Special Relativity from Heisenberg’s Uncertainty Relation

Luca Nanni

Luca Nanni

In this note, we consider the implications of the Heisenberg uncertainty principle (HUP) when computing uncertainties that affect the main dynamical quantities, from the perspective of special relativity. Using the well-known formula for propagating statistical errors, we prove that the uncertainty relations between the moduli of conjugate observables are not relativistically invariant. The new relationships show that, in experiments involving relativistic particles, limitations of the precision of a quantity obtained by indirect calculations may affect the final result.

Pavle Ilija Premović

B. Kivel

Vishnu M. Bannur

Recently, Maccone and Pati \cite{pa.1} derived new uncertainty relations which they claim to be stronger than Heisenberg-Robertson or Schrodinger uncertainty relations. Here we comment that their work is a special case of a more general uncertainty relation and we reexamine some of their conclusions.

A. G. Karavaev

In this paper we investigate the problem of minimizing the Heisenberg's uncertainty relation with the trajectory-coherent states. The conditions of minimization for Hamiltonian and trajectory are obtained. We show that the trajectory-coherent states minimize the Heisenberg's uncertainty relation for special Cauchy problem of the Schrödinger equation only.