Supernova explosion is a phenomenon described very well by the laws of quantum mechanics
meaning that the Heisenberg uncertainty principle (HUP) restricts the achievable information from
this source, and indeed, the accuracy of measurements on Hubble parameter by using this source is
bounded by HUP. On the other hand, cosmic microwave background (CMB) stores quantum gravity
(QG) effects dominant in the early universe. Hence, its physics is supposed to be under the influence of
the modified forms of HUP (obtained in the QG scenarios). This means that the most accurate H0
measurements, by using this source, may meet modified forms of HUP instead of HUP itself.
Therefore, photons coming from these sources satisfy different uncertainty principles. Here, we show
that the difference between these two regimes (or equally, the difference between the uncertainty
principles) establishes an eternal discrepancy between the H0 values obtained by these sources.
Consequently, more accurate observations and estimations on the value of Hubble parameter may
help us find out the values of QG parameters.