The 3 great constants of Nature are well known :
- The Speed of light $c$ (special relativity)
- The Plank constant $\hbar$ (quantum mechanics)
- The Newton gravitational constant $G$ (general relativity)
However, is it possible that they play, in fact, a similar role, a moderator role, in the precise sense of decreasing energy ?.
Consider the following baby model : We consider a particle of radius r and mass m. We admit an auto-gravitational potential, and a pseudo auto-quantum potential.
The energy of the particle is given by :
$$E(m,r) = m c^2 - \frac{\hbar^2}{m r^2} - \frac{G m^2}{r}$$
(Do not care of possible coefficients of order unity)
We demand the physical condition : $$E(m,r) >=0$$
We may easily observe that, putting $\hbar$ = 0, we recover the gravitational limit for the radius of particle when she becomes a black hole, and, by putting $G=0$, we recover the "quantum limit" for the radius (a taste of Heinsenberg inequalities) .
What is the effect of choosing $c^{-1}$ > 0 ($c$ not infinite), or choosing $\hbar$ > 0, or choosing $G$ > 0 ?
This is the same effect, that is, it decreases the energy $E(m,r)$.
So the team ($c^{-1}, \hbar, G$), when they are not zero, decreases the energy, it appears as a (dream) team of moderators of energy.
Of corse, we are working with a baby (particle) model.
But do you think that these conclusions could be extended to the real word?
