Strongly Violated Scale Invariance of Space-Time (Quantum-Mechanical Aspect)

Abstract

The hypothesis that the Universe in its evolution exhibits, to one degree or another, strongly violated scale invarianceis discussed. The fundamental group of space-time now is not the Poincaré group, but the Poincaré-Weyl group. In case with a very high probability a particle is found near its classical trajectory, but there is an extremely small (but nonetheless nonzero!) probability of detecting this particle far from its classical trajectory, providing quantum mechanical nonlocality both in space and in time. The considerations presented here, in their further study, may lead to the formulation of a new interpretation of quantum mechanics. А possible change in Planck’s constant over time is discussed.