Thank you for this question, I did not yet know the angle lever paradox.I read the Wikipedia article that you get to a search: Trouton-Noble Experiment – Wikipedia.I find it incomprehensible written and overloaded for physical laymen:
- Two different paradoxes are described together: the Trouton-Noble experiment describes an electrical paradox in the SRT.
The angular lever paradox is a mechanical.
Experimental setup with two different observer points
The experimental setup from the point of view of an observer resting in relation to the angle lever (left side of the image)
There is an angle that is suspended rotatably (blue).
The arms are equal in length (green). Percennitily to both arms attacks a force, the amount of which is also the same for both arms (red). A force attacking a rotatable arm exerts a torque.
|My| = Fy * y
|Mx| = Fx * x
|Mx| = | My|
Both torques are the same size but directed in the opposite direction, so the angle lever does not move.
The test setup from the point of view of an observer moving with respect to the angle lever (right side of the image)
The Special Theory of Relativity says here that lengths shorten in relation to the direction of movement (Lorentz contraction 鈥?Wikipedia), therefore should apply
|Mx| < | My|
because the arm x is now shorter than the arm y.
Therefore, the angle lever would have to rotate.This is paradoxical,because even in the SRT it is true that events for different observers can take place at different times and can therefore change the order of their observation, but the events remain the same for all observers.If the angle lever does not rotate in the dormant reference system, it must not rotate in the moving system.
The Wikipedia article mentions two different mathematical solutions to the problem:
- The first solution takes into account that the two angle ends fly past the observer at different times.
- In the second solution, the tensor character of the force is used in the SRT.
F = m * a
The mass m is a scalar size.It has increased for the moving observer, but this applies to both lever arms regardless of the direction of movement and therefore shortens away.
Force F and acceleration a, however, are both vectorial variables with amount and direction.You can point in different directions in the SRT! To show this is obviously too much math even for this formula-heavy Wikipedia article and is not elaborated there. (More precisely, this is described here: Acceleration (Special Theory of Relativity) – Wikipedia.)