Trouton–Noble experiment
The Trouton–Noble experiment was an attempt to detect motion of the Earth through the luminiferous aether, and was conducted in 1901–1903 by Frederick Thomas Trouton and H. R. Noble.
It was based on a suggestion by George FitzGerald that a charged parallel-plate capacitor moving through the aether should orient itself perpendicular to the motion.
Like the earlier Michelson–Morley experiment, Trouton and Noble obtained a null result: no motion relative to the aether could be detected.
[1][2] This null result was reproduced, with increasing sensitivity, by Rudolf Tomaschek (1925, 1926), Chase (1926, 1927) and Hayden in 1994.
Several solutions have been proposed to solve this kind of paradox, all of them in agreement with special relativity.
In the experiment, a suspended parallel-plate capacitor is held by a fine torsion fiber and is charged.
If the aether theory were correct, the change in Maxwell's equations due to the Earth's motion through the aether would lead to a torque causing the plates to align perpendicular to the motion.
On the other hand, the assertion of special relativity that Maxwell's equations are invariant for all frames of reference moving at constant velocities would predict no torque (a null result).
Thus, unless the aether were somehow fixed relative to the Earth, the experiment is a test of which of these two descriptions is more accurate.
Its null result thus confirms Lorentz invariance of special relativity.
towards bc must be equal to obtain equilibrium, thus no torque is given by the law of the lever: where
However, due to length contraction, ba is longer than bc in a non-co-moving system, thus the law of the lever gives: It can be seen that the torque is not zero, which apparently would cause the lever to rotate in the non-co-moving frame.
Since no rotation is observed, Lewis and Tolman thus concluded that no torque exists, therefore: However, as shown by Max von Laue (1911),[10] this is in contradiction with the relativistic expressions of force, which gives When applied to the law of the lever, the following torque is produced: Which is principally the same problem as in the Trouton–Noble paradox.
The detailed relativistic analysis of both the Trouton–Noble paradox and the right-angle lever paradox requires care to correctly reconcile, for example, the effects seen by observers in different frames of reference, but ultimately all such theoretical descriptions are shown to give the same result.
In both cases an apparent net torque on an object (when viewed from a certain frame of reference) does not result in any rotation of the object, and in both cases this is explained by correctly accounting, in the relativistic way, for the transformation of all the relevant forces, momenta and the accelerations produced by them.
In addition, if two point charges are connected by a flexible string, no molecular force could produce a turning moment.
This was further elaborated by Max von Laue (1911), who gave the standard solution for these kind of paradoxes.
It was based on the so-called "inertia of energy" in its general formulation by Max Planck.
[10] [13] [14] [15] Since then, many papers appeared which elaborated on Laue's current, providing some modifications or re-interpretations, and included different variants of "hidden" momentum.
The role played by the concept of force in relativity is very different from that of Newtonian mechanics.
So the paradoxes are resolved, because the two accelerations (as vectors) point to the center of gravity of the system, although the two forces do not.
