More on the Right-Angled Lever at Equilibrium in Special Relativity

Aranoff, Sanford

doi:10.1119/1.1987485

Cited by 3 publications

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“…Topics covered here have been analysed for a long time [38], especially in discussions around the 'relativistic lever paradox' [39]). They are scattered in the literature vaguely [40] or incompletely [41]. To the best of our knowledge, the relativistic rotational dynamics fourtensor equation developed here no has been explicitly written in the form presented here.…”

Section: Discussionmentioning

confidence: 99%

“…From the inertia of energy principle, in describing rotation, it is not only work performed and energy variation produced that matter, but also points at which these quantities are considered. Equation (40) indicates that the sum of terms (F k • u k )dt, the kth introduced at point vector R k , must correspond to the sum of kinetic energy variations d[γ v i M i c 2 ], the ith at point vector r i .…”

Section: By Defining (Withmentioning

confidence: 99%

“…For an arbitrary distribution of elements, inertias (suppose that the ith element has its own different inertia M i , for instance), distances, (arbitrary) forces and torques, relationship (40) would not be fulfiled. That would mean that the rigid-rotation condition, which has been assumed to obtain previous Poinsot-Euler and Newton's second law equations, is not fulfiled and that part of work performed on the system has been transformed into internal elastic energy, deforming the system's springs.…”

Section: By Defining (Withmentioning

confidence: 99%

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Relativistic mechanics and thermodynamics. III. Rotation

Güémez¹

2021

Eur. J. Phys.

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A covariant four-tensor rotation equation—for bi-dimensional composite body—, by generalising cross product to four-vectors, is obtained. From it, a relativistic angular impulse-angular momentum variation equation (Poinsot–Euler rotation equation) and its pseudo-work-rotational kinetic energy variation equation (Poinsot–Euler pseudo-work equation), are obtained for a body spinning—with constant angular momentum direction—by external torques. Two rotational processes are analysed by using this four-tensor formalism—completed by a four-vector fundamental equation (Newton’s second law and thermodynamics first law)—: a rotating body subjected to conservative and friction forces torque—a mechanical energy dissipation process—, and a device spinning by torque produced by chemical reactions—a mechanical energy production process.

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Section: Discussionmentioning

confidence: 99%

Section: By Defining (Withmentioning

confidence: 99%

Section: By Defining (Withmentioning

confidence: 99%

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Relativistic mechanics and thermodynamics. III. Rotation

Güémez¹

2021

Eur. J. Phys.

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“…one obtains the Poinsot-Euler equation (40) complementary dynamical relationship [9] or rotational kinetic energy equation. equations' redundancy, when the rotational kinetic energy equation is obtained from the Poinsot-Euler equation, guarantees the systemʼs rigid-rotation during the process [15].…”

Section: Newton's Second Law Adding Of 4-tensors Componentsmentioning

confidence: 99%

“…This explanation, involving a flow of energy with no known speed, is against the local character of relativity. Some authors have considered that internal torques exactly cancel external torques [4], but this explanation is not operative and refuted [15]. In order to carry out a coherent relativistic description for a process evolving by applying forces on a composite system, it is necessary to admit that the system undergoes some kind of motion (linear translation or rotation) and/or some deformation [16] (otherwise nothing happens and equations are fulfilled in a trivial way).…”

Section: Introductionmentioning

confidence: 99%

On the relativistic lever paradox

Güémez¹

2021

Phys. Scr.

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As the 'relativistic lever paradox' is a characteristic topic in the theory of relativity application to rotation processes, a covariant four-tensor equation is developed to describe the relativistic rigidrotation of an extended body subjected to external torques, and its Lorentz transformation between frames S and S in the standard configuration is analysed, to discuss this paradox. From the four-tensor rotation equation applied to an L-shaped body submitted to several torques it is concluded that although the system does not vary its angular momentum in frame S-in which simultaneously applied forces resultant torque is zero -, in frame S, it does vary its angular momentum and exerted torque on it is non-zero. From this formalism (asynchronous formulation of relativity), in frame S, angular momentum variation is related to Einsteinʼs inertia of energy principle, and the non-zero torque is a consequence of the relativity of simultaneity, showing that this description is coherent and that there is no paradox.2 [1]. In frame S, on element 1, located at L 1 = (L 1 , 0, 0), force F 1 = (0, F 1 , 0), and on element 2, located at L 2 = (0, − L 2 , 0), force F 2 = (−F 2 , 0, 0), are applied. The pivot, located at O, RECEIVED

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Basic assumptions and black holes

Aranoff¹

2009

Physics Essays

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Science develops by initially proposing hypotheses to explain phenomena, then creating a formal consistent mathematical framework, verified by experiment and observation, called a scientific theory. This theory must exclude solutions that violate basic physical principles or yield inconsistent mathematics. New observations may challenge the theory, but do not necessarily invalidate it as a basic mathematical inconsistency would. Science continues by developing hypotheses to explain what the current theory cannot. The paper discusses objects falling into black holes using general relativity as examples of both valid theory and developing hypotheses. The existence (according to most physicists) of a black hole is part of a valid theory. The crossing of the event horizon of the black hole is an extension of the theory, but is not part of the theory, for the mathematics is not consistent, and the results violate basic principles. Another example of an invalid extension of a theory is given from special relativity. Since this theory is easier to understand, it helps clarify the point. One needs to be clear what is part of the theory, and what is not part of the theory. The statement "an observer crossing the event horizon and losing all contact with the rest of the universe is part of physics" is a counterexample to the proper understanding of theories. Statements incorrectly based on theories may be obstacles to the advance of science. One needs to understand the philosophical underpinnings of science, and how one can tease out the hidden assumptions of a theory.Resume: La science se développe en proposant tout d'abord des hypothèses pour expliquer les phénomènes, puis ensuite en créant un cadre mathématique adéquat, validé par le biais de l'expérience et de l'observation. Ce cadre rigoureux devient alors synonyme d'une théorie scientifique. Cette théorie se doit cependant d'exclure les solutions qui mettent en porte-à-faux les principes physiques élémentaires ou encore celles qui donnent la primauté à une mathématique inconsistante. De nouvelles observations peuvent venir remettre en question la théorie, mais elles ne la rendent pas nécessairement nulle comme le ferait une mathématique incohérente. En réalité, la science se construit en développant des hypothèses à même d'expliquer ce qui ne peut l'être par la théorie actuelle. Le présent article traite des objets qui entrent dans la catégorie des trous noirs en utilizant le concept de la relativité générale comme exemple tout à la fois d'une théorie valide et d'hypothèses en cours de construction. L'existence (selon la plupart des physiciens) d'un trou noir fait partie intégrante d'une théorie valable. La traversée de l'horizon de l'événement du trou noir est une extension de la théorie, sans pour autant relever de cette dernière, dans la mesure où les mathématiques ne sont pas consistantes, car les résultats ne cadrent guère avec les principes de base. Un autre exemple d'un usage incorrect de la théorie peut s'observer dans le cadre de la relativité spéciale. Étan...

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More on the Right-Angled Lever at Equilibrium in Special Relativity

Cited by 3 publications

References 0 publications

Relativistic mechanics and thermodynamics. III. Rotation

Relativistic mechanics and thermodynamics. III. Rotation

On the relativistic lever paradox

Basic assumptions and black holes

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