- Published 2015

We investigate the relations between the physical quantities and the physical constants by the dimensional analysis. From normal form of uncertainty relations (URs), we propose an assumption which the physical quantities have the formal symmetry with the physical constants; and find three basic formulas. A physical quantity has a corresponding Planck scale and many physical quantities have the same Planck scales because of the same dimensions. All Planck scales can be classified by two methods, one is the basic Planck scale and derived Planck scale, and another is Femi-Planck scale, Bose-Planck scale and other-Planck scale. The basic formulas can be rewritten as the ones of corresponding Planck scales. We find the generalized relation which the power products of physical quantities are equivalent to the ones of corresponding Planck scales. Heisenberg UR is part of the generalized relation when the reduced Planck constant ħ appears. We also find the Big Bang UR between its temperature and volume by the generalized relation, and the Schwarzschild black holes (SBH) UR between its mass and volume. These suggest no singularity at Big Bang and in SBH with the quantum effect. We show that the generalized relation is interesting and significant.

@inproceedings{Bao2015GeneralizedRO,
title={Generalized Relation of Unifying All Uncertainty Relations with Dimension},
author={Yong Bao},
year={2015}
}