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Tuesday, March 31, 2015

Derivation MpRp=4LM #5

This Equation is (9) on page 274 (which is page 5) of Nassim's paper Quantum Gravity and the Holographic Mass, black hole mass in terms of R, $\eta$, and Planck mass $m_l$:
$$m_h={R \over \eta} \times m_l$$

$m_h=$mass of black hole
$m_l=$Planck mass

$R=V_S/V_l =$ geometric arguments - LARGE NUMBER RATIO!!!
  $V_S={4 \over 3} \pi  r_s^3=$ Volume of black hole
  $V_l={4 \over 3} \pi  r_l^3=$ Volume of Planck Spherical Unit (PSU)
    $r_s=$ Schwarzschild radius
    $r_l={l \over 2}$ Planck Length divided by to for radius of PSU
      $l=$Planck length

$\eta=A_S/A_l =$ informational arguements - LARGE NUMBER RATIO!!!
  $A_S=4 \pi r^2=$ Surface Area of black hole
  $A_l=4 \pi r_l^2=$ Equitorial cross-sectional Area of Planck Spherical Unit (PSU)

From this, we can use $T={m_l \over V_l}$ from The Derivation of MpRp=4LM #3.

If we re-write $m_h={R \over \eta} \times m_l$ using $T={m_l \over V_l}$, we can see that The Surfer's attempt in part #4 is part of this equation, so let's re-write it substituting T for $m_l \over V_l$:

$$m_h={R \over \eta} \times m_l$$
$$m_h={V_S \over \eta} \times T$$

This is the SAME equation The Surfer came up with in part #4, however, with the addition of this $\eta$ term. A little clean up work on that to better see it: in part #4 The Surfer was using the simple concept of the total mass of an object is the density of the matter of the object times the volume of the object. Density is mass/volume, so mass/volume times volume is mass, so, it is simply definitions.

So, now we can see why the Surfer's attempt to perform this black hole derivation ALMOST worked, yet he forgot, in his rush to get ready for the Survival of Humanity Alchemy Event to include the $\eta$ term, which is related to the information theory aspect of this derivation.  One could also say it is related to the fact that the black hole is "floating" in the vast sea of space-time of huge density T. More on that later...

So, now this $\eta$ is the gating item to finish the derivation of the mass.radius relationship of a black hole.  As Master Moe said, "it's the $\eta$ that'll gate ya".  We will dive deeper into this $\eta$ thing, as now we can see it is the only thing barring us from finishing this simple derivation. No advanced math is needed.  Basic geometry and a little insight is all that is needed.

Tune in next time to wrap up this black hole relationship, then we can quickly finish the proton mass.radius relationship, then makes some comments, and move on to bigger and better things. There's a lot of work to be done, a lot of physics and science to create and re-write.

Some closing comments on the significance of R and $\eta$. Both of these numbers are related to Dirac_large_numbers_hypothesis. This will be discussed in more detail in a future post that goes over the interesting aspects of this type of approach to the solution to these previously very challenging problems, and, as one will soon see, exactly how easy it really is compared to the previous method(s) and we will compare these equations to actual measurements and previous mainstream physics analytical solutions to see how well they agree.

The Surfer, OM-IV