Uniform Scaling: Relativistic Energy-Momentum Relationships

A number of the most often cited results of relativity theory deal with the relationships between energy, momentum and inertial mass. The history of how Einstein and Planck came to these conclusions is reviewed. It is pointed out that considerations of how the speed of light is affected by the motion of the Earth played a determining role in these developments. After the Michelson-Morley null-interference result became available, Voigt introduced a new space-time transformation by amending the classical Galilean transformation so that the speed of light in free space has the same value of c regardless of the state of motion of both the light source and the observer. This led to the Lorentz transformation which has been the cornerstone of relativity theory for the past century. A thought experiment is presented which proves, however, that there are many situations for which the measured speed of light is NOT equal to c. Furthermore, it is pointed out that the rate of an inertial clock cannot change spontaneously, which result is perfectly compatible with Newton’s First Law of Kinetics (Law of Inertia). This result contradicts the space-time mixing characteristic of the Lorentz transformation and leads to the conclusion that events which are spontaneous for one inertial frame will also be so for every other one. The uniform scaling procedure is a generalization of this result for all other physical properties than elapsed times. Its application shows that the commonly accepted relationships between energy and momentum are only special cases in which it is assumed that the observer is stationary in the rest frame in which force has been applied to cause the object’s acceleration

Inverse-transformation of 4-dimensional Rindler spacetim

In special relativity theory, we discovered 4-dimensional transformation of general Rindler spacetimefrom 4-dimensional Lorentz transformation in inertial frames.We try to discover 4-dimensional inverse-transformation of general Rindler space-time.

Transformation of 4-dimensional Rindler spacetime

In special relativity theory, we discover 4-dimensional transformation of general Rindler spacetimefrom 4-dimensional Lorentz transformation in inertial frames.

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.

On Fundamentality of Heat

Motivated by the well-known contradiction of special relativity and the heat equation, a wave equation for temperature scalar field is presented that also resolves the old controversy of (Lorentz) transformation of temperature and entropy. After showing that the current dogma of temperature and entropy being emergent concepts is based on but a logical fallacy, it is proposed that single particles posses entropy. This principle of fundamentality of entropy is then shown to be compatible with the equipartition theorem by yielding corrections in the quantum gravity regime.

Pinpointing a disastrous limitation of Special Relativity and Proposing a new explanation for Light Speed’s constancy

This paper pinpoints a severe infirmity of the Lorentz Transformation in the Special Theory of Relativity. Even if it were true, its ambit is very much limited. Out of infinite events happening in the universe, it covers only the events of detecting light signals at the spatial points lying on a straight line in the direction of the relative velocity between the two inertial frames. This paper points out that the slowing down of moving clocks is not a prediction of Lorentz Transformation and hints at the possibility of attributing the observed slowing down of fast-moving clocks to the Relativistic Variation of Mass with Velocity. This paper concludes that from the fact that the same Reality is perceived differently by the observers in different inertial frames, we can draw a straightforward explanation for the constancy of light's speed in all inertial frames without any need for bringing in narrow-scoped and unrealistic Lorentz Transformation.

The Lorentz transformation

“The Lorentz transformation” derives the Lorentz transformation by an unusual route, from application of simple postulates: space is uniform and isotropic; inertial frames exist; physics is invariant under a change between inertial frames. The speed of light is an invariant, but this property is input last.

Four-vectors in relativity

“Four-vectors in relativity” gives a “soft” introduction to four-vectors by first setting up corresponding properties of three-vectors. These include the triangle rule for vector addition, and rotation of axes by a matrix multiplication. The physics of a three-dimensional system is unchanged by a rotation of the axes within which it is observed. Likewise the physics of a relativistic system is unchanged (“invariant”) under application of a Lorentz transformation.

Special Relativity sans Lorentz Transformation (OR) Perceptional Relativity

This paper shows that from the fact that the same Reality is perceived differently by the observers in different inertial frames, we can draw a simple and straightforward explanation for the constancy of light's speed in all inertial frames without any need for bringing in paradoxical Lorentz Transformation. This paper shows that the premise that each inertial frame has its unique time, which Lorentz Transformation introduced to explain the constancy of the speed of light in all inertial frames is incompatible with the interchangeability of the frames, an essential requisite of the First Postulate of the Special Theory of Relativity. This paper also points out the misconceptions regarding the claimed experimental verifications of Lorentz Transformation's predictions in the Hafele–Keating experiment and μ meson experiment. This paper hints at the possibility of attributing the observed slowing down of fast-moving clocks to the Relativistic Variation of Mass with Velocity instead of Time Dilation. This paper concludes that Einstein's Special Theory Relativity can stand on its own merits without Lorentz Transformation.

Dendrogramic Representation of Data: CHSH-Violation vs. Nonergodicity

This paper is devoted to the foundational problems of dendrogramic holographic theory (DH-theory). We use the ontic-epistemic (implicate-explicate order) methodology. The epistemic counterpart is based on representation of data by dendrograms constructed with hierarchic clustering algorithms. The ontic Universe is described as the p-adic tree; it is zero dimensional, totally disconnected, disordered, and bounded (in p-adic ultrametric). Interrelation classical-quantum loses its sharpness; generally simple dendrograms are ``more quantum’’ than complex one. We use the CHSH-inequality as a measure of quantum(-likeness). We demonstrate that it can be violated by classical experimental data represented by dendrograms. The seed of this violation is neither nonlocality nor rejection of realism. This is nonergodicity of dendrogramic time series. Generally, violation of ergodicity is one of the basic features of DH-theory. We also consider DH-theory for Minkovski geometry and monitor the dependence of CHSH-violation and nonergodicity on geometry as well as a Lorentz transformation of data.