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Thursday, April 2, 2015

Derivation of MpRp=4LM #6

Interesting growth pattern
Let's check that the derived equation matches the Schwarzschild solution:
$$M_S={{V_S T} \over \eta}?\leftrightarrow ? R_S={2GM_S \over c^2}$$
$V_S={4 \over 3}\pi R_S^3$

$T={m_l \over V_l}$

$\eta={A_S \over A_l}$
$$M_S={{V_S T} \over \eta}$$
$$M_S={{{4 \over 3}\pi R_S^3}{m_l \over V_l} \over {A_S \over A_l}}$$
$V_l={4 \over 3}\pi r_l^3$

$A_S=4\pi R_S^2$

$A_l=\pi r_l^2$

$R_S=$ Schwarzschild radius

$r_l={l \over 2} =$ Planck radius = Planck length, l, over 2

$$M_S={{{4 \over 3}\pi R_S^3}{m_l \over {4 \over 3}\pi r_l^3} \over {4\pi R_S^2 \over \pi r_l^2\pi r_l^2}}$$
$$M_S={{R_S m_l} \over {4 r_l}}$$
$r_l={l \over 2} =$ Planck radius = Planck length l divided by 2
$$M_S={{R_S m_l} \over {2 l}}$$
 Planck Mass: $m_l=\sqrt {\hbar c \over G}$
 Planck Lenght: $l=\sqrt {\hbar G \over c^3}$
After substituting Planck's units and simplifying:
$$M_S={{R_S c^2} \over {2 G}}$$
$$R_S={2GM_S \over c^2}$$

Therefore we see the derived equation matches the Schwarzschild solution to Einstein's Field Equations, however, it is a very simple derivation.  There are new fields being developed that are very advanced that give answers more simply, and Nassim's approach is a major theory behind that effort. Some of this can be seen in the jewel of quantum mechanics that replaces 500 pages of QED Feynman diagrams with 1 page.

derivation-of-mprp4lm-7.html (#7)

The Surfer, OM-IV