Several contradictions inherent for relativistic dynamics get evident in the case of mechanical systems of cyclic type. In the present paper a version of situation taking place in the moving belt transmission is examined. It is shown that non-Euclidean intrinsic geometry, appearing during acceleration, does not abolish the real paradox in this mechanism. An unavoidable discrepancy between Special and General relativities is established. So, the very existence of wormholes becomes a moot point.
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