2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/158044We formulate and prove a new, universally valid uncertainty relation for the necessary errors bar widths in any approximate joint measurement of position and momentum.Version 2 has minor corrections and a new referenceMathematical PhysicsQuantum Physics81P15, 81P05Universal joint-measurement uncertainty relation for error barstext