Why the Sagnac effect favors absolute over relative simultaneity

We consider a thought experiment, equivalent to the Sagnac effect, where a light signal performs a round trip over a closed path. If special relativity (SR) adopts Einstein synchronization, the result of the experiment shows that the local light speed cannot be c in every section of the closed path. No inconsistencies are found when adopting absolute synchronization. Since Einstein and absolute synchronizations can be discriminated, the conventionality of the one-way speed of light holds no longer. Thus, as sustained by specialists, it might be a viable formulation of SR that reinstates the conservation of simultaneity, even though it allows for relativistic effects, such as time dilation. Such an approach may lead to the discovery of new effects and a better understanding of relativistic theories.

Testing Absolute vs Relative Simultaneity with the Spin-orbit Interaction and the Sagnac Effect

All the experiments supporting special relativity (SR) formulated with Einstein synchronization support as well SR with absolute synchronization, if the corresponding coordinate transformations foresee time dilation and length contraction. We first test absolute vs relative simultaneity with a non-relativistic model of the spin-orbit interaction by taking into account either the effect of the electron hidden momentum or the relativistic effect of the Thomas precession, based on non-conservation of simultaneity. As second test, we consider a thought experiment equivalent to the Sagnac effect, where a clock measures the time taken by a counter-propagating light signal to perform a round trip on a closed path. While these experiments are coherently described with absolute simultaneity, the result of our tests points out inconsistencies in the case of relative simultaneity, thus favoring the formulation of SR with absolute synchronization, while advocating that further research and tests on simultaneity are needed for the comprehension of relativistic theories.

Practical Measurement of Absolute Velocity of Earth

In 1880, Albert Michelson conceived the idea of optically measuring the speed of earth through the solar system. However, the Michelson-Morley experiment conducted for detecting the expected motion of earth, gave null result. Einstein propounded his theory of Relativity on the assumption that speed of light is isotropic in ECI reference frame. The Relativity model can be invalidated through an unambiguous physical experiment that confirms anisotropy of light speed in ECI reference frame. Let us consider a 3 km long line segment AB, fixed on surface of earth. The proposed experiment for measuring absolute velocity of earth involves sending a picoseconds Laser pulse from location A at time T0 and detecting it at location B at time T1 to measure the time of flight Tab of the laser pulse from A to B. On the other hand, by sending a picoseconds Laser pulse from location B at time T0 and detecting it at location A at time T2 we can measure the time of flight Tba from B to A. For accurate measurement of times of flight Tab and Tba the precision atomic clocks located at A and B must be in absolute synchronization. The absolute velocity Uab will be given by Uab/c = (Tab - Tba)/(Tab + Tba). Final absolute velocity U of earth can be computed from pulse flight timing record of 24 hours. For this we need to use the latest cutting-edge technology in Atomic Clocks, Pulsed Lasers, Ultrafast Detectors and Picosecond Time Interval Counters.

Systematic approach to the relativistic Doppler effect based on a test theory

Numerous experiments have been carried out to validate the Lorentz transformation or to find possible violations of Lorentz invariance, based on test theories to test special relativity. The test theory of Mansouri and Sexl (MS) provides a general framework for the transformation of inertial frames, presuming a preferred system of reference. Based on the MS framework, this paper systematically approaches the relativistic Doppler effect such that its dependency on transformation coefficients and parameters can be investigated. The Doppler effect is formulated in a complex Euclidean space where time is represented with imaginary numbers. Two formulae of the Doppler effect, which have been derived in an arbitrary transformation within the MS framework, are presented: one between an inertial frame and the preferred one and the other between arbitrary inertial frames. It is shown from the former formulation that the Doppler effect is independent of the synchronization of clocks, which implies that the Doppler-shifted frequency in the absolute synchronization is the same as that in the standard synchronization. The latter formula can allow us to find Doppler shifts without information on the velocities of inertial frames relative to the preferred frame. Exploiting these theoretical results, we examine the transverse and the longitudinal Doppler effects in detail.

Revisiting Barry Cox and James Hill's theory of superluminal motion: a possible solution to the problem of spinless tachyon localization

In 2012, Barry Cox and James Hill published a new and elegant way to deduce the formulae of extended relativity, developed by Erasmo Recami and others during the 1960s and 1970s. Extended relativity applies to superluminal or FTL (faster than light in the vacuum) particles, called tachyons by the late American physicist Gerald Feinberg. However, tachyons generate causality paradoxes in special relativity when used for signalling. These paradoxes are safely removed only in a space–time containing a preferred inertial reference frame. Moreover, quantum properties should be taken into account. They cause further trouble for tachyons because, for instance, spin-zero FTL particles satisfying the Klein–Gordon equation cannot be localized as pointlike particles, contrary to all other known fundamental constituents of matter. Perhaps the most interesting suggestion in Cox and Hill's paper is that a certain freedom is allowed in the theory of superluminal particles as no such particle has been reliably detected until now, so that it is worthwhile exploring theoretical alternatives. We shall prove that an idea from Cox and Hill's paper, when applied not in the context of extended relativity but in the framework of F. R. Tangherlini's absolute synchronization, allows the problem of tachyon localization for spinless particles to be solved.

EFFECTS OF SHORT-CUT IN A DELAYED RING NETWORK

This paper presents a detailed analysis on the dynamics of a ring network with short-cut. We first investigate the absolute synchronization on the basis of Lyapunov stability approach, and then discuss the linear stability of the trivial solution by analyzing the distribution of zeros of the characteristic equation. Based on the equivariant branching lemma, we not only obtain the existence of primary steady state bifurcation but also analyze the patterns and stability of the bifurcated nontrivial equilibria. Moreover, by means of the equivariant Hopf bifurcation theorem, we not only investigate the effect of connection strength on the spatio-temporal patterns of periodic solutions emanating from the trivial equilibrium, but also derive the formula to determine the direction and stability of Hopf bifurcation. In particular, we further consider the secondary bifurcation of the nontrivial equilibria. These studies show that short-cut may be used as a simple but efficient switch to control the dynamics of a system.