It is shown that, due to Rosenfeld's inequality relations, there is no possibility of defining states of the Friedmann universe in a physically sensible manner when the world radius becomes equal to or smaller than Planck's length.

We give picture-covariant formulations of the equations of motion for observables and states such that the Hamiltonian operator is transformed asH-0304;=U(t)HU † (t) under a time-dependent unitary transformationU(t). Next, we consider the explicit and implicit covariance of Heisenberg's equations of motion for observables with respect to general transformations of coordinate operators. Most of our representation is spread out over a number of textbooks and articles, where the subject has been considered with greater or lesser clarity from different points of view.

Planck's units define the limits of super GUT and also the possibilities of classical measurements. A “planckion'” is the largest ultrarelativistic elementary particle and also the smallest body that can serve as a classical standard.

As is well known, the law of parity conservation does not hold in weak interactions. This type of asymmetry created a number of theoretical problems which were solved, first of all, by a new understanding of the features of neutrinos and their role in weak interactions. These solutions were based, however, essentially on the handedness (chirality) of neutrinos which is closely related to their vanishing rest mass. The thesis of neutrinos with nonvanishing rest mass, newly considered in the literature, therefore (...) requires a rediscussion of the early arguments concerning the relation between the neutrino theory and some weak interaction essentials. When one does this, as in the present paper, it is noted that neutrinos with rest mass lead to some difficulties, in particular to a violation of T invariance. (shrink)