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Trouton-Noble paradox revisited

Tomislav Ivezic
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Abstract

An apparent paradox is obtained in all previous treatments of the Trouton-Noble experiment; there is a three-dimensional torque in an inertial frame S in which a thin parallel-plate capacitor is moving, but there is no 3D torque in S', the rest frame of the capacitor. In this paper instead of using 3D quantities and their ``apparent'' transformations we deal with 4D geometric quantities their Lorentz transformations and equations with them. We introduce a new decomposition of the torque N (bivector) into 1-vectors N_{s} and N_{t}. It is shown that in the frame of ``fiducial'' observers, in which the observers who measure N_{s} and N_{t} are at rest, and in the standard basis, only the spatial components N_{s}^{i} and N_{t}^{i} remain, which can be associated with components of two 3D torques. In such treatment with 4D geometric quantities the mentioned paradox does not appear. 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.

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Tomislav Ivezic. 2006-06-20. Trouton-Noble paradox revisited. https://doi.org/10.1007/s10701-007-9116-x

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