Reference spaces in Special Relativity Theory: an intrinsic approach

A free system, considered to be a comparison system, allows for the notion of objective existence and inertial frame. Transformations connecting inertial frames are shown to be either Lorentz or generalized Galilei.

Old and New Concepts of Physics, 2007

Several new ideas related to Special and General Relativity are proposed. The black-box method is used for the synchronization of the clocks and the space axes between two inertial systems or two accelerated systems and for the derivation of the transformations between them. There are two consistent ways of defining the inputs and outputs to describe the transformations and relative motion between the systems. The standard approach uses a mixture of the two ways. By formulating the principle of special and general relativity as a symmetry principle we are able to specify these transformations to depend only on a constant.

Relativity in Celestial Mechanics and Astrometry, 1986

The treatment of the coordinate systems is briefly reviewed in the Newtonian mechanics, in the special theory of relativity, and in the general relativistic theory, respectively. Some reference frames and coordinate systems proposed within the general relativistic framework are introduced. With use of the ideas on which these coordinate systems are based, the proper reference frame comoving with a system of masspoints is defined as a general relativistic extension of the relative coordinate system in the Newtonian mechanics. The coordinate transforma tion connecting this and the background coordinate systems is presented explicitly in the post-Newtonian formalism. The conversion formulas of some physical quantities caused by this coordirate transformation are discussed. The concept of the rotating coordinate system is reexamined within the relativistic framework. A modification of the introduced proper reference frame is proposed as the basic coordinate system in the astrometry. The relation between the solar system barycentric coordinate system and the terrestrial coordinate system is given explicitly.

International Journal of Theoretical Physics, 1985

By using the principle of relativity alone (no assumptions about signals or light) it is shown that a relativisitic group Of linear transformations of a spacetime plane is, if infinite, either Galilean, Lorentzian or rotational. Th e largest such finite group is a Klein 4-group, generate d by space-reversal and time-reversal. In the infinite case an invariant of the group, denoted c, appears. When c is real, nonzero, noninfinite, then the group is a Lorentz group and c is identified with the speed of light. Lorentz transformations are represented through an algebra D of iterants that provides a link among C!ifford algebras, the Pauli algebra and Herman Bondi's K-calculus.

Foundations of physics, 2003

New four coordinates are introduced which are related to the usual space-time coordinates. For these coordinates, the Euclidean four-dimensional length squared is equal to the interval squared of the Minkowski space. The Lorentz transformation, for the new coordinates, becomes an SO(4) rotation. New scalars (invariants) are derived. A second approach to the Lorentz transformation is presented. A mixed space is generated by interchanging the notion of time and proper time in inertial frames. Within this approach the Lorentz transformation is a 4-dimensional rotation in an Euclidean space, leading to new possibilities and applications.

2007

Starting with two light clocks to derive time dilation expression, as many textbooks do, and then adding a third one, we work on relativistic spacetime coordinates relations for some simple events as emission, reflection and return of light pulses. Besides time dilation, we get, in the following order, Doppler k-factor, addition of velocities, length contraction, Lorentz Transformations and spacetime interval invariance. We also use Minkowski spacetime diagram to show how to interpret some few events in terms of spacetime coordinates in three different inertial frames. * nilton.

Relativity in Rotating Frames, 2004

The peculiarities of rotating frames of reference played an important role in the genesis of general relativity. Considering them, Einstein became convinced that coordinates have a different status in the general theory of relativity than in the special theory. This line of thinking was confused, however. To clarify the situation we investigate the relation between coordinates and the results of space-time measurements in rotating reference frames. We argue that the difference between rotating systems (or accelerating systems in general) and inertial systems does not lie in a different status of the coordinates (which are conventional in all cases), but rather in different global chronogeometric properties of the various reference frames. In the course of our discussion we comment on a number of related issues, such as the question of whether a consideration of the behavior of rods and clocks is indispensable for the foundation of kinematics, the influence of acceleration on the behavior of measuring devices, the conventionality of simultaneity, and the Ehrenfest paradox.

the orthogonal transformations are the path to a geometrical approach to the theory of relativity. the Euclidean space and the orthogonal transformations are the early forms of Minkowski's space and Lorentz' transformations.

Eprint Arxiv Gr Qc 9606035, 1996

We argue that space-time geometry is not absolute with respect to the frame of reference being used. The space-time metric differential form ds in noninertial frames of reference (NIFR) is caused by the properties of the used frames in accordance with the Berkley -Leibnitz -Mach -Poincaré ideas about relativity of space and time . It is shown that the Sagnac effect and the existence of inertial forces in NIFR can be considered from this point of view.

arXiv: History and Philosophy of Physics, 2023

In order to ask for future concepts of relativity, one has to build upon the original concepts instead of the nowadays common formalism only, and as such recall and reconsider some of its roots in geometry. So in order to discuss 3-space and dynamics, we recall briefly Minkowski's approach in 1910 implementing the nowadays commonly used 4-vector calculus and related tensorial representations as well as Klein's 1910 paper on the geometry of the Lorentz group. To include microscopic representations, we discuss few aspects of Wigner's and Weinberg's 'boost' approach to describe 'any spin' with respect to its reductive Lie algebra and coset theory, and we relate the physical identification to objects in $P^{5}$ based on the case $(1,0)\oplus(0,1)$ of the electromagnetic field. So instead of following this -- in some aspects -- special and misleading 'old' representation theory, based on 4-vector calculus and tensors, we provide and use an alternat...