Lorentz Transformation Equations Research Articles

Derivation And Applications of The Lorentz Transformation

The Lorentz transformation is a foundational mathematical construction that has revolutionized people’s comprehension of space, time, and motion within the realm of special relativity. Crafted through the collaborative insights of Lorentz and Einstein, it offers a profound perspective on the intricate fabric of the universe. By delving into the intricate interplay between space and time, the Lorentz transformation transcends traditional Newtonian notions, providing a groundbreaking framework to grasp the behavior of matter and energy in the cosmos. This paper embarks on a meticulous exploration, deriving the Lorentz transformation equations from first principles. It subsequently delves into a captivating journey through its multifaceted applications. From unraveling the mysteries of high-energy particle interactions to enhancing the accuracy of global navigation systems, the reach of the Lorentz transformation extends across diverse scientific and technological domains. The applications include elucidating counterintuitive effects like time dilation and length contraction, elucidating the mass-energy equivalence principle, and facilitating precise measurements in high-speed scenarios like medical imaging. Moreover, the Lorentz transformation guides people’s understanding of electromagnetic fields and underpins advancements in nuclear energy and aerospace technology.

Description Of Natural Events with Correct Reference Body

The beginning of life could not be described on Earth, yet. For this reason, natural phenomena have been described with the starting point uncertainty. Natural events could not be described by a single field. In H. Brown’s study [1], the main lesson that emerges is described as the special theory of relativity is incomplete. For that reason, the aim of this study is to describe physical reality in a single field. In the light of this aim, first of all, coordinate systems which are under-established are defined. The reason for the deficiency is explained. The system of unified coordinates, which is based on the correct basis, is explained. Moreover, in this study, the coordinate systems which are defective with respect to each other are described. In addition, in this study, the theory describing the relation of these coordinates with the reference body with a single field is explained and proved by equations. Furthermore, the beginning of life is explained by Lorentz Transformation Equations and Gauss Coordinate Systems. At the end of the description, new interpretations, interpretations supporting previous interpretations of scientists, or equations stating that they are wrong are explained. As a result, in this study, the equivalent of the reference body in the natural system is explained

An Implicit and Untested Premise of the Special Theory of Relativity

The derivation of Lorentz Transformation Equations in the Special Theory of Relativity, besides being explicitly based on the two postulates of that theory is also critically based on an implicit premise that the detection of a light signal/particle at a point in space at an instant of time is an event that is not exclusive to any inertial reference frame but it is capable of being measured by the observers in other inertial reference frames as well. This paper explains how this untested paradoxical premise vitiates the entire theory and suggests its replacement with a contrary postulate that the detection of light in an inertial reference frame is an event that is exclusive to that frame. This paper shows that if that contrary postulate is accepted, then the absoluteness of space and time declared by Newton can coexist with the absoluteness of the speed of light in vacuum declared by Einstein without any conflict between them.

Reinterpretation of Lorentz transformation according to the Copenhagen school and the quantization of gravity

In this paper, I propose a quantization of gravity that leads to photons mediated gravitation. The quantization of general relativity depends now on the modified special relativity [A. Almosallami, e-print viXra:1111.0001v1 (2011); e-print viXra:1401.0043 [High Energy Particle Physics](2014)], which introduces a new interpretation of the Lorentz transformation equations depending on quantum theory (Copenhagen school) [A. AlMosallami, IJSER 5, 128 (2014); Int. J. Mod. Theor. Phys. 3, 44 (2014); e-print viXra:1111.0001v1 [Relativity and Cosmology] (2011); e-printviXra:1401.0043 [High Energy Particle Physics] (2014); IJSER 5, 451 (2014)]. In these new transformations, I propose there is no space-time continuum, as in special relativity; it is only time, and space is invariant. This new interpretation of the Lorentz transformations leads to thetransformation being vacuum energy dependent instead of relative velocity dependent as in Einstein's interpretation of the Lorentz transformation equations of the theory of special relativity. Furthermore, the Lorentz factor is equivalent to the refractive index in optics. In this new interpretationof the Lorentz transformations, I refuse the reciprocity principle adopted by Einstein in the theory of special relativity. Refusing the reciprocity principle in this theory leads to the disappearance of all the paradoxes of the theory of special relativity: The Twin paradox, Ehrenfest paradox,the Ladder paradox, and Bell's spaceship paradox. Furthermore, according to my interpretation, one could explain the experimental results of quantum tunneling and entanglement (spooky action), Casimir effect, and Hartman effect. The new interpretation of the Lorentz transformation equationsleads also to the wave-particle duality as in the quantum theory, and thus agrees with Heisenberg uncertainty principle. The generalization of the transformation leads also to the concept of acceleration or deceleration as vacuum fluctuations as in the quantum field theory. In the proposedquantized force, the force is given as a function of frequency, where in this paper I defined the relativistic momentum as a function of frequency equivalent to the relativistic kinetic energy held by a body and time, and then the quantized force is given as the first derivative of the momentumwith respect to time. Subsequently, I introduce Newton's second law as its relativistic quantized force. Further, I introduce the relativistic quantized inertial force, and then, by my equivalence principle, which agrees completely with the experimental results of quantum field theory, I introducethe relativistic quantized gravitational force, and the quantized time dilation.

Deriving a unified equation for Doppler effect for any wave in any medium from Lorentz transformations

We use the Lorentz transformation equations to derive a unified equation for the Doppler effect–that can be used for any one-dimensional (sound, water, EM, etc.) wave in any medium. This unified equation includes the effects of motion, if present, of the medium relative to the observer as well as the relative velocity between the observer and the source. This master equation can be applied to both relativistic and nonrelativistic situations to recover the more familiar Doppler effect expressions and it clarifies that the Doppler equations given in standard textbooks for both sound and EM waves, are basically the same. The advantage of this unified equation is that it reduces the effort in solving complex problems. Basic knowledge of Lorentz transformations and their physical effects is enough to understand this derivation.

Armenian Theory of Relativity Letter

By using the principle of relativity (first postulate), together with new defined nature of the universal speed (our second postulate) and homogeneity of time-space our third postulate, we derive the most general transformation equations of relativity in one dimensional space. According to our new second postulate, the universal (not limited) speed c in Armenian Theory of Special Relativity is not the actual speed of light but it is the speed of time which is the same in all inertial systems. Our third postulate: the homogeneity of time-space is necessary to furnish linear transformation equations. We also state that there is no need to postulate the isotropy of time-space. Our article is the accumulation of all efforts from physicists to fix the Lorentz transformation equations and build correct and more general transformation equations of relativity which obey the rules of logic and fundamental group laws without internal philosophical and physical inconsistencies.

The Critical Error in the Formulation of the Special Relativity

The perception of events in two inertial reference frames in relative motion was analyzed from the perspective of the Special Relativity postulates, leading to the Lorentz transformation equations for the time and space coordinate in the relative motion direction. Yet, straightforward inconsistencies were identified upon examining the conversion of the time interval between two co-local events in the traveling reference frame. The approach used in the Special Relativity formulation to get around the identified inconsistencies was revealed. Subsequent mathematical contradictions in the Lorentz transformation equations, disproving the Special Relativity predictions, were shown.

The Quantization of General Relativity: Photon Mediates Gravitation

In this paper I propose a quantization of general relativity of Einstein which leads to photon mediates gravitation. My quantization of GR depends on the modified special relativity MSRT which introduces a new interpretation to the Lorentz transformation equations depending on quantum theory (Copenhagen school) [25, 26, 27, 43]. My new interpretation to the Lorentz transformation leads to the Lorentz transformation is vacuum energy dependent instead of the relative velocity in Einstein’s interpretation to the Lorentz transformation equations in the SRT. Furthermore the Lorentz factor is equivalent to the refractive index in optics. In my interpretation to the Lorentz transformation I refuse the reciprocity principle which was adopted by Einstein in the SRT. Refusing the reciprocity principle in my theory leads to disappearing all the paradoxes in the SRT; the Twin paradox, Ehrenfest paradox, Ladder paradox and Bell's spaceship paradox [25, 26, 2,7, 43]. Furthermore, according to my interpretation I could reconcile and interpret the experimental results of quantum tunneling and entanglement (spooky action), —Casimir effect, Hartman effect— with the SRT in this paper [25, 26, 27, 43]. My new interpretation to the Lorentz transformation equations leads also to the wave-particle duality as in quantum theory, and thus agrees with Heisenberg uncertainty principle. The generalization of my transformation leads also the concept of acceleration or deceleration is vacuum fluctuations as in quantum field theory. In my proposed quantized force, the force is given as a function of frequency [1]. Where, in this paper I defined the relativistic momentum as a function of frequency equivalent to the relativistic kinetic energy held by a body and time, and then the quantized force is given as the first derivative of the momentum with respect to time. Subsequently I introduce Newton’s second law as it is relativistic quantized force, and then I introduce the relativistic quantized inertial force, and then by my equivalence principle which agreed completely with the experimental results of QFT, I introduce the relativistic quantized gravitational force, and the quantized gravitational time dilation.

Time Contraction: The Possibility of Faster Than Light without Violation of Lorentz Transformation or Causality and the Vacuum Energy Dependent

Faster than light is impossible according to the special relativity theory of Einstein SRT. In this paper I'll propose a new concept in physics called contraction. This concept will solve many problems in physics related to faster than light without violation Lorentz transformation or causality. According to this concept, it is possible measuring the speed of an electromagnetic wave or a particle which owns rest mass greater than zero to be faster than the speed of light in vacuum without violation of Lorentz transformation or causality. Time contraction is proposed by a new understanding to the Lorentz transformation equations depending on the concepts of quantum theory (Copenhagen School). It is a new formulation to the time dilation and the length contraction and the speed of light which are vacuum energy dependent. By this new formulation, I could rescue the special relativity from the Twin paradox, Ehrenfest paradox, Ladder paradox and Bell's spaceship paradox. Furthermore, I could reconcile and interpret the experimental results of quantum tunneling and entanglement (spooky action), —Casimir effect, Hartman effect— with the SRT in this paper.

On Lorentz transformation and special relativity: Critical mathematical analyses and findings

In this paper, the Lorentz transformation equations are closely examined in connection with the constancy of the speed of light postulate of the special relativity. This study demonstrates that the speed of light postulate is implicitly manifested in the transformation under the form of space-to-time ratio invariance, which has the implication of collapsing the light sphere to a straight line, and rendering the frames of reference origin-coordinates undetermined with respect to each other. Yet, Lorentz transformation is shown to be readily constructible based on this conflicting finding. Consequently, the formulated Lorentz transformation is deemed to generate mathematical contradictions, thus defying its tenability. A rationalization of the isolated contradictions is then established. An actual interpretation of the Lorentz transformation is presented, demonstrating the unreality of the space-time conversion property attributed to the transformation.

Armenian Theory of Special Relativity

By using the principle of relativity (first postulate), together with new defined nature of the universal speed (our second postulate) and homogeneity of time-space (our third postulate), we derive the most general transformation equations of relativity in one dimensional space. According to our new second postulate, the universal (not limited) speed c in Armenian Theory of Special Relativity is not the actual speed of light but it is the speed of time which is the same in all inertial systems. Our third postulate: the homogeneity of time-space is necessary to furnish linear transformation equations. We also state that there is no need to postulate the isotropy of time-space. Our article is the accumulation of all efforts from physicists to fix the Lorentz transformation equations and build correct and more general transformation equations of relativity which obey the rules of logic and fundamental group laws without internal philosophical and physical inconsistencies.

Derivation of Lorentz transformation equations from the new concept of reaction-at-a-distance

Derivation of Lorentz transformation equations from the new concept of reaction-at-a-distance

Derivation of the Lorentz force law, the magnetic field concept and the Faraday–Lenz and magnetic Gauss laws using an invariant formulation of the Lorentz transformation

It is demonstrated how the right-hand sides of the Lorentz transformation equations may be written, in a Lorentz-invariant manner, as 4-vector scalar products. This implies the existence of invariant length intervals analogous to invariant proper time intervals. An important distinction between the physical meanings of the space–time and energy–momentum 4-vectors is pointed out. The formalism is shown to provide a short derivation of the Lorentz force law of classical electrodynamics, and the conventional definition of the magnetic field, in terms of spatial derivatives of the 4-vector potential, as well as the Faraday–Lenz law and the Gauss law for magnetic fields. The connection between the Gauss law for the electric field and the electrodynamic Ampère law, due to the 4-vector character of the electromagnetic potential, is also pointed out.

On Einstein's 1905 electrodynamics paper

Examination of Einstein's 1905 landmark paper On the electrodynamics of moving bodies reveals that his obtaining of the Lorentz transformation equations contains shortcomings apparently previously unnoticed or unremarked. Modifications of his analysis as well as extension of the procedures he has chosen allows his approach to be made into a complete proof, while still remaining within the framework of his method.

Comment on the Comment by G. Schäfer on the Paper "Non-kinematicity of the Dilation-of-time Relation of Einstein for Time-intervals" by S. Golden

Abstract In his comment G. Schäfer [1] points out that S. Golden's [2] time-dilation equations (12) and (13) are of kinematic type and that the title of Golden's paper is therefore a misconception. He also states that Golden's treatment of the time-dilation problem is incomplete, since Golden has not considered particle decay in his paper. I should like to present my comment on these two points raised by G. Schäfer. Although Golden describes his equation (13) as "spatially dependent," he says at the beginning of Sect. 4 of his paper that his equations (12) and (13) can be regarded as "either velocity dependent or spatially dependent." But this is not at all the essence of his paper. The essence of his paper is that the two time-dilation equations that he has derived do not imply "any actual dilation-of-time in clocks that may be stationed in the systems." Hence he concludes that Einstein's time-dilation relation is merely a transformation relation and that the motion of the systems does not affect "the intrinsic time-rates of any clocks stationed within them." In order to judge the significance of Golden's paper, it is important to remember that Einstein arrived at the ideas of kinematic time-dilation and length contraction in moving systems not as a result of a rigorous deduction from any mathematical, physical or logical relations, but simply by interpreting in his own way the physical significance of transformation equations for space and time (Lorentz transformation equations) [3]. Ever since the publication of his 1905 article, Einstein's ideas of kinematic length contraction and time dilation

Special theory of relativity, conceptual change and history of science

The problem of the learning of Special Theory of Relativity by secondary and college students is analysed. It is stressed that the results of the studies which attempted to evaluate students' learning are ambiguous and intriguing. Also the history of the emergence and acceptance of the theory by the scientific community itself at the beginning of the 20th century is analysed. Three fundamental steps are described: a) the publication of Lorentz's Transformation Equations, their interpretation in the context of the Electron Theory and their consequent acceptance by the scientific community; b) the presentation by Einstein of two postulates, namely the Relativity Principle and Einstein's Principle of the Invariance of the Speed of Light, and their partial acceptance; c) the rejection of the Electron Theory and the final acceptance of the Theory of Relativity simultaneously with the development of the General Theory of Relativity. The analogy between historical and learning processes provides some suggestions to improve the teaching of the theory.

The observed intensity of a radiating moving object

The Lorentz transformation equations for emission rates are calculated from the equations for the time dilation, the Doppler effect and aberration. Radiation from accelerated charges and from diffuse surfaces in motion is considered. The theory is applied to a model of an expanding star, and the modification of its apparent magnitude due to the expanding motion is calculated.

The co-ordinatization of the kinematical vectors

The process of transforming the co-ordinates of a three-dimensional vector, conceived as a geometric object, between inertial co-ordinate systems is defined as a co-ordinatization process. The vectors obtained by co-ordinatizing the kinematical vectors represent an extension of kinematical theory, existing on a par with the standard Lorentz transformation equations. These two different approaches to the transformation of the kinematical vectors represent transformations of two forms of spatial information between inertial co-ordinate systems. The new co-ordinatization approach potentially allows a classical geometrization of the vector laws of physics. The kinematical vector results obtained from the co-ordinatization process can be experimentally verified.

The Rod Contraction-Clock Retardation Ether Theory and the Special Theory of Relativity

This paper is a historical and critical review of an ether theory which starts with rod contraction and clock retardation, and a comparison between this ether theory and the special theory of relativity. The two theories are generally equivalent since they both lead to the Lorentz transformation equations. The possibility of an experimental difference between the two theories may lie in a one-way experiment, and this subject is briefly explored with the tentative conclusion that so far it seems that no one has made a specific proposal for such a crucial one-way experiment nor has anyone conclusively demonstrated the impossibility of such a test.

Elementary Treatment of Relativistic Cross Sections

The primary purpose of this paper is to show that, when relativity must be taken into account, there is no need to revise the ordinary definition of a cross section. Rather, a slight rearrangement of factors will obtain Lorentz invariant quantities. To demonstrate invariance is quite simple. Next, the reaction rate density can easily be written down just by bringing together, from a particle viewpoint, the various factors we know on physical grounds should be present. Again, by judicious grouping, the result can be expressed as a product of factors that are separately invariant. We go on to discuss the Lorentz transformation of an angular distribution (without explicitly using the Lorentz transformation equations), the relativistic normalization of wave functions, and finally, the connection of our simple approach with S-matrix theory.