Bernhard Rothenstein
Handling substance-like physical quantities in the limits of special relativity theory we should make a net distinction between those which present a proper (rest) magnitude and those which have not. We show how the theory relates them via relativistic transformation equations.
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In this Comment it is shown that the principle of relativity is naturally satisfied and there is no paradox if an independent physical reality is attributed to the four-dimensional (4D) geometric quantities (GQs) and not, as usual, to the 3D quantities. Hence, there is no need either for the change of the expression for the Lorentz force, but as a 4D GQ, or for the introduction of some "hidden" 3D quantities.
Invariance of the counted number of photons and the Lorentz-Einstein transformations enable us to derive transformation equations for the physical quantities introduced in order to characterize energy emission and transport in a plane and in a spherical electromagnetic wave propagating in vacuum.
Different approaches to special relativity (SR) are discussed. The first approach is an invariant approach in which physical quantities in the four-dimensional spacetime are represented by true tensors or equivalently by coordinate-based geometric quantities comprising both components and a basis. This approach we call the ''true transformations (TT) relativity.'' It is compared with the usual covariant approach, which mainly deals with the basis components of true tensors. The third approach is the usual noncovariant approach to SR in which some quantities are not tensor quantities, but rathe…
In this paper it is shown that the real cause of Jackson's paradox is the use of three-dimensional (3D) quantities, e.g., $\mathbf{E}$, $% \mathbf{B}$, $\mathbf{F}$, $\mathbf{L}$, $\mathbf{T}$, their transformations and equations with them. The principle of relativity is naturally satisfied and there is no paradox when the physical reality is attributed to the 4D geometric quantities, e.g., to the 4D torque $N$ (bivector) or, equivalently, to the 4D torques $N_{s}$ and $N_{t}$ (1-vectors), which together contain the same physical information as the bivector $N$.
In this paper we present an invariant formulation of special relativity, i.e., the ''true transformations relativity.'' It deals either with true tensor quantities (when no basis has been introduced) or equivalently with coordinate- based geometric quantities comprising both components and a basis (when some basis has been introduced). It is shown that this invariant formulation, in which special relativity is understood as the theory of a four-dimensional spacetime with the pseudo-Euclidean geometry, completely explains the results of the Michelson-Morley experiment. Two noncovariant approach…
It is shown that if we can define a physical quantity with proper character in a given inertial reference frame (kinematic, dynamic, electromagnetic in its nature) which transforms when detected from a reference frame relative to which it moves with velocity $u_x$ as $F=\f{F^o}{\sqrt{1-\f{u_x^2}{c^2}}}$ then we can derive for it transformation equations following one and the same procedure, which involves the addition law of relativistic velocities which can be derived without using the Lorentz transformations. The transformation equation derived that way, generates the physical quantities $u_…
Invited report at the 8th Meeting of the Working Group ``Base units and fundamental constants'' of the French Academy of Sciences. June 14, 2004. The text consists of seven sections: 1. Great importance of SI. 2. The necessity of updating SI. 3. Special relativity: four-dimensional quantities. 4. Maxwell equations in vacuum in CGSG units. 5. Maxwell equations in vacuum in SI. 6. $c \hbar$ units. 7. Systems CGSG and $c \hbar$ should be legalized.
Periodic relativity: the theory of gravity in flat space time
周期相对论提出时间本质上是周期性的，通过平坦时空和洛伦兹不变加速度统一量子力学与引力理论，并预测黑洞事件视界半径和阴影机制，同时解释引力红移和引力波辐射。
The transformation rules for the basic electrodynamical quantities are routinely derived from the hypothesis that the relativity principle (RP) applies for Maxwell's electrodynamics. These derivations leave open several questions: (1) Is the RP a true law of nature for electrodynamical phenomena? (2) Are, at least, the transformation rules of the fundamental electrodynamical quantities, derived from the RP, true? (3) Is the RP consistent with the laws of electrodynamics in one single inertial frame of reference? (4) Are, at least, the derived transformation rules consistent with the laws of el…
In this paper it is shown that in the approach to special relativity which exclusively deals with the four-dimensional geometric quantities (4D GQs), the invariant special relativity (ISR), there is not recently posed paradox that in a static electric field a magnetic dipole moment (MDM) is subject to a torque in some frames and not in others. In the ISR, there is no need either for the change of the Lorentz force, but as a 4D GQ, or for the introduction of some "hidden" 3D quantities. Furthermore, in the ISR, contrary to all previous approaches, an electrically neutral current-loop in its res…
Using properties of the nonstandard physical world, a new fundamental derivation for all of the effects of the Special Theory of Relativity is given. This fundamental derivation removes all the contradictions and logical difficulties in the original derivation and leads to the fundamental expressions from which Prokhovnik derives the basic transformations. However, it is shown that the correct interpretation is completely distinct from Prokhovnik's. It is shown that the Special Theory effects are but manifestations of the interaction between our natural world and a nonstandard substratum. This…
The paper focuses on finding out several physical quantities to exert an influence on the spatial parameters of complex-octonion curved space, including the metric coefficient, connection coefficient, and curvature tensor. In the flat space described with the complex octonions, the radius vector is combined with the integrating function of field potential to become a composite radius vector. And the latter can be considered as the radius vector in a flat composite-space (a function space). Further it is able to deduce some formulae between the physical quantity and spatial parameter, in the co…
Special relativity theory is well established and confirmed by experiments. This research establishes an operational measurement way to express the great theory in a geometrical form. This may be valuable for understanding the underlying concepts of relativity theory. In four-dimensional spacetime continuum, the displacement field of matter motion is measurable quantities. Based on these measurements, a finite geometrical field can be established. On this sense, the matter motion in physics is viewed as the deformation of spacetime continuum. Suppose the spacetime continuum is isotropic, based…
The paper is intended to clarify operational meaning of mass and time quantities as main characteristics of an atomic clock, which is considered a quantum oscillator in association with the de Broglie wave concept. The specification of the concept of clock in quantum terms reflects the idea of relativistic mass and time complementarity, which is important for avoiding ambiguity of such notions as ``time rate'', ``time record'', and ``elapsed time'' under relativistic conditions. We used this approach in SRT Kinematics to conduct a detailed analysis of the clock paradox; results are discussed. …
One of the main results of Scale Relativity as regards the foundation of quantum mechanics is its explanation of the origin of the complex nature of the wave function. The Scale Relativity theory introduces an explicit dependence of physical quantities on scale variables, founding itself on the theorem according to which a continuous and non-differentiable space-time is fractal (i.e., scale-divergent). In the present paper, the nature of the scale variables and their relations to resolutions and differential elements are specified in the non-relativistic case (fractal space). We show that, owi…
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