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 opposite direction giving that the total 3D torque is zero. In this paper, it is considered 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 decomposition of the electromagnetic field F (bivector) into two 1-vectors E and B we introduce decomposition of the 4D torque N (bivector) into 1-vectors N s , 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 T and T t . In such treatment with 4D geometric quantities the mentioned paradox does not appear. The presented explanation is in complete agreement with the principle of relativity and with the Trouton–Noble experiment without the introduction of any additional torque.
Similar content being viewed by others
References
Trouton F.T., Noble H.R. (1903). Philos. Trans. R. Soc. Lond. Ser. A 202: 165
Hayden H.C. (1994). Rev. Sci. Instrum. 65: 788
von Laue M. (1911). Phys. Zeits. 12: 1008
Pauli W. (1958). Theory of Relativity. Pergamon, New York
Singal A.K. (1993). Am. J. Phys. 61: 428
Teukolsky S.A. (1996). Am. J. Phys. 64: 1104
Jefimenko O.D. (1999). J. Phys. A: Math. Gen. 32: 3755
Ivezić T. (2005). Found. Phys. Lett. 18: 401
Ivezić T. (2006). Found. Phys. 36: 1511
D. Hestenes, Space-Time Algebra(Gordon & Breach, New York, 1966); New Foundations for Classical Mechanics (Kluwer Academic, Dordrecht, 1999), 2nd. edn.; Am. J. Phys. 71, 691 (2003).
C. Doran, and A. Lasenby, Geometric algebra for physicists (Cambridge University, Cambridge, 2003).
Jefimenko O.D. (1997). Retardation and Relativity. Electret Scientific, Star City
Jackson J.D. (2004). Am. J. Phys. 72: 1484
Jackson J.D. (1977). Classical Electrodynamics, 2nd edn. Wiley, New York
A. Einstein, Ann. Physik. 17, 891 (1905); in The Principle of Relativity, tr. W. Perrett and G. B. Jeffery, eds. (Dover, New York, 1952).
Rohrlich F. (1966). Nuovo Cimento B 45: 76
T. Ivezić, Found. Phys. 33, 1339 (2003); Found. Phys. Lett. 18, 301 (2005); Found. Phys. 35, 1585 (2005).
Ivezić T. (2002). Found. Phys. Lett. 15: 27 physics/0103026; physics/0101091
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Ivezić, T. Trouton–Noble Paradox Revisited. Found Phys 37, 747–760 (2007). https://doi.org/10.1007/s10701-007-9116-x
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10701-007-9116-x