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.
