The non-conservation of generally-accepted expressions for relativistic energy and momentum at collisions of particles results, in the general case, in the non-conservation of the angular momentum in SRT as well. However, the relativistic expression of the angular momentum can be easily discredited for much simpler examples . Let us recall, for example, the paradox of a lever. Let two forces, equal in magnitude, , to act on two identical arms , disposed at angle (Fig. 4.10).
The total moment of forces equals zero. The structure remains motionless. In the classical physics the result does not depend at all on the frame of reference, and, hence, it is not necessary to invent any new physical concepts, processes, phenomena or mathematical derivations.
Different is the situation in SRT. If somebody will only look at this system from a missile moving at velocity along one of arms, then the total moment will occur to be nonzero. Owing to contraction of lengths and transformation of forces we have: . The lever must begin to rotate. It would seem that such an inconsistency should entail refusal from SRT and returning to the classical physics, that provides an obvious and true result. However, the relativists (following Laue and Sommerfeld) have gone another way . "For the sake" of pseudo-science it was necessary to sacrifice something. Since the common sense is less significant for relativists, than SRT, it was necessary for them to invent the missing pseudo-moment. Now, if you simply rest upon something (on the wall, for instance) or use a lever, then you should store some additional clothes: "something" (the energy) will begin to flow through you, and this quantity can occur huge! Besides, the fluxes (of sweat, probably?) can occur to be different simultaneously, if somebody "spies" upon you from different moving missiles. If you keep both levers with your hands with identical force, then the energy from one hand merely flows away to an axis and "settles" somewhere. Do not worry, however! This "something" can not be measured in any way, but this is just not necessary for relativists: this is not engaging in physics, you see! Simply, the literal expressions should be met with an obvious (from the common sense viewpoint) result. Thus, instead of one principally undetectable relativistic effect (otherwise the inconsistency would be detected) we would obtain two principally undetectable relativistic effects exactly balancing each other. Similar tricks have an effect on many people (the letters just converge!), in spite of the fact that "the dry remainder" of all similar "inventions" is a priory obvious classical result.