de Vaucouleurs-Ikeuchi Diagram and Commutation Relations among Phase Space Coordinates

Details de Vaucouleurs-Ikeuchi Diagram and Commutation Relations among Phase Space Coordinates de Vaucouleurs-Ikeuchi Diagram and Commutation Relations among Phase Space Coordinates

2005-04-23

arxiv.org/abs/astro-ph/0504516v2

Mod.Phys.Lett.A24:1669-1676,2009

Astronomy and Astrophysics

Astrophysics

10 pages, 2 figures, the enlarged version to which one auhtor was added

Scientific paper

10.1142/S0217732309031077

We consider the relations between de Vaucouleurs-Ikeuchi diagram and generalized commutation relations among the coordinates and momenta. All physical objects in the Universe ranging from elementary particles to super cluster of galaxies are confined within the Triangle of the de Vaucouleurs-Ikeuchi diagram on the matter density versus scale length plane. These three boundaries are characterized by the quantum uncertainty principle, gravitational event horizon, and cosmological constant. These are specified by the non-zero commutation relations $[x_\mu,p_\nu], [x_\mu, x_\nu]$ (strictly $[x_i,t]$) and $[p_\mu,p_\nu]$, respectively. The canonical commutation relation $[x_i,p_j]$ are slightly modified, which preserves the self consistency as a whole.

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