Interesting growth pattern
Let's check that the derived equation matches the Schwarzschild solution:
$$M_S={{V_S T} \over \eta}?\leftrightarrow ? R_S={2GM_S \over c^2}$$
$V_S={4 \over 3}\pi R_S^3$
$T={m_l \over V_l}$
$\eta={A_S \over A_l}$
$$M_S={{V_S T} \over \eta}$$
$$M_S={{{4 \over 3}\pi R_S^3}{m_l \over V_l} \over {A_S \over A_l}}$$
$V_l={4 \over 3}\pi r_l^3$
$A_l=\pi r_l^2$
$R_S=$ Schwarzschild radius
$r_l={l \over 2} =$ Planck radius = Planck length, l, over 2
$T={m_l \over V_l}$
$\eta={A_S \over A_l}$
$$M_S={{V_S T} \over \eta}$$
$$M_S={{{4 \over 3}\pi R_S^3}{m_l \over V_l} \over {A_S \over A_l}}$$
$V_l={4 \over 3}\pi r_l^3$
$A_S=4\pi R_S^2$
$A_l=\pi r_l^2$
$R_S=$ 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
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
Inside Black Holes | Leonard Susskind
ReplyDeleteThis point in the derivation of MpRp=4LM is to the black hole mass.radius relationship part derived. A few more steps to complete the review of the mass.radius relationship of the proton: (#7, and upcoming and likely final #8)
ReplyDeletehttp://phxmarker.blogspot.com/2015/04/another-preview-to-derivation-of.html