Lorentz's theory and special relativity are completely identical

Comment on "Trouble with the Lorentz Law of Force: Incompatibility with Special Relativity and Momentum Conservation"

This Comment addresses a recent paper by M. Mansuripur (Phys. Rev. Lett. 108, 193901 (2012)), who claims that the Lorentz law of force should be abandoned because it violates relativity. The Comment argues that this is not necessarily the case and also takes issue with Manusripur's approach to classical electromagnetism.

Time Isotropy, Lorentz Transformation and Inertial Frames

Homogeneity of space and time, spatial isotropy, principle of relativity and the existence of a finite speed limit (or its variants) are commonly believed to be the only axioms required for developing the special theory of relativity (Lorentz transformations). In this paper it is shown, however, that Lorentz transformation cannot actually be derived without the explicit assumption of time isotropy (time-reversal symmetry) which is logically independent of the other postulates of relativity. Postulating time isotropy also restores the symmetry between space and time in the postulates of relativ…

使用lorentz R包系统搜索狭义相对论中的三速度陀螺分配律

A systematic search for a three-velocity gyrodistributive law in special relativity with the lorentz R package

本文介绍了用于处理相对论物理的lorentz R包，该包支持四维矢量变换和非交换、非结合的三速度加法，作者利用它系统搜索狭义相对论中的三速度陀螺分配律，虽未获成功，但为相关研究提供了工具支持。

Space-Time Exchange Invariance: Special Relativity as a Symmetry Principle

Special relativity is reformulated as a symmetry property of space-time: Space-Time Exchange Invariance. The additional hypothesis of spatial homogeneity is then sufficient to derive the Lorentz transformation without reference to the traditional form of the Principle of Special Relativity. The kinematical version of the latter is shown to be a consequence of the Lorentz transformation. As a dynamical application, the laws of electrodynamics and magnetodynamics are derived from those of electrostatics and magnetostatics respectively. The 4-vector nature of the electromagnetic potential plays a…

Does Lorentz Force Law Contradict the Principle and Theories of Relativity for Uniform Linear Motion?

I show that no force or torque is generated in cases involving a charge and a magnet with their relative velocity zero, in any inertial frame of reference. A recent suspicion of an anomalous torque and conflict with relativity in this case is rested. What is distilled as `Lorentz force' in standard electrodynamics, with relative velocity as the parameter, is an under-representation of two distinct physical phenomena, an effect due to Lorentz contraction and another due to the Ampere current-current interaction, rolled into one due to prejudice from special relativity applied only to linear mot…

Comment on "Trouble with the Lorentz Law of Force"

A recent article claims the Lorentz force law is incompatible with special relativity. The claim is false, and the "paradox" on which it is based was resolved many years ago.

Does special relativity theory tell us anything new about space and time?

It will be shown that, in comparison with the pre-relativistic Galileo-invariant conceptions, special relativity tells us nothing new about the geometry of spacetime. It simply calls something else "spacetime", and this something else has different properties. All statements of special relativity about those features of reality that correspond to the original meaning of the terms "space" and "time" are identical with the corresponding traditional pre-relativistic statements. It will be also argued that special relativity and Lorentz theory are completely identical in both senses, as theories a…

Change of basis and Gram-Schmidt orthonormalization in special relativity

While an explicit basis is common in the study of Euclidean spaces, it is usually implied in the study of inertial relativistic systems. There are some conceptual advantages to including the basis in the study of special relativistic systems. A Minkowski metric implies a non-orthonormal basis, and to deal with this complexity the concepts of reciprocal basis and the vector dual are introduced. It is shown how the reciprocal basis is related to upper and lower index coordinate extraction, the metric tensor, change of basis, projections in non-orthonormal bases, and finally the Gram-Schmidt proc…

The Normalization Problem of Special Relativity

For the special theory of relativity, the normalization problem is formulated as the question how observers in constant relative motion may reach an agreement on space and time scales. As the normalization problem does not receive a thorough treatment in the standard development of the theory, two possible solutions called normalization at rest and normalization in motion are suggested. It is shown that normalization in motion makes the validity of the Lorentz transformation the result of mere conventions. The non-conventional approach following from normalization at rest requires an assumptio…

True Transformations of Spacetime Lengths and Apparent Transformations of Spatial and Temporal Distances. I. the Theory

It is shown in this paper that the difference between the two forms of relativity - the ''true transformation (TT) relativity'' and - the ''apparent transformation (AT) relativity'' is essentially caused by the difference in the concept of \emph{sameness} of a physical system, i.e., of a physical quantity, for different, relatively moving, observers. In the ''TT relativity'' the same quantity for different inertial frames of reference is covariantly defined four-dimensional (4D) tensor quantity, which transforms according to the Lorentz transformation as the TT. In the ''AT relativity'' parts …

Cosmological Constant, Classical "Vacuum" and Special Relativity (From the Lorentz boost to the Milgrom acceleration)

We show that Cosmological Constant (CC) is not optional in GR (General Relativity) because it is required by SR (Special Relativity). This completely unexpected result is obtained by introducing a minimal acceleration (Milgrom), square root of CC, in Einstein boost with Lorentz Transformation (LT). We prove that hyperbolic rotation (LT) is an hyperbolic motion with a centrifugal acceleration. In SR with CC (CSR or CR), the universe is not only in expansion (with the law of Hubble) but even in accelerated expansion (cosmological parameter is minus one). Given that the structure of space-time in…

Hyperbolic triangle in the special theory of relativity

The vector form of a Lorentz transformation which is separated with time and space parts is studied. It is necessary to introduce a new definition of the relative velocity in this transformation, which plays an important role for the calculations of various invariant physical quantities. The Lorentz transformation expressed with this vector form is geometrically well interpreted in a hyperbolic space. It is shown that the Lorentz transformation can be interpreted as the law of cosines and sines for a hyperbolic triangle in hyperbolic trigonometry. So the triangle made by the two origins of ine…

A Case for Lorentzian Relativity

The Lorentz transformation (LT) is explained by changes occurring in the wave characteristics of matter as it changes inertial frame. This explanation is akin to that favoured by Lorentz, but informed by later insights, due primarily to de Broglie, regarding the underlying unity of matter and radiation. To show the nature of these changes, a massive particle is modelled as a standing wave in three dimensions. As the particle moves, the standing wave becomes a travelling wave having two factors. One is a carrier wave displaying the dilated frequency and contracted ellipsoidal form described by …

Special Relativity: Einstein's Spherical Waves versus Poincare's Ellipsoidal Waves

We show that the image by the Lorentz transformation of a spherical (circular) light wave, emitted by a moving source, is not a spherical (circular) light wave but an ellipsoidal (elliptical) light wave. Poincare's ellipsoid (ellipse) is the direct geometrical representation of Poincare's relativity of simultaneity. Einstein's spheres (circles) are the direct geometrical representation of Einstein's convention of synchronisation. Poincare adopts another convention for the definition of space-time units involving that the Lorentz transformation of an unit of length is directly proportional to L…

相对论中的速度极限与无粘流体流动中声障的相似性

Similarities between the speed limit in relativity and the sound barrier in inviscid fluid flows

本文综述了普朗特-格劳厄特-洛伦兹变换所揭示的可压缩势流理论与狭义相对论之间的数学对应关系，并借助附加质量概念表明线性化可压缩势流理论可精确镜像狭义相对论的整个数学框架。

The Theory of Relativity - Galileo's Child

We determine the Lorentz transformations and the kinematic content and dynamical framework of special relativity as purely an extension of Galileo's thoughts. No reference to light is ever required: The theories of relativity are logically independent of any properties of light. The thoughts of Galileo are fully realized in a system of Lorentz transformations with a parameter 1/c^2, some undetermined, universal constant of nature; and are realizable in no other. Isotropy of space plays a deep and pivotal role in all of this, since here three-dimensional space appears at first blush, and persis…

"Meta" relativity: Against special relativity?

We introduce a Lorentz-covariant description of tachyons, free of inconsistencies. Our approach is based on an appropriate extension of the special relativity beyond the light barrier, owing to the freedom of synchronization of distant clocks.

Space Time Measurements in Special Relativity

The conventional discussion of apparent distortions of space and time in Special Relativity (the Lorentz-Fitzgerald Contraction and Time Dilatation) is extended by considering observations of : (i) moving objects of limited lifetime in their own rest frame (`transient luminous objects') and (ii) a moving extended array of synchronised `equivalent clocks' in a common inertial frame. Application of the Lorentz Transformation to (i) shows that such objects, viewed with coarse time resolution, appear to be longer in the direction of the relative velocity $\vec{v}$ by a factor $1/\sqrt{1-(v/c)^2}$ …

Diffusion in the special theory of relativity

The Markovian diffusion theory is generalized within the framework of the special theory of relativity using a modification of the mathematical calculus of diffusion on Riemannian manifolds (with definite metric) to describe diffusion on Lorentzian manifolds with an indefinite metric. A generalized Langevin equation in the fiber space of position, velocity and orthonormal velocity frames is defined from which the generalized relativistic Kramers equation in the phase space in external force fields is derived. The obtained diffusion equation is invariant under Lorentz transformations and its st…

On some consequences of the Snyder-Sidharth deformation of Special Relativity

The hypothesis on a minimal scale existence in the Universe leads to noncommutative geometry of Spacetime and thence to a modification of the Special Relativity constraint. Sidharth has deduced that this is equivalent to the Lorentz symmetry violation. This latter consideration was also used by Glashow, Coleman and other scholars though based on purely phenomenological models that have been suggested by the observation of Ultra High Energy Cosmic Rays and Gamma Bursts. On the other hand a parallel development has been the proposal of a small but nonzero photon mass $m_γ>0$ by some authors incl…