Abstract
Three new mass dimension quantities have been derived by dimensional analysis, in addition to the famous Planck mass mP ~10-8 kg. These masses have been derived by means of fundamental constants-the speed of light (c), the gravitational constant (G), the Plank constant (h) and the Hubble constant (H). The enormous mass m1 ~1053 kg practically coincides with the Hoyle-Carvalho formula for the mass of the observable universe. The extremely small mass m2 ~10-33 eV has been identified with the minimum quantum of energy, which seems close to the graviton mass. It is noteworthy that the Planck mass appears geometric mean of the masses m1 and m2. The mass m3 ~107 GeV could not be unambiguously identified at present time. Besides, the order of magnitude of the total density of the universe has been estimated by this approach.
Highlights
The Planck mass mP ~hc has been introduced from GPlanck (1959) by means of three fundamental constantsthe speed of light in vacuum (c), the gravitational constant (G) and the reduced Plank constant (ħ)
The extremely small mass m2 ~10−33 eV has been identified with the minimum quantum of energy, which seems close to the graviton mass
Three new mass dimension quantities mi have been derived by dimensional analysis, in addition to the mP ~
Summary
Planck (1959) by means of three fundamental constantsthe speed of light in vacuum (c), the gravitational constant (G) and the reduced Plank constant (ħ). G and ħ represent three very basic aspects of the universe (i.e., the relativistic, gravitational and quantum phenomena), the Plank mass appears to a certain degree a unification of these phenomena. The Plank mass formula has been derived by dimensional analysis using fundamental constants c, G and ħ. The dimensional analysis is applied in the mechanics and other fields of the modern physics, where there are many problems with a few determinative quantities. Because of the importance of the Hubble constant, in the present paper we include H in the dimensional analysis together with c, G and h aiming to find the new mass dimension quantities mi. The Hubble constant will represent the cosmological phenomena in new derived fundamental masses.
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