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In this note, we consider the implications of the Heisenberg uncertaintyprinciple (HUP) when computing uncertainties that affect the main dynamicalquantities, from the perspective of special relativity. Using the well-knownformula for propagating statistical errors, we prove that the uncertaintyrelations between the moduli of conjugate observables are not relativisticallyinvariant. The new relationships show that, in experiments involvingrelativistic particles, limitations of the precision of a quantity obtained byindirect calculations may affect the final result.

A Discussion on the Heisenberg Uncertainty Principle from the Perspective of Special Relativity