Planck Scale Constants

Factual Questions
1

There are three main constants in the Planck Scale:
Planck Mass = ((h-barc)/G)^1/2 = 2.1766510^-5 gram

Planck Length = ((Gh-bar)/c^3)^1/2 = 1.616110^-35 meter

Planck Interval = ((Gh-bar)/c^5)^1/2 = 5.3907210^-44 sec

These three constants are based on:
c, the speed of light
G, the constant of gravitation
h-bar, based on h, the planck constant, the quantum constant

I was wondering, if Mp, Lp, and Tp are defined using c,G, and h-bar as units defining the Planck scale, you should be able to work the other way…defining c,G, and h-bar in terms of the Planck scale itself.

I already figured out c = Lp/Tp,
so how is G and h-bar defined?

2

Substitute your value of c into one of the expressions, then solve for (e.g.) G in terms of the Planck scale values and hbar. Substitute this value of G and your value of c into another one of the expressions, and you can solve for hbar in terms of the Planck scale constants. Substitute this and c into one of the expressions, solve for G.

3

c = L[sub]p[/sub] / T[sub]p[/sub],

G = (L[sub]p[/sub] / M[sub]p[/sub]) * c
= L[sub]p[/sub][sup]2[/sup] / (M[sub]p[/sub]T[sub]p[/sub]),

h-bar = M[sub]p[/sub]L[sub]p[/sub]c
= M[sub]p[/sub]L[sub]p[/sub][sup]2[/sup] / T[sub]p[/sub].

I don’t think it gets much simpler.

4

Thanks for the help…I was a failure at math.

5

Thanks for the help…I was a failure at math.