Synchrony parameter dependent transformation equations and some of their particular values - Kinematics

Derivation and New Interpretation of the Lorentz Transformations and Einstein's Theorem of Velocity Addition

It is traditionally believed that the Lorentz transformations (LT) and Einstein's theorem of velocity addition (ETVA), underlying special relativity, cannot be obtained from non-relativistic (classical) mechanics. In the present paper it is shown, however, that both the LT and the ETVA are derivable within the framework of classical kinematics if the speeds of material points are bounded above by a certain universal limit $c_+$ which can coincide with the speed of light $c$ in a vacuum.

Coordinate System And Coordinate Transformations Based On Wave Nature Of Light

The Classical Coordinate System is geometrical by nature with time being an external variable. Constructing a classical coordinate system employs a point-like signal with infinite speed. In Special Relativity Theory the speed is limited but the signal is a point-like particle (photon). If the oscillatory nature of light is considered, an event in absolute space is to be characterized by three coordinates namely, distance, time and phase. The Galilean transformation equations for space and time coordinates should be complemented by a third equation that accounts for the phase transformation. Wa…

Opera's neutrinos and the Robertson test theory of the Lorentz transformations

The difference in light's travel time from CERN to GPS to Gran Sasso, on the one hand, and light going the direct route in vacuum (mimicked by neutrinos), on the other hand, is analyzed with a modified Robertson test theory of the Lorentz transformations. The modification consists simply in removing the restriction of what Robertson referred to as agreement to equate the to and from speeds of light. For reasons that will be contained in a paper to soon follow, we restrict ourselves, within the new freedom, to the case of preferred frame kinematics with absolute simultaneity. At the level of no…

Special Relativity and Time Travel Revisited

In this paper, Lorentz Transformation(LT) is derived by an alternate method, using photon clocks, placed at the locations of the concerned events, which are initially synchronised using a light signal(Einstein synchrony). Then, it is shown that the second term in the time dilation equation of the LT, is the term responsible for time travel and further it is shown that this term arises merely due to non-simultaneous initial clock synchronisation and that this term does not correspond to any actual time elapsed while timing events, thus ruling out the possibility of time travel, from the framewo…

多重态的洛伦兹不变方程及其规范

Lorentz Invariant Equations for Multiplets and Their Gauge

本文研究描述两个自旋1/2粒子多重态的洛伦兹不变方程，发现其存在三种运动学规范变换群，而这种规范在粒子单独处理时不存在，并分析了解的基本性质。

Turns and special relativity transformations

We advance an universal approach to the construction of kinematics in non-inertial and, in particular, rotating reference frames. On its basis a 10-dimensional space including three projections of velocity vector and three turn angles in geometric space as additional coordinates to time and geometric coordinates is introduced. In a specific case, the turns in 10-space describe the uniform rotation of reference frame as well as its accelerated motion. Transformations for coordinates and angular velocities are derived. Definitions of dynamic quantities contain a fundamental constant $Ω$ with dim…

With the relativistic velocity addition law through special relativity

It is shown that if we can define a physical quantity with proper character in a given inertial reference frame (kinematic, dynamic, electromagnetic in its nature) which transforms when detected from a reference frame relative to which it moves with velocity $u_x$ as $F=\f{F^o}{\sqrt{1-\f{u_x^2}{c^2}}}$ then we can derive for it transformation equations following one and the same procedure, which involves the addition law of relativistic velocities which can be derived without using the Lorentz transformations. The transformation equation derived that way, generates the physical quantities $u_…

An approach to directly probe simultaneity

The theory of special relativity derives from the Lorentz transformation. The Lorentz transformation implies differential simultaneity and light speed isotropy. Experiments to probe differential simultaneity should be able to distinguish the Lorentz transformation from a kinematically-similar alternate transformation that predicts absolute simultaneity, the absolute Lorentz transformation. Here, we describe how published optical tests of light speed isotropy/anisotropy cannot distinguish between the two transformations. We show that the shared equations of the two transformations, from the per…

Special Theory of Super Relativity and a Possibility to Exceed the Speed of Light

Modification of special theory of relativity is proposed to describe the propagation of signals with superluminal velocity. Modified kinematics and Lorentz transformations of Maxwell's equations are described. A possible experiment on measuring the speed of light for verification of the theory is discussed. It is shown that replacing the maximum speed in special theory of relativity by the neutrino superluminal velocity measured by the OPERA collaboration leads to lower value of the muon mass reconstructed from the muon decay products with the modified relativistic kinematics. This value is in…

Kinematics of an Ideal Fluid into a Spatially Flat Anisotropic Axisymmetric Universe

The Standard Cosmological Model assumes that the Universe is, on average, homogeneous and isotropic for large scales (z>1), but this principle has been questioned from the results about Cosmic Microwave Background. This radiation has anomalies that are not explained from the Standard Model, such as temperature fluctuations in the order of 10-5K or aligning polar moments. These anomalies could be explained by anisotropic cosmological models. We propose a transformation to spherical coordinates considering different temporal scale factors in the Cartesian axes, from which a reducible to flat spa…