arXiv subjects
Publications and source records attributed to Andor Frenkel.
It is shown in the present note that the degree of the complexity of the time-reading process of the Salecker--Wigner clock depends on the size of the clock. This dependence leads to a relation between the size and the accuracy of the clock, and suggests a precise optimal value for the size in agreement with the order of magnitude value established by Salecker and Wigner.
In classical electrodynamics all the measurable quantities can be derived from the gauge invariant Faraday tensor $F_{αβ}$. Nevertheless, it is often advantageous to work with gauge dependent variables. In [4],[2] and [8], and in the present note too, the transformation of the vector potential in Lorenz gauge to that in Coulomb gauge is considered. This transformation can be done by applying a projection operator that extracts the transverse part of spatial vectors. In many circumstances the proper projection operator is replaced by a simplified transverse one. It is widely held that such a replacement does not affect the result in the radiation zone. In this paper the action of the proper and simplified transverse projections will be compared by making use of specific examples of a moving point charge. It will be demonstrated that whenever the interminable spatial motion of the source is unbounded with respect to the reference frame of the observer the replacement of the proper projection operator by the simplified transverse one yields, even in the radiation zone, an erroneous result with error which is of the same order as the proper Coulomb gauge vector potential itself.
The space-time foam formulas, quoted below in Eqs (1) and (3), express the minimal amount of quantum uncertainty to be introduced into the structure of the Einsteinian space-time in order to make that structure compatible with quantum mechanics. In addition to their theoretical significance, the formulas lead to far reaching observable consequences shortly recalled below in the last section. The main purpose of the present note is the examination of the reliability and the comparison of various derivations of the said formulas.
Half a century ago H. Salecker and E. P. Wigner examined the functioning of a quantum clock of very simple construction [1]. They raised the question whether such a clock can be microscopic or not, but no clear-cut answer has been reached in [1] (see also [2]). In this note it is shown that their clock can have a microscopic mass and size only if its accuracy is poor, but if the size is macroscopic, a decent accuracy can be achieved even if the mass is microscopic.
In the existing expositions of the Karolyhazy model, quantum mechanical uncertainties are mimicked by classical spreads. It is shown how to express those uncertainties through entities of the future unified theory of general relativity and quantum theory.