Using the notion, developed in an earlier paper, of "representation" of "position" by a vector in a vector space with an inner product, we show that the Lorentz Transformation Equations relating positions in two different reference frames can be put in a particularly simple form which could be said to be "Galilean". We emphasize that two different reference frames can use a common vector space for representation but with two different inner products. The inner products are defined through the observational set-up of each frame.
A calculus based on pointer-mark coincidences is proposed to define, in a mathematically rigorous way, measurements of space and time intervals. The connection between such measurements in different inertial frames according to the Galilean or Lorentz transformations is then studied using new, simple, and practical clock synchronisation procedures. It is found that measured length intervals are Lorentz invariant, whereas moving clocks show a universal time dilatation effect. The `relativistic length contraction' and `relativity of simultaneity' effects of conventional special relativity theory…
We present a pedagogical approach to the Lorentz group. We start by introducing a compact notation to express the elements of the fundamental representation of the rotations group.Lorentz coordinate transformations are derived in a novel and compact form. We show how to make a Lorentz transformation on the electromagnetic fields as well. A covariant time-derivative is introduced in order to deal with non-inertial systems. Examples of the usefulness of these results such as the rotating system and the Thomas precession, are also presented
It is generally expected from intuition that the electromagnetic force exerted on a charged particle should remain unchanged when observed in different reference frames in uniform translational motion. In the special relativity, this invariance is achieved by invoking the Lorentz transformation of space and time. In this investigation an entirely different interpretation of the invariance of force is presented. We propose a new model of the electromagnetic force given in terms of the augmented potentials, which are derived from the electric scalar potential by incorporating a velocity differen…
Using post-Galilean space and time derivatives transformations and quantum mechanics, we have found a new particle-wave equation besides the Klein-Gordon equation describing a spinless scalar particle. This new equation can also be obtained from Dirac's equation if $β=γ(1\pm\frac{v}{c})$. Biot-Savart law and additional continuity equations are obtained as a consequence of the invariance of Dirac's equation and Maxwell's equations under these transformations.
Transformation equations for the kinetic energy of the same bullet in Galileo's and Einstein's special relativity are derived. The special relativity result is extended to the case of a photon.
We report the discovery of an exact mapping from Galilean time and space coordinates to Minkowski spacetime coordinates, showing that Lorentz covariance and the spacetime construct are consistent with the existence of a dynamical 3-space, and "absolute motion". We illustrate this mapping first with the standard theory of sound, as vibrations of a medium, which itself may be undergoing fluid motion, and which is covariant under Galilean coordinate transformations. By introducing a different non-physical class of space and time coordinates it may be cast into a form that is covariant under "Lore…
The Lorentz Transformations are derived without any linearity assumptions and without assuming that y and z coordinates transform in a Galilean manner. Status of the invariance of the speed of light is reduced from a foundation of the Special Theory of Relativity to just a property which allows to determine a value of the physical constant. While high level of rigour is maintained, this paper should be accessible to a second year university physics student.
The incompatibility between the Lorentz invariance of classical electromagnetism and the Galilean invariance of continuum mechanics is one of the major barriers to prevent two theories from merging. In this note, a systematic approach of obtaining Galilean invariant field variables and equations of electromagnetism within the semi-relativistic limit is reviewed and extended. In particular, the Galilean invariant forms of Poynting's theorem and the momentum identity, two most important electromagnetic identities in the thermomechanical theory of continua, are presented. In this note, we also in…
Evaluation of the additive constants in the space-time Lorentz transformation equations required, according to Einstein, to correctly describe synchronised clocks at different spatial locations, reveals the spurious and unphysical nature of the 'relativity of simultaneity' and 'length contraction' effects of conventional special relativity. Unlike time dilation, there is no experimental evidence for these putative effects. Only a universal (position independent) time dilation effect for different inertial frames distinguishes special from Galilean relativity.
We show that a derivation of the Lorentz-Einstein transformation based on length contraction or on time dilation is faster then "World's fastest derivation of the Lorentz transformation"
We show that starting with the fact that special relativity theory is concerned with a distortion of the observed length of a moving rod, without mentioning if it is a "contraction" or "dilation", we can derive the Lorentz transformations for the spacetime coordinates of the same event. This derivation is based on expressing the length of the moving rod as a sum of components with all the lengths involved in this summation being measured by the observers of the same inertial reference frame.
We show that the transformation equations for the parameters that characterize a plane acoustic wave: period, (frequency), wave vector, wave length and phase velocity can be derived without using phase invariance and Lorentz-Einstein transformation
Generalized Lorentz transformations with modified velocity parameter are considered. Lorentz transformations depending on the mass of the observer are suggested.The modified formula for the addition of velocities remarkably preserves the constancy of the velocity of light for all observers. The Doppler red shift is affected and can provide a test of such generalisations.
The Lorentz Transformation is traditionally derived requiring the Principle of Relativity and light-speed universality. While the latter can be relaxed, the Principle of Relativity is seen as core to the transformation. The present letter relaxes both statements to the weaker, Symmetry of Reference Principle. Thus the resulting Lorentz transformation and its consequences (time dilatation, length contraction) are, in turn, effects of how we manage space and time.
In the line of thought of Einstein's 1905 paper on relativity, I get a physical derivation of Lorentz transformation (LT) answering its main criticism and considerably enlarging the area of applications of the theory of relativity.
Some solutions to the anomalies of ultra high energy cosmic-ray(UHECR) and TeV $γ$-rays require disturbed non-quadratic dispersion relations, which suggest the Lorentz violation. Also, some new theories such as quantum gravity, string theory and the standard model extension imply the Lorentz violation. In this paper, we derive some transformation laws for the classical parameters of nonlinear field system, and then provide their dispersion relations. These dispersion relations also have non-quadratic form but keep the Lorentz invariance. The analysis of this paper may be helpful for understand…
We show that starting with the addition law of parallel speeds derived as a consequence of the invariance of the speed of light, the Lorentz transformations for the space-time coordinates can be derived.
The Lorentz Transformation, which is considered as constitutive for the Special Relativity Theory, was invented by Voigt in 1887, adopted by Lorentz in 1904, and baptized by Poincaré in 1906. Einstein probably picked it up from Voigt directly.
Symmetry breaking is discussed in this paper which comes from the Lorentz transformation of special relativity and changes our view that two relatively moving bodies always have the relative speed equal in magnitude and opposite in direction. An appeal was made for the test of Lorentz transformation in a multimedia environment which has the fundamental significance that it may reveal the origin of symmetry breaking in many physical phenomena.
It is recently discovered that the usual transformations of the three-dimensional (3D) vectors of the electric and magnetic fields differ from the Lorentz transformations (LT) (boosts) of the corresponding 4D quantities that represent the electric and magnetic fields. In this paper, using geometric algebra formalism, this fundamental difference is examined representing the electric and magnetic fields by bivectors.
An interpretation of the inertial mass increase due to an object's velocity which is derived from the theory of special relativity is discussed. A Lorentz transformation of the reference time causes the inertial mass increase. It is assumed that the real physical phenomenon that occurs is an expansion of the reference time by a Lorentz transformation (that is, a dilation of time). Only the reference time is assumed to be variant, which causes relativistic mass. Time dilation is real. Relativistic mass originates in a Lorentz transformation of reference time.
Introducing the primed inertial coordinate system, for each inertial frame of reference, in addition to the usual inertial coordinate system, we assume that gravity-free space and time possess the Euclidean structures in the primed inertial coordinate system and the generalized Finslerian structures in the usual inertial coordinate system. We combine these assumptions with two fundamental postulates, (i) the principle of relativity and (ii) the constancy of the speed of light in all inertial frames of reference, to derive the localized Lorentz transformation as a linear transformation between …
We show that the Lorentz transformations for the space-time coordinates of the same event are a direct consequence of the principle of relativity and of Einstein's distant clocks synchronization procedure. In our approach, imposing the linear character of the Lorentz transformations we guess that the transformation equation for the space coordinate has the form x=ax'+cbt'. Imposing the condition that it accounts for the time dilation relativistic effect and taking into account the fact that due to the clock synchronization a la Einstein the space-time coordinates of the same event in the two f…
Starting with a thought experiment proposed by Kard, which derives the formula that accounts for the relativistic effect of length contraction, we present a "two line" transparent derivation of the Lorentz-Einstein transformations for the space-time coordinates of the same event. Our derivation make uses of Einstein's clock synchronization procedure
In a recent article [1] we have explored alternative decompositions of the Lorentz transformation by adopting the synchronization convention of the target frame at the end and alternately at the outset. In this note we develop the decomposition by assuming a correct universal synchronization that may be outside the two inertial frames that are involved.
In this paper we develop a framework allowing a natural extension of the Lorentz transformations. To begin, we show that by expanding conventional four-dimensional spacetime to eight-dimensions that a natural generalization is indeed obtained. We then find with these generalized coordinate transformations acting on Maxwell's equations that the electromagnetic field transformations are nevertheless unchanged. We find further, that if we assume the absence of magnetic monopoles, in accordance with Maxwell's theory, our generalized transformations are then restricted to be the conventional ones. …
A new method of derivation of Lorentz Transformation (LT) is given based on both axioms of special relativity (SR) and physical intuitions. The essence of the transformation is established and the crucial role played by the presumptions is presented for clarification. I consider the most general form of transformations between two sets of events in two inertial reference frames and use the most basic properties expected from such a transformation together with the principle of the constancy of the velocity of light to derive LT. The method is very simple, succinct and useful for students tryin…
Starting from the well-known light-clock thought experiment to derive time dilation and length contraction, it is shown that finding the Lorentz Transformation requires nothing more than the most trivial vector addition formula. The form which is obtaine for the L.T. allows an easy derivation of the velocity and acceleration transformations which are also given.
The Lorentz transformation is entirely derived from length contraction, itself established through the known light-clock thought experiment . This makes the derivation accessible to beginning students once Eintein's two postulates have been admitted. The formula derived for the space part of the general rotation-free Lorentz transformation is very compact and allows for an easy derivation of the velocity and acceleration transformations. A possibly new and very simple relation is found between proper acceleration and acceleration in an inertial frame.
The standard Lorentz transformations establish a relationship between the space-time coordinates of the same event when detected from two inertial reference frames I and I' in the standard arrangement. This event is characterized by the space-time coordinates E(x,tE) and E'(x',t'E), tE and t'E representing the readings of the standard synchronized clocks C(x) and C'(x') located in the two frames where the event takes place. We obtain the nonstandard Lorentz transformations establishing a "physically" correct relationship between the readings of the standard synchronized clocks and the readings…
The Lorentz transformation is derived without the postulate of the universal limiting speed, and the general Edwards transformation is obtained by using the principle of permutation invariance (covariance). It is shown that the existences of the one-way universal limiting speed (in the Lorentz transformation) and the constancy of the two-way average speed of light (in the Edwards transformation) are the necessary consequences of the principle of permutation invariance that is consistent with the postulate of relativity. The connection between the Edward transformation and the general coordinat…
In this paper it is exactly proved by using the Clifford algebra formalism that the standard transformations of the three-dimensional (3D) vectors of the electric and magnetic fields E and B are not the Lorentz transformations of well-defined quantities from the 4D spacetime but the 'apparent' transformations of the 3D quantities. Thence the usual Maxwell equations with the 3D E and B are not in agreement with special relativity. The 1-vectors E and B, as well-defined 4D quantities, are introduced instead of ill-defined 3D E and B.
We discuss transormation laws of electric and magnetic fields under Lorentz transformations, deduced from the Classical Field Theory. It is found that we can connect the resulting expression for a bivector formed with those fields, with the expression deduced from the Wigner transformation rules for spin-1 functions of massive particles. This mass parameter should be interpreted because the constancy of speed of light forbids the existence of the photon mass.
