Volume Charge Density in Geometric Product Lorentz Transformation

Lorentz Transformation is the relationship between two different coordinate frames time and space when one inertial reference frame is relative to another inertial reference frame with traveling at relative speed. In this paper, we have derived the transformation formula for the volume charge density in Geometric Product Lorentz Transformation. The changes of volume charge density of moving frame in terms of that rest frame in Geometric Product Lorentz Transformation at various velocities and angles were studied as well.

Superluminal Lorentz transformations

In this article, linear transformations of coordinates to a superluminal inertial reference frame are presented. Even if there is no need to use imaginary numbers to maintain c invariant, these functions are just intended as a mathematical curiosity not necessarily having a real physical meaning. Possible applications to our world, if any, are left to the reader.

On the Relativity of the Speed of Light

Einstein's assumption that the speed of light is constant is a fundamental principle of modern physics with great influence. However, the nature of the principle of constant speed of light is rarely described in detail in the relevant literatures, which leads to a deep misunderstanding among some readers of special relativity. Here we introduce the unitary principle, which has a wide application prospect in the logic self consistency test of mathematics, natural science and social science. Based on this, we propose the complete space-time transformation including the Lorentz transformation, clarify the definition of relative velocity of light and the conclusion that the relative velocity of light is variable, and further prove that the relative variable light speed is compatible with Einstein's constant speed of light. The specific conclusion is that the propagation speed of light in vacuum relative to the observer's inertial reference frame is always constant $c$, but the propagation speed of light relative to any other inertial reference frame which has relative motion with the observer is not equal to the constant $c$; observing in all inertial frame of reference, the relative velocity of light propagating in the same direction in vacuum is $0$, while that of light propagating in the opposite direction is $2c$. The essence of Einstein's constant speed of light is that the speed of light in an isolated reference frame is constant, but the relative speed of light in vacuum is variable. The assumption of constant speed of light in an isolated frame of reference and the inference of relative variable light speed can be derived from each other.

Calibrating Range Measurements of Lidars Using Fixed Landmarks in Unknown Positions

We consider the problem of calibrating distance measurement of Light Detection and Ranging (lidar) sensor without using additional hardware, but rather exploiting assumptions on the environment surrounding the sensor during the calibration procedure. More specifically we consider the assumption of calibrating the sensor by placing it in an environment so that its measurements lie in a 2D plane that is parallel to the ground, and so that its measurements come from fixed objects that develop orthogonally w.r.t. the ground, so that they may be considered as fixed points in an inertial reference frame. We moreover consider the intuition that moving the distance sensor within this environment implies that its measurements should be such that the relative distances and angles among the fixed points above remain the same. We thus exploit this intuition to cast the sensor calibration problem as making its measurements comply with this assumption that “fixed features shall have fixed relative distances and angles”. The resulting calibration procedure does thus not need to use additional (typically expensive) equipment, nor deploying special hardware. As for the proposed estimation strategies, from a mathematical perspective we consider models that lead to analytically solvable equations, so to enable deployment in embedded systems. Besides proposing the estimators we moreover analyse their statistical performance both in simulation and with field tests, reporting thus the dependency of the MSE performance of the calibration procedure as a function of the sensor noise levels, and observing that in field tests the approach can lead to a ten-fold improvement in the accuracy of the raw measurements.

On the Support that the Special and General Theories of Relativity Provide for Rock’s Argument Concerning Induced Self-Motion and Vice Versa

Though Einstein and other physicists recognized the importance of an observer being at rest in an inertial reference frame for the special theory of relativity, the supporting psychological structures were not discussed much by physicists. On the other hand, Rock wrote of the factors involved in the perception of motion, including one’s own motion. Rock thus came to discuss issues of significance to relativity theory, apparently without any significant understanding of how his theory might be related to relativity theory. In this paper, connections between Rock’s theory on the perception of one’s own motion, as well as empirical work supporting it, and relativity theory are explored. Paper available at: https://arxiv.org/abs/physics/9908025v1 .

ETHER AND EQUIVALENCE OF INERTIAL FRAMES OF REFERENCE

The paper discusses the problem of equality of Inertial frames of reference IFR. The hypothesis of a physical ether, whose properties do not depend on the choice of an inertial reference frame, is proposed. Based on the concept of the physical ether, it turns out the features of instantaneous action at a distance. It is shown that there is a class of transformations that preserves Maxwell’s equations unchanged. The problem of choosing a transformation is posed. This choice should be based on experimental research.

The “twin paradox”: the role of acceleration

The “twin paradox” corresponds to the situation where two twins begin at rest in an inertial reference frame, one of them takes a journey, normally very fast and to a distant place, and then returns to the twin at rest. The “twin paradox” evokes the idea that each twin would say that it should be the other who is younger because of their relative motion. A complete resolution of the paradox corresponds to the calculation of the elapsed proper time of each twin, by each twin, and the subsequent observation that they actually get the same answer, that the travelling twin is indeedthe younger twin. Acceleration has a role to play; indeed, if one tries to calculate the age difference from the point of the view of the travelling twin, then the role of the acceleration is crucial and cannot be dismissed. In this tutorial, we show in complete and pedagogical detail, how to do the necessary calculations according to each twin using simple transformations of coordinates.

Accelerated frames and galactic rotation curves

In this paper, the galactic rotation curve is analyzed as an effect of an accelerated reference frame. Such a rotation curve was the first evidence for the so-called dark matter. We show another possibility for this experimental data: non-inertial reference frame can fit the experimental curve. We also show that general relativity is not enough to completely explain that which encouraged alternatives paths such as the MOND approach. The accelerated reference frames hypothesis is well-suited to deal with the rotation curve of galaxies and perhaps has some role to play concerning other evidences for dark matter.