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Addressing the cosmological $H_0$ tension by the Heisenberg uncertainty

The uncertainty on measurements, given by the Heisenberg principle, is a quantum concept usually not taken into account in General Relativity. From a cosmological point of view, several authors wonder how such a principle can be reconciled with the Big Bang singularity, but, generally, not whether it may affect the reliability of cosmological measurements. In this letter, we express the {Compton mass} as a function of the cosmological redshift. The cosmological application of the indetermination principle unveils the differences of the Hubble-Lemaître constant value, $H_0$, as measured from the Cepheids estimates and from the Cosmic Microwave Background radiation constraints. In conclusion, the $H_0$ tension could be related to the effect of indetermination derived in comparing a kinematic with a dynamic measurement.