Naslov
Trouton-Noble paradox revisited

Autori
Ivezić, Tomislav

Izvornik
Physics/0606176

Vrsta, podvrsta
Ostale vrste radova, rukopis

Godina
2006

Ključne riječi
Trouton-Noble paradox

Sažetak
An apparent paradox is obtained in all previous treatments of the Trouton-Noble experiment ; there is a three-dimensional (3D) torque T in an inertial frame S in which a thin parallel-plate capacitor is moving, but there is no 3D torque T′ in S′ , the rest frame of the capacitor. Different explanations are offered for the existence of another 3D torque, which is equal in magnitude but of oppo- site direction giving that the total 3D torque is zero. In this paper instead of using 3D quantities, e.g., E, B, F, L, T, .. and their “ apparent” transforma- tions we deal with 4D geometric quantities E, B, K, M, N, ... their Lorentz transformations and equations with them. It is considered in our approach that 4D geometric quantities and not the usual 3D quantities are well-defined both theoretically and experimentally in the 4D spacetime. In analogy with the de- composition of the electromagnetic field F (bivector) into two 1-vectors E and B we introduce decompositions of the torque N and the angular momentum M (bivectors) into 1-vectors Ns, Nt and Ms, Mt respectively. The torques Ns, Nt (the angular momentums Ms, Mt), taken together, contain the same physical information as the bivector N (the bivector M). It is shown that in the frame of “ fiducial” observers, in which the observers who measure Ns and Nt are at rest, and in the standard basis, only the spatial components Ni s and Ni t remain, which can be associated with components of two 3D torques T and Tt. In such treatment with 4D geometric quantities the mentioned paradox does not ap- pear. The presented explanation is in a complete agreement with the principle of relativity and with the Trouton-Noble experiment without the introduction of any additional torque.

Izvorni jezik
Engleski

Znanstvena područja
Fizika

POVEZANOST RADA