Relativistic Relative Velocities and Relativistic Acceleration

Koczan, Grzegorz

doi:10.12693/aphyspola.139.401

Cited by 6 publications

(7 citation statements)

References 8 publications

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“…which is the same as for the Oziewicz-Bolós binary velocity and with the accuracy to the sign as for the Einstein velocities composition (see Statement 2 in [9]). Since • > 0 then applying (41) to (35) we directly obtain the last formula (42) of the thesis according to [14].…”

Section: Theorem 4 (Covariant Passive Lorentz Transformation Of Veloc...mentioning

confidence: 92%

“…If the conditions v. and vi. are set for the binary velocity (1), then we can easily obtain the canonical binary velocity of Oziewicz-Bolós (see [9] and Fig. 1):…”

Section: The Binary 4d Relative Velocity Of Oziewicz-bolós and Its Tr...mentioning

confidence: 99%

“…where ⃗ = ⃗ ∕ is 3D binary velocity [9] or jet velocity [10]. The ⃗ velocity satisfies the full version of condition i.…”

Section: The Binary 4d Relative Velocity Of Oziewicz-bolós and Its Tr...mentioning

confidence: 99%

“…(27) Thus, the addition of the ternary velocity in the sense of Oziewicz can rightly be called the addition of Oziewicz-Einstein. Proof. In the 3D Dragan approach, the relationship between the ternary velocity (as "inverse" velocity) with the Lorentz transformation and Einstein velocities composition is not in doubt and results almost from the very definition of ternary velocity (see [9,11]). Oziewicz 4D approach is more general and, apart from the definition of ternary velocity, must be based on the definition of its addition in the form (24) or (25).…”

Section: Theorem 2 (Oziewicz's) Ternary Velocities Composition In The...mentioning

confidence: 99%

“…The application of the covariant Lorentz transformation allowed for a significant simplification of the proof of the theorem. For example, in Dragan [5], the calculations extend through three subsections, and the previous relatively simple heuristic derivation of the author [9] was not fully general and had to be based on a computationally complex proof of the relevant lemma.…”

Section: ⊓ ⊔mentioning

confidence: 99%

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Relative binary, ternary and pseudo-binary 4D velocities in the Special Relativity: Part I. Covariant Lorentz transformation

Koczan¹

2021

Preprint

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Zbigniew Oziewicz was a pioneer of the 4D space-time approach to covariant relative velocities. In the 1980s (according to private correspondence) he discovered two types of 4D relative velocities: binary and ternary, along with the rules for adding them. They were first published in conference materials in 2004, and the second time in a peer-reviewed journal in 2007. These physically logical and mathematically precise concepts are so subtle that Oziewicz's numerous preprints have yet to receive the recognition they deserve. Part I of the work was planned to be a more review, but a thorough review of the little-known results was made in an original synthetic manner with numerous generalizations. The Part I presents the Oziewicz-Bolós (and Bini-Carini-Jantzen) binary relative velocity and the Oziewicz-Dragan ternary relative velocity. The Einstein-Oziewicz and Einstein-Minkowski velocities, which are a four-dimensional generalization of Einstein velocities addition, also have a ternary character (or at least pseudo-binary). It turns out that the Lorentz transformation of velocity itself is already ternary anchored. This fact is explicitly revealed by the covariant Lorentz transformation of velocity, which is the main tool in Part I of the work. Part II of the work will be fully original and introduces two 4D ternary generalizations of relative binary velocity called pseudo-binary relative velocities: cross and axial. A longer description of Part II follows after the conclusion of Part I of the work.

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Section: Theorem 4 (Covariant Passive Lorentz Transformation Of Veloc...mentioning

confidence: 92%

“…If the conditions v. and vi. are set for the binary velocity (1), then we can easily obtain the canonical binary velocity of Oziewicz-Bolós (see [9] and Fig. 1):…”

Section: The Binary 4d Relative Velocity Of Oziewicz-bolós and Its Tr...mentioning

confidence: 99%

“…where ⃗ = ⃗ ∕ is 3D binary velocity [9] or jet velocity [10]. The ⃗ velocity satisfies the full version of condition i.…”

Section: The Binary 4d Relative Velocity Of Oziewicz-bolós and Its Tr...mentioning

confidence: 99%

Section: Theorem 2 (Oziewicz's) Ternary Velocities Composition In The...mentioning

confidence: 99%

Section: ⊓ ⊔mentioning

confidence: 99%

See 3 more Smart Citations

Relative binary, ternary and pseudo-binary 4D velocities in the Special Relativity: Part I. Covariant Lorentz transformation

Koczan¹

2021

Preprint

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The Mechanical Behavior of a Multispring System Revealing Absurdity in the Relativistic Force Transformation

Javanshiry¹

2021

International Journal of Mathematics and Mathematical Sciences

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The mechanical motion of a system consisting of simple springs is investigated from the viewpoint of two inertial observers with a relativistic relative velocity. It is shown that the final displacement of the springs is not measured the same by the observers. Indeed, it is demonstrated that there is an incompatibility between kinematics and dynamics in Einstein’s relativity regarding the force transformation.

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Multiple velocity composition in the standard synchronization

Choi

2022

Open Physics

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Mansouri and Sexl (MS) presented a general framework for coordinate transformations between inertial frames, presupposing a preferred reference frame the space-time of which is isotropic. The relative velocity between inertial frames in the standard synchronization is shown to be determined by the first row of the transformation matrix based on the MS framework. Utilizing this fact, we investigate the relativistic velocity addition. To effectively deal with it, we employ a diagram of velocity that consists of nodes and arrows. Nodes, which are connected to each other by arrows with relative velocities, represent inertial frames. The velocity composition law of special relativity has been known to be inconsistent with the reciprocity principle of velocity, through the investigation of a simple case where the inertial frames of interest are connected via a single node. When they are connected through more than one node, many inconsistencies including the violation of the reciprocity principle are found, as the successive coordinate transformation is not reduced to a Lorentz transformation. These inconsistencies can be cured by introducing a reference node such that the velocity composition is made in conjunction with it. The reference node corresponds to the preferred frame. The relativistic velocity composition law has no inconsistencies under the uniqueness of the isotropic frame.

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Relativistic Relative Velocities and Relativistic Acceleration

Cited by 6 publications

References 8 publications

Relative binary, ternary and pseudo-binary 4D velocities in the Special Relativity: Part I. Covariant Lorentz transformation

Relative binary, ternary and pseudo-binary 4D velocities in the Special Relativity: Part I. Covariant Lorentz transformation

The Mechanical Behavior of a Multispring System Revealing Absurdity in the Relativistic Force Transformation

Multiple velocity composition in the standard synchronization

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