The Conjugate Frame Method Relativity (original) (raw)
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Journal of Physics: Conference Series, 2019
This work presents the form that the special theory of relativity takes when only the first postulate and the properties of homogeneity and isotropy of space and time are considered valid. The transformations of Lorentz coordinates are obtained in terms of a universal constant parameter k, developing from these the relativistic kinematics, dynamics and electrodynamics and their respective invariances before these transformations. 1. Introduction Over time, relativity work has been developed from two postulates of special relativity enunciated by Einstein [1]. In our case the electrodynamic formulation is developed only taking into account the first postulate of special relativity [2], where the basic equations of electrodynamics are found. Some researchers on the subject, such as N. David Mermin, in an article from 1983 [3], find the theorem of velocity addition, only counting on the principle of relativity and the properties of homogeneity and isotropy of space-time, arriving at a result that suggests a more general way of describing special relativity. In 1994 J. P. Hsu and L. Hsu [4], used the first postulate of special relativity to develop a theory called Taiji relativity, which is physically different from special relativity where it presents a simpler contextualization. Subsequently U. Molina and collaborators [2], who find the law of adding velocities from the first postulate and properties of homogeneity and isotropy, remaining in terms of a universal constant that depends on the velocity of the inertial frame í µí± ′ respecting to í µí±. Similarly in 2006 Ingrid Steffanel [5], as a continuation of the 2005 work by Molina, focuses on studying relativistic dynamics without the second postulate of relativity where are found expressions for energy, force and relativistic momentum. In 2009 H.O. Di Rocco [6], was able to deduce equations for time dilation, length contraction, Doppler effect among other important aspects of the Special Theory of Relativity, TRE, in which it was not necessary to use Lorentz transformations or space-time diagrams. In 2008 M. J. Feigenbaum [7], obtains the relativistic kinematics and dynamics by making an extension of the Galilean theory without using the second postulate. Similarly in 2012 Peng Cheng Zou and colleagues [8], show that the invariance and constancy of the speed of light were originated from the principle of special relativity, but not from the arbitrary implementation of the second postulate. Also in 2009, A. Sfarti, [9], makes a special simplified theory with the first postulate. On the other hand, in 2015 Alón Drory [10] speaks of the need for the second postulate in relativistic physics and that the principle of relativity together with the homogeneity and isotropy of
A new approach to special relativity
The success of Special Relativity (SR) comes from the requirement of Lorentz covariance to all physical equations. The explanation with regard to the Lorentz covariance is based on two hypotheses, namely the principle of special relativity and the constancy of the speed of light. However, the statements of the principle of special relativity are various and confusing. The covariance of physical equations and the equality of inertial frames of reference are mixed up. The equality of inertial frames of reference is obvious, but the covariance of the physical equations is a more advanced requirement. Additionally, the way that the propagation property of light is placed in a central position of SR has caused people misunderstandings towards space-time, and also there is a logical circularity between the measurement of speed of light and the synchronization of clocks. These have obstructed to correctly extend the theory of space-time from an inertial frame of reference to a non-inertial frame of reference. These are the main reasons why many people criticize SR. In present paper, the two hypotheses have been discussed in detail and a new requirement to the equations of Physics has been proposed. The requirement is the Requirement of Special Completeness, namely, the physical equations used to describe the dynamics of matter and/or fields should include the descriptions that not only the matter and/or fields are at rest relative to an inertial frame of reference, but also they move relative to this frame. Basing on this requirement and the equality of the inertial frames of reference, we can approach to SR. Thereby let the theory of Lorentz covariance has a clear and solid foundation. The constancy of the speed of light is just a deduction, not a premise. The Lorentz covariance is just a characteristic of the Special Complete equations. Maxwell equations automatically satisfy the Lorentz transformations without any modification, while Newton law of gravity does not, because Newton law of gravity is not Special Complete and Maxwell equations are. The new approach has paved a road leading towards the generalizing of the theory of space-time from the inertial frame of reference to non-inertial frame of reference without considering gravitation. Résumé: Le succès de la relativité restreinte (RR) provient de l'exigence de la covariance de Lorentz à toutes les équations physiques. L'explication en ce qui concerne la covariance de Lorentz est fondée sur deux hypothèses, à saa
The Real Quaternion Relativity
arXiv: General Physics, 2018
In this work, we use real quaternions and the basic concept of the final speed of light in an attempt to enhance the standard description of special relativity. First, we demonstrate that it is possible to introduce a quaternion time domain where a coordinate point is described by a quaternion time. We show that the time measurement is a function of the observer location, even for stationary frames of reference. We introduce a moving observer, which leads to the traditional Lorentz relation for the time interval. We show that the present approach can be used in stationary, moving, or rotating frames of reference, unlike the traditional special relativity, which applies only to the inertial moving frames. Then, we use the quaternion formulation of space-time and mass-energy equivalence to extend the quaternion relativity to space, mass, and energy. We demonstrate that the transition between the particle and observer reference frames is equivalent to space inversion and can be describ...
Classical Mechanics, Second Edition, 2013
Special Relativity is taught to physics sophomores at Johns Hopkins University in a series of eight lectures. Lecture 1 covers the principle of relativity and the derivation of the Lorentz transform. Lecture 2 covers length contraction and time dilation. Lecture 3 covers Minkowski diagrams, simultaneous events and causally connected events, as well as velocity transforms. Lecture 4 covers energy and momentum of particles and introduces 4-vectors. Lecture 5 covers energy and momentum of photons and collision problems. Lecture 6 covers Doppler effect and aberration. Lecture 7 covers relativistic dynamics. Optional Lecture 8 covers field transforms. The main purpose of these notes is to introduce 4-vectors and the matrix notation and to demonstrate their use in solving standard problems in Special Relativity. The prerequisites for the class are calculus-based Classical Mechanics and Electricity & Magnetism, and Linear Algebra is highly recommended.
The Relativity Equations of Uniformly Accelerating Frames of Reference
International Journal of Physics
The work presented here is an extension of the work done in the article titled "The Conjugate Frame Method Relativity" [1]. In that work, we considered a moving reference frame that traveled at a constant speed v in a flat or curved space-time manifold. The moving reference frame traveled along a geodesic trajectory in a direction that was either directly towards or directly away from the stationary reference frame. The scalar acceleration a of the moving reference frame was equal to zero. In this work, we consider a moving reference frame that travels with a uniformly changing speed v in a flat or curved space-time manifold. The moving reference frame travels along a geodesic trajectory in a direction that is either directly towards or directly away from the stationary reference frame. The scalar acceleration a of the moving reference frame is a constant that is greater than or equal to zero. The Augmented Conjugate Frame Method is utilized in this work to derive the relativity equations of uniformly accelerating reference frames. These equations can apply to objects that are uniformly accelerated by gravitational, electric, or magnetic fields; as well as by other means, such as rocket propulsion. The relativity equations derived in this work reduce to the equations of Special Relativity when the moving reference frame has a zero scalar acceleration. The Augmented Conjugate Frame Method uses only scalar quantities in the derivation of the relativity equations of uniformly accelerating frames of reference.
The Physical and Mathematical Foundations of the Theory of Relativity
2019
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A Reformulation of Special Relativity
This paper presents a reformulation of special relativity, whose kinematic and dynamic magnitudes are invariant under transformations between inertial and non-inertial reference frames, which can be applied in massive and non-massive particles, and where the relationship between net force and special acceleration is as in Newton's second law. Additionally, new universal forces are proposed.
An alternative to relativistic transformation of special relativity based on the first principles
A new relativistic transformation in the velocity space (here named the differential Lorentz transformation) is formulated solely from the principle of relativity and the invariance of the speed of light. The differential Lorentz transformation is via transforming physical quantities, instead of space-time coordinates, to make laws of nature form-invariant. The differential Lorentz transformation may provide a way to resolve the incompatibility of the theory of special relativity and the quantum theory.
Relativityworkshop.com, 2018
This scientic article develops the theory of relativity regardless of the principles "constancy of light speed", "homogeneity and isotropy of space", and "timing of clocks" in a minkowskian space-time on the basis of electromagnetic fields and reference frames features. In this article we do not think into the invariance of Maxwell equations. It is proved that in this context, orthogonal transformation preserves the skew-adjoint property of electromagnetic field. Thereby it is derived the Lorentz transformations and (in part II) the Lorentz boost. Some possible appealing generalizations arise from the hints that appear in the analysis of this work. * c General Register of Intellectual Property ; Dossier 09/RTPI-03090.4/2018 Madrid(Spain) April 20th 2018 ; M-002741/2018 † Article on line published in the website relativityworkshop.com ‡ The theory of relativity is rediscovered from new standpoints and principles.