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Volume 29: Pages 309-312, 2016
A discussion on the Heisenberg uncertainty principle from the perspective of special relativity
Luca Nannia)
San Maiolo 5, I-36023 Longare, Italy
In this note, we consider the implications of the Heisenberg uncertainty principle 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.
Dans cette note, nous considérons les implications du principe d\\\'incertitude de Heisenberg (HUP) lors du calcul des incertitudes qui influent sur les principales grandeurs dynamiques, du point de vue de la relativité restreinte. En utilisant la formule bien connue pour la propagation des erreurs statistiques, nous prouvons que les relations d\\\'incertitude entre les modules des observables conjugués ne sont pas invariant relativistes. Les nouvelles relations montrent que, dans les expériences impliquant des particules relativistes, les limites de la précision d\\\'une quantité obtenue par des calculs indirects peuvent affecter le résultat final.
Key words: Heisenberg Uncertainty Principle; Special Relativity; Conjugate Variables; Quantum Tunneling
Received: June 16, 2015; Accepted: June 8, 2016; Published Online: July 21, 2016
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