near Planck's mass

• To: mathgroup at smc.vnet.net
• Subject: [mg68434] near Planck's mass
• From: Roger Bagula <rlbagula at sbcglobal.net>
• Date: Sat, 5 Aug 2006 03:46:25 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```Back about 1987 or before
I was studying gravitation and quantum mechanics
and I came across  this:
r = e^2/(m*c^2)
(* Riemannian Curvature*)
R = -2/r^2
(* 3 space volume*)
V = (4*Pi/3)*r^3
(*scalar energy densidty*)
T = m*c^2/V
(* solution for R = -8Pi*G*T(v, v) : scalar reduction of Einstein's
general relativity*)
Solve[R + (8*Pi*G/c^4)*T == 0, m]
e = 4.80325*10^(-10)
G = 6.6732*10^(-8)
(* mass in grams*)
m = e/Sqrt[3*G]
1.073513458510097`*10^-6

At the time I hadn't run into Planck's mass.
If you put in
r=h/(m*c)
in this calculation  you get a version of the Planck mass.

I was wondering if this was a well known calculation like Planck's mass?
Roger

```

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