Objects

Uncertainty principle (un)

Absolute certainty principle (ac)

Microcosm and mesostructures

Relationship: $\Delta a\cdot \Delta p\approx \hslash /2$

Growth laws: ${\langle a\rangle }^{3/2}\text{d}\langle a\rangle \approx {\left(\frac{\hslash a_0^{3/2}}{2m_0{t}_i}\right)}^{1/2}\text{d}t$ ,

${\langle a\rangle }^{3/2}\text{d}\langle a\rangle \approx {\left(\frac{a_0^3\Delta E}{2m_0}\right)}^{1/2}\text{d}t$

Maximum size $a_{\max }^{un}\approx \frac{2m_0{a}_0^3}{9\hslash \Delta t_{\min }}$

Relationships: $ap=\hslash /2$ , $Et=\hslash$

Growth law $a^4\text{d}a=\left(\hslash /2\alpha \rho \right)\text{d}t$

Maximum size $a_{\max }^{ac}\approx {\left(\frac{\hslash t_i^{\max }}{6m_0}\right)}^{1/2}\cong \frac{\hslash }{{\left(6m_0{E}_{\min }\right)}^{1/2}}$

Objects of astrophysics and cosmology

Relationships and growth law

$\left|\Delta a\right|\cdot \left|\Delta p\right|\cong K_c/2$ . $\left|\Delta E\right|\cdot \left|\Delta t\right|\cong K_c$

${\langle a\rangle }^2\text{d}\langle a\rangle =\left(1/\sqrt{2}\right){\left({\rho }_c/\rho \right)}^{1/2}{a}_0^{2}c\text{d}t$

Relationships and growth law

$ap\cong K_c/2$ , $Et\cong K_c$

${\langle a\rangle }^2\text{d}\langle a\rangle =\left(1/2\right)\left({\rho }_c/\rho \right)a_0^{2}c\text{d}t$