Minimal Length at All Energy Scales and Measurability

Abstract

This paper is a continuation of the earlier studies conducted by the author and of his latest publication devoted to the inferences concerning the introduction of a minimal length in quantum theory and in gravity. It is demonstrated that, provided a minimal length is actualized at all energy scales, a theory inevitably involves associated new parameters, discrete in their nature. Taking two gravitational models as an example, it is shown that the indicated parameters in fact are discrete at high (Planck's) energies only, varying slowly (smoothly) at low energies which are far from the Planck energies, and we get a "nearly continuous theory" that is close to the initial one.