Oh No wrote:
Thus spake "

Parenthetically, the revised Schwarschild radius for the proton is
about 0.8 x 10^-13 cm, which is about equal to the charge radius of the
proton and the revised Planck length.


I should just like to add that the Schwarzschild radius of the proton
is not something which appears in standard physical models, the reason
being that a classical massive point particle is not a consistent idea
in general relativity. In fact a proton must be treated quantum
mechanically, and we do not have an accepted theory on that, but if the
Schwarzschild radius of the proton were considered then it would have a
magnitude given by

2Gm/c^3 =3D 8.28 x 10 e^-63 m

Planck length also has a formal definition

l_p =3D sqrt(hbar*G/c^3) =3D 1.61605e-35 =B1 1.0e-39 m

Neither of these figures is open to revision beyond that allowed by
experimental margins of error. If you are defining other quantities, you
should give them other names.


Gentlemen:

Given:

Planck's constant hb 1.054572675E-27 g cm^2 sec^-1
gravitational constant G 6.6725985E-8 cm^3 sec^-2 g^-1
speed of light c 2.997924580E10 cm sec^-1

The following is list of some of the Planck scale parameters:

Planck length (hb G/c^3)^(1/2) 1.61605E-35 cm
Planck time (hb G/c^5)^(1/2) 5.39056E-44 sec
Planck mass (hb c/G)^(1/2) 2.17671E-08 g
Planck energy (hb c^5/G)^(1/2) 1.95610E-16 g cm^2 sec^-2
Planck momentum (hb c^3/G)^(1/2) 6.52483E+05 g cm sec^-1
Planck force (c^4/G) 1.21027E+49 g cm sec^-2
Planck density (c^5/(hb G^2) 5.15500E+93 g/cm^3
Planck acceleration (c^6/(hb G)) 1.03145E+97 cm/sec^2
Planck kinematic viscosity (c^7/(hb G))^(1/2) 5.56077E+53 cm^2/sec
Planck absolute viscosity (c^9/(hb G^3))^(1/2) 2.49779E+71 g cm^-1 sec^-1

It is difficult to say which has a 'physical meaning'.

Using dimensional units of mass, length & time
the constants hb, G, c can be arranged in an infinite number of possibilities.

Richard