Characteristic actions ħ^(s) in the structure of the universe

Abstract

It is suggested that gravitationally bound systems in the Universe can be characterized by a set of actions ħ^(s). The actions

$$\hbar ^{\left( s \right)} = \left( {{\hbar \mathord{\left/ {\vphantom {\hbar {\frac{1}{{2\pi }}\frac{{C^5 }}{{GH_0^2 }}}}} \right. \kern-\nulldelimiterspace} {\frac{1}{{2\pi }}\frac{{C^5 }}{{GH_0^2 }}}}} \right)^{s/6} \left( {\frac{1}{{2\pi }}\frac{{C^5 }}{{GH_0^2 }}} \right)$$

,derived from general theoretical consideration, are only determined by the fundamental physical constants (Planck's action ħ, the velocity of lightC, gravitational constantG, and Hubble's constantH ₀) and a scale parameters. It is shown thats=1, 2, and 3 correspond, respectively, to the scales of galaxies, stars, and larger asteroids.

The spectra of the characteristic angular momenta and masses for gravitationally bound systems in the Universe are estimated byJ ^(s) andM ^(s)=(ħ^(s) Cα/G)^1/2. Taken together, an angular momentum-mass relation is obtained,J ^(s)=A(M^(s))², where$A = G/C\alpha ,{\text{ }}\alpha \simeq \tfrac{{\text{1}}}{{{\text{137}}}}$, for the astronomical systems observed on every scale. ThisJ-M relation is consistent with Brosche's empirical relation (Brosche, 1974).