Trouton-Noble paradox revisited

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.

References in corpus (4)

• The Proof that the Standard Transformations of E and B are not the Lorentz Transformations. Clifford Algebra Formalism
• The Proof that Maxwell Equations with the 3D E and B are not Covariant upon the Lorentz Transformations but upon the Standard Transformations. The New Lorentz Invariant Field Equations
• Axiomatic geometric formulation of electromagnetism with only one axiom: the field equation for the bivector field F with an explanation of the Trouton-Noble experiment
• The 4D geometric quantities versus the usual 3D quantities. The resolution of Jackson's paradox

Cited by in corpus (5)

• Lorentz Transformations of the Electric and Magnetic Fields According to Minkowski
• Generalized Uhlenbeck-Goudsmit hypothesis 'Magnetic' S^{a} and 'Electric' Z^{a} Spins
• The Lorentz transformations of the vectors E, B, P, M and the external electric fields from a stationary superconducting wire with a steady current and from a stationary permanent magnet
• The manifestly covariant Aharonov-Bohm effect in terms of the 4D fields
• Electric and magnetic fields as explicitly observer dependent four-dimensional vectors and their Lorentz transformations according to Minkowski-Ivezić