers them to be equal. So, what is under scrutiny is the exhaustivity of the electromagnetic equivalency of inertial systems. A null time-of-flight difference would strengthen the Lorentz symmetry, while a non null result would bring a threshold to the equivalency of inertial systems and at the same time would provide a tool to define their speed, which should be equal to that relative to the CMB for being congruent.

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.

Special Relativity over the Field of Rational Numbers

Abstract: We investigate the question: what structures of numbers (as physical quantities) are suitable to be used in special relativity? The answer to this question depends strongly on the auxiliary assumptions we add to the basic assumptions of special relativity. We show that there is a natural axiom system of special relativity which can be modeled even over the field of rational numbers.