On Uncertainty Relations at Planck's Scale

Abstract

A brief review of the previous research on the Heisenberg uncertainty relations at the Planck scale is given. In this work, investigation of the uncertainty principle extends to p-adic and adelic quantum mechanics. In particular, p-adic analogs of the Heisenberg algebra and uncertainty relation are introduced. Unlike ordinary quantum theory, adelic quantum approach provides a promising framework to probe space below the Planck length.