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

TL;DR

This paper examines how the Heisenberg uncertainty principle's limitations are affected by special relativity, revealing that uncertainty relations are not invariant under relativistic transformations and impacting experimental precision.

Contribution

It demonstrates that the uncertainty relations between conjugate observables are not relativistically invariant, highlighting implications for high-speed particle experiments.

Findings

Uncertainty relations are not invariant under special relativity.

Relativistic effects influence the precision limits of measurements.

Indirect calculations of quantities may be limited by relativistic uncertainties.

Abstract

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.