Bernhard Rothenstein
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.
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This paper considers the question of whether Aryabhata's direct and indirect references to relativity of motion are equivalent to Galilean Relativity. Examining verses fom different sections of the text Aryabhatiya, we show that there is explicit mention of relativity of space and motion, although there is no explicit reference to the motion being uniform.
An odd look at "standard" physics (Galileo, Newton, Einstein, Dirac) leading to a radical change of our concept of inertial motion and to new heuristic approaches of gravitation and the cosmological constant.
We deduce the most general space-time transformation laws consistent with the principle of relativity. Thus, our result contains the results of both Galilean and Einsteinian relativity. The velocity addition law comes as a bi-product of this analysis. We also argue why Galilean and Einsteinian versions are the only possible embodiments of the principle of relativity.
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 first define the functions which ensure the transformation of momentum and energy of a tardyon, the transformation of the wave vector and the frequency of the associated wave. Having done this, we show that they ensure the relativistic invariance of the quotient between momentum and wave vector and between energy and frequency if the product between particle velocity u and phase velocity w is a relativistic invariant (uw=c^2), a condition which is a natural combination of special relativity theory and quantum mechanics.
It is demonstrated that the measured spatial separation of two objects, at rest in some inertial frame, is invariant under space-time transformations. This result holds in both Galilean and Special Relativity. A corollary is that there are no `length contraction' or associated 'relativity of simultaneity' effects in the latter theory. A thought experiment employing four unsynchronised clocks and a single measuring rod reveals that the physical basis of the time dilatation effect is a relative velocity transformation law, not `length contraction'. Time dilatation, which is universal and transla…
All About the Galilean Group SGal(3)
本文研究了伽利略群 SGal(3) 的结构及其李代数，探讨了时间在伽利略相对论中的作用以及时空不确定性的关系。
It is well known that the field equations of teleparallel theory which is equivalent to general relativity (TEGR) completely agree with the field equation of general relativity (GR). However, TEGR has six extra degrees of freedom which spoil the true physics. These extra degrees are related to the local Lorentz transformation. In this study, we give three different tetrads of flat horizon space-time that depend only on the radial coordinate. One of these tetrads contains an arbitrary function which comes from local Lorentz transformation. We show by explicate calculations that this arbitrary f…
The work is devoted to the critical analysis of theoretical prediction and astronomical observation of GR effects, first of all, the Mercury's perihelion advance. In the first part, the methodological issues of observations are discussed including a practice of observations, a method of recognizing the relativistic properties of the effect and recovering it from bulk of raw data, a parametric observational model, and finally, methods of assessment of the effect value and statistical level of confidence. In the second part, the Mercury's perihelion advance and other theoretical problems are dis…
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.
Recently, [3], it was shown that Special Relativity is in fact based on one single physical axiom which is that of Reciprocity. Originally, Einstein, [1], established Special Relativity on two physical axioms, namely, the Galilean Relativity and the Constancy of the Speed of Light in inertial reference frames. Soon after, [4,5], it was shown that the Galilean Relativity alone is sufficient for Special Relativity. Here it is important to note that, implicitly, three more assumptions have been used on space-time coordinate transformations, namely, the homogeneity of space-time, the isotropy of s…
In this paper, Lorentz Transformation(LT) is derived by an alternate method, using photon clocks, placed at the locations of the concerned events, which are initially synchronised using a light signal(Einstein synchrony). Then, it is shown that the second term in the time dilation equation of the LT, is the term responsible for time travel and further it is shown that this term arises merely due to non-simultaneous initial clock synchronisation and that this term does not correspond to any actual time elapsed while timing events, thus ruling out the possibility of time travel, from the framewo…
In 1945 Einstein concluded that [1]: 'The present theory of relativity is based on a division of physical reality into a metric field (gravitation) on the one hand, and into an electromagnetic field and matter on the other hand. In reality space will probably be of a uniform character and the present theory be valid only as a limiting case. For large densities of field and of matter, the field equations and even the field variables which enter into them will have no real significance.'. The dichotomy can be resolved by introducing a scalar field/potential algebraically related to the Ricci ten…
We propose a parallel introduction to Galilean and Einsteinian relativity based on the causal structure and inertial motions. Galilean and Poincare transformations, as objects secondary to the geometrical structure, are left aside.
In this paper Maxwell equations are used to analyze the propagation of oscillating electric and magnetic fields from a moving electric dipole source. The results show that both the magnetic field and electric fields generated propagate faster than the speed of light in the nearfield and reduce to the speed of light as they propagate into the farfield of the source. In addition, the results show that the speed of the fields are dependant on the velocity of the source in the nearfield and only become independent in the farfield. These effects are shown to be the same whether the source or observ…
A theory of vector gravitational waves is presented on the basis of an additional gravitational field, recovering ideas that go back to H. A. Lorentz, field that A. Wheeler called ``gravitomagnetism''. The theory is independent of Einstein's General Relativity Theory, but is consistent with the Einstein-Lorentz framework of Special Relativity, so that the resulting equations are considered exact from the start, and not approximations valid for velocities small compared with the speed of light. A simple model of mass formation and presence of angular momentum started with a new type of singular…
Following an early observation of Ignatowsky, we present a derivation of the transformation rules between inertial systems making no other assumptions than the existence of the latter, and show that generically these rules are characterized by a constant of nature with the dimensions of an inverse velocity squared having the same value in all inertial frames. No independent postulate of the existence of an absolute velocity for light waves or other carriers of physical information is necessary. Aside from the usual Lorentz- and galilean transformations, our analysis also allows for the existen…
An in-depth and mathematically-detailed analysis of Langevin's popular 1911 article on the special theory of relativity is presented. For the reader's convenience, English translations of large parts of the original French text are given. The self-contradictory nature of many of Langevin's assertions is pointed out. Of special interest is the analysis of the exchange of light signals between the travelling and stay-at-home twins in Langevin's thought experiment, in which antinomies are found in the conventional relativistic treatment. Their resolution shows that the physical basis of the diffe…
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…
The distinction between the real positions of moving objects in a single reference frame and the apparent positions of objects at rest in one inertial frame and viewed from another, as predicted by the space-time Lorentz Transformations, is discussed. It is found that in the Rockets-and-String paradox the string remains unstressed and does not break and that the pole in the Barn-and-Pole paradox never actually fits into the barn. The close relationship of the Lorentz-Fitzgerald Contraction and the relativity of simultaneity of Special Relativity is pointed out and an associated paradox, in whi…
In this paper, we establish a theory of Special Relativity valid for the entire speed range without the assumption of constant speed of light. Two particles species are defined, one species of particles have rest frames with rest mass, and another species of particles do not have rest frame and can not define rest mass. We prove that for the particles which have rest frames, the Galilean transformation is the only linear transformation of space-time that allows infinite speed of particle motion. Hence without any assumption, an upper bound of speed is required for all non-Galilean linear trans…
The kinematics of particles refer to events and tangent vectors, while that of waves refer to dual gradient planes. Special relativity [1-3] applies to both objects alike. Here we show that spacetime exchange symmetry [7] implicit in the SIdefinition of length based on the universal constant c has profound consequences at low velocities. Galilean physics, exact in the limit c \to \infty, is mirrored by a dual so-called Carrollian superluminal kinematics [4-6] exact in the limit c \to 0. Several new results follow. The Galilean limit explains mass conservation in Newtonian mechanics, while the …
The kinematics of the two-scale relativity theory (new relativity) is revisited using a simplified approach. This approach allows us not only to derive the dispersion equation introduced earlier by Kowalski-Glikman, but to find an additional dispersion relation, and, even more important, to provide a physical basis for such relations. They are explained by the fact that in the observer invariant two-scale relativity (new relativity) the Planck constant does nor remain constant anymore, but depends on the universal length scale. This leads to the correct relation between energy and frequency at…
The root of the divergence problem in the current quantum field theory seems to be in the special theory of relativity. Here we propose a modified special relativity theory by introducing the primed inertial coordinate system, in addition to the usual inertial coordinate system, for each inertial frame of reference, assuming the flat structures of gravity-free space and time in the primed inertial coordinate system and their generalized Finslerian structures in the usual inertial coordinate system, and combining this assumption with the two fundamental postulates, (i) the principle of relativi…
In 1945 Einstein concluded that [1]: "The present theory of relativity is based on a division of physical reality into a metric field (gravitation) on the one hand, and into an electromagnetic field and matter on the other hand. In reality space will probably be of a uniform character and the present theory be valid only as a limiting case. For large densities of field and of matter, the field equations and even the field variables which enter into them will have no real significance.". The dichotomy is resolved by introducing a complex Randers metric with a real valued scalar field and comple…
In this paper, we revisit the two theoretical approaches for the formulation of the tachyonic Dirac equation. The first approach works within the theory of restricted relativity, starting from a Lorentz invariant Lagrangian consistent with a spacelike four-momentum. The second approach uses the theory of relativity extended to superluminal motions and works directly on the ordinary Dirac equation through superluminal Lorentz transformations. The equations resulting from the two approaches show mostly different, if not opposite, properties. In particular, the first equation violates the invaria…
Galilean Relativity and Einstein's Special and General Relativity showed that the Laws of Physics go deeper than their representations in any given reference frame. Thus covariance, or independence of Laws of Physics with respect to changes of reference frames became a fundamental principle. So far, all of that has only been expressed within one single mathematical model, namely, the traditional one built upon the usual continuum of the field $\mathbb{R}$ of real numbers, since complex numbers, finite dimensional Euclidean spaces, or infinite dimensional Hilbert spaces, etc., are built upon th…
On the Special Theory of Relativity and Electromagnetism
该研究提出狭义相对论表述，从伽利略空间变换出发，经分析得出公理结构与洛伦兹变换，还考虑惯性电荷系统，推导电磁场方程和力定律，为林德曼断言提供框架，且结果与单位选择无关，能推断现象在不同时空的表现。
To consider a medium carrying light and electromagnetic waves is impossible, when this medium shall have properties according to the principle of constant speed of light, that is, isotropy of speed of light in every system of reference. Therefore, with principle of constant speed of light abandoned, the so-called medium synchronization of clocks is defined, yielding isotropy solely in the system at rest and anisotropy in all moving systems. From medium synchronization the appropriate coordinate transformation is developed, the so-called medium transformation, a Galilean type of transformation,…
Groups of Worldview Transformations Implied by Einstein's Special Principle of Relativity over Arbitrary Ordered Fields
本文在任意有序域上重构Borisov公理系统，证明非阿基米德域上存在欧几里得、伽利略和庞加莱模型及无限下降链，且欧几里得等距变换无法被自然公理消除。
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